The Hunt for Absolute Motion
The Special Theory of Relativity from a New Perspective
Cam Jeroncic
Copywrite © November 2010 The Hunt for Absolute motion: The Special Theory of
Relativity from a New Perspective by Cam Jeroncic at Montreal, Quebec, Canada
Contents
…back in ‘95 .................................................................................................................................................. 1
The Idea That Started it all ............................................................................................................................ 2
The absolute second ..................................................................................................................................... 3
.333…c and .7142857 c ............................................................................................................................... 11
The Interferometer ..................................................................................................................................... 13
Strange devices ........................................................................................................................................... 17
Pythagoras? I know what time it is!............................................................................................................ 19
Aberration of light....................................................................................................................................... 22
One of My First Attempts ........................................................................................................................... 24
Length alterations ....................................................................................................................................... 30
“If you are moving at 1/2 c and you throw a ball at 1/2 c what will…?” .................................................... 35
Disks and Angles.......................................................................................................................................... 40
Mutual Illumination .................................................................................................................................... 43
Now that you’re an expert… ....................................................................................................................... 47
A simple observation .................................................................................................................................. 57
Third Frame of Reference ........................................................................................................................... 58
The Absolute Doppler Shift ......................................................................................................................... 61
The “Wave-chopper” .................................................................................................................................. 63
More Doppler Shifting ................................................................................................................................ 65
2/7 c ............................................................................................................................................................ 67
Kinetic Energy ............................................................................................................................................. 69
More Inertia and less Energy ...................................................................................................................... 73
The Conjecture ............................................................................................................................................ 75
Why Colour?................................................................................................................................................ 75
The Spectral Speedometer.......................................................................................................................... 75
Red Sun ....................................................................................................................................................... 77
There is no Such Thing as Time ................................................................................................................... 79
Temperature X! ........................................................................................................................................... 80
Relativistic Thermodynamics ...................................................................................................................... 82
Cooler Tea and a Luke-warm Bath .............................................................................................................. 83
But is it Warm?............................................................................................................................................ 83
Cold Photons ............................................................................................................................................... 84
If .................................................................................................................................................................. 84
That’s a lot of Constants ............................................................................................................................. 85
An Inter-Reference Frame Two-Particle Collision ....................................................................................... 86
.5 From Frame to Frame ............................................................................................................................. 91
So! Which is it?............................................................................................................................................ 96
Out on a Limb .............................................................................................................................................. 97
The Final Appeal........................................................................................................................................ 103
Afterword .................................................................................................................................................. 104
…back in ‘95
When I was younger - and smarter than I am now - I was certain that the Special
Theory of Relativity was wrong! Now that I am older, dimmer and presumably wiser, I see
how simple and obvious the whole concept is and, in hindsight, how natural it is for the
universe to incorporate the rules of Relativity into the movements of things.
I started my search for absolute motion back in ’95 while studying planetary orbital
systems. I had always known that satellites could be placed into a geo-synchronous orbit
but on that particular day I noticed something that brought my attention back to what little
I had understood of the Special Theory at the time and to a dim recollection of the concept
of absolute motion. Intrigued, I began to study the Special Theory in depth. I had thought
at the time, as I do to this day, that the mass gain of an object couldn’t be a relative
measure since an object gained mass as it approached that absolute velocity of light.
Since everything is moving relative to the velocity of light, I had reasoned, then those
lesser motions must be absolute too. After all, an object that moves can’t be where it once
was, right? And saying you can’t measure the absolute motion of an object is not the
same as saying that there is no absolute motion at all.
Another thing that had, and still does, bother me is the fact that nobody really knows
where we are in the universe. There must have been a center in the beginning. Where is
it now? What about an edge? And if there are only relative measures of motion and time
then how can we be sure of the true age of the universe?
And how aberrated is the light that reaches us from the stars in the Hubble Deep Field
images due to our unknown velocity through space? We know that those stars were
formed billions of years ago when the universe was younger and smaller, so we are not
really seeing what is there now and we can’t trace things back as well as we might if we
don’t know how we are moving in the absolute.
I saw recently a diagram of the observable universe, complete with stellar distances
and velocities and look-back times and, of course, there we were right at the center.
It reminded me instantly of those representations from the middle-ages of an
earth-centered solar system.
Now that’s obviously a natural result of empirical observation but these early
observations are usually inaccurate reflections of reality. What we need is an “Absolute
Standard of Time” and a “speedometer” that works in an enclosed room.
Well, anyway, I couldn’t help myself. I was so sure that I could find a way to measure
absolute motion since I was then, and I am still, certain that all motion is absolute Though these days I say; “Be it measureable or not!”
So let’s take a look at the idea that set me on my path and get a feel for things and
then we’ll ease into some concepts and some of the devices for measuring one’s absolute
motion and we’ll see why they all fail. And once you have joined me in my defeat I will
invite you to ponder a conjecture that was born from my inability to measure through time
- which I so wanted to do - which just might point the way to an answer!
1
The Idea That Started it all
A satellite in a geo-synchronous orbit around the earth must orbit at a distance of
about 6.6 earth-radii. I like to call this the geo-synchronous orbital point, or GSOP. At this
distance from the earth's surface the orbital velocity is about 3.07 kps - if we use as a
surface velocity of the earth a speed of about .465 kps - and our satellite will in effect be at
rest above the surface of the earth. It is at rest relative to earth and yet it moves - it must
move or it will fall and 6.6 radii is the only place where an orbiting body can remain
stationary over the surface. If we would want to change this geo-synchronous orbital
distance we would have to change the rate of the earth's rotation.
Right at the surface of the earth the orbital velocity is about 7.9 kps. If we wanted a
satellite in a geo-synchronous orbit this close to the surface we would have to speed the
earth up so that the surface velocity would match that of any satellite placed there. Of
course everything upon the earth would then also be in geo-synchronous orbit, freely
falling and floating - just inches above the surface even - and chaos would be just a nudge
away.
Conversely, if we were to slow the earth down, its surface velocity could be made to
match any orbital velocity we choose. The moon orbits at about 1 kps and being 60.3
earth radii away we would have to slow the earth to about 1/28 its present speed or not
quite 1/60 the present speed of the moon. The slower the central body rotates the further
out our geo-stationary orbit becomes until finally, if our planet were to stop rotating
completely, the GSOP would basically disappear or could be considered to be at an
infinite distance - there being no place in the universe whereby a body in orbit could be at
rest above the surface of the orbited body. Rotationally, our planet could be considered to
be at absolute rest relative to the edge of the universe or, if the reach of our planet's
gravity is truly infinite, at absolute rest in an infinite universe. Well, if our planet can be at
absolute rest rotationally then doesn't that mean that if it isn't at absolute rotational rest it
must possess an absolute rotational motion?
We could state further that the equatorial bulge should disappear as our GSOP
reaches an infinite distance and therefore, if we do have a GSOP and we do have
rotational motion relative to infinite co-ordinates, then the equatorial bulge should be an
indicator of that absolute rotational motion.
However, the argument has been put forth that "... the equatorial bulge must be a result
not just of the rotational motion of our planet alone in an absolute space but of it's motion
relative to the rest of the universe..." and that "...the inertial effects of rotation are not an
indicator of anything absolute and the creation of the bulge could just as well be a result of
the mass of the entire universe rotating around the body itself."
But consider this; in order to cause a body to rotate you must input energy. So we could
say that the inertial bulge is an indicator of an input of energy. And if you wish to consider
the body to be at rest relative to infinite co-ordinates as a finite universe rotates around
you, you would have to have applied an energy to have kept our body from rotating with
that universe - hence our inertial bulge could still be considered to be an indicator of an
input of energy. An input of energy and the inertial effects that result from that energy
therefore must indicate a change in the position of that body relative to the universe and,
if the universe is infinite, a change in position relative to infinite co-ordinates. We might
2
even state that all inertial effects indicate a shift in an object's position relative to nothing
other than where it once was!
But could our planet still possess a bulge if it could exist alone in a universe? Well, all of
the particles that create that body are not alone relative to each other. If a force was
impressed upon a few particles at a particular point of that body the remaining particles
would resist the movement of those particles - by virtue of the fields that keep the particles
together as a body - and stresses within that body should be created. The mere
resistance of the remaining particles to being moved and their subsequent inclination to
remain moving tangentially should create a bulge. And if we were to imagine a subtly
lopsided Big-Bang which caused a universe to rotate I suspect that that universe would
possess a bulge too.
The absolute second
While these ideas might help to show that the inertial effects of acceleration do seem
to indicate an absolute change in one's position within the universe it has so far proven to
be impossible to measure any form of absolute changes in position when dealing with
uniform linear motion. Only relative measures can be made. The thing is, though, that the
Special Theory of Relativity which deals solely with uniform linear motion will still work if
one assumes that all bodily motions, particles of light or otherwise, to be absolute and that
all of the relative measures one makes occur against an absolute framework which is
defined by where you once were and how fast you are moving relative to that speed of
light. That would mean that time dilation, mass gain and length contraction are all
absolute alterations in the properties of the objects involved as they move through space
and without these absolute alterations Relativity wouldn’t work.
The first basic rule of the Special Theory is that any experiment performed in a uniformly
moving inertial frame of reference will always render the same results as that same
experiment performed in any other uniformly moving frame of reference. And that means
that every observer, regardless of the motion of his frame of reference, can always
consider himself to be at rest at the center of an expanding sphere of light, for example,
that has originated from his position. It seems counter-intuitive but even if he had moved
from where his flash had originated and isn’t at the center, in an “absolute” sense, he will
always measure himself to be equidistant from every point on the surface of that
expanding sphere. And we can conceive of an inertial frame of reference whereby one
could actually be at absolute rest at the true center of a sphere of light so that when his
clock would show that 1 second had passed the radius of that sphere would be an actual
299,792 km.* Common sense dictates that such a scenario should easily exist but
according to the rules of relativity we could never really be sure that we were ever in such
a situation.
*(Let’s set the velocity of light to an even 300,000 kps.)
3
From a theoretically omniscient point
of view we will consider this inertial
frame to be at absolute rest. When
the radius of the sphere of light is
300,000 km the clock at the center
will show that 1 second will have
passed.
P
If our observer at P had set up a long pole with a
reflector at the 300,000 km mark, the light would
return to him after an elapsed time of 2 seconds.
That would tell him that he was at the center.
300,000 km
from P
Since all observers must consider themselves to be at the center of an expanding
sphere of light, which originates at their position, then if our second subject's inertial
frame is moving at 1/2 the velocity of light relative to the inertial frame which we
considered to be at absolute rest, we would have to visualize things a little differently.
4
To be truly moving at what we will consider to be an absolute velocity of .5 c, our
second subject would have to have travelled 150,000 km, from P to P1, when the radius
of his flash of light reaches 300,000 km. According to the inertial frame that we
considered to be at absolute rest, 1 second will have passed.
Direction of
motion
150,000 km
.
P
P1
Pole
Reflector
At this point, when T has reached 1 "absolute rest frame second",
the light still hasn't reached the reflector at the end of his pole.
This scenario is quite different from our first example and in order to see how our .5 c
observer is going to measure the same thing as our absolute rest frame observer we have
to understand the changes that an object undergoes with velocity. The first change is the
contraction of the moving observer’s pole and we can obtain that value by multiplying the
length (L) of that pole of 300,000 km by the answer produced by the following equation:
𝐿 = √1 − 𝑣 2 /𝑐 2
which becomes, letting c = 1,
𝐿 = √1 − .52 /𝑐 2 or .8660254.
86,60254 % of 300,000 gives us a contracted length of 259,807.62 km.
The next thing we have to consider is the slowing of time - or time dilation (t). Using the
same equation we will just divide our answer into 1;
𝑡=
1
√1 − .52 /𝑐 2
or 1.1547005
When one second has passed aboard our .5 c craft, 1.1547005 seconds will have passed
for our absolute rest frame observer. Or we could say that the .5 c clock will show
86,60254% of a second when that sphere of light has an absolute radius of 300,000 km.
5
Now the relativists will say that the measured velocity of light is always c. True. But what
isn’t always apparent is that if your velocity was .5 c relative to the absolute then the part
of the flash that would be ejected in the direction of your motion would only be receding
from you at .5 c as you chased it while light ejected in the direction opposite of your motion
would actually be receding at 1.5 c. With this in mind let’s see what we will measure with
a time-dilated clock and with a reflector at the end of a contracted 300,000 km pole.
Dir. of motion .5 c
P
The reflector (r) at the end of our contracted pole at .5 c was only 259,807 km away (at P1) from the point
P where the flash originated and, travelling only 1/2 as fast as the light, will be overtaken when the light
has travelled twice that distance or 519,615 km (at P2).
When the flash arrives
at P2 and the
reflector, the observer
has moved from P to
P1. The reflected light
will now return to the
still moving observer
and meet him at the
point P4.
Starting position
of contracted pole
259,807 km
P1
P2
P
Since the light has travelled at
the absolute velocity of c an
absolute distance of 692,820 km
then, according to our inertial
"absolute rest frame" time,
2.3094011 seconds will have
passed when the .5 c clock is
stopped(at P4). Multiply that rest
frame time by the dilated value
of 86,60254% for our slower .5 c
clock and we get 2 seconds
exactly. Our .5 c observer
concludes that he is at rest at the
center of his flash of light.
259,807 km
Light travels 519,615 km
Observer has
travelled 346,410 km
P
P4
P1
(r)
P2
(r)
Light has travelled 519,615, reflected back 173,205, for a total distance of 692,820 km.
6
Dir. of motion
1/2 c
...reaches tail
of craft's
pole...
.
flash at P...
This is how it would look
conceptually from an omniscient
point of view with our observer
now at the center of a
contracted 600,000 km pole.
519,615 km
.
.
...and the front of
craft's pole...
.
P
The foreward and aft flashes both travel the same distance
of 692,820 km in the same time of 2.309401 absolute seconds.
.8660254 times 2.309401 equals 2 time-dilated seconds for our observer in the 1/2 c frame.
7
...with both fore and aft
reflected beams
returning to P in two
1/2 c seconds
We can now say that when an observer is truly at rest at the center of an expanding
sphere of light his measure of distance will be un-contracted, or absolute, and his clock
will measure time at the fastest rate possible – being un-dilated, un-slowed. If we could
ever be sure of being at absolute rest we might consider measurement there as being a
universal standard. And, as we will see later, we might be able to include the experience
of energy in that conjectural universal standard.
So we have, conceptually, established that a "true" or "absolute" second has passed
when an expanding sphere of light has an “absolute” radius of 300,000 km and that your
absolute motion is how far you have moved from where you were when that light flashed
to where you are when that radius reaches 300,000 km. If in that same time you would
have moved 150,000 km from the flash-point then we could say that you would have an
absolute velocity of 1/2 c. The length of your craft will have contracted to 86,60254% of it's
rest length, everything aboard ship will have increased in mass to 1.1547005 times it's
rest mass (same equation for mass gain) and time will have slowed so that one second at
1/2 c would equal 1.1547005 times what it would be if you were still sitting at the center of
that sphere at absolute rest. These are all absolute alterations in the substance itself of
the craft and all of the mechanisms aboard. All of the relative inter-reference frame
measurements one makes must include these hidden, un-measureable, absolute
changes.
Remember, these observations are all from an intellectual, omniscient point of view clear and self-evident. But let’s see how things will appear to an observer aboard that .5 c
craft. Imagine once again that there is a pole 300,000 km long that is at rest within that
sphere of light and all along that pole are indicators of distance - from flashpoint to
circumference. After one absolute second, when the light has reached the 300,000 km
mark, you would be beside the 150,000 km mark on that pole and the elapsed time from
the flash, had you been measuring it in your time dilated reference frame, would show that
only .8660254 of a second had passed. If you could ever know that the pole was at
absolute rest (hereafter referred to as the rest frame) you could easily deduce your true
velocity and you'd realize your clock was slow.
The problem is though that an observer in the rest frame at the flashpoint had the
same idea and is making measurements off of the pole that is attached to your craft.
Remember, you and your pole are moving at 1/2 c and so your pole is only 86,60254% it's
rest frame length. Because of this, when the 150,000 km mark on your pole passes him,
you will have only actually travelled 129,903 km and so only .8660254 of a rest frame
second will have passed when he makes his measurement.
