Grade Distribution, second exam
Comments on CTEC
• Will be done by the web.
• The TA’s offical, sections are 6 & 8
Time Reversal Invariance
• Then when the slightly different amounts
of baryon/anti-baryons meet up, we end
up with with just a small (about 1 part in
109) of excess of baryons. Just enough to
explain the current ratio of photons to
baryons. And the process is hot by
definition of having so many more
photons. =>Annihilation of baryons and
anti-baryons (almost completely) leads to
a hot Big Bang.
Time Reversal Invariance
• When X and X’ particles decay the X
decays faster to produce MORE baryons
when going forward in time than the X’
particles, and vice versa. Therefore, as
the Universe expands as time increase
(runs forward), we end up with our
imbalance.
CPT Theory and Observations
• The CPT theorem says if I do a calculation of a
particle collision probability and I (flip the
positive charges to negative and vice versa plus
change all the “lefty” particles to “righty”
particles and vice versa, and change the sign on
the time I use, I will get the same answer.
• This means if I observe a reaction in which I
change charge and parity (description of
left/right handiness)
CPT Theory and Observations
• And I see a difference. Then assuming
CPT holds ( and it better!), then this
means sub-atomic particles can sense the
arrow of time.
• Such a “CP violating” reaction was
detected in the laboratory. =>
• This makes it plausible that a much
higher energy CP violating and hence T
violating reaction did occur in the early
Universe.
CPT Theory
• In mathematical terms, C x P x T = 1 means CPT
is not violated. But if CP is violated this means by
convention C x P = -1, but this then means T
better = -1 (means T invariance is violated) so as
to get C x P x T and keep CPT “true.”
• This is why we say CP = - 1 implies T = -1, or we
have a reaction that is not invariant under time
reversal or in other words can sense the direction
of time.
•
More on Inflation
• Why does inflation make the universe flat?
• starts with KE +kc2/R2 = PE for radiation and
matter
• PLUS a cosmological constant term for inflation
that does not depend on R.
• KE Lambda term therefore doesn’t change while
kc/R2 hence decreases “dramatically”
• Therefore the kc2/R2 term becomes negligible =
the same a 0 = same as flat!
Review of inflation’s raison d’etre
1. It can’t be a cosmic coincidence that the
value of Omega is relatively close to 1. If
Omega starts out 1, it stays one. This is more
natural and inflation will produce a flat
universe.
2. Inflation says we must explain why objects
that apparently never could exchanged
information (were never in causal contact) in the
age of the Universe had nearly exactly the same
temperature at the time of decoupling.
Review of inflation’s raison d’etre
3. The initial “perturbation spectrum” needs
to be explained and inflation gives a simple
one that can evolve to what we see in the
CMB.
4. Inflation people say we need to explain why
the Big Bang started out so hot and or why
there are so many more photons than baryons
and why there aren’t any anti-baryons. Inflation
provides a mechanism for such process.
OK, Now yet another
model:http://feynman.princeton.edu/~steinh/
The official title is “The Endless Universe”
Replace Inflation with the existence of a mirror
universe.
This universe can communicate with ours only
by gravity.
IF there were people there we could
communicate with them via gravitational waves.
Brane Power to the Max
•Each Universe is on a “brane.”
•The branes keep colliding with each other and
starting a new cycle of big bang to big crunch and
on to another big bang.
•The branes pull in fresh material from an extra
dimension
•This allows the universe to start “anew” at low
entropy
Brane power to the max, cont
Besides the existence of another universe, BPM has
two special features (at least);
1. We won’t find and non-baryonic dark matter
because there isn’t any. Rather the gravitational
interaction with the other Universe mimics this
effect.
2. We won’t find gravitational radiation
Now, on to reality: Measurements!
“Just the facts ma‘am”
• First we’ll do the distance scale
• The overall GERNAL concepts of designing
and carrying out a measurement.
Before you even start you have to ask:
• Why is this interesting?
• Is somebody else already doing this?
•If so, can I do better? And why do it think I can do
better?
General Considerations continued
• How long is it going to take me?
• How much is it going to cost?
• Are the time and money worth it?
Other Considerations
• When to hold’em and when to fold’em
• What are the cost drivers in my design?
• Do I need any instrument development
to allow me to achieve my goals?
• Do I have all the skills I need?
• If not, can I assemble a winning team?
Technical Considerations
• What limits the accuracy of my
measurement?
• How will I calibrate my measurements so
that somebody else can judge the results.
• What assumptions will I have to make
from theory or experiment to build my
case.
• If I’m looking for an effect (such as
WIMPs), will my result be interesting even if
I don’t find the effect?
Why Distance
• Why bother with the distance scale?
• Because nearly every thing we derive in
astronomy depends on knowing the distance.
