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

[Moses Fayngold <moshfarlan@yahoo.com>]

Regarding point 3) of my non-geometric presentation:
3). Due to relativity of time, the object's clocks along N read different times at one moment of A-time.


To this, John Mallinckrodt wrote:
  > Not if I'm reading you correctly. In frame A, each clock behaves identically so, at any specific instant of time in A all clocks along the object read the same time (assuming, reasonably, they were synchronized before the acceleration phase.)

  I think, precisely if reading correctly one should say "Yes". There are TWO sets of clocks along the object - one belonging to A, all of them stationary in A and reading the same A-time. But they are NOT the OBJECT''S clocks referred to in 3)! (Maybe I should have specified "The object after acceleration", but that must be clear from the context!). The object's clocks are forming the second set sliding with a speed V relative to A. Even if they have all been synchronized IN THEIR FRAME B, they read DIFFERENT MOMENTS at one moment of A-time (relativity of simultaneity!). For instance, at noon of A-time, all A-clocks read 12 pm. The middle clock attached to B also reads 12 pm. But the front B-clock reads EARLIER time, say, 11 am, whereas the rear B-clock reads 1 pm. To simplify here, without changing the initial conditions and without loosing the generality of conclusions, let us assume that accelerating forces are applied to rear and the front, and are
 practically instantaneous but huge (to transfer the finite impulse I=F delta t = delta P). Initially the object is stationary in A and accordingly moving backwards at a speed V relative to B. At noon of A-time the two forces applied to the rear and front of the object instantly transfer the object from A to B. Now the object is stationary in B but moving forward at speed V in A. The length of the object in A remains the same due to synchronous action of both forces in A. But in B, the force on the front (which is rear in B due to object's reverse initial motion relative to B!) was applied earlier (at 11 am of the B-time) whereas the force on the rear (the front in B!) was applied later (at 1 pm of the B-time). The rear of moving object was stopped relative to B 2h earlier than the front. As a result, the whole object, when finally stopped in B, is stretched and is thus longer than it was initially. The whole process is instantaneous in A, but lasts 2h
 in B. Since the object is now at rest in B, its new length in B is its proper length. And since it was subjected to stretch, this new proper length is greater than the initial one. We came to the same conclusion as before in a slightly different way, but again, without geometry, using only relativity of space and time and dynamics of forces. 
  All this is in much more details in references I gave in earlier messages.

Moses Fayngold,
NJIT   
    




On Friday, November 7, 2014 11:11 AM, John Mallinckrodt <ajm@cpp.edu> wrote:
 


On Nov 6, 2014, at 5:19 PM, Moses Fayngold wrote:

> 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.

Right.

> 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.  

Right again.

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

Not if I'm reading you correctly.  In frame A, each clock behaves identically so, at any specific instant of time in A all clocks along the object read the same time (assuming, reasonably, they were synchronized before the acceleration phase.)

> 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. 

I can't really follow this as it makes frame-specific assertions without specifying the frame.  

It's a little difficult to talk about what things look like according to ride-along observers since each one finds that all of the others are moving at different velocites at any given time DURING the acceleration phase.  For instance, in the instantaneous inertial reference frame of an oberver riding along at the middle, M, the observer riding along at the front, F, is always moving faster than M (i.e., is pulling away from M) and has a clock that reads a later time than M's.  Similarly, in the instantaneous inertial reference frame M, the observer riding along at the rear, R, is always moving slower than M (i.e., is lagging further and further behind M) and has a clock that reads an earlier time than M's.  As observed in the sequence of instantaneous inertial frames for M, the acceleration phase ends earlier for F and later for R.  When all parts of the object have attained speed V, and the observers once again are at rest in a single inertial
 reference frame, B, moving at speed V 
relative to A, the clocks will not be synchronized in B.  Specifically, clocks will read read later and later times as one moves toward the front of the object.  

Note again, however, that in A, all clocks ALWAYS read the same time since each one moves identicaly in that frame.

John Mallinckrodt
Cal Poly Pomona
johnmallinckrodt.com

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