When one rest frame second actually does pass and you really are 150,000 km
distant, your contracted pole will show to the rest frame observer the mark at 173,205 km.
8
rest frame pole
300,000 km
After 1 second, rest frame
observer sees on
1/2 c pole the
173,205 km mark
1/2 c observer sees
150,000km mark on the rest
frame pole at .8660254 of a
relative second
259,807 km
1/2 c pole
T = 1 second
Direction of motion
1/2 c
1/2 c observer sees 173,205 km
after 1 relative second
T = 1.1547005 seconds
When your slower clock shows that one second has passed you will have actually
been travelling for 1.1547005 rest frame seconds and so you too will see the
173,205 km mark on that rest frame pole.
9
Neither you nor our rest frame observer will be able to tell who is truly moving at 1/2 c
and who is at rest. The rest frame observer has "true" time but reads a contracted pole
and, while you actually have the true measure of distance, time for you is running slow.
And this is the fundamental problem presented by nature when one wishes to make
any absolute measurements. Whenever one sets up an experiment in one frame one
must perform the same experiment in the other. In other words, the results collected from
an experiment or observation in one frame will always equal the results collected by that
same experiment and observation in any other frame.
(For ease of calculation I would prefer to represent the velocity of light as a simple 3
and all subsequent velocities and distances as divisions or multiples of 1. As long as the
proportions and ratios are right we can use any units we wish. Long decimals and
repetitive values will help to ingrain the information and instantly verify your calculations.
I have always found it very satisfying to see those long numbers come up after fumbling
through messy drawings and primitive mathematics!)
Let’s see how relativity works within our conceptual absolute framework.
10
.333…c and .7142857 c
Now, there are innumerable combinations of absolute velocities whereby two
observers will measure their relative velocities as being 1/2 c. And that means they must
get the same results as in our rest frame/1/2c example. If they were to get different results
then the rules of Relativity wouldn’t hold. For example we could consider the velocities of
.333...c and .7142857 c. In order to duplicate the particulars of our rest frame/1/2 c
example above we must remember that the .333 c observer is really moving in the same
direction as the .71c guy even though he is facing “left”. As the faster .71 c craft passes
by, they both set their clocks. The slower moving pole of .333 c is contracted to
94,28091% of 3 being 2.8284273 in length while the pole moving at .7142857 c is
contracted to 69,98542% of 3 for an absolute length of 2.0995626.
direction of motion
of both craft
T= 0
.333 pole length
(2.8284273)
.71 c pole length
(2.0995626)
As .71 c observer passes
.333 c observer,
clocks
are set.
After both craft have been travelling for a rest frame time of 1.0606602 absolute, or rest
frame, seconds, 1 time dilated second will have passed for the .333 c guy and he will have
to see on the .71 c pole the 1.7320508 mark – just as in our rest frame/1/2c example. In
that time, the .333 c guy has travelled a distance of, coincidently, 1.0606602 while the
11
.71 c observer has travelled 2.2728432 and these shifts in their position have occurred
within the sphere of that flash of light which now has a radius of 3.1819806. The
difference in the positions of our observers at that point is 1.212183. Since it is the .333c
guy that is making the measurement off of the .71c pole, we have to consider the rate of
contraction of the .71 c pole. 1 divided by the .6998542 contraction for .71c equals
1.428869 multiplied by the difference in the positions of our observers at this point, which
is 1.212183, and we get 1.7320508 – as we should!
when T = 1.0606602 seconds
T = 0
.333 c observer has travelled 1.0606602 after
1 ( of his relative seconds) and sees 1.7320508 on .71 c pole.
.71 c observer has travelled
2.2728432
1.212183
Difference in position
After 1.428869 rest frame seconds 1 relative second will have passed for the .71c guy
and the difference in their positions would then be 1.6329934 which, when multiplied by
1.0606602 (1 divided by the percentage of contraction for .333…c) will be read by the
.71c guy on the lesser contracted .333…c pole as 1.7320508. Once again, both
observers can claim to be either at rest or moving at 1/2 c though neither point of view is
“absolutely” true!
12
when T = 1.428869 seconds
T=0
.333 c observer
has travelled
1.4288687
1.6329934 difference in
position is measured on
.333 c pole as 1.7320508
by .71 c observer.
.71 c observer's distance travelled is
3.0618621 after one of his seconds.
Against an absolute framework, delineated only by the velocity of light, all of our
relative observations hide the absolute changes that occur with movement through space
and any measurement of absolute motion remains elusive.
The Interferometer
Now, a machine or optical device designed to measure absolute motion should, by its
very nature, work within the confines of an enclosed room. One would be able to tell how
fast they were moving and in which direction. This was the purpose of the Michelson Morley Interferometer. The basic idea was that if a beam of light was split and the two
halves were sent in different directions they might not arrive at the point of measurement
at the same time, gaining or losing speed or arriving with unsynchronized wavelengths
depending on whether they moved with or against or perpendicular to the direction of the
earth's motion. It's easy to see why this experiment failed!
Let's build an interferometer 300,000 km long by 300,000 km wide. Imagine it to be at
absolute rest in the rest frame. A laser is projected towards the center where it is split by a
half silvered mirror - one half of the beam is redirected "upwards" perpendicular to the
initial direction of propagation while the other half is allowed to continue to the far side of
13
the box. Upon reaching their respective walls they are reflected back to the center where
they meet and are directed "down" to the measuring device. Each half takes two seconds
to travel their respective distance. If we perform the same experiment at 1/2 c we know
what to expect as per the rules of relativity but, relative to the rest frame, things will appear
a little differently.
Since our experiment is now moving at 1/2 c (see diagrams) we know that our length
will be contracted to 86,60254% of 3 or 2.5980762. Our beam splitting mirror is at the
center of our square which is half that distance or 1.2990381 distant. However, our laser
will have to catch up to the mirror, the light having to travel twice that distance or
2.5980762 for a total elapsed time of .8660254 of an absolute second. As the light splits,
the half that is redirected perpendicularly to the direction of motion has to travel "up" a
distance of 1.5. Because of the motion of our device, of course, there is a lateral
component to that beam's motion and it will have to actually travel 1.7320508 angularly
taking .5773503 of a second for a total elapsed time of 1.4433757. Remember, this is
“true” time because these measurements depend solely upon the distance that the light is
travelling. The other half, moving in the direction of motion, has also travelled 1.7320508
and still hasn't hit the mirror on the far wall. It's still only 2/3 of the way there. When
T = 1.7320508 and it does catch up to the mirror, having travelled the remaining .8660254
and reflects, the beam that was sent perpendicularly will still be on its return trip to the
center. The center will now be rushing towards the returning straight line beam so that the
distance of 1.2990381 will be reduced by 1/3 so that that beam will recombine with the
lateral beam when T = 2.027259 seconds and both will then travel "down" to the point of
measurement in another .5770354 seconds for a total elapsed time of 2.5980762
seconds.
If, in the rest frame experiment, we had started a clock at the final point of
measurement by sending a separate signal from the laser's starting point 1.5 down to a
separate mirror at the lower left-hand corner and 1.5 across the perimeter of our square, it
would have taken a second to arrive and the recombined laser, taking two seconds to
complete it's route would have turned the clock off after one second had passed. We
know an observer at 1/2 c must reach the same conclusion as an observer in the rest
frame but we are seeing an elapsed time, from our omniscient point of view, that is much
greater than 2 seconds. If we plot the course of the signal that starts our 1/2 c clock we
know that it must travel laterally 1.7320508, strike the mirror and then catch up to the
measuring point - that is to say 2 times 1.2990381 or 2.5980762 for a total distance of
4.330127. The absolute time for our light signal to travel that far is 1.443357 seconds. If
we subtract that from the laser's time of 2.5980762 we get a difference of 1.1547005 - and
then there is one more step. We may theoretically have an omniscient point of view but, if
we were actually in the 1/2 c reference frame, time would be passing more slowly. The
time dilation factor for 1/2 c is 86,60254% the rest frame value. If we multiply 1.1547005
by this value we will measure the elapsed time to be 1 relative second!
14
Direction of Motion
1/2 c
T = 0
mirrors
Lasers to
mirror...
...and
to
clock
2.598067
T = .8660254
beam
splits
Mirror redirects laser to clock.
T=
1.4433757
clock starts
15
T=
1.7320508
Laser reaches far
wall and returns
to center
where...
T = 2.027259
...beams
re-combine...
T=
2.5980762
...and stop clock after
after 1 time-dilated second
16
And I say 1 relative second because the time on the clock is not an accurate
representation of the actual distance that the light has travelled. It is an illusion relative to
the "absolute" truth. A relative truth which the occupants of each reference frame must
live by. And all the observations of the universe - about its age and breadth and
movements - are cast into doubt without that absolute standard of motion and time!
. There must be a way to measure this secret of the universe!
Strange devices
Well, my fellow human being, now that you have entered into my little world let us
continue with your training. A simple light clock can be constructed by placing a disk at
either end of a long shaft and turning them at a known speed, say once a second, and
then marking them with a flash of light sent from a central point. If the shaft is aligned with
the direction of motion one might deduce that the light would reach the "rear" disk before
the "leading" one and, upon stopping each disk, the unaligned marks could tell you what
you would need to know. If our shaft was once again 3 units long at 1/2c it would be
contracted to 86,60254 % or, once again, 2.5980762. If we now send out our marking
flash from the center to the "fore" and "aft" positions, the rearward flash will meet the
oncoming disk after travelling 2/3 of 1.2990381, or a distance of .8660254 for an absolute
time of .2886751 seconds which converts to .25 for any measurements in the 1/2 c frame.
The forward flash will have to catch up to that receding disk having to travel 2.5980762 for
a time of .8660254 seconds - which is .75 relative time and three times that taken by the
aft flash - for a difference of .5773503 seconds which converts to .5 or 1/2 of a relative
second. If we didn't know better we might think that those disks, upon being stopped,
would show a 1/2 second difference and we could then conclude that we were moving at
1/2 c.
The problem is that the impulse that produces the motion of the shaft takes different
times to reach those disks just as the opposing ends of our flash of light does. The light
arrived .5773503 seconds apart - 1/2 a relative second – and, though the impulse that
started the shaft turning may have taken much longer to reach each disk than a flash of
light would have, the arrival times at each end by those impulses would have been
separated by the same value. This means that the disk at the rear started turning 1/2 of a
relative second sooner than the forward disk. When the rear-ward disk is stopped by the
light flash, the forward disk, which started late, will continue turning for an additional 1/2 of
a relative second, or 1/2 of a revolution, so that the disks end up being aligned when at
rest. This also means that when the shaft is turning at 1/2 c, the physical substance of the
shaft is twisted through time and space! The ends - the disks - cannot be synchronized as
they would've been at rest. There is a twist in the shaft! The substance of the shaft itself is
no longer straight and true. Poetically speaking, there is a twist through time!
17
Dir. of Motion 1/2 c
T=0
Flash is sent from center
Note the 1/2 of a relative second
twist in the shaft due to different
start-up impulse arrival times.
2.5980762
Light flash turns rear disk off after
.2886751 (or .25 of a 1/2 c second.)
Forward flash still has to travel for
another .5773503 (or .5 of a relative
second) ...
.8660254
...during which time the forward disk
will turn 1/2 of a revolution to end up
in the synchronized position.
2.5980762
Rest frame results at 1/2 the velocity of light!
Note: Disks are disproportionally large for visual ease. If drawn to scale they wouldn't be visible. They should be
assumed to be small and slow moving incurring no relativistic effects and existing only for our time-keeping
experiments as primitive clocks and separated by great distances.
18
Pythagoras? I know what time it is!
Let's see another example of how it all works. Once again we will set a pole of 3 moving
in the direction of motion at 1/2 c. Instead of moving left to right let's move our pole
upwards. At the mid-point, perpendicular to the first pole and the direction of motion, let’s
place another pole possessing also a length of 3. A laser, flashed from the end of the
perpendicular pole and along its length, would take 1 second to arrive at the mid-point of
our "directional" pole. At 1/2 c the laser will take on the momentum of the source and
travel straight along the pole to an observer in that frame. But because the pole is moving
the actual path of any segment of the laser through free space would be a straight line
from the point of origin to the point of reception which would basically create an
hypotenuse of a great triangle.
Now let's add another pole of a length of 3 which is at absolute rest and also
perpendicular to the direction of the motion of our 1/2 c apparatus. We'll make this the
trigger pole. As the 1/2 c perpendicular pole neatly passes by, a switch, (of any type of
your choosing), causes not only the 1/2 c laser to fire but also turns on a clock at the other
end where it joins the directional pole. At the same time on the trigger pole the switch that
turned on the 1/2 c clock also sets off a laser on the rest frame pole and at the other end,
a rest frame clock. Because everything is arranged perpendicularly, this is the only time
that you can have synchronized multi-reference frame events - for there is no length
contraction or "twist" through time between trigger and target. The clocks and the lasers
all fire at the same instant in both frames. But only theoretically! Without knowing how to
measure absolute motion you could never really be sure if the poles were really
perpendicular to the direction of motion.
Anyway, we know that the rest frame laser will turn the rest frame clock off after one
second. We also know that the 1/2 c laser will turn the 1/2 c clock off in one relative
second and we can draw an interesting conclusion from this fact. Without using the
Pythagorean theorem, we can calculate the distance that the 1/2 c laser travels since we
know all about the times that must be measured. After one relative second our 1/2 c guy
would have actually travelled for 1.1547005 absolute seconds for a distance of
1.7320508. The laser light itself, travelling at c, or twice as fast, for the same absolute time
would have to have traversed an hypotenuse, from the end of that 300,000 km pole to the
point of reception, of 3.4641016.
19
rest frame
trigger pole
direction
of
motion
1/2 c
1/2 c trigger pole
1/2 c laser will turn off 1/2 c
clock
after 1 relative second.
Rest frame
clock
starts
Rest frame laser will
turn
clock off after 1 second
20
1/2 c clock
starts
The 1/2 c laser has travelled parallel to its pole all the
way with each segment of the ray forming its own
"hypotenuse".
1/2c
1.7320508
Rest frame clock
showed
1 second when
his laser reached
him while
"now", at
1/2 c...
When the light reaches
the 1/2 c observer it has
also travelled for
1.1547005 seconds
(at the velocity of c)
and d must therefore
equal 3.4641016.
1/2c laser
rest frame
laser
Perpendicular un-contracted poles are
3.000000
21
...after
1.1547005
seconds ,
slower 1/2 c
clock will also
show 1 second
having travelled
1.7320508.
Aberration of light
If we now imagine that our perpendicular poles in both frames had "directional" poles at
either end so that we had two "H" shaped apparatus we could then make some actual
measurements. When the rest frame clock flashes after 1 second with the purpose of
marking the "left" leg of the 1/2 c "H" it will actually be side by side with the 1.7320508
mark on that contracted 1/2 c pole though the 1/2 c craft has only travelled in that second
a distance of 1.5. When the 1/2 c laser stops the 1/2 c clock after one relative second, we
know as before that the whole 1/2 c craft will have actually travelled 1.7320508 and that's
what our 1/2 c observer will measure as well on the rest frame pole. But there is
something else to notice! The rest frame observer, upon looking down his pole when the
laser arrives and stops his clock, would have seen the event of 1 second ago and he
would have seen the 1/2 c clock at the far end trigger point. We know that our 1/2 c
observer must see the same thing at the end of his pole but while the rest frame observer
is at rest and would actually see where the event took place - the actual position in space.
The 1/2 c observer can't possibly! While he must see the rest frame clock from 1 relative
second ago at the end of his pole, the end of his pole has moved, as he has,173,205 km
from the event's point of origin. But he will see what the rest frame observer sees and this
is because of the effect called the aberration of light.
