Length contraction of space with multiple reference frames

[Dale]

Nobody can 'explain' this. SR asserts that clocks show elapsed times that are equal to the proper-lengths of their worldlines.

I know what you mean, but I wouldn't go quite this far. You can in fact explain the elapsed time on a clock in terms of the two postulates of SR. I.e. time dilation is a derived result.

What we cannot explain in SR is why the postulates are correct, that is simply asserted by the theory.

 

[1977ub]

Why does the fast moving a-naut think the universe contracts in his direction of motion?

1) on the initial level of pure optics, he experiences all kinds of distortions, such as Penrole-Terrell effect which turn sides of moving bodies around.

2) on the the next level - inertial frames, he finds that times and lengths along the direction of motion come out contracted as compared with when at rest wrt them.

3) if he understands SR, he doesn't "think" that anything has contracted.

 

[Mentz114]

I know what you mean, but I wouldn't go quite this far. You can in fact explain the elapsed time on a clock in terms of the two postulates of SR. I.e. time dilation is a derived result.

What we cannot explain in SR is why the postulates are correct, that is simply asserted by the theory.

Noted.

I see a fairly trivial proof that this must be so (the flat spacetime conclusion). Consider some inertial observer constructs Minkowski coordinates. Some event is labeled (x,t). What coordinates would this same observer assign use radar convention? The time would be the same, since radar is the simultaneity convention for Minkowski coordinates. The distance would be c*(1/2 round trip light time). Suppose this isn't the same as x. Then 2x/c does not give the round trip light travel time to event at x from the origin. This violates the axioms used to construct Minkowski coordinates (speed of light is isotropically c in Minkowski coordinates). Thus radar coordinates are identical to Minkowski coordinates for inertial observers. Then all measurements made on a coordinate basis must be the same (e.g. length measured as proper distance at a given time in said coordinates).

Are you saying that using the radar metric of Dolby&Gull, distant measurements show the γ-factor of SR ? As opposed to the naive method where length ( and wavelength) transform like Doppler ?

 

[Dale]

This thread seems to be degenerating into a discussion about "true" and "real". Closed pending moderation.