• For cosmology, we want to know:
• The expansion rate (Hubble constant) which
requires distance versus velocity measurements.
• We want to measure the mass density of the
universe, we need to know the mass within a
given volume, which means a knowledge of the
distance.
Why Distance
• For cosmology, we want to know:
• The distance along with a measure of the redshift
so we can test different geometries of the
Universe
• The distance to objects can tell us how these
objects form and evolve.
• The spatial distribution objects is another test of
cosmology.
Back to distance
• Overall design calls for a “bootstrap”
approach. We start with small distances
we can effectively measure with a ruler.
Now, our next step in the design is to
figure out that the “parallax” can tell us
distances.
• Parallax is the effect of noting you can
discern the distance to an object if you
can measure how much it appears to
move around as you do.
• Overall design calls for a “bootstrap” approach.
• We start with small distances we can effectively measure with a
ruler.
• Next step in the design is to figure out that the “parallax” can
tell us distances.
• Parallax is the effect of noting you can discern the distance to
an object if you can measure how much it appears to move
around as you do.
Parallax Demo
• Take a piece of paper and draw a stripe on it.
Hold the paper at arm’s length with your nose
pointed at the stripe. Then hold 1 finger (your
choice; I used my index one) about half way.
Then close your left eye. Then open it and close
your right eye. Notice how much your finger
appears to move RELATIVE to the stripe. Now
move this same finger to arm’s until it is almost
touching the stripe and try again. Now there
won’t be much apparent motion of your finger
relative to the stripe.
OK now what?
• The effect is caused by moving your vision relative
to your finger and you have accomplished the
“motion” by using different eyes. The effect is the
same as using one eye and moving it the distance
between you two eyes perpendicular to the line-ofsight.
• Now how far can we determine distances that way?
We need to answer two questions first: (1) How far
apart are our eyes, and (2) how small a change in
apparent motion can we measure.
OK now what, cont.
• My eyes are separated by about 7 cm, and I
know also I can see an angular separation of
about 1 arc minute. So the diagram I draw is
like this:
So using
Apparent motion trigonometry,
Each right
d*sin(0.5arc min)
triangle has a
= 3.5 cm or d =
base of 3.5
q
d
240 meters tops,
cm and the
l
q = 0.5 arc min.
apex angle of
s
l about = d,
eyes
0.5 arc
s = 3.5 cm
minutes
Parallax cont.
• => If we know s and q we can calculate d (and or
l). This give us the distance. A person’s distance or
depth perception via binocular vision” is about 15
times worse than what I’ve calculated. The true
number is about 50-60 feet.
(cf., http://online.sfsu.edu/~psych200/unit6/66.htm)
• Where did I go wrong? (a) Our eye needs a
reference frame and the reference frame should be
distant enough not to show parallax; (b) the eye
doesn’t have the luxury of being able to accumulate
data for hours and to look at objects with extremely
well defined centers.
Parallax and astronomy
• We want the equivalent of s to be as large as
possible and accurately measured. => Here
to Chicago won’t “do it.” One side of earth
to the other can allow us a low tech way of
measuring the distance to the Moon. Fine,
but the closest star besides the sun is four
million times further away. We need a
larger “s.” This is
Parallax and astronomy
• The Earth’s orbit around the sun!
• Our most accurate measure now is by?
Radar!
And 1 arc second for q in our diagram with the
earth’s motion around the sun to define s, we
find that 1 arc second gives a distance called a
Parsec (for parallax and arc second!)
The parsec
Taking s = 1.50 x 1013 cm and q = 1 arc second and
sin(1 arc second) = 4.85 x 10-6. Or, d = (1.50
x1013)/(4.85 x 10-6) = 3.09 x 1018 cm! Or in round
numbers, 3 x 1018 cm = 1 par sec. A year = p x 107
sec of time=> p x 107 sec x 3 x 1010 cm/sec = 1018
cm, or 1 par sec = about 3 light years, where speed
of light = c= 3 x 1010 cm/sec
1 parsec (pc) = 3 x 1018 cm
3 light years = 1 parsec
But will parallax work beyond
the stars in our galaxy?
• NO! => We need to determine parallax to
a standard candle, if we can get it.
• What do we need? Precise, small images, the
better to find the centers of, and a well defined
non-moving background for reference.
• Stars are good for making small images,
and distant stars or small galaxies are good
for reference.
Limitations to parallax method
• Swing around sun: Going to Pluto would
get us a much larger swing, but the period is
over 200 years!
• Image quality; Rule of thumb is we can
measure a center to about 1/10 of an object’s
width. The best we could do on the ground a
few years ago was 0.5 arc second images =>
about 20 pc distance. If can go into space can
get a factor of 100 improvement without the
blurring effects of the Earth’s atmosphere.