The basic idea is that at a high velocity one's eye or camera strikes the particles and
waves of light at an angle and this distorts the discernment of true direction. The best
example is that of a telescope pointed straight up at a star. If the earth did not move, a
particle of light would enter the telescope, travel straight down the tube and strike the
optical receptor dead center. However, because the earth does move, by the time the
particle reaches the bottom, the center will have moved minutely and the image will be off
center. In order to counteract this effect one must tilt the telescope slightly in the direction
of motion thereby altering the apparent position of the star in the heavens. This effect is
miniscule on earth but it is there and at great velocities it becomes an integral part of
relativistic phenomena. In fact at very high velocities the majority of the visible stars in the
universe would be focused almost directly in front of you while all around you would be a
great darkness. (But another effect of high velocity is that the light of those stars would be
so blue-shifted that you would be blinded and irradiated to death without proper shielding.
High speed travel is dangerous!)
22
4.00
Contracted 4.0 equals
(3.4641016)
The Abberration of light
.
1.73
1/2 c "H" passes rest
frame "H"
Abberrated image and
apparent position of
event.
In
At this point rest
frame clock shows
1.1547005 seconds.
At 1 second he would
have seen the
unstarted 1/2 c
clock's image arrive
with the rest frame
laser...
rom
nf
tio
a
m
for
At one relative
second, ("now"),
1/2 c observer
sees his laser arrive
with the rest frame
clock image when he
reaches the 1.7320508
mark on the rest
frame pole.
Since he and his pole
have moved he cannot
be seeing the event's
true position in space.
(Any starlight in the
background will also
shift with the event.)
nt
eve
1/2 c
Path of rest frame laser and 1/2 c image along rest
frame pole.
.
1.73
T = 1.1547005
...at the 1.7320508
mark on the 1/2c pole.
* Note: I have staggered "H" shapes for visual ease.
23
One of My First Attempts
Now let's stay sharp with one more example and put some disks at the ends of our
directional poles. This time, instead of using clocks we'll set off simultaneous flashes from
the ends of our perpendicular poles which will expand spherically and turn the disks off
after laser signals from the center of our directional poles set them in motion so that they
turn at a rate of once a second. Once each flash is triggered we can ignore the other
reference frame.
The rest frame is easy. It takes 1/2 of a second for the laser's light to reach the disks
and turn them on. We can calculate the distance from the flash point at the end of the pole
to either disk as being 3.354102 and it takes light 1.118034 seconds to simultaneously
reach each disk. From the time of them being turned on to the time of our flash's arrival
each disk will have turned .618034 of a revolution.
(See Fig. 1)
No surprises there and I'm sure that you know by now what to expect in considering the
end result in the 1/2 c example - but there is beauty and mystery in the journey!
The flash expands spherically around its fixed point of origin as our 1/2 c contraption
continues its straight line course up the page. At the same time the signal from the center
heads towards each disk. In the direction of the trailing disk the laser will travel 2/3 of the
contracted pole's distance of 1.2990381 which is .8660254 and the disk will meet it after
moving 1/3 that distance or .4330127 for an absolute time of .2886751 - which converts to
.25 of a relative second. It is 1.0704662 away from the flash’s arrival point at .2044408
past the perpendicular point of origin (T = 0) where it will be turned off. The time that it will
take to travel to that point is .7136441 of an absolute second which converts to .618034 of
a relative revolution.
(See Fig. 2 and 3)
24
Rest Frame
(Fig. 1)
R
=3
.35
41
02
R
=
5
1.
laser fired from here
T=0
Flash arrives after 1.118034
seconds and turns off
synchronized disks at the .618034
mark.
25
Lasers reach
disks and turn
them on when
flash has
travelled for
1/2 of a second.
(Figures 2 and 3)
Dir. of motion
1/2 c
Lasers to
disks
T= 0
Flash
T=0
T = .2886751
Flash after .2886751
seconds.
Device has travelled 1/2 as far as flash.
T=0
R
Laser starts
rear disk
=
54
02
66
.8
26
Now the laser that was directed to the forward disk, which is also 1.2990381 away, will
have to travel twice that distance, 2.5980762, and it will take .8660254 of an absolute
second to get there - .75 in the 1/2 c frame. Once again notice the 1/2 of a relativie second
difference in the start up laser arrival times for each disk. It's that twist in the shaft again that perfect example of our inability to synchronize anything with certainty in the direction
of motion.
(Fig. 4)
Flash after .8660254
seconds
Laser starts
forward
disk...
T = .8660254
2.5980762
8
2.59
R =
2
076
T= 0
...while rear disk has
already turned for 1/2
of a relative second.
27
Once the forward disk is started it too will travel for a distance of 1.0704662 to the point
at 3.6685424 past the perpendicular point of origin where, after .618034 of a revolution, it
too will be turned off. Both disks are synchronized and the 1/2 c observer concludes he's
at rest and all is right within the universe! (Fig. 6)
(Fig. 5)
Flash at T = 1.0023193
Forward disk
shows .118034
(relative)
seconds...
78
95
006
3.
R=
...when rear
disk stops,
showing
.6118034 at...
....2044408 past
T=0
T = 0
28
(Fig. 6)
light reaches forward
disk after 1/2 a relative
second more and stops
it too at
.6118034
R=
3.4641016
4.7
39
008
7
3.6685424
Flash at T = 1.5796696
Rear disk had stopped here at .2044408 past T = 0
T=0
29
The only time you can be sure of position is when your marks are not moving. Once
they move, uncertainty is certain! Hmmm…that sounds familiar!
Length alterations
Here's a good one! Since two guys can agree that they are passing each other at 1/2 c
they decide to shorten the rest frame pole to 93,06049% of 3 which is 2.7918146 and
lengthen the 1/2 c pole by 1 divided by 93,06049%, or 1.0745699 times the contracted
pole of 2.5980762 so that it too will be 2.7918146. When the two poles pass each other
now, all four disks will start simultaneously. Flashes from their respective centers will turn
off the rest frame's disks at the same time while the 1/2 c disks, being stopped at different
times, will show a twist of .5372849 of a relative second - which is 1.0745698 times .5 of a
relative second – the increased twist in the shaft is in exact proportion to the lengthening.
Length Alterations
Direction of Motion
1/2 c
2.7918146
Shortened rest frame
pole
lengthened 1/2 c pole
All four disks and the flashes at the centers
start at the same time
30
T=0
Rest frame flash will stop
synchronized disks
1/2 c flash turns off rear
disk after
.3102016 seconds.
However, time dilated disk
shows a time of .2686425
1/2 c
Synchronized rest frame
disks have already stopped
and show a time of
.4653024 of a second.
Rear disk
stopped after
.3102016 but
shows
.2686425...
...and forward
disk stops now
after .9306049
and shows
.8059275...
...the difference being .6204032 in the
absolute which translates to .537285 in
the 1/2c frame.
31
Both guys measure the true values of the event without really knowing it and the 1/2 c
guy puts forth the notion that maybe he should've shortened his pole while the rest frame
guy should've lengthened his. Shall I continue?
O.K. So the rest frame observer lengthens his pole of 3 by 1.0745699 to 3.2237097
while the contracted pole of the 1/2 c observer is further shortened to .9306049 of
2.5980762 or 2.4177824. Now the rear disk of the 1/2 c craft will be turned on with the
"forward" disk of our rest frame craft and it will take exactly .5372849 of an absolute
second for the forward 1/2 c disk to reach the rest frame "rear" disk. When the rest frame
disks are turned off simultaneously, the measurement that is supposed to tell you how
“fast” you are moving is waiting.
And what about our 1/2 c guy? Well, an absolute time difference of .5372849 in this
frame means that his disks are un-aligned by .4653024 of a relative second. That's the
new twist for his shorter shaft. When he sends the light signal that will turn those disks off
we know that they will have to show that he is at rest. Let's see - 1/2 of 2.4177824 is
1.2088912 and 2/3 of that is .8059274 taking light .2686425 of a second to go "aft" while
for the light to reach the forward disk it takes 2 times 1.2088912 which is 2.4177824 or
.8059274 of a second for a difference of exactly .5372849. .5372849 times our time
dilation factor for 1/2 c of .8660254 equals .4653024. It is perfect!
Length Alterations
cont...
1/2 c
3.2237097
Rest frame
"forward"
disk starts
with 1/2c
rear disk.
Flashes at the
center
haven't gone
off yet!
Lengthened rest
frame pole.
Shortened 1/2c
pole
2.4177824
.8059273
T = 0
32
Flash goes off
when rest frame
"forward " disk
shows .2686425
of a second...
1/2 c
Mutual flashes
...while 1/2c
disk shows
only
.2326512
.4029637
T=0
1/2 c forward disk reaches rest frame "rear"
disk after .5372849 absolute seconds. The rest
frame flash will turn the rest frame disks off
simultaneously in .2686424 seconds showing a
.5372849 "twist" in the shaft. The rest frame
guy will then
have a 1/2 c measurement!
T=0
1/2 c flash
reaches rear disk
which stops at
.4653024 just as
forward disk
starts. Flash must
now catch up to
forward disk...
1.6118546
...reaching it here after an absolute time of .5372849.
33
Rest frame disks have already stopped at .8059273 and
.2686425 showing a difference of .5372849.
Light stops 1/2 c forward disk after .5372849
which is actually .4653024 1/2 c time. Disks
are synchronized and show the rest frame
synchronized measurement!
1.6118546
Of course, however, where-ever there is a relative measurement between two
observers of 1/2 c, such as our .333… and .71c example, and they make the same
alterations as depicted above they will always get the same results. It’s as if the rest
frame/1/2 c example becomes a mathematical template for all other situations where
there is a relative measurement of 1/2 c between two observers. The next example shows
this well.
34
“If you are moving at 1/2 c and you throw a ball at 1/2 c what will…?”
Imagine now that you propel a clock to the left at 1/2 c along a rest frame pole of 3. It
will take 2 rest frame seconds to reach the end but will show on its face a time of only
1.7320508 seconds. Imagine, too, that at the instant you propelled your clock an observer
moving past you to the right at 1/2 c also threw a clock at what he considered to be 1/2 c
in his frame of reference in the same direction of his motion down the length of his pole of
3.
Now, when the rest frame clock reaches the end of its two-second flight at the end of its
pole the 1/2c observer will be 600,000 km distant. If the 1/2 c observer also had a pole of
some great length attached behind him, that contracted pole would show him that when
the rest frame clock arrived at the end of its pole it would have been alongside the
6.928203 mark on the .5 c pole showing that rest frame time of 1.7320508. Identical
experiments done in different frames of reference must render the same results so we
can deduce that the clock which the 1/2 c guy launched at what he considers to be 1/2 c,
and possesses a velocity relative to the rest frame of which we don’t know yet, must arrive
at the 6.928203 mark on the rest frame pole also showing a time of 1.7320508. Since we
know that the clock and its destination at the end of the 1/2 c pole must arrive at the
6.928203 mark and we know that the end of the pole travels at 1/2 c we can calculate the
time it will take. The difference between the end of the contracted 1/2 c pole, which is
2.5980762 from where the clock was launched, and the 6.928203 rest frame mark is
4.3301268 and it will take both the end of the pole and the clock 2.8867512 rest frame
seconds to arrive there. Since it would have taken light 2.309401 seconds to travel the
same distance of 6.928203 we can divide that time by 2.8867512 and come up with a
velocity for our fast moving clock of .8 c. If you divide 2.8867512 by 1.7320508 you get
1.666… which is how long a second lasts at that velocity of .8 and, for the length
contraction, 1 divided by 1.666…. gives us .6. Using the equations of relativity are a lot
simpler than plotting everything out thusly but you can really see what those equations
are saying by setting it up like this!
35
6.928203 mark
on 1/2 c pole
6.000000
(6.928203 on the contracted
pole trailing behind our 1/2 c
observer's craft.)
.5 c
After travelling
for 2 rest frame
seconds the
rest frame
observer's 1/2c
clock shows
1.7320508
when 1/2 c
observer is
6.000000 away.
Point where observers passed
each other and launched their
clocks: t = 0.
Position of
contracted
1/2 c forward
pole at t=0.
2.5980762
End of forward pole
travels
4.3301268
taking 2.8867512
seconds...
...which is the same time it takes the clock to
travel 6.928203.
Rest frame 6.928203
t=0
Light would travel 6.928203 in 2.309401 seconds.
Divide that by 2.8867512 and you get a velocity
for our second clock of .8 c.
36
Now how would we fare if we tried using the same technique with the velocities of
.333…and .7142857 c? Since our observers will only be able to tell that they are moving
past each other at what they think is 1/2 c they will be looking for the same results that we
just encountered in our 1/2 c/rest frame example. We can begin by calculating how long it
will take for the 6.928203 mark on the .71 c pole to reach the end of the .333…c pole.
When it does reach the end the .333…c clock should have just arrived showing a time of
1.7320508.
Now, just as the observers had passed each other and allowing for their contracted
poles, the .71 c pole’s 6.92 mark was an absolute distance of 2.020305 from the end of
the .333…c pole and it would have to take 1.767767 absolute seconds for the 6.92 mark
to arrive. The clock that was launched in the .333…c frame had to travel from the point
where the two observers passed each other to the point where the .71 c mark and the
.333…c clock and pole-end meet for a distance, in that same time of 1.767767, of
1.0606602. If it would take light .3535534 of a second to travel that distance of
1.0606602, simple division shows us that our clock would have travelled five times slower
rendering a velocity of .2 c. The time dilation of our clock at .2 is 1.0206208 or 97,97959%
of a rest frame second. You could divide our absolute time of 1.767767 by 1.7320508 to
get the same result.
Both clocks are launched down their respective
poles as .71 c observer passes the .333...c
observer at T= 0.
6.928203 mark on .7142857 c pole.
.7142857c
2.020305
.333...c
End of .333
pole...
...which is
2.8284272 long
37
Remember! The
.333 clock is
moving towards
the oncoming end
of the .333 pole!
T=0
6.928203 mark
arrives along with
.333...c clock at
end of .333...c
pole showing a
time of
1.7320508.
This clock still hasn't reached the
end of the .71 c pole.
Clock has travelled from T= 0 a distance of 1.0606602 in a time of 1.7677659. Since light would've
taken .3535534 of a second to travel that distance the velocity of the clock must be .2c.
1.7677659 divided by 1.7320508 equals time dilation factor for .2c showing 97,97965% to a rest
frame second.
Now let’s see how fast the other clock is travelling. Once again, when the two
observers are side by side and the .71 c clock is launched to the right of the page towards
the front end of his pole of 3 which is contracted to 2.0995627, the end of his pole is
4.4324101 away from the 6.928203 mark on the contracted .333…c pole where they are
supposed to meet. And they will meet at a point 10.410331 from the clock’s starting
position taking 3.8783583 rest frame seconds. Since it would take light 3.4701103
seconds to travel that distance we can divide that time by our clock’s travel time of
3.8783583 to obtain a velocity for our clock of .8947369 c. Time dilation at that velocity is
.4465938 to the second, multiply that by 3.8783583 and we get 1.7320508.
38
T=0
.7142857 c
.333...c
.71 c clock arrives at the 6.928203
mark on the .333...c pole also
showing a time of 1.7320508.
When T
equaled 0,
end of .71c
pole was
2.0995627
from clock's
launch
point...
...and 8.3107679 from
clock's point of arrival
3.8783583 seconds later.
Clock travels the total distance of 10.410331 in 3.8783583 seconds.
Light would take 3.4701103 seconds.
The light's time of 3.4701103
divided by the clock's time of
3.8783583 gives us a velocity
for the clock of .8947369 c.
Time dilation at .8947369 c is
.4465938 to the rest frame second.
44,65938% of 3.8783583 gives us
1.7320508 for our fast moving clock.
39
Disks and Angles
Let’s say we had a pole of 3 in the rest frame and we decided to launch a disk from the
“leading” end, which would travel at a rate of 1 km a second, perpendicular to the direction
of our supposed motion. If at the same time we sent a flash of light to the other end of the
pole and launched a second disk, that disk would be 1 second behind the first and if we
were to draw a line from the first disk down to the second that line would be at an angle to
the perpendicular. If we now were to send a second pair of disks which were to travel at
twice the speed of the first two we would notice that a line connecting the two faster
moving disks would form an angle which was more inclined to the perpendicular than the
first. We know that the faster moving disks will catch up to the slower two and we could
reason that since the angle formed by the faster disks is a result of the upper one being 2
km distant from the pole when the lower disk is released then if we were to shift the upper
disk back 1 km we would then have equal angles and the two faster disks would each
reach their respective slower counterparts at the same time. Synchronized flashes could
be set off and the light from those flashes would reach an observer at the center of the
pole at the same time telling our rest frame observer that indeed he was at rest.
