Notes on Relativity and Cosmology - Physics Department, UCSB

Chapter 4
Special Relativity is
Minkowskian Geometry
Read Einstein, ch. 16,17, Appendix 2
Let’s take a look at where we are. In chapter 2 we were faced with the baffling
results of the Michelson-Morely experiment and the stellar aberration experiments.
In the end, we decided to follow Einstein and to allow the possibility that
space and time simply do not work in the way that our intuition predicts. In
particular, we took our cue from the Michelson-Morely experiment which seems
to say that the speed of light in a vacuum is the same in all inertial frames
and, therefore, that velocities do not add together in the Newtonian way. We
wondered “How can this be possible?”
We then spent the last chapter working out “how this can be possible.” That is,
we have worked out what the rules governing time and space must actually be
in order for the speed of light in a vacuum to be the same in all inertial reference
frames. In this way, we discovered that different observers have different notions
of simultaneity, and we also discovered time dilation and length contraction.
Finally, we learned that some of these strange predictions are actually correct
and have been well verified experimentally.
It takes awhile to really absorb what is going on here. The process does take
time, though at this stage of the course the students who regularly come to my
office hours are typically moving along well. If you are having trouble making
the transition, I encourage you to come and talk to me.
There are lots of levels at which one might try to “understand” the various
effects 1 . Some examples are:
1 This is as opposed to why you should believe in these effects. The fundamental reason to
believe them must always be that they predicted new phenomena (like time dilation) which
were then experimentally verified.
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