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

• From: John Mallinckrodt <ajm@cpp.edu>
• Date: Thu, 6 Nov 2014 18:28:08 -0800

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