1 kps
Supposed
direction of
motion
Light flash
travels "down"
3
in 1 second
Light flash from "top" of pole launches
second disk 1 sec. later.
40
A one-time, 1 km adjustment in position
renders similar angles...
1 km
Second pair of
faster moving
disks are
launched in
the same
manner.
O
...which will set
off synchronized
flashes when
faster disks catch
up to the slower
ones.
An observer at O
can then measure
the flashes'
arrival times.
2 kps
At 1/2 c when we launch our disk and send a light signal down to the bottom of our
pole, the top disk will only be able to travel 1/2 of a km before the bottom one is started
because it will take only 1/2 a relative second for the light flash to get there, right?
(Two-thirds of our contracted pole of 2.5980762 is 1.7320508 taking our beam .5773503
absolute seconds which converts to 86,60254% of that for .5 of a 1/2 c second.) If we
were to draw a line now from one disk to the other we would have an angle representing
that 1/2 second difference. When we send the two faster disks a little later at twice the
speed of the first two the top one will also travel for just 1/2 of a relative second reaching
only to the 1 km mark when the lower one is ejected. Now when we make our adjustment
by moving the upper disk back 1 km we can easily see that we will no longer have
synchronization. The lower flash will go off 1/2 a second sooner, take .75 of a second to
reach the center while the light from the top flash will “rush” down in .25 of a second and,
in arriving at the same time as the lower flash, the observer will once again conclude that
he is at rest.
41
1/2 km
1/2 c
light flash travels
"down" 2/3 of the 1/2
c pole length of
2.5980762 in 1/2 of a
relative second
meeting lower disk
here.
Upper disk has only
travelled 1/2 of a km
when light flash reaches
and starts lower disk.
1 km adjustment is too much
in the 1/2 c frame...
1 km
O
...and so there is no synchronicity in disk arrival times. The
top disk will set off the flash 1/2 of a relative second later
giving the lower flash the head start it needs to arrive at
the center at the same time!
42
And if the 1/2 c observer decides to move his disk back only 1/2 of a km, reasoning
deductively that which we can see on the page, then indeed he will synchronize his
flashes and derive a 1/2 second difference in arrival times at his central point of
measurement. However, any alterations in one frame, as we know, must be made in the
other and so a rest frame alteration of only 1/2 of a kilometer will cause the faster upper
disk to reach the slower one 1/2 of a second sooner causing the light from that flash to
arrive 1/2 of a second sooner at the center just as in the 1/2 c example. Both observers
conclude that they are both moving at 1/2 c!
You just can’t win!
Mutual Illumination
Let’s build two boxes that are each illuminated within and which each possess a
window which is facing the other and let’s move one at 1/2 c past the rest frame one. As
the 1/2 c box approaches and the windows pass, each observer will be able to see into
the other’s box. The illuminated area will increase until each window is filled with light and
then once again diminish as the 1/2 c window passes completely by.
(Fig. 1)
In studying these drawings one might be tempted to think that since the 1/2 c window
at one point was entirely “bracketed” by the larger perimeter of the rest frame window and
at no time was the situation reversed then the 1/2 c guy shouldn’t ever be able to see the
same thing and we might finally be able to say that there is an observational difference
between the two frames and absolute motion should finally be measureable. But we know
better than that!
(Fig. 2)
The 1/2 c observer is not only seeing into the past but he is seeing the different
positions that his box has occupied at different times in the past. In using the concept of
time merely as a tool for measurement we can say that he is not only looking back through
time but he is seeing his box smeared through multiple positions - multiple events blended
together creating the illusion of a rest frame “bracketed” observational result. Nothing
mystical about it! Just the simple mechanics of light’s motions and the differing distances
that it must travel on the way to striking the eye! Here’s that twist in the shaft again!
(Fig. 3)
43
(Fig. 1)
Light begins to enter
each box as windows
pass each other!
window
A
A
Observer at B in
1/2 c box
B
Observer at A in
rest frame box
window
B
Notice that the 1/2 c window is
entirely bracketed by the larger rest
frame window...
B
A
B
A
As the 1/2 c box
passes, the mutual
illumination reduces.
...but at no time could the
rest frame window ever be
"bracketed" by the 1/2 c
window.
(Fig. 2)
44
...and the light from point B from the right
perimeter of the 1/2 c window from a
later position...
1/2 c
B
A
Light from point A at the left
perimeter of the 1/2 c window and
an earlier position...
Abberated line of sight for B
1/2 c observer must see rest frame
box as being contracted.
AB
Abberated line of sight for A
...will arrive at the
same time at point AB
and abberate thereby
showing our 1/2 c
observer a "bracketed"
rest frame window.
B
Point B in the past...
A
45
...and point A even further in
the past.
(Fig. 3)
...and the light from disk
B...
B
A
Light from disk A...
AB
...arrive at point AB and
abberate showing a
synchronized result.
In order for the 1/2 c
observer to see this
"rest frame" result we
must consider the
"shaft" to be physically
twisted as it moves
through space and the
particles of light to
possess absolute
motions and to have
originated from fixed
points in space.
46
Now that you’re an expert…
Let's say that our 1/2 sec. difference is equivalent
to 1/8 the rotation of our disks. The lower sphere
is therefore, upon ejection, linearly, ahead of the
upper one by 1/8 of a unit of rotation and we
will call their difference in postion the natural
angle for this particular apparatus at 1/2 c.
.
.
p
2.5980762
Note: The spheres are ejected at points "p" but
do not actually travel around the circumference
of the disks unless we want to delay them for
one rotation. All ejections are initiated upon the
arrival of a flash of light whereupon they fly out
at a tangent to the radius of the disk and
perpendicular to the direction of motion.
Natural Angle at
1/2 c for 1/2 of a
relative second
difference.
.
.
p
disk rotation 1/8 per 1/2 second
1/2 c
.
.
p
.
p
.
disk rotation - 7/8 per 1/2 second
47
If we now spin similar disks 7times
faster and which rotate in the
opposite direction and we delay the
ejection of the lower sphere by one
rotation then when 1/2 of a second
has elapsed and the upper sphere is
ejected the lower one will still not
have completed its extra circuit - It
being 1/8 of a rotation behind.
.
.
We now have an angle created by the
faster moving spheres which is equal to
the natural one created in our first
example. The result will be
synchronized flashes when they meet.
.
.
If we then cause our spheres to enter onto a stationary track(s)
which is the circumference of a large circle then those
synchronized flashes can be made to transmit the information
of each event equal distances to the point at the center
whereby two robotic craft, for instance, could be made to
simultaneously accelelerate or decelerate to any velocity we
wish. Since they would be programmed to do exactly the same
thing - and they would be doing it at the same absolute time they would remain separated by an absolute distance of
2.5980762.
..
Flash at impact
directed to center
The position of both impact points
upon the circumference show a
"natural" angle of 1/2 of a second.
Flash at impact
directed to center
..
48
.
Before we launch our synchronized 1/2 c
robotic devices let's consider what the
rest frame guy's set up is going to look
like. His spheres, of course, are going to
be naturally synchronized forming no
angle and being in line with his "direction
of motion"...
v = 1/8 of a rotation
per 1/2 rest frame
second
.
Rotation
...but remember that we have to apply the
same rules to the faster spinning disks that we
used in the 1/2 c frame. Relative to the 1/2 c
observer then, the rest frame's apparent
motion is to the bottom of the page and we
would have to delay the "aft" disk, which is the
upper one, in the same way. Since both spheres
will start at the same time the "lead" sphere
will be, linearly,
7/8 of a rotation ahead of the "aft" after 1/2 of
a second and 8/8 ahead when the "aft" sphere
is finally ejected.
.
"Direction of motion"
.
Rotation
49
Aft flash
.
.
When the forward spheres meet and flash the aft spheres are still
8/8 apart. In 1/2 of a second more the "natural" sphere will move 1/8 and the other,
moving 7 times as fast, will move 7/8 and they will meet upon the circumference of
our great circle showing a 1/2 second "natural" angle - as in our
1/2 c example. Remember that actual 1/2 second difference in impact times, though.
..
..
While our 1/2 c robotic craft can be started in a
synchronized manner, here, in the rest frame, the "forward"
flash will start it's robot 1/2 of a second sooner.
..
50
.
.
.
.
(2.5980762 at 1/2 c)
.
2.25
If we bring the 1/2 c robots
into the rest frame the rest
frame observer will claim that
the distance separating them is
2.5980762.
2.5980762
.
(3.0 at 1/2 c)
.
3.0
2.5980762
.
Of course, in the rest frame, the forward robot has a 1/2 of a second
head start as it chases after the 1/2 c mothership. If we ignore the
time it takes to accelerate and just consider each robot capable of
virtually instantly attaining any desired velocity then in that 1/2
second the robot will travel a distance of .75 (at a velocity of 1/2 c)
when the aft robot starts up. The distance separating them would
then be reduced to 2.25 from 3 which on a contracted 1/2 c pole
would be measured as 2.5980762.
When the 1/2 c robots reach the rest frame, the pole
One might have the brilliant idea that since the
has reached its maximum, un-contracted length
1/2 c robots would always maintain a separation
showing 2.5980762 and as they re-accelerate, still
of 2.5980762, a pole could be made to accompany
moving away from the 1/2 c mothership, the pole
them and they could measure the varying
begins to contract again. When they reach "negative"
distances that the pole would show as it expanded
1/4 c, or .666...c to the 1/2 c observer, measurement
as they approached the rest frame.
relative to the pole once again shows the robot
separation of 2.6832816.
.
At 2/7 c the pole
would show a
separation of
2.7110883
.
2.5980762
.
At 1/4 c the
distance would
be 2.6832816
.
-"1/4 c"
2.5980762
2.5980762
.
.
51
.
.
Absolute
velocity of
.666...c
1/2 c
mothership
The absolute velocities of
.2857143 and .666...c will both be
measured by the 1/2 c observer
as 1/4 c on "either side of zero".
.
.
Robots at 1/4 c
measure 2.6832816
off of accompanying
pole...
.
Absolute
velocity of
.2857143
...which the 1/2c
craft measures
as a recessional
velocity of
.2857143.
.
..
T=0
..
.
At "negative" 1/4 c
the measurement is
again 2.6832816...
At the rest frame
mothership after 1/2 of a
second at a velocity of
.2857143 the "forward"
robot has reduced the
separation between itself
and the aft robot to
2.5714286 which will be
measured upon the
accompanying pole as
2.6832816 at that
velocityof .2857143...
...while 1/2 of a second at
.666... reduces their
separation to 2.0 which will
be measured once again as
2.6832816 at .666...c.
...which is measured
as receding from the
1/2c craft as .666...c
.
52
Well that didn't tell us anything! Maybe if we were to find an intermediate velocity which
both observers could agree upon we might be able to make some interesting measurements.
Letting C = 1 ,
.5 - .2679492
1 - .5 x .2679492/c 2
= .2679492 c
1 - .2679492/c 2 =
Our intermediate velocity.
1 / .963433
=
.
1.0379549...
...which we
will apply
to our pole.
.
1/2 c
96,3433 % of a rest
frame second
Robots simultaneously
decelerate to a measured
velocity relative to 1/2 c
frame of .2679492 c which
is...
Rotation once every two seconds
this frame's time.
...equal to an absolute
velocity of .2679492 for
both "1/2 c" and "rest
frame" devices.
Sychronized "1/2 c" disks
.4817165 time difference
.
Launching our rest frame "forward" robot for 1/2 of a
second at .2679492 c will reduce the separation between it
and the "aft" one to 2.5980762. Multiply that by 1.0379549
and it will be measured as a distance, upon our
accompanying contracted pole, of 2.6966859. If we now
replace our robots with spinning disks we would see that
after 1/2 of a second at .2679492 the forward disk would
show that only .4817165 of a second had passed when the
aft disk was launched.
53
Rotation once every two seconds
this frame's time.
0c
.
0
0
It would be quite easy to bring the
crafts side by side without ruining the
proportions that they were launched
with and then each observer could
compare disk positions. They could
each agree that, at the moment, the
forward *1/2 c disk is synchronized
with the aft *rest frame disk and the
rest frame forward disk is ahead by
.4817165.
+ .4817165
0
If we were to synchronize the rest frame
forward disk with the 1/2 c aft disk then
the rest frame aft disk would be
.4817165 behind the 1/2 c forward disk
or the 1/2 c guy could say that his was
ahead by that amount. Even though
both observers will agree that their
crafts must both be, in this example,
travelling at .2679492 c neither one can
once again be sure whose disks are
synchronized.
- .4817165
*Having originated from either the 1/2 c or
rest frame.
flash from center arrives aft
.2408583 before arriving "up
top".
Now, the twist in the shaft for an absolute
distance of 2.5980762 at v = .2679492 c is
.2408583 of a relative second. Which, of course,
as nature would have it, is exactly half the value
of the difference between our rest frame disks.
+ .2408583
54
Rest frame "tail"
1/2 c "forward"
0
-.48
-.24
C
Late flashes
0
+.24
Dir. of
rotation
1/2 c "tail"
+.48
Rest frame "forward"
.2679492 c
Now if, in the .26 c frame, we doubled each pair of disks, added our green "naturally" twisted ones and
synchronized the "tails" at zero (the left triplet corresponds to the 1/2 c observer and the right to the rest frame
observer) to the 1/2 c disks in the "forward" positions we would have all six pairs locked in these positions
relative to each other. If we were to set off flashes when the synchronized tails hit zero we would have, in
comparing the tail flashes alone, a difference in arrival times at the center, C, of .2408583 with the late flashes
arriving from the 1/2 c "tail" side. This would tell both observers that the disks were moving at .26 c up the
page - or following the now receding 1/2 c mothership. We also see that the rest frame disks have a .48 "twist"
in the shaft while our "natural" disks, which were started with a flash from the center, show .24.
Notice, too, that when our synchronized tails are at zero the forward disks exactly mirror their counterparts. If
we stagger everything then we could say that when the forward disks mirror their counterparts, and, only when
they are in this one position, then the tails can be said to be synchronized at zero.
So far we have absolute measurements and our observers are measuring their absolute motion. But we have
set everything up to the 1/2 c disk postions and, to be fair, we must use the rest frame disk postions and see
what results we get.
- .48
- .24
+ .24
+ .48
Synchronized tail flashes will arrive
.48 apart indicating an absolute
motion of .26 up the page.
55
These disks were synchronized at zero...
...with rest frame forward disk
+48
0
+48
In synchronizing our tails now with the rest frame disks we get the positions depicted above. We can see
that the three tails at the left have already flashed .48 sooner than the upper right tails and the difference
in arrival times, with the upper flashes coming to the center .24 later, will indicate that the "absolute"
motion of our observers is .26 to the bottom of the page. Aligning everything with the rest frame disks tells
the observers that they are "following" the rest frame mothership.
If we once again stagger our disks thusly and align the forward rest frame disks at the center to zero as we
did with the 1/2 c disks earlier we see that the mirrored disks are opposite the positions in our first example.
The lower left triplet flashed .48 of a second ago and the upper right triplet will flash in another .48 of a
second from now - the difference in flash times is .96 with the upper flashes arriving .48 late indicating once
again an "absolute" motion down the page of .26 c.
0
0
We have only scratched the surface here and it is tempting to think that with all the possible combinations
and comparisons that you can make you might find some subtle difference in measurement but it has
been my experience that you will always end up with a result that will tell you absolutely nothing about
the absolute. If you really want to test the theory further try the same set-up at .8 c and .5 c with the
intermediate velocity being .6772191 c. You will have to start right at the beginning though!
