Axis Alignment in Einstein's 1905 Paper: Symmetry Impact

[jason12345]

In Einstein's 1905 paper he says that, by reasons of symmetry, we can assume the coordinate axis of the stationary and moving frame are aligned.

If the y and z axis rotate towards/away from the x-axis in the moving frame in a way dependent upon the velocity, how does this break the symmetry of the problem?

Thanks.

 

[tiny-tim]

Einstein's stationary and moving frame are both inertial … the axes cannot rotate.

 

[Matterwave]

If instead you are saying that I have 2 frames which are not aligned (e.g. the x-axis doesn't point where the x'-axis points), what happens? The math gets a lot more complicated, but the physical results stay the same. There's no reason to construct 2 coordinate systems which don't align in SR.

 

[starthaus]

In Einstein's 1905 paper he says that, by reasons of symmetry, we can assume the coordinate axis of the stationary and moving frame are aligned.

If the y and z axis rotate towards/away from the x-axis in the moving frame in a way dependent upon the velocity, how does this break the symmetry of the problem?

Thanks.

You get a set of transforms that look very similar to Lorentz , see for example :

H. Nikolic,
"Proper co-ordinates of non-inertial observers and rotation",
gr-qc/0307011, invited contribution to the book "Relativity in Rotating Frames", editors G. Rizzi and M. L. Ruggiero, Kluwer Academic Publishers, Dordrecht (2004)

 

[jason12345]

Einstein's stationary and moving frame are both inertial … the axes cannot rotate.

I wasn't implying that they rotate continuously with time.

If a set of axis are at right angles in their proper frame, why should they remain at right angles when viewed from a moving frame?

Einstein suggests they must remain so for symmetry reasons and i think i can see why now, partly.

The y and z axis can be flipped with the negative to give another stationary frame with the moving frame traveling along the same x-axis in the same direction. This means the transformation at (x,-y,z) = (x,y,z) and likewise (x, 0+dy, z)= (x, 0-dy, z), for example. So there is no variation of the moving axis y' wrt x and likewise with z'.

 

[starthaus]

I wasn't implying that they rotate continuously with time.

If a set of axis are at right angles in their proper frame, why should they remain at right angles when viewed from a moving frame?

Then, what you want is this. This is the most general form of the Lorentz transform.