Axis Alignment in Einstein's 1905 Paper: Symmetry Impact

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Discussion Overview

The discussion centers on the implications of axis alignment in Einstein's 1905 paper on special relativity, particularly regarding the symmetry of coordinate systems in stationary and moving frames. Participants explore the conditions under which the axes can be considered aligned and the consequences of potential misalignment.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions how rotating the y and z axes in a moving frame could break the symmetry of the problem, referencing Einstein's assertion of aligned axes.
  • Another participant asserts that both the stationary and moving frames are inertial, implying that the axes cannot rotate.
  • A different viewpoint suggests that if the axes are not aligned, the mathematics becomes more complex, but the physical results remain unchanged, indicating no necessity for misaligned coordinate systems in special relativity.
  • One participant reiterates the importance of axis alignment and discusses the implications of maintaining right angles between axes when viewed from a moving frame, suggesting that symmetry reasons support this alignment.
  • Another participant introduces a reference to a paper discussing proper coordinates of non-inertial observers, hinting at alternative transformations that resemble Lorentz transformations.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and implications of axis alignment in special relativity. There is no consensus on whether rotating axes in a moving frame affects symmetry or the physical results.

Contextual Notes

Participants discuss the implications of axis alignment and rotation without resolving the mathematical complexities involved. The discussion reflects varying interpretations of Einstein's principles and their application to coordinate systems.

jason12345
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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.
 
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Einstein's stationary and moving frame are both inertial … the axes cannot rotate.
 
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.
 
jason12345 said:
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)
 
tiny-tim said:
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'.
 
jason12345 said:
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.
 

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