56
A simple observation
While, when an object passes in a straight line motion, two observers cannot come to
any absolute conclusions concerning their true motions, consider the following. If one
observer is at rest while another circles him at a constant distance at a velocity of 1/2 c
then if the central observer sends a signal every second it will reach the circumference of
that circle every second regardless of where our circling observer may be. That means
that the 1/2 c observer will receive a signal, according to his slower time keeping, every
.8660254 of a relative second while his signal, sent every relative second, would actually
be emitted 1.1547005 absolute seconds apart which the central observer would measure
as such - he too always being equidistant from the 1/2 c signal's source. Now imagine that
circle to be 1/2 the breadth of the universe and at the center once again is a source that
sends out a signal every second. Our 1/2 c traveler, moving along the circumference of
that great circle would actually be travelling virtually in a straight line, but he will still see
that each signal is arriving every .8660254 of a second because the straight line that he
would travel would deviate, if even by just an atom's width per unit of time, from a truly
straight path keeping him equidistant from that far-away source. In this scenario, both
observers would have true measures of their states of motion without being able to say
that they know their true states of motion. (I’m ignoring the time dilation effects of
acceleration which would depend upon the size of their respective circular orbits.)
57
Third Frame of Reference
Speaking of circles, let's take a different look at the famous "Twin Paradox" that graces
the pages of so many texts on relativity. Firstly, the rules of Special Relativity concern
uniform motion through space whereas the twin that travels through space to the star
experiences inertial effects when he slows, changes direction and begins his return
journey. Because the earth experiences no inertial effects we can assume the earth to be
moving uniformly with time passing at a constant rate while the astronaut must actually be
the one who is moving a greater distance and at a greater velocity. We can simplify it a bit
by imagining that he takes a circular route to that star and back so that the earth and that
star are opposite each other at points on the circumference of that great circle.
When time dilation was tested by flying an atomic clock around the earth it could be
said that the motions of the earth and that of the plane comprised a third frame of
reference within which the earth's motion was zero and the plane's was what it was. The
plane's motion is not uniform as it describes a circle around the earth and the inertial
effects that it encounters, though negligible, are still there and indicate a constant
absolute change in its position. Since the earth bound observer will not experience any
inertial effects he can state that his rate of time has not changed. The inertially affected
clock is therefore going to show that time had passed at a slower rate. Magnify this
reasoning to our great circle from earth to star and you basically have the same scenario.
If the astronaut had never stopped and returned but had continued moving uniformly
in a straight line away from earth then, as we have seen, no measurement could ever
have been made to show that his clock was actually the slower of the two. Because he
does turn around, the inertial effects of doing so prove that he is the one who is making
the greater journey through space and therefore the astronaut twin will be younger. The
astronaut twin's motion is greater not only in our "third" frame of reference but also
relative to the absolute frame. The fact that his clock is slower in the end proves that he
actually has travelled at a greater absolute velocity, and, in this case, presumably a
greater distance (see next example) through space though the absolute motions of the
bodies in our third frame of reference relative to the absolute frame are un-measureable.
Consider this scenario, too! If the earth's absolute motion was 1/2 c to the left and our
rocket was fired in the opposite direction to the right at what happened to be 1/2 c then our
astronaut would actually be at absolute rest. His clock would be keeping faster time and
he would age at a greater rate. But as soon as he "slows" his craft and those inertial
effects show up as he turns around, he would have to head home at a much greater
velocity than 1/2 c and he would experience a much more severe time dilation than that of
the earth or than what he would have experienced had he actually been travelling at 1/2 c.
By the time he finally caught up to the earth his clock would show that time had slowed
as if he had actually travelled through space away and back and this would prove that he
had still travelled at a greater absolute velocity through space - though in this case both
will have travelled the same distance.
58
Twin Paradox Revisited
Earth is moving at 1/2 c
Rocket is at rest
After 1 rest frame unit of time rocket
turns to catch up.
1/2 c
The 1/2c measure of
time is .8660254
1.00000 unit of
time
59
Rocket reaches earth after 2 additional units of time for a total of 1 absolute unit plus 2 time
dilated units at .75 c which equals a time of 2.3228757 versus earth's constant 3 units at
1/2 c which equals 2.5980762.
Distance per unit of time
at .75 c
T = 2.3228757
v = .75 c
v = .5 c
Distance per unit of
time at 1/2 c
T = 2.5980762
While one cannot, by using inertial effects, measure one's absolute
velocity, the resultant time dilation can prove that one's absolute
velocity was greater.
60
Well, it's time to move on!
The Absolute Doppler Shift
The main recurring theme in all of this is the continuity of measurement from reference
frame to reference frame which prevents us from measuring any form of absolute motion.
Let us now consider some other aspects of the theory in our attempts to find a loop-hole in
the law.
If you have an oscillating electro-magnetic charge in the rest frame that produces a ray
of light of a wavelength of 5000 (A)ngstroms, that same source will oscillate at only 86%
at, you guessed it, 1/2 c. A comparable oscillation in the rest frame of 86% would produce
a longer, less energetic wavelength of 5773 A so we might deduce that our 1/2 c ray of
light will be energetically equivalent to a rest frame ray of 5773 A. We also know that the
1/2 c guy must measure 5000 A and any signals back and forth between reference frames
must show identical results. But first consider the following!
In the 1/2 c craft, let's place our light source in the rear and direct our beam to the front.
Since the oscillation is producing a 5773 A equivalence then we might deduce that as the
wave leaves the source and the distance from crest to crest is halved as the source
chases the emitted light, we will end up with an ultra-violet ray of 2886 A that travels freely
through the space in the cabin of the craft on the way to the front wall. When that
ultra-violet ray touches the point of reception - the eye or photographic paper, etc..., - that
point of reception will red-shift that ray back down to a 5773 A equivalent. The energy that
was emitted must be seen to have the same value upon arrival regardless of the changes
that it may have undergone on the way there. If our light source was in the front of our
craft, a ray directed towards a point of reception at the rear would travel in a red-shifted
manner on its way through free space where it would promptly blue-shift back “up” to that
5773 A equivalence.
V=C
Source at
rest
.
Source
moves
.
5773 A
If in the same time
the source moves at
1/2 c, wavelength
will be halved.
.
.
5773 A
2886 A
61
1/2 c
source
.
.
eye
The ray moves freely through space on
the way to the eye as an ultra-violet ray
of 2886 A!
.
.
As the light
strikes the eye,
the eye moves
away and robs
the ray of its
energy...
...redshifting it to
a 5773 A
equivalent.
.
.
5773 A
2886 A
Note: The depiction of the 5773 A redshifted ray is a representation of the
absorption of energy in the 1/2c frame and does not exist in the absolute!
Remember, the wave-front’s velocity may be c in the absolute but relative to the 1/2 c
craft its only moving 1/2 as fast. The red-shift will hide this and the expected energy
reading will “verify” that measured constant velocity of c.
62
The “Wave-chopper”
If we had a ray with a wavelength 300,000 km long, it would take 1 second from crest to
crest to pass. At 1/2 c it must also appear to take 1 second to pass so we'd have to
visualize it thusly: That 1/2 c wave, in order to form, would have to first be emitted for 1
relative second, or 1.1547005 absolute seconds, so that the beginning of the wave would
be 3.4641016 from the point of origin after that second. At the same time the craft would
have travelled 1.7320508 (to the right of the page) when the end of the wave is emitted,
compressing, or blue-shifting, the wave to the same length of 1.7320508. When the wave
reaches the other side and is red-shifted back to the original emission energy, the second
or end crest will be 1.7320508 away from the first and will travel 3.4641016 as it catches
up and is absorbed for a measure of 1 relative second. 3.4641016 is exactly the length
that it would’ve been had it been emitted from a rest frame source which was oscillating at
our 1/2 c value of 86%. (It is interesting to note the recurring distance of 3.4641016 for
both examples! At rest, the length is actual while at 1/2 c the length becomes actual once
the motion of the craft is included. It's as if the delivery of a specific energy implies a
specific wavelength ( wavelength equivalence) and distance regardless of the motion of
the source. We will revisit this idea.)
And, if we had a "wave-chopper", our rest frame disks would chop into the crests in a
synchronized manner while at 1/2 c the rear disk would chop into the trailing crest first and
1/2 a relative second later, when the lead crest would reach the first disk...but you know
how that works by now! So even though we had, in our previous example a 5773 A
equivalent, it will be measured as being 5000 A.
Once again our sense of time at 1/2 c is telling us that our wave is 300,000 km long.
Rest frame synchronized "chops".
300,000 km
63
1/2 c
First "chop"
1.7320508
wavelength
2.5980762
Pole length
.8660254
Leading crest will be
"chopped" after
travelling twice this
distance or 1.7320508
which will take .5773503
of a second which
converts to 1/2 a second
in the 1/2 c frame.
There's that 1/2 a relative second
twist in the shaft again!
Second
"chop"
1.7320508
64
More Doppler Shifting
At 1/2 c, a 5773 A ray, if we were to direct it out the "back door" to a rest frame
observer, would red-shift. As the first crest left and travelled a distance, the forward
motion of the craft would have moved the emission point 1/2 of that distance again before
the second crest was emitted, causing that wave to stretch to an absolute value in free
space of 8660 A. And that's the red-shift that would be measured, being absolute, by the
rest frame observer. The rest frame 5000 A ray, upon being received in the1/2 c frame,
would stretch out to double the wavelength, or 10,000 A - which also would be measured
as 8660 A - (remember our wave-chopper). Both observers measure the same thing - as
they should.
1/2 c to Rest frame Redshift
5773 A
equivalence...
...plus movement of 1/2 c source...
Wave's
direction:
V=C
towards
rest frame
observer
8660 A
...equals an absolute redshift!
65
Rest frame to 1/2 c Redshift
.
Rest frame light
source
5000 A
Wave direction
1/2 c observer
5000 A ray doubles to a 10,000 A
equivalence which is measured as
8660 A in 1/2 c frame!
They could reason with each other and decide that if they each fired an ultra-violet ray
of an agreed upon value towards each other it should red-shift down to an equal value in
their respective frames. We've seen the 1/2 c example of 2886 A doubling to 5773 A and
being measured as 5000! And when the 1/2 c guy creates what he thinks is a 2886 A ray
it's actually going to be equivalent to 3333 A due to time dilation. Multiply this number by
1.5 as it leaves aft and you get an absolute ray moving through space of 5000 A.
66
2/7 c
At a velocity of 2/7 c, or .2857143 c, our 5000 A ray aboard ship would be time-dilated
to 5217 A which if multiplied by 1.2857143 as it leaves aft becomes 6708 A. That's the
absolute red-shift for 2/7c.
.
Rest Frame - 2/7 c
...becomes 7000 A which is
measured as 6708.
Rest Frame 5000 A...
Rest
frame
observer
Absolute ray of 6708 A is
ejected by 2/7 c craft.
2/7 c
Now, if a 1/2 c craft was passing a 1/4 c craft, with both moving in the same direction,
their mutually measured velocity would be 2/7 c. Let's check the theory using the
Doppler-shift. At 1/2 c we know that a measured 5000 A is actually 5773 A which will
red-shift to 8660 A. As the 1/4 c guy moves into that ray he will blue-shift it up by 4/5 to
6928 A which will be measured as being, by applying the time dilation value for 1/4 c,
6708. Conversely, 5000 A in the 1/4 c frame is equivalent to 5163 A which upon leaving
the front of the craft promptly blue-shifts to 3/4 of that to a ray in the ultra-violet of 3872 A
which will then red-shift at the 1/2 c craft to 7745 A which will be measured as 6708. And,
once again, we are bound by measurement to never know what’s going on in between.
67
Relative 2/7c
1/4 c
1/2 c
1/2 c guy passes the 1/4 c guy and both measure the
velocity of the other as being 2/7 c.
1/4 c
1/2 c observer redshifts ray to 7745 A which he
measures as being 6708.
3872 A
(7745 A)
8660 A
(6928 A)
1/2 c
1/4 c observer blueshifts
ray to 6928 A and
measures 6708.
Both observers can claim to be at rest measuring an absolute 2/7 c redshift!
68
Kinetic Energy
Relative to the rest frame, or as I like to see it in this book, the absolute frame, a moving
body’s kinetic energy increases dramatically as it approaches the velocity of c and this
causes the mass gain. It is more immoveable. Once we know and calculate the mass gain
for a given reference frame we can, when calculating the movement of particles within
that frame, from an omniscient point of view, use the classical equation for kinetic energy
and simply halve that greater mass. For example a rest frame mass of 1 moving at a
velocity of 1 will be read as .5 times 1 squared. Whereas at 1/2 c we would halve a mass
of 1.1547005 to .5773503 and multiply it by the square of the lesser distance travelled in
the same rest frame unit of time of 1 which is .8660254. And that will give you 86% of the
rest frame value of kinetic energy. You know the mass gain, you know the lesser distance
travelled relative to our absolute “standard time”, or rest frame time, and you can now
know, from an omniscient point of view, the absolute value of the kinetic energy of an
object in that reference frame. This applies within any reference frame when the velocity
of the object or particle, as it shifts within that frame, is much less than c.
Now, the kinetic energy of a 5000 A wave, being ascribed an arbitrary value of .5, will
propel a receiving particle a perpendicular distance of 1 in a time of 1 and impart to that
particle that kinetic energy of .5 while a 5773 A wave will impart a kinetic energy of
86,60254% of .5, which is .4330127, and propel our particle a distance of .9306048 in the
same time of 1. Simple ratios and proportions!
At 1/2 c we know that a measured 5000 A wave is equivalent to a rest frame 5773 A
wave and therefore should also possess only 86% the kinetic energy. At 1/2 c an
impacted particle will take 1.1547005 seconds to go that un-contracted perpendicular
distance of 1 so that we can deduce that after 1 absolute second, it will have only traveled
.86,60254% of that distance. While in the rest frame a distance of 1 squared times half the
rest mass gives us .5, a distance of .8660254 squared times half of our more massive
particle of 1.1547005, which is .5773503, equals a kinetic energy within the 1/2 c frame of
.4330127 - as it should since that is what a 5773 A wave imparts as compared to what is
rendered by a 5000 A wave. What this means is that while the energy input from frame to
frame may appear to be equivalent as measured by an observer within that frame, it
actually diminishes with increased velocity relative to the absolute. Movement within the
frame is lessened and so is the kinetic energy!
Throwing a ball against the wall in the rest frame with all your might involves more
kinetic energy than at 1/2 c where a more massive arm is moved with 86% the rest frame
energy and hurls a more massive ball at a slower speed which then impacts that wall with
less force. The dent that the ball may leave is supposed to be identical to a rest frame
dent though because the atomic forces that hold the wall together are weaker and the ball
has more inertia, staying in contact with the wall for a longer time before rebounding. And
because your sense of time is supposed to have slowed in direct proportion with all of
these changes you’re not supposed to be able to tell that anything has changed relative to
a comparable rest frame experience.
69
Kinetic Energy
.
Time
.5
1
.4330127
1
.9306048
.4330127
1
.8660254
d
=
1
5000 A
Kinetic
energy
Distance
1
Rest Frame
.
d
=
1
5773 A
5773 A
equivalence at
1/2 c
d
=
1
.
5773 A wave imparts same kinetic energy in each frame but 1/2 c particle is more
massive and moves with greater reluctance!
Please note: I stated in the text that the particles are impelled in a manner perpendicular
to direction of motion for ease of visualization and measurement as there is no length
contraction. On paper, however, it is easier on the eyes to depict them as I have above.
70
Distance and Delivery
Because of the rules of time dilation and the continuity of measurement we see the
delivery of energy as being a slowed down version of rest frame values. But if you
consider the true wavelength of the light in each frame as it masquerades as some rest
frame value, you'll see that the time of delivery for each rest frame wave equivalence
actually matches the time that it would take that wave to arrive in the rest frame. It's as if
the wave, the energy delivered and the time it takes to deliver that energy are constant
and require an absolute distance.
In the rest frame a 5000 A ray will take a certain time from crest to crest to strike the
eye and the kinetic energy delivered is .5. A 5773 A wave, in the rest frame, takes
1.1547005 units of time and delivers 86% of our 5000 A kinetic energy of .5, or .4330127.
