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# Re: [Phys-L] relativistic acceleration of an extended object

• From: John Mallinckrodt <ajm@cpp.edu>
• Date: Sun, 2 Nov 2014 10:44:29 -0800

There's nothing that is the least bit controversial about the points that John Denker has made. They are very well known even if seriously under-appreciated. The simplest way to see that uniform acceleration of an extended object will not preserve its shape, is to consider two displaced rockets that start from rest with the same constant acceleration (in a direction FROM the "rearward one" TOWARDS the "forward one") at the same instant in the initial rest frame of the rockets. Clearly, as time goes on they will remain the same distance apart as viewed from that initial rest frame. Thus, as a direct consequence of "Lorentz contraction," they will be FARTHER apart as viewed from an instantaneous rest frame attached to either rocket.

John Mallinckrodt
Cal Poly Pomona

On Nov 2, 2014, at 9:12 AM, Moses Fayngold wrote:

I reread carefully the previous correspondence. UNDER THE CONDITIONS THAT I TOOK CARE TO EXPLICITLY FORMULATE, I do not see any errors in my conclusions. If you admit that they may be correct "...perhaps in the non-relativistic limit... ", this is already killing for your statements since the non-relativistic limit is merely a part of relativistic domain. The high school relationship between given acceleration and resulting displacement (starting from rest) which I used, is universal, mass-independent, and applies at any, even superluminal, speed. The latter may be realized, e.g., by an appropriate light spot zipping across a screen (the mathematical structure of Relativity treats superluminal and subluminal motions on the same footing).

As to your article, I had explained why I could not read it. Reciprocally, you could read my article with much more detailed analysis of the whole situation than presented here, and under different possible conditions. As to your statement "Shape is determined by proper length..." , I can also refer to another relevant article, "Two Permanently Congruent Rods May Have Different Proper Lengths" in the arXiv.

I would appreciate if anyone could show where and why my arguments are wrong.

Moses Fayngold,