Warning: I'm so depressingly out of practice at mathematical
things that I could well have stupid mistakes in the following. Sorry!
If you spot anything wrong, please mail and correct me...
So, I'm slowly working through Taylor and Wheeler's Spacetime
Physics, which is a reasonable pile of fun. I reached the halfway
point during my gardening leave, and have basically been on hold while
I've been learning the new job. However, I thought it worth starting
to write up some notes on the things I've been thinking about while
learning special relativity.
- Invariance of interval is a great starting point for the
book. I'd previously read explanations based on Lorentz
transformation, and this is a much more intuitive explanation.
- Change of reference frame The fundamental point is that a
change of reference frame that changes velocity is no longer a shear,
but a hyperbolic rotation. Talk of hyperbolic functions was in the
first edition of the book (which I "trialed" before I bought the paper
copy), but sadly taken out of the second edition.
- Lorentz contraction is weird If we go past each other at
speed, you seem shorter, with time going slower to me, and you see me
as shorter with time going slower? Yep. This is not entirely alien -
you get the same thing in a non-relativistic world where, if we run
past each other while making a noise, we both hear the same Doppler
effect coming from the other person. It does seem a bit odd, doesn't
- The garage paradox I finally understand the question about
"Imagine you drive a long car really fast into a short garage. The car
fits from the reference frame of the garage, why can't you park it?"
If you want to stop the front and rear of the car at the same point in
time from the reference frame of the garage, you'll be stopping them
at different times in the reference from of the car - namely stopping
the front rather earlier than stopping the back!
- How come we get contraction if the Lorentz transform increases
coordinates? The Lorentz transformation has x' = (x + vt) /
(1-v^2)^0.5. The term on the bottom is less than 1, so we're
stretching out x coordinates. But we're supposed to have a
contraction. What's going on? While the transform changes x
coordinates, it also changes t coordinates. The transformed points
that have the same t' coordinates have x' coordinates that are closer
together. I should draw a diagram.
I've got some more complicated bits to cover (even before I get
onto the second half of the book), but that'll do for now.