At 1/2 c our 5773 A wave equivalence is formed when that 2886 A ultra-violet ray
red-shifts so that the second crest, which is 2886 A distant when the first crest touches the
eye has to actually travel 5773 A to catch up and be measured. And this takes 1.1547005
units of time, just as it would in the rest frame, to deliver 86% the kinetic energy or
.4330127. At a velocity of .8660254 c, when the first crest of an ultra-violet ray of 773 A
touches the eye, the second crest will have to travel 7.461014 times that wavelength, or,
once again, 5773 A before it will reach the eye, taking an absolute time of 1.1547005 and
the delivered kinetic energy will once again be .4330127. (Of course in that frame it will be
measured as 2886 A which took, from crest to crest, .5773503 units of time and delivered
a kinetic energy of .8660254. Those being the rest frame values for a 2886 A ray).
Not only is the velocity of light constant but the wavelength equivalence (the distance)
and the time involved with the delivery of a specific amount of energy seems to be also!
71
Same Distance - Same Wavelength Equivalence - Same Kinetic Energy
5000 A
.
Rest frame wave of
5773 A
.
Wave of
2886 A
Screen's motion of 1/2 c
in 1.15...units of time.
Wave of
773 A
As the moving screens redshift
each ray, the ends of the rays will
have to travel 5773 A to catch up.
The kinetic energy delivered in
each frame depicted here is
equivalent to that delivered by
the rest frame 5773 A ray.
Screen's motion of .8660254 c
in 1.15...units of time.
5773 A
End of wave's motion in 1.15...units of time.
72
.
Each particle
receives the
kinetic energy
equivalent to a
rest frame
5773 A wave.
Their different
masses dictate
the distance
they will travel
in the same unit
of time.
More Inertia and less Energy
Though time dilated movement within the 1/2 c frame is accompanied by a diminished
kinetic energy, the kinetic energy of the 1/2 c frame has increased overall relative to the
rest frame. This causes the mass gain - the greater immovability. And the mass gain is a
very real and absolute effect, giving all the objects in the 1/2 c frame more inertia. At a
velocity of .8660254 c, the rest frame mass will have doubled while our light source would
now only deliver an energy equivalent to that of a 10,000 A ray, or half the rest frame
5000 A value. At .9999999... c, when the mass is 2,236.068 times the rest mass, the
emitted light is reduced to a much longer wavelength equivalence (in the millimeter
range) and delivers 1/2,236 the rest frame energy. In theory, at some "…incredibly close
to the velocity of light…” speed, you could have a virtually infinite mass with virtually no
energy, stretching a second to millions of years and, according to the theory, no one
aboard that craft would be able to tell.
With increasing velocity, the energy diminishes as the mass increases in a way that is
disproportionate to rest frame values. Diminishing energy, increasing mass! If you
visualize the system from frame to frame, from an omniscient point of view, it seems as if
the system is slowly winding down - like an inter-reference frame power failure!
(Fig. 1)
And with that observation we will look at the Special Theory from a different angle!
73
(Fig. 1)
Multi-frame Comparison
.
d
=
1
5000 A
Ek = .5
V=0
d= 1
.
=
1
5773 A
d
Ek = .4330127
V = .5c
d = .8660254
d
=
1
.
10,000 A
Ek = .25
V = .8660254 c
V = .9999999 c
=
.
d
11,180,340 A
(About a millimeter)
1
d = .5
Ek = .0002236
d = .0004472
At .9999999 c our particle's rest frame
mass of 1 has become 2,236 times as
great and the kinetic energy of any
radiation in that frame is 1/2236th what
would be delivered in the rest frame!
* T = 1 for all frames
74
The Conjecture
Why Colour?
I suffer from, though as I have aged it has diminished, mild synesthesia. The word itself
has a gentle, gold and yellow, multi-colour accent. Numbers are slightly colourful, the
days of the week or month and even strong smells can possess body and colour. Once,
while working part-time at a refinery, I smelled something sulphurous and I sensed or saw
or visualized a dense, pale yellowish cloud hugging the ground. Even the word sulphur is
yellow. Music was often hard to learn because the intensity, duration and quality of the
notes created colourful, metered lines which were very distracting. And when I had the
idea that somehow the experience of traveling at high velocity would somehow be
experienced or sensed, it wasn't long before the idea that colour might be
reference-frame specific, among other things, imposed itself upon me! Now I know that I
am leaving the purely mathematical path that we’ve been travelling as we’ve tried to
synchronize flashes of light or find some way to outwit time but, having been frustrated at
this task over the years, I have been forced to imaginatively contemplate other means of
measuring absolute motion. And though I cannot present an actual proof I believe that my
arguments, being rooted in all of the rules of the physics of Relativity, are logical and
possible. Without changing any of the mathematics of the Theory let’s take another look.
The Spectral Speedometer
Let's say that we had passed a beam of light through a prism and noticed a spectral
line of some element at the 5000 A mark, which is basically in the green portion, and we
were at theoretical absolute rest. At 1/2 c we know that the journey from the source,
through the prism and to the point of observation is a little more complex, but the end
result is that the 1/2 c observer will see the spectral line of that element in the 5000 A
range and if it had been green in the rest frame it would have to be, according to the rules
of Relativity, green at 1/2c.
Now, we know that 5000 A in the 1/2 c frame is energetically equivalent to a rest frame
5773 A which is more yellow but, of course, you’re not supposed to see yellow at 1/2 c. As
I understand it, the wavelength may be energetically equivalent to a rest frame yellow but
we would still see green because the more massive, slower moving particles of the eye or
camera would "blue-shift" the lesser energy - sort of like when that burst of adrenalin
during an accident or stressful event heightens your senses so that everything seems to
be moving in slow motion, except in reverse - your slowness "speeds" things up. But in all
of my studies I have never really come across this point discussed in depth and/or proven.
It was, the one time I came across colour being mentioned, simply stated that it must be
so. And it's true that anyone in their right mind must agree with the Special Theory unless
they have really given it a lot of thought and/or is working on a sober-minded, objectively
reasoned out intuitive hunch!
75
Rest Frame
b
Rays m
n
a
o
b
c
The "Spectral Speedometer"?
While each ray, m,n,o, must strike their respective points on the
screen at a,b or c, regardless of the motion of their frame of
reference, the rays themselves, at 1/2 c for example, will lose
energy. As a result, the red should slip into the infrared, the
spectral line in our rest-frame 5000 A green ray would remain in
position "b" while that wavelength would shift to a 5773 A "yellow"
equivalent and our blue would shift to green. Measurement would
remain true to relativistic principles but do those principles include
the sensation of heat and energy?
b
Actual trajectory
of rays...
Rays m
a
n
o
b
c
...and apparent
trajectory
1/2 c
76
Think about it, though, for a second. Seeing yellow at 1/2 c, let's say, instead of green
after your light has gone through a prism with the spectral line of our element still in the
same rest frame position would give us an absolute red-shift! A spectral speedometer!
Whereas a relative red-shift causes spectral lines to move through the colours, this sort of
red-shift, from frame to frame, would cause the colour to move over stable spectral lines The spectral lines are the measurement and must remain true to the rules of relativity, but
what about colour? Colour is merely a measurement of heat. Do the rules of relativity also
include the sensation of heat which we call colour?
Red Sun
Now imagine a sun that appears orange because of its temperature. It radiates more
waves in the orange frequencies than in any other visible range as per the rules of Black
Body Radiation. If we and that sun were to be suddenly transported to a frame whereby
we had an absolute motion of 1/2 c, theoretically every ray that would have struck the eye
in the rest frame would still have to strike the eye at our new velocity. There can be no
difference in amounts or measurement or position as I am sure you know by now. If,
however, in considering this idea we suppose that there is an absolute red-shift, then
every orange ray will lose energy becoming red while every yellow ray will have to have
changed to orange and so on from colour to colour. If we transported everything to a
slightly higher velocity still, then our original orange might go from red to infrared, while
our yellow, which had turned orange, would now become red.
77
Relativistic Reddening?
In the rest frame our
imaginary sun radiates
more in the orange
range though all
wavelengths are present
in varying degrees.
At 1/2 c, as the waves
lose energy relative to
rest frame values, the
colors will shift - exactly
as if the sun had cooled
- with the majority of
orange radiation now
reddened and the
previous red rays having
become infrared.
At some higher velocity
still the rest frame
orange majority will
have also shifted into
the infrared leaving a
lesser number of rays in
the red.
The sun should still be
red but dimmer... and
cooler still?
78
Now, when in the rest frame, let’s say that our orange light possessed x number of
waves per unit of measurement while our yellower light possessed a lesser number of
waves per that same unit and the green a lesser number of waves still. At our higher
velocity our once rest frame orange number of x waves will have receded into the infrared
while the yellower ones will have become red. Since our new red is being produced by the
same number of what were once yellow rays, which were lesser in number than those of
our original orange, our sun should also appear to be dimmer. This shifting of waves as
they lose energy is exactly what happens with the relative Doppler-shift measurements of
the stars made here on earth. The difference is that the energy loss and reddening just
discussed would be due to relativistic phenomena, basically the loss of energy as a result
of time dilation, as opposed to the stretching out of the waves due to the motions of those
stars relative to earth.
That same time dilation, however, is supposed to hide from the eyes within that sun’s
reference frame what I have just described from an omniscient point of view. And so, it is
time to look at time!
There is no Such Thing as Time
While I agree whole-heartily that measurement from frame to frame will follow the rules
of motion as put forth in the Special Theory, I have seriously considered this idea that
measurement and sensation will diverge! While every bounce of a ball, dent in a wall,
measure of length and distance and time and weight and mass will give you rest frame
results regardless of your motion, I would like to think that the disproportionate ratio from
frame to frame between energy and mass may affect the sensation that accompanies
those measurements. To move your arm in the rest frame you must move the rest mass
of your arm a certain distance using a certain amount of energy which takes a certain
amount of time. To do the same thing at .9999999...c, for example, you must move an
arm that is 2,236 times as resistant to being moved with only 1/2,236th the amount of
energy. And to move it the same rest frame (perpendicular) distance would take 2,236
times as long - that's how it's supposed to work. But one of the arguments against being
able to sense this effect of diminishing energy and increasing mass is that time dilation is
supposed to hide the effects of this disproportion. All of your senses are time dilated so
you're not supposed to be able to tell.
It’s sort of like being unaware of being drunk.
But is the slowing down of time really responsible for hiding this disproportion or does
the lack of energy and the mass increase create a slowing down of things which somehow
you may still be aware of – creating within you an altered state of mind.
And it isn't really that time is slowing down in and of itself. There is no “thing” that is time
that is affected by velocity. It is by virtue of the relative motions of material objects that
have been altered by mass gain and diminishing energy - the slower clock or heartbeat –
that we have an altered measure of events. Time doesn’t slow down – physical processes
do! Why shouldn’t one be aware of these altered physical processes? Time is apparently
malleable only because of the changes that bodies undergo at high velocities. Earlier I
79
mentioned the twist that the shaft with the disks underwent and poetically referred to that
“twist through time”. But, once again, time isn’t “twisting” – it is the substance of the shaft
itself that is physically distorted thereby affecting measurement.
Time dilation is a result of the altered physical properties of matter and we have to ask
if you would be aware of those altered physical properties if you were to experience
them? Does the time dilation of the senses hide the effects of high speed motion or is
there a sensation accompanying the effects of time dilation? That is to say, the sensation
of being more massive and being less energetic!
The increasing disproportion between these two things - energy and inertia - is all we
need to consider for now as we ignore the problem of time dilation in order to visualize
further relativistic phenomena.
Temperature X!
Now, color and heat go together. A 5000 A ray, in the rest frame, will produce a certain
amount of heat. It will cause the mercury to expand in the thermometer and rise and
produce a reading...of x. If our source is now moving at .8660254 c, our 5000 A ray's
wavelength will double to a 10,000 A equivalence and the delivered kinetic energy will be
half of our rest frame value. But our thermometer will still show a temperature of x! A
temperature in the rest frame produced by a 10,000 A ray should logically be cooler and
so I ask the question: What temperature would a rest frame finger feel if it could be
inserted into the .86 c frame? The answer is obvious. We must then be able to state quite
confidently that the energy that is moving that .86 c thermometer is actually equivalent to
a cooler temperature. The kinetic energy is half the rest frame value and the doubled
mass of the slower moving particles impart to their neighbours and the glass walls of the
thermometer that lesser kinetic energy. That .86c measurement of x is, according to rest
frame values, misleading. And that leads us to the next question - the sort of question
that, if satisfactorily answered, changes everything: What is the sensation of this cooler
temperature equivalence to the more massive .86 c finger? How is the greater inertia of
that more massive finger supposed to compensate for the lesser oscillation? Isn't warmth
a certain amount of oscillation in a certain time versus the surrounding lack of movement
that is cold?
80
Temperature X!
X
5000 A in the rest frame rendering a temperature of X.
Same experiment done at .8660254 c
X
1339 A wavelength
enroute...
...redshifts to 10,000 A and takes twice as long to impart 1/2 the
rest frame value of kinetic energy. It would have taken the
mercury twice as long to reach the position showing X.
81
s
Relativistic Thermodynamics
There seems to be some controversy over the inter-reference frame measurement of
temperature. Some say that if you try to get a reading as some object speeds by it will be
lower. Some say it will be higher and others say it will be the same. One example that I
read concerned measuring the temperature of a gas as it sped by and included doubts
about how to measure the temperature of a gas in the first place – even in the rest frame!
So let’s simplify it a bit and use in our thought experiment an old water radiator that’s
giving off heat in the infrared at 10,000 A in the rest frame. We know by virtue of the
workings of the Doppler-shift that a similar radiator moving at 1/2 c would send to our rest
frame observer a time-dilated 11,547 A ray equivalence that would red-shift to 17,320 A
while the 1/2 c observer would receive from the rest frame a ray of 20,000 that he too
would measure as 17,320. In this case, the measurement of temperature reflects
relativistic continuity - as it should! If one were to get a different reading then that elusive
measurement of absolute motion could be made. So, if measuring the temperature of a
gas involves measuring the kinetic energy of individual particles within different frames as
they speed by each other, I’m willing to bet, that however the experiment is set up, both
observers will reach the same conclusions – and we’ll look at a thought experiment
concerning inter-reference frame interactions between particles a little later. Besides,
since the radiator readings will match up, any attempts to read the temperature of the air
(which is a gas, right?) surrounding those radiators would have to match up too. It would
be strange if they didn’t.
The question should be about the temperature equivalence to rest frame values and
the way energy is experienced within these high velocity frames of reference and not
about actual measurement! Actual measurement should - and seems to always - reflect
relativistic continuity.
Before I continue let me re-assert that it is said that the energy of a moving system
increases with velocity. But this is only relative to the rest frame! Movement within a high
velocity system is really being reduced – It is losing energy within that reference frame!
The movement of the atoms and electrons themselves is reduced as the potential energy
of the materials in that frame is partially converted to mass. And with each incremental
increase in velocity, matter becomes more and more inert. That said, let’s continue.
Let’s bring the conditions in the .8660254 c frame into the rest frame in order to further
understand the problem. Imagine, in the rest frame, a perfect pool player who shoots a
hundred balls with precisely the same force against a metal plate. At the end of his run the
metal plate will have heated up by a certain value by virtue of the transfer of kinetic
energy.
If, still in the rest frame, we now doubled the mass of those hundred balls and our pool
player were to shoot them with half the previously imparted force, the total kinetic energy
delivered to the plate would then be halved and the temperature will show this. This is
exactly what happens at .86 c. The extra kinetic energy produced by the .86 c frame’s
absolute motion doubles the mass of our pool balls but their movement within that frame
is halved so that they, as in our rest frame experiment, behave in exactly the same
manner imparting half the kinetic energy. There is no difference between the inertial
behaviour of a ball with the added mass of actual material or one with the added mass
82
produced by motion through space. Inertia is inertia! At .86 c, not only does our metal
plate receive only half the kinetic energy but its molecular oscillations will pass on that
lesser energy to the atoms in the thermometer which will (eventually) show the expected
relativistic rest frame reading but not reflect that lesser energetic rest frame equivalent
input. If our pool player was actually in the .8660254 c frame shooting those one hundred
balls, we could once again say that the metal plate should be receiving half the rest frame
value of kinetic energy and, relative to rest frame values, should be cooler.
