# Alignment of axis

1. Apr 18, 2010

### 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.

2. Apr 19, 2010

### tiny-tim

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

3. Apr 19, 2010

### 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.

4. Apr 19, 2010

### starthaus

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)

5. Apr 23, 2010

### jason12345

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 travelling 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'.

6. Apr 23, 2010

### starthaus

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