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

[Moses Fayngold <moshfarlan@yahoo.com>]

On Sunday, November 9, 2014 6:43 PM, John Mallinckrodt <ajm@cpp.edu> wrote, in part, about my earlier statement 3):

> Again, no. You are misapplying a result of relativity that applies only 
to an array of comoving clocks that--importantly--are synchronized in  >   their own rest frame.


John,
  Thank you for your latest comment regarding my statement 3), in which I wrongly identified the object's clocks after acceleration with the system of synchronized B-clocks, where B is permanently inertial reference frame (RF). It was due to my negligence, by considering only spatial properties of the object and omitting its temporal characteristics. That did not affect my basic conclusions about the object's proper length (which increases in the described process),  but made them incomplete. 

   I cannot explain even to myself how I could have written nonsense 3) and then defend it.

  Now I want to reformulate all my argument, corrected in the light of your comments.
We have an extended stable object S of length D, originally at rest in an inertial reference frame (RF) A. We subject all its parts to equal and synchronous accelerations along D (as observed from A), say, to the right (R). In the end, the object winds up at rest in another inertial RF B moving with a speed V in the R-direction relative to A. Since all parts of S have been translated uniformly from A to B, the length D remains the same in A. But since S is now moving with respect to A, it is Lorentz-contracted by a factor gamma (V). Hence it must have a new proper length D(new) = gamma(V) D. The increase D ---> D(new) is a manifestation of dynamics AND of relativity of time.  Due to the latter, the accelerations of different parts of S were not simultaneous in B. Specifically, the R-end started earlier than the left (L) one. Since S was initially moving to the L relative to B, this stretches S. 

  Now about time. Since displacement of S in temporal dimension was also uniform in A, all of S-clocks as observed from A, keep on reading equal times in the end of the process. But in the end, they become part of B, and the synchronized B-clocks cannot read equal times at one moment of A-time. This means that S-clocks are now de-synchronized. At any moment t of the B-time, those closer to the R read generally a later time than t and those closer to the L read earlier time than t. This is consistent with gravitational red - or blue-shift. The gravitational field in S during its acceleration is L-directed. The local S-clocks at L are in the lower gravitational potential and accordingly tick slower, and the clocks close to the R-end are at higher potential and tick faster. 
   Conclusions: 

1. There is no such thing as a rigid body in Relativity. Even if a body behaves as rigid in one RF, it will be deformed in some other RF. 

2. All considered effects can be explained without geometry. 

3. This is not to discard geometry, but to emphasize that geometry and dynamics are both necessary for a deeper understanding of the   

     relativistic world. 

Moses Fayngold,
NJIT





On Sunday, November 9, 2014 6:43 PM, John Mallinckrodt <ajm@cpp.edu> wrote:
 


Yesterday Moses Fayngold defended his earlier statement:

> 3). Due to relativity of time, the object's clocks along N read different times at one moment of A-time.

Again, no. You are misapplying a result of relativity that applies only to an array of comoving clocks that--importantly--are synchronized in their own rest frame.  Let's review:

I. ASSUMPTIONS

We have a linear array of clocks, perhaps (but irrelevantly) attached to points along a deformable object. All clocks are initially at rest in inertial frame A. All clocks are initially synchronized with themselves and other clocks that will remain stationary in A. 

The clocks in the linear array begin accelerating in a direction along the line of clocks so that there are identifiable "front" and "rear" clocks, F and R respectively.   The accelerations begin simultaneously in A and the acceleration versus time profile is identical for each of the accelerating clocks as measured in A. 

The accelerations end when each clock reaches speed V as measured in A. 

II. THINGS THAT FOLLOW IMMEDIATELY FROM THESE ASSUMPTIONS

1. The proper (i.e. "felt") acceleration versus proper time (i.e. the reading of the clock itself) profile is also identical for each of the accelerating clocks.

2. At any given instant in frame A each accelerating clock is moving at the same speed and displays the same time reading. 

Corollaries: In reference frame A the accelerating clocks maintain their initial spacing, all reach speed V simultaneously, and all display the same time when they reach speed V. 

Note: The accelerating clocks all run slow as determined by observers in A and, therefore, read earlier times than clocks in A as measured in A.

3. When all of the clocks have stopped accelerating they will be found to form a linear array that is at rest in a new inertial frame, B, that moves at speed V relative to A. 

4. The final spacings of the clocks in B will be larger than the respective initial spacings in A by the standard relativistic factor, gamma(V). 

5. In frame B after the acceleration phase has ended, the array of now motionless clocks is not synchronized. In particular, clock F will read a later time than clock R.  Indeed, the clocks will show precisely the times required by the fact that they remain, at all times during and after the acceleration phase, synchronized as observed in A. 

Note: This result is nicely compatible with the qualitative requirement of General Relativity that "higher clocks run faster than lower clocks."  During the acceleration phase, the clocks experience the effects of a gravitational field in which F is "higher" than R.

John Mallinckrodt
Cal Poly Pomona
johnmallinckrodt.com

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