Cooler Tea and a Luke-warm Bath
Measurement from frame to frame may reflect relativistic continuity but the sensation
of light, heat and colour may not! Consider the following earth-bound examples:
When water boils it does so at a certain temperature. And if we were to use the boiling
point of water as a standard of measurement we'd find a divergence between that
standard and the sensation of heat if we try to make a tea atop Mt. Everest. Water will boil
there at a lower temperature. Of course, if your fingers are cold, you might not be able to
tell, or care, if the temperature of the rising steam is different from the sea level value but
that doesn't change the fact that the measurement and the sensation of heat should differ.
(I suppose that once your fingers were accustomed to the new temperature of the steam
you might notice the difference. See next example.)
Earlier in the text I mentioned the idea that the more massive particles of the eye in a
high velocity frame would “blue-shift” the lesser energy received so that that energy would
seem more energetic thereby rendering a rest-frame sensation of colour or heat that is
supposed to match the measurements in that frame. It’s like getting into a luke-warm bath
when you are extremely cold and the water feels really hot. And that seems like a really
good way to explain how a more massive – and “cooler?” - body could experience a rest
frame equivalent sensation of warmth with that lesser energy input. But it has been my
experience that here on Earth as your skin becomes accustomed to your new liquid
surroundings you’ll begin to realize that the water is really not that hot after all as you
reach for the tap. Maybe initially at 1/2 c when that lesser ray strikes the eye and warms it
the eye expects green but then “realizes”, in a nano-second, that things are cooler than
they seem!
But is it Warm?
When you are removed from a star or in the shadow of a planet, the temperature of
space is near absolute zero. What would it be like to be travelling through that cold of
space at some incredibly great velocity whereby a second would last for a million years?
Mathematically there is nothing in the Theory of Relativity that forbids such a scenario!
Your source of light or heat would be delivering miniscule amounts of energy and the
molecular oscillations in your body would be slower than those in the bones of an
ice-interred mammoth. It could take you a couple of million years to reach for the
thermostat if you were feeling a chill and all that time that constant temperature in free
83
space of absolute zero would be trying to rob you of whatever rest frame value of warmth
you still possessed. In the rest frame, those miniscule amounts of energy would have
allowed the cold of space to instantly freeze a substance so that the molecular structure of
that substance would possess virtually no warmth-giving oscillation. It's true that at our
great un-named velocity, the tremendous mass and momentum of those particles will
keep them in motion despite the greatly diminished energy input. And it's true that just as
a rest frame particle will trace out a particular path in a given unit of time, that moving
particle, possessing a million times more mass, will also trace out in its frame the same
path after a million of those given units of time so that measurement remains
relativistically continuous - but is it warm?
If it isn't, then why would you see a warmer color? Why would you see green at .86 c for
instance when the wavelength equivalence is actually in the cooler infrared at 10,000 A?
Does a more massive eye really “blue-shift” that lesser energy thereby “fooling” the
senses of the observer?
If it isn't as warm, then that coldness of space, which is everywhere, becomes an
absolute frame of reference!
Cold Photons
I have often had the image before me of two photons travelling parallel to each other
having originated from the same source. Now we know that had they struck the skin they
would have imparted their warmth and that warmth would be a direct result of their kinetic
energy which is a direct result of their tremendous velocity relative to the skin. But relative
to each other there is no interaction. They are, relative to each other, cold!
And if the molecules of the skin were travelling at some tremendous velocity so that
their oscillations were virtually non-existent, couldn’t we say the same thing of them?
Relative to the rest frame the kinetic energy of those molecules could be great while
relative to each other they would be sharing virtually none.
If
If a high velocity frame of reference were to come to rest then if the temperature had
actually been cooler than measured it should warm up as the molecules would begin to
oscillate once more at rest frame values. The mass of our traveler would also return to
rest frame values and the particles of his body would be more easily moved. Color also
would return to "normal" as the wavelength of our source would shorten and so there
would be no record of any supposed changes due to high velocity motion. If you had tried
to send an image of this color difference, we have seen by virtue of the Doppler-shift, that
that information would have been altered to fit the expected results. And what if, in the
1/2 c frame for instance, you had taken a physical picture of the actual color difference on
our "spectral speedometer". I suspect, as you returned to the rest frame, that just as the
temperature would warm and the color of your light source would energize, the atoms
84
upon that photographic paper that were affected in the 1/2 c frame by those less energetic
waves and showed you yellow would have their rest frame measure of oscillation returned
and what was yellow would become green. There would still be no trace of your 1/2 c
“sensational” experience!
While in the 1/2 c frame of reference the wavelength and energy delivered is equivalent
to a rest frame value of a yellow ray. I concede that the altered mass of the retina or
photographic paper may not record the same rest frame color of yellow, or even a
particular shade of that color, but I wonder if they will truly record the rest frame
experience of the color that measurement in that frame dictates?
That’s a lot of Constants
So we have a constant speed of light, a constant wavelength equivalence
accompanying a constant time of delivery of kinetic energy which imparts a constant rest
frame temperature equivalence which opposes the constant of the cold of absolute zero.
The gain in mass, the length contraction and the slowing down of physical processes,
which are responsible for relativistic continuity of measurement, are actually
mis-measuring these constants in the name of relativistic continuity! We know that the
true measurement of these constants are perfectly masked and hidden but do those
same relativistic alterations in length, mass and time also mask so perfectly the
sensations that accompany the experience of those constants?
By now you may have mentally protested against all of this by thinking… “But isn’t
sensation a measurement?” and, “If all measurements are relativistically continuous then
why should sensation differ from frame to frame?”
Maybe it’s a question of the order in which you place each effect. It is generally said
that relativistic phenomena hide any deviation from continuity of measurement and
therefore sensation must be included. But if sensation is a direct result of an input of
kinetic energy and how the receiving mass responds then there definitely is a difference
in proportions from frame to frame according to our omniscient point of view. And saying
that, “…time slows down so you can’t tell…” may not be a satisfactory explanation since
time dilation is merely one of those altered physical processes – nothing more! But you
could say instead that the altered physical processes which cause relativistic continuity of
measurement create a new sensation! That different sensation accompanies the new
measurement! And time dilation is just another product of these initial conditions.
So let’s divide things up even further and relate kinetic energy with the sensation of
heat and colour and couple momentum with continuity of measurement.
85
An Inter-Reference Frame Two-Particle Collision
Imagine two perfect pool players this time who each shoot a cue ball towards a central
point on the pool table so that the balls impact each other perfectly and rebound directly
back to their respective points of origin. Consider each impact to be perfectly elastic so
that all of the kinetic energy and momentum that they possessed before the impact is
restored. And let’s keep it simple by ascribing to each a kinetic energy of .5 – a mass of 1
moving 1 unit of distance in 1 unit of time.
Now that you have a mental image of our set-up, let’s re-arrange it so that we now
move one of those pool players at 1/2 c, remove the cushions on the tables, one table per
frame, and have them both take their shots so that as the 1/2 c table moves past the rest
frame table the two balls impact each other in such a way as to restore to each ball exactly
the momentum and kinetic energy that they were launched with within their respective
frame of reference. This means that the rest frame ball moved towards the impact point
with a kinetic energy of .5 and a momentum of 1, impacted the 1/2 c ball and rebounded
with the same kinetic energy and momentum while within the 1/2 c frame the more
massive ball did the same thing, possessing a kinetic energy of .4330127 and also a
momentum of 1 (The momentum within the 1/2 c frame is the mass of 1.1547005 times
the velocity of .8660254).
Of course the true motion of the 1/2 c ball is basically a straight line as it speeds by the
impact point. If you’ve ever played pool you know that you can hit the white ball very hard
and just nick a ball so that it just barely moves while the course of the white ball is only
imperceptively altered. And that is what we have here – a pool shot in space!
If we consider these pool shots to be the parts of an experiment designed to measure
absolute motion then we know that they will fail to do so. If everything is impossibly
perfectly timed and executed then we know that each observer must measure the same
thing. Each ball will take one unit of their respective times to cross the table, which we will
say is one perpendicular unit of distance, impact the other ball and return. Each observer
can say that the kinetic energy and momentum that their balls possessed before the
impact was exactly restored post impact and we know that if we set up the same
experiment with different velocities each observer will always get the same result. At 1/2c
it would take 1.1547005 units of time for a mass of 1.1547005 times the rest mass to shift
from one side of the table to the other and the momentum of that mass of 1.1547005
times that slower speed of .8660254 of the rest frame value would equal 1 and its kinetic
energy would equal .4330127. At the velocity of .8660254 c it would take twice as long to
cross the table, its kinetic energy within that frame would be half the rest frame value, or
.25, and its momentum would be a mass of 2 times 1/2 the rest frame velocity which
would also equal 1. At .9999999…c it would take 2,236 times as long for a mass 2,236
times as great to cross the table which once again would give us a momentum of 1 and a
kinetic energy of 1/2,236, or .0004472.
86
Launch points
Point of impact
The result of a collision between two
rest frame balls of the same mass.
Kinetic energy = .5
In the same post-impact time the 1/2 c ball
will have travelled within it's frame a distance
of .8660254. Multiplied by its mass of
1.1547005 we have a momentum of 1.
Ek = .4330127
At .8660254 c the ball will have travelled only
half way back. Multiplied by twice the mass
and we have once again a momentum of 1.
Ek = .25
1/2236.068 x 2236.068 = 1.
That's the momentum at .9999999 c.
Ek = .0004472
Rest frame mass always returns to point of origin in the same time with a kinetic energy of .5. The force of the
shared impact therefore should be considered to be constant for each example.
We could say, too, that in each example the restoring force is equivalent to the rest frame mass impacting an
infinite mass! And therefore, since the momentum is restored exactly in each high velocity frame as well, the same
can be said for each of them. The restoring force is always equivalent to an impact with an infinite mass regardless
of the differing amounts of mass or kinetic energy in the opposing frame!
87
Every time our rest frame observer performs his experiment with any one of these
other moving frames of reference his ball will always be returned possessing the same
kinetic energy and momentum. Likewise, in each of the other frames, they too will
measure the same thing and reach the same conclusions as per the rules of relativity.
It is interesting to note that the force of impact is always the same for the rest frame
mass regardless of the different values of the other masses involved. Since the rest frame
mass shares each impact with its more massive counterparts then we must conclude that
each more massive ball is being affected by that same force of impact as well. The shared
force of impact is constant from frame to frame.
Now let’s do some imagining. If our rest frame pool ball was to strike a ball of infinite
mass it would bounce off and return with all of its momentum and kinetic energy while that
infinite mass would experience nothing. It would remain un-moved and unchanged. It
would feel no heat or vibration. Since our infinite ball had no momentum of its own it must
have returned to the rest frame ball its motion only by virtue of that infinite inertia.
The transfer of force, then, and the conservation of momentum involves not only the
kinetic energy of the masses but the inertial resistance to motion that those masses
possess and offer.
If we had a ball that was not quite infinite then if the rest frame ball were to impact that
great mass that great mass would move, if even by a billionth of the diameter of an atom
in some vast stretch of time, and it would not quite restore to the rest frame ball all of its
qualities of motion. In order for it to do so, it would have to possess a slight motion of its
own in the direction of the rest frame ball. Our near infinite mass, possessing a near
infinitely slow velocity, would then possess a momentum equal to that of our rest frame
ball, of 1.
As the masses involved decrease in each respective frame of reference, more and
more motion is required to maintain that momentum of 1.
We can see that if you vary the mass you must vary the velocity to maintain an equal
momentum.
Now, the rest frame ball’s round trip from its launch to impact and return always takes
the same time and the ball always possesses the same momentum for each
inter-reference frame collision. Because of this we have concluded that the force of
impact in each collision is constant. And, if the energy of impact is the same for the rest
frame ball in each successive example, it must be the same for each of the respective
masses that it shares that impact with. Earlier we surmised that an infinite mass would
experience nothing upon impact and we might say too that a virtually infinite mass would
experience virtually nothing. We might reason then that since the impact from frame to
frame is constant and we know that each different measure of mass must experience an
energy that corresponds to the lesser value of kinetic energy that is already present in its
frame of reference then it might make sense to state that the increase in mass deadens,
or dulls, the energy that each mass experiences for the sake of that measurement.
88
Each mass cannot be experiencing that constant value of the impact energy in the
same way by virtue of the varying amounts of inertia that each mass possesses.
In other words, the mass increase deadens the experience of energy! It doesn’t
“blue-shift” it! The force of impact is modified by the increased inertia of each faster
moving mass and the lesser kinetic energy, post impact, will equal the lesser pre-impact
value.
The more immoveable the mass becomes the less aware it is of that impact until,
nearing the infinite, it is virtually unbothered by what it would consider to be such a faint
disturbance!
So, the total energy of impact is a result of the momentum of the masses. The
momentum, from frame to frame, is a combination of varying amounts of mass and kinetic
energy. Since, in each frame the total energy of impact was the same by virtue of a
constant degree of momentum and that momentum was a product of varying degrees of
mass and kinetic energy, then we might reason that relativistic continuity of measurement
is dependant upon the overall momentum and not the amounts of mass gain or kinetic
energy taken separately. The rest frame ball cannot tell whether the total energy of impact
possessed this amount of mass or that amount of kinetic energy. It only knows that there
is an equivalent impact from frame to frame and responds accordingly. And the same can
be said for all of the other balls in each of their frames of reference when striking the rest
frame ball. It doesn’t matter how much heat the rest frame ball possesses in the form of
kinetic energy. All that matters is the total energy of impact.
You could, without altering the values of our experiments in any way, have a .86 c
observer pass a .5 c observer and both balls would respond to that shared impact in a
way that was identical to their impacts with the rest frame ball. If the temperatures
produced by any combination of post-impact pool balls are measured, the thermometers
will all once again, regardless of the balls’ respective kinetic energies, eventually, show
the same result.
89
.866 c
.5 c
Rest frame balls have
returned to starting
point while .5 c ball is
only 86% of the way
back and .866 c ball is at
the 1/2 way mark.
Rest frame
balls
Launch points
Whether the .5 c ball impacts the
rest frame ball or the .866 c ball
the shared impact is constant
and each ball must return to its
starting position in 1 unit of its
frame's time.
We could even say then that the motions of the particles of the mercury in a
thermometer, in any frame, are really conserving momentum when that thermometer
shows a rest frame equivalent reading of 70 degrees. The more massive particles of
mercury are not registering a reading which is an accurate reflection of the kinetic energy
that they actually receive. They are responding to particles that impart a specific
momentum which imparts a relativistic continuity of measurement regardless of the
varying amounts of kinetic energy and mass that accompany that momentum.
We could also see it like this! As the potential energy is slowly being converted to mass
in each successively faster frame and as the kinetic energy lessens and could not be
considered to be rendering the temperature that our thermometer is showing us, the
momentum takes over. The momentum must cause the particles of mercury to register
the same result from frame to frame though the trade off, in becoming more massive and
90
losing kinetic energy, is that it takes longer. The temperature reading slowly becomes an
empty shell of measurement produced mainly by momentum and lacking in energetic
substance! As the kinetic energy within the frame diminishes the momentum will remain
to do the work! Momentum without kinetic energy means no heat!
The next time you look at a thermometer here on earth you might consider the
possibility that part of that measurement is due to the momentum of the particles and you
are not experiencing a true “absolute rest frame” measure of temperature. In other words,
at absolute rest, the proportion of heat accompanying a particular momentum would be at
the maximum.
In fact, we might even say that the inter-reference frame readings that a thermometer
makes are not a measure of heat - they are a measure of momentum. The actual
sensation of heat that accompanies those readings is a reflection of the interpretation of
the kinetic energy that the particles in each particular frame possess in tandem with that
momentum. And therefore, the proportion of heat that accompanies a particular
momentum must vary from frame to frame.
.5 From Frame to Frame
Now, we’ve been using a ball of a mass of 1 which moves at a velocity of 1 as our
“original” rest frame standard of measurement of .5. Let’s reduce the rest mass to 86% of
that and increase the velocity to 1.1547005. That would still give us a momentum of 1 but
a greater proportion of the total energy of impact would be due to a greater amount of
kinetic energy which would now have a value of .5773503, not .5.
