The Twins Paradox in Relativity

Hi Kevin

What is the speed of a photon from the photon's POV? I think it must be infinite, am I right?

Likewise, a sufficiently fast spaceship would have a speedometer showing its speed as being >c? Is that right?

As I mentioned upthread, the pistons would be going up and down at impressive speeds too. ;)

The garage thing can be crispened up so as to be practically measurable. The point of the doors is that if a collision occurs, it occurs in all reference frames.

Cheers

Phil Hobbs

There are also a few other practical problems, e.g. that the kinetic energy of a 2000 kg car going at c/2 is

m c**2 (gamma -1) =

That's 6653 megatons, at the usually quoted rate of 1 MT = 1e15 cal (4.18E15 J).

The XKCD baseball is a mere 8 MT.

Phil Hobbs

That never happens. Their relative velocity is *always* less than c as viewed from one of their fast moving rest frames (doesn't matter which one).

You are applying a Galilean/Newtonian addition of velocities as measured in the rest frame of the Earth in a situation where the full relativistic treatment for addition of velocities is required. see

Mr stay at home with v=0 sees his two twins going away from him at +/-w

u[stay at home] = w

On either of the fast moving rockets they also see Mr Stay at home receding from them at velocity w and their other twin receding at

u[other traveller] = (w+w)/(1+w^2/c^2) = 2w/(1+(w/c)^2)

To see why set w = c*(1-e)

= 2c*(1-e)/(1+(1-e)^2) = c*(2-2e)/(2-2e+e^2)

Common sense doesn't work with relativity at all. You can really only trust the mathematics and the laws of physics always remaining self consistent. Everything else derives from that basic axiom.

Spacetime itself can expand faster than the speed of light but that is a consequence of GR. There are parts of the (presumed infinite) universe that will remain forever inaccessible to us at any sub light speed.

heh Einstein skeptics have been trying to do that for a hundred years.

Playing around with the the numbers does make a nice exercise for the student.

You can also gin up variations on this paradox. For instance, the garage becomes a two lane highway, with north and southbound lanes. Two cars approach, simultaneously, as seen from the garage. In the garage frame, it's much the same as before, both cars fit inside.

Then work out the various door sequences, as seen from each vehicle, for some real brain twisting -

There's a class of things, called _Lorentz_scalars_, that are the same in all reference frames, i.e. hitting them with a Lorentz transform doesn't change the answer. On example is phase. (It's based on counting, not length measurements.) Whether a collision occurs is one of those.

Cheers

Phil Hobbs