# The relative speed between two Inertial frames are the same

1. Mar 10, 2015

I'm wondering .. if there is an argument could prove that the relative speed of two inertial frames must be the same .

2. Mar 10, 2015

### PeroK

I guess you mean as measured in each frame?

If the two frames measured different relative speeds, then which one would measure the higher speed?

3. Mar 10, 2015

### A.T.

It would violate the equivalence of inertial frames, if their relative speed weren’t symmetrical.

4. Mar 10, 2015

### wabbit

To convince myself of the complete validity of the symmetry argument, I expanded it as follow:

Let A and B start by agreeing, through communication over EM waves, to build identical measuring equipments - i.e. they agree on physical units, then how to build an atomic clock, a Doppler radar, and sighting equipment for angular speeds. Each observer's equipment, as well as the results of their measurements (velocity and distance of the other observer) are unambiguously defined in terms of their local laws of physics.

Now assuming the local laws of physics are the same for both, it follows that they mut get identical results: the distance of B from A, and the speed of B's movement relative to A, are the same as those of A relative to B.

Not saying anything more than previous posters of course, just being pedantic I guess.

Last edited: Mar 10, 2015