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

[Moses Fayngold <moshfarlan@yahoo.com>]

  Thank you for the corrected links. Now I opened safely your site and read it. It is well written. But its conclusions are the same as in my first two comments.  Let me summarize the whole thing again.
  1).  If all parts of an object undergo equal and synchronous accelerations along some fixed direction N in a fixed inertial reference frame (RF) A, the object's shape conserves in this frame.
  2).  Assuming the object started from rest and acquires final velocity V, it is now Lorentz-contracted along N, which in view of 1) means that its PROPER  length along N has increased by Lorentz factor gamma (V). The proper shape in these conditions does not conserve in the comoving frame B.  
  3). Due to relativity of time, the object's clocks along N read different times at one moment of A-time. The front clock reads earlier time than the rear clock. This means that acceleration program works earlier at the front than at the rear in B, which stretches the object along N, thus increasing its proper length. This explains the underlying dynamics of the process and shows that Geometry alone is not the whole story. 

   Properties 1) - 3) are expressed in a few lines, and in doing this I have used old-fashioned length contraction and local time, without any geometry. Nevertheless, I remained alive - to see again that Physics and Geometry are two sides of the same coin. This is the best coined by Misner, Thorne, Wheeler in their famous "Gravitation":  "Matter tells the spacetime how to curve. Spacetime tells the matter how to move."

Moses Fayngold,
NJIT    



On Saturday, November 1, 2014 1:19 PM, John Denker <jsd@av8n.com> wrote:
 


On 11/01/2014 09:51 AM, Moses Fayngold wrote:
> But I have some comment on the basic statement in the text itself:
> "...in order for the object to maintain its shape, different parts
> will need to accelerate at different rates".
>
> This statement is ambiguous. Its truth value depends on the chosen
> reference frame (RF) and on definition of "shape".

If you would read the article, you would find the answers
to those questions.  Acceleration means proper acceleration
at each point.  Shape is determined by proper length, measured 
along a contour of constant time.  All observers agree that 
the contour in question *is* a contour of constant time, so
there is no ambiguity whatsoever.

>  Let us define the
> shape as an instantaneous configuration of the object in a given RF.
> Then it is easy to see that in the initial rest frame of the object
> (frame A), the statement is wrong. 

It's not wrong. 

> Different acceleration rates for
> different parts will surely distort the shape.

False.  Read the article already.

>  In order to conserve
> it in A, we need the same acceleration a for all parts.

False    (except perhaps in the non-relativistic limit, which
is not what we are talking about here).

Would it kill ya to read the article?

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