At 1/2 c, however, our new values of mass and velocity would now cause the mass to
increase to 1 and the velocity within the frame to lessen to 1. That would give us within the
1/2 c frame a kinetic energy which matches our “original” rest frame standard of
measurement of .5. If we now compare our “original” rest frame value of kinetic energy to
our new 1/2 c value we can see that we would have two balls, or particles which impact a
thermometer, moving within their respective frames which possess identical kinetic
energies and momentums. Of course we know that the 1/2 c thermometer is going to
show a higher temperature reading but each particle must be imparting to their respective
thermometers the potential for identical rest frame values of heat.
And we can adjust our masses and their velocities to always render a kinetic energy of
.5 in any frame we choose. Half a rest mass moving at a velocity of 2 and giving a kinetic
energy of 1 would become twice as massive at .8660254 c and move half as fast and
would render an absolute kinetic energy within that frame of .5 - though we know that
within the frame it will be measured as having a kinetic energy of 1 and will produce a
higher temperature reading to match it. As we continually strike the thermometers in each
successively faster moving frame with particles that possess our .5 rest frame value of
kinetic energy they will progressively produce higher and higher temperature readings
and, the higher the reading, the longer it will take for the mercury to rise. In theory, in our
frame possessing virtually infinite mass, that kinetic energy of .5 would render a reading
of millions of degrees and those virtually immoveable particles in the thermometer could
take, literally, a billion years or more to get there.
91
.5 in Every Frame
Rest Frame
.5 c
.8660254 c
.9999999 c
Virtually infinite mass at our
" incredibly close to the
velocity of light" velocity
Infinite mass
virtually infinite
1.1547005
2236.068
2
virtually zero
.8660254
.0004472
.5
Virtually zero
Ek = .4330127
.0002236
.25
Regular relativistic progression produces constant temperature
reading of X in every frame except infinite one.
m=1
m = .8660254
v=1
v = 1.1547005
Ek = .5
Ek = .5773503 Temp. reading
Temp. 1.15X
1.15X
mass = 1
velocity = 1
Ek = .5
m = .5
v=2
Ek = 1.0
Temp. 2X
infinite
zero
zero
m=1
v=1
Ek = .5
Temp. reading
2X
m = .0004472
v = 2,236.068
Ek = 1,118.034
Temp. 2,236X
m=1
v=1
Ek = .5
Temp. reading
2,236X
m = virtually zero
v = virtually C
Ek = virtually
infinite
Temp. Virtually
infinite
m=1
v= 1
Ek = .5
Temp. reading Virtually
infinite
.5 impacting an
infinite mass
produces zero
response
These rest frame values produce the same heat
input of .5 for each of the frames marked diagonally
in blue from an omniscient point of view.
Note: All measurements, except for temperature, are for a given time of 1 rest frame unit.
Temperatures are rendered simplistically as proportions of kinetic energy over whatever time that
frame dictates.
92
That brings us once again to our totally impossible and imaginary infinite mass. That’s
one step further than our virtually infinite mass - which is mathematically allowed by
Relativity. The infinite mass isn’t going to respond at all to that .5 energy input. In keeping
with the series of measurements in each frame we would like to say that it would take an
infinite time for that thermometer to reach an infinite temperature reading. But if the
particles in the thermometer are moving infinitely slowly, which is to say they aren’t going
to move at all, how could they ever begin to move towards that infinite temperature
reading? The infinite mass remains unmoved by our .5 impact and therefore experiences
no heat. There is no sensation of temperature and no temperature reading in an infinite
time.
The virtually infinite mass, being one infinitesimally small step less massive and
virtually as immoveable, would give us a reading that would be off the chart – but it would
take almost an infinite time! The particles in our thermometer are going to move virtually
infinitely slowly! If we were to make our measurements of temperature in a given time
instead we could equate that “off the chart” reading with an infinitesimally small degree of
warmth that is just greater than the zero degree reading produced by the infinite frame. A
virtually infinitely massive thermometer is virtually as immoveable as an infinitely massive
one and should render a sensation that is virtually as cold regardless of whatever
numbers the momentum of the particles of that virtually infinitely massive thermometer
will eventually produce! As the temperature readings reduce in each successively slower
frame, an “omniscient reverse scale thermometer” (see next page) would show higher
readings instead which would be based upon the greater oscillations of lesser masses
and upon the lessening time that it would actually take for the temperature readings to be
made.
In other words the higher the original reading, the longer it took to get there as a result
of the increasing inertial resistance to our constant .5 input of heat and the colder it should
feel!
93
Measurement according to the
rules of Special Relativity for
multi-frame uniform inputs of
energy
Infinitely hot
Conjectured temperature
according to sensation on
our "reverse scale"
thermometer
Infinitely cold
...or just barely warmer than infinitely cold
Millions of degrees...
Could an energetic input of .5 really
produce in a virtually infinite mass a
sensation of warmth and heat and
energy in the millions of degrees over
a billion years?
Sensationally warmer
Relativistically warmer
From the omniscient point of view the
kinetic energy of .5 is impacting the
particles in the thermometer which
possess a mass of 2,236 times their rest
mass and are very inert - relatively
speaking. Things might feel really cold in
this frame!
At .9999999 c the kinetic energy
of .5 is measured as being 1,118
and the temp. as 2,236 X.
.5 at .866 c produces kinetic
energy reading of 1.
Temp. is measured as being 2X.
.5 input is further deadened and things are
beginning to feel...noticeably cooler?
Mass at 1/2 c deadens .5 input so
that experience of heat should be less
than rest frame value.
.5 at 1/2 c measured as .5773503.
Temp. is measured as being
1.1547005 X
Rest frame temperature of
X degrees as a result of a .5
kinetic energy input.
Sensation matches temperature
reading.
Note: Temperature representation is simplistically expressed as being proportionally equal to the different
values of measured kinetic energy.
94
Temp. reading and length
of time it takes to render
the reading
"Blue-shifted" Temp.
sensation which should
match measurement
according to Relativity
Proposed
"deadened"
Temp.
sensation
.
...
Virtually
infinite frame
infinite frame
The Relativistic progression for a constant rest frame .5 input of energy renders higher and higher temp.
readings and, presumably, an increasing sensation of heat that will match those readings in increasing amounts
of time. The next step after our virtually infinite temp. reading is that our chart shows a sudden drop at our
infinite mass - We go, all of a sudden, from "millions"of degrees to zero!
rest frame
.5 c
.866 c
.9999999... c
The sensation of heat, on the other hand, according to the idea that the mass increase "deadens" the
experience of energy, would seem to show instead that the cooling from frame to frame gently eases into that
infinite cold.
95
The sensation of heat is dependant upon the response of a mass to a stimulus in a
given time. The thermometers in each frame, In order to follow the rules of relativistic
continuity of measurement, will fulfill their duties but the increasing length of time that it
takes to render each reading is in a direct proportion to the supposed lessening sensation
of heat and their increased immoveability!
I don’t believe that a deadened response over a billion years will produce a rest frame
value of heat - which is easy to see - and I don’t see how that same scenario could
produce within the skin of an observer in that frame a rest frame experience of heat – as
the Special Theory of Relativity predicts! That virtually infinite thermometer is supposed to
give us a temperature reading from that paltry .5 impact in the millions of degrees – over a
billion years! But in the same given time as a rest frame reading that virtually infinitely
massive thermometer isn’t going to even budge.
So! Which is it?
The idea that the mass gain alters the sensation of energy is actually presumed to be
so by the Special Theory. According to the theory, our rest frame equivalent .5 input in
every frame must produce, from that constant rest frame heat potential, widely differing
sensations that will match those extreme and differing temperature readings.
I suppose that could mean that the idea that an observer in these high velocity frames
will not be able to experience any sensational difference in his state of existence is
actually as much of an assumption on the part of the Special Theory as my opposing point
of view is!!
And I guess that brings us back to time. Would one be aware of the slowing of time that
would accompany the experience of our supposed lessening sensation of energy? We
know that every measure made in the rest frame must be made in any other. Every tick of
the clock, every wave and particle, must appear to arrive or move in exactly the same
manner as before. So while the waves that produce the sound in the rest frame of a
ticking clock must also strike the ear in some other frame in the same number and
progression which will match the slower senses of our time dilated subject’s brain, the
deadening of energy, as has been proposed, should produce a different sensation. After
all, all sense of time involves the interpretation of some sort of energy or another. Every
sound wave or visual clue involves an oscillation and the energy that is a result of that
oscillation. Perhaps the sound of the clock will appear muffled, matching a dimmer light
whose colour has changed in a cooler environment, beating out the seconds in tandem
with your slowed heart as you try to figure out what exactly was different…
There is no such thing as time - Just varying experiences of energy and motion in three
dimensions. One might be aware of the dilation of time by virtue of one’s “lethargic”
response to a lesser energetic impulse. As such, the sensual experience of the passage
of events must be linked to the altered physical properties of the masses involved –
including the particles that make up the body and brain. You should feel what you cannot
measure! You might experience the slowness that is the deadening despite the fact that
96
the clock is keeping the same rhythm as your slowed heart and thoughts!
There is only energy in the universe. And all that we see and know and feel and
measure is a result of the sensation of the inertia of that energy.
The conservation of momentum may give us continuity of measurement from frame to
frame but as our mass increases and our energy disappears, as colors cool and our
sources of light dim, we might just feel ourselves slowly going numb - all relative to a
universal standard of a time that doesn’t exist!
Out on a Limb
Many authors have used the "... if you could travel at the velocity of light..." example to
make points concerning the stoppage of time at that velocity or the infinite gain in mass
which would prevent the achievement of that velocity of light, so I'm going to continue to
do the same thing to make my point. Aside from being contracted to less than the
thickness of a hair, "...if one could attain the velocity of light..." then all physical processes
would stop, time would stop but your clock would still show a measurement and even
though your light source would cease to radiate any energy, your thermometer would still
show that last temperature reading of x ! Measurement would remain but without
movement there would be no heat or sensation - the two, measurement and sensation,
will have completely diverged! We know that we can't move at c, so, by choosing a
velocity that is the tiniest fraction imaginable less than the velocity of c can we not say that
that is close enough to saying that the same basic conditions of timelessness and cold
that would exist at the velocity of light would still basically be prevalent?
97
Rest Frame
T = 1 rest frame second
Atomic oscillation
of Y
Mass
is
1.00
.
.
Light
source
5000 A
Kinetic
energy
of
particle
is .5
Distance
is 1.00
.
70 degrees
Spectral
line in
green at
5000 A
According to the rules of Special Relativity, all of the conditions and measurements in the rest
frame must remain true regardless of the absolute changes that the room will undergo with
any increase in its absolute velocity.
98
1/2 C frame
T = 1 rest frame second
Mass increase
is
1.1547005
Atomic
oscillation
86,6254 %
Movement of
Light source
blueshifts light
to 2886 A...
.
.
...which redshifts to 5773 A
equivalence upon particle
interaction.
.
Particle's
Kinetic
energy
is .4330127
Particle
moves a
distance
within frame
of .8660254
Spectral line
still in same
position but
wavelength is
5773 A
equivalent.
.
70 Degrees
While measurement will remain true to the previous rest frame
example, the true values of the events as they occur relative to
the absolute are represented here at 1/2 c! The mass begins to
increase and the energy begins to wane.
99
.8660254 C
T = 1 rest frame second
Atomic
oscillation
is
50 %
Moving light
source
blueshifts to
1339 A...
.
.
...redshifts to
10,000 A
equivalence
.
70
degrees
.
It's still "70 degrees" but the radiation moving the doubled mass of the mercury is only
half as energetic as in the rest frame and the delivery of that energy takes twice as long!
100
Mass
is
twice
as
great
Kinetic
energy of
particle is
.25
Distance is
50 %
Spectral line
is still in
"green"
position but
wavelength is
equivalent
now to
infrared
10,000 A
.9999999 C
T = 1 rest frame second
Atomic oscillation is 1/2,236th rest frame value.
.
Wavelength is in the millimeter range and
imparts 1/2,236th the energy over 2,236 rest
frame units of time.*
.
The impacted particle, possessing 2,236 times the
mass, will take 2,236 times as long to travel the
comparable rest frame unit of distance and possess,
within its frame of reference, 1/2,236th the kinetic
energy!
The work being done within this frame of reference
has been greatly reduced relative to rest frame
values but we still have a temperature reading of 70
degrees and the spectral line upon the screen, visible
or not, would still be in the
5000 A position.
* 1 second at .9999999... c equals about 37.5 minutes.
101
No
Colour
left on
screen?
.
Our "...incredibly close to the velocity of light..." Velocity!
At this point any atomic oscillation is virtually
non-existant with all the constituant parts of the atom
travelling side by side like the pellets of a shotgun
blast.
..
..
The light source, relative
to rest frame standards ,
is just a cold, dead
conglomeration of
matter, thinner than a
hair, radiating, for all
intensive purposes,
nothing!
.
.
The thermometer should, inspite of virtually no energy
input, still show 70 degrees. As good an example as any
of the divergence of sensation and measurement!
It may all be possible, mathematically, according to the Special
Theory, but, realistically, it all seems quite improbable that an
observer in this frame could ever hope to survive for an instant. If
consciousness would even be possible I would expect our observer
to feel the worst cold imagineable along with the sensation of
being squashed flat by the virtually infinitely massive substance of
his body while, in horror, he would realize that he wouldn't be able
to move a muscle - or, if he could, it would take a billion years to
call home with a warning!
102
Our particle, being
virtually infinitely
unmoveable,
receives basically
nothing from its
"source" of energy
and might take
longer than the life
of the universe to
move a rest frame
distance of 1.
.
The Final Appeal
We exist within the narrow band of an atmosphere where at one extreme we'd freeze
and at the other we'd bake. The universe at large is a very inhospitable place for our
fragile bodies and to find another world where we can exist as we do here will be
incredibly difficult. And I think, too, that high velocity travel through space might not be as
easy as we would like to believe. If just being in zero gravity is very disorienting and
adversely affects the bones and senses, among other things, what new stresses would
the gain in mass cause? Would we really not be able to tell that our forearm possessed
the inertia of a small car - or even, in theory, the mass of a battleship - while the energy
that you would have at your disposal to move these great masses would be greatly
diminished or even virtually non-existent?
Have you seen the footage of helium being cooled to absolute zero? As the atoms of
the glass beaker, and the helium within, lose their oscillatory qualities the liquefied helium
begins to seep through the spaces between the atoms in the glass. The qualities of the
materials are compromised by their altered state of existence! At an extremely high
velocity the oscillations of the atoms within that frame of reference could approach a
similar quiescence and who can say what the conditions in that frame would really be
like? Did the mathematics involved in the super-cooling of substances predict this effect
on the helium and the glass?
We know that the universe is expanding. The high red-shifts of those distant heavenly
bodies show this and if we too are moving then we too are probably at rest within our
section of that expanding universe...
…and maybe it is that at rest within our sector of space we have evolved - A "narrow
band" of velocity within which we are comfortable!
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Afterword
By now you must have surmised that I am a layman and lack credentials of any kind.
But please do not belittle any of that which you have read for any reasons other than
those based upon your own scientific reservations. As much as I would have loved to find
a nice, neat mathematical solution to the problem which could be called a proof I have not
allowed that desire to sully or corrupt any of my logical reasoning or deduction. I have
coupled and tempered my imagination with the rules of empirical investigation and have
put forth an idea, the Conjecture, which was the result of two weeks of basic inspiration
and three years of contemplation and research. That’s in addition to the many years
before that which I had spent teaching myself the Special Theory and hunting for that
magic combination which would allow me to measure that which I am sure is there!
I would like to point out, too, that the imagination is an extremely important part of the
scientific process. Albert Einstein’s thought experiments are great examples of this and,
though I don’t remember his exact words, he did stress the importance of the imagination.
Michael Faraday, who knew no mathematics – just as my swirling mind prevents me, too,
from excelling thusly – was also a great imaginer, visualizing the magnetic field’s lines of
force, among other things, and thereby contributing greatly to the body of knowledge
which is science. Of course his ideas could be backed up experimentally.
Hmm, if I could just fly through space at 1/2 the velocity of light…!
Cam Jeroncic
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