Special relativity
Einstein originally proposed his theory of
special relativity in 1905 and it is often
taken as the beginning of modern physics.
It opened the door to whole new ways of
thinking about the universe.
VIDEO
2+2=3
Imagine you are on a train going at 60 mph. You are travelling
at 60 mph when viewed by an observer at the side of the track,
but you are at rest when viewed by the passenger sitting
opposite you. These two points of view are known as frames of
reference in physics and relativity is all about how the physics
measured in these frames of reference compares. If the
observer was on a train travelling at 60 mph in the opposite
direction, then in their frame of reference you would be
travelling at 120 mph. This works well for objects travelling at
low speed but we find that it doesn't work so well when moving
close to the speed of light.
Use this calculator to see what speed objects appear to
approach when the speeds are close to the speed of light.
Experiment to find the speed of light
Can we produce a simulation version?
The principles
1. When two observers are moving at constant speeds
relative to one another, they will observe the same laws of
physics.
2. The speed of light (in a vacuum) is the same for all
observers.
Einstein started with just these two principles. These were two
almost philosophical statements that he could not prove to be
true, but using them he was able to derive his theory of special
relativity. The consequences of this theory could then be tested
against what we observe to be true in the universe. It was also
impressive that Einstein was able to derive all the results of his
predecessors using just a few pages rather than the volumes of
scientific writing they had needed.
Time dilation
A very simple thought experiment shows that one consequence
of the speed of light being the same for all observers is that
time experienced by all observers is not necessarily the same.
There is no universal clock that we can all refer to - we can
simply make measurements of time as we experience it.
This calculator can be used to see how much time dilation
takes place at various speeds.
This song (Queen, 39) is about the effects of special relativity.
See if you can work out what is going on.
Animations:
http://www.phys.unsw.edu.au/einsteinlight/jw/module4_time_dil
ation.htm,
http://www.upscale.utoronto.ca/PVB/Harrison/Flash/#relativity
Why do we not notice these time
differences in everyday life?
We can see that for
small speeds (ie less
than 0.1 times the
speed of light) the
Lorentz factor is
approximately 1 and
relativistic effects are
negligibly small.
Even 0.1 times the
speed of light is a
tremendously fast
speed compared to
everyday life.
Implications for everyday life
The speed of satellites is fast enough that even these small
changes will add up over time and affect the synchronisation
of global positioning systems (GPS) and television
broadcasters with users on the Earth.
Satellites have to be specially programmed to adapt for the
effects of special relativity (and also general relativity, which
is not covered here). Very precise measurements of these
small changes in time have been performed on fast aircraft
and agree with predicted results within experimental error.
Muon detection
Further evidence in support of special relativity comes from the
field of particle physics, in the form of the detection of a particle
called a muon at the surface of the Earth. Muons are
produced about 25 km up in the atmosphere by cosmic rays.
Their measured lifetime is about 2.2 μs and their speed is
99.9653% of the speed of light.
Flash Simulation
Calculate how far muons can travel in their lifetime.
How can we detect them?
Calculate the lifetime of the muon as seen from our stationary
reference frame.
How far can muons travel in this time?
Length contraction
Another implication of Einstein's theory is the shortening of
length when an object is moving. Consider the muons
discussed above. Because of their large speed they experience
a longer lifetime as a result of time dilation. An equivalent way
of thinking about this is that muons experience the height of the
atmosphere as smaller (or contracted) by the same amount as
the time has increased (or dilated). There is a symmetrical
formula to that for time dilation, which can be derived. Note that
the contraction only takes place in the direction that the object
is travelling.
Formula
http://www.physicsclassroom.com/mmedia/specrel/lc.cfm
Ladder paradox
Consider a ladder that is just longer than a garage. If we fly the
ladder at high speed through the garage does length
contraction mean that from our stationary perspective it fits
inside the garage? How can this be reconciled with the fact that
from the ladder's reference frame the garage appears even
shorter as it moves towards the ladder?
http://en.wikipedia.org/wiki/Ladder_paradox
Or produce one like
http://www.yteach.com/index.php/search/results/Twin_Paradox,
0,0,0,twin_paradox,25,1,tn,1.html