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From: Edward Green on 16 Jun 2010 20:13
On Jun 15, 10:06 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
> Edward Green wrote:
> > Still, thinking about it a little more: assume the rivet is initially
> > unstressed. In the rest frame of the rivet, the initially undeformed
> > foot of the rivet strikes the bottom of the hole, and a compressional
> > wave starts toward the head at a speed bounded by c. In the rest frame
> > of the plate, the initially undeformed head hits first, and a
> > dilational wave starts towards the foot of the rivet at a speed
> > bounded by c. (The "bounded by c" obviously applies to either frame in
> > both cases). The ordering of these events varies, but they both must
> > be observed in either frame, and hence the two waves meet at an event
> > somewhere in the middle of the rivet. After that all bets are off. :)
>
> No. You must pick one frame and describe the situation entirely in that frame.
> Then, if you wish, you can select another frame and describe the situation
> entirely in that frame.

We may still use insights gleaned in one frame to describe events in
another frame.

Again taking the pictures at

http://hyperphysics.phy-astr.gsu.edu/Hbase/Relativ/bugrivet.html

as our model, we deduce in the rivet's frame, for example, that the
rivet bottoms out in the hole, and thus that this is true in any
frame. Further, we deduce that the bit of rivet hitting the bottom of
the hole is undisturbed before the collision takes place, and this is
true in every frame also. Similarly we deduce in the plate's frame
that the head of the rivet hits the plate, and that the material
immediately adjacent to this collision was also undisturbed
immediately prior to the collision, and this remains true in any
frame.

Now, in the rivet's frame we know a disturbance travels up the rivet
from the collision with the bottom of the hole, and we also know that
it does not reach the head before the head collides with the plate
(since we know the material is initially undisturbed). Upon this
second collision a second disturbance begins propagating _down_ the
rivet, and meets the first disturbance at an intermediate point. The
description in the plate's frame is similar. Thus in either frame we
have disturbances propagating inwards from the ends of the rivet and
meeting in the middle.

> The "dilational" and "compressional" waves are in different frames, and
> attempting to combine them in one description is wrong.

I think in this case the waves will have the character I mention in
either frame. I concede that if the disturbances travel at less than c
their direction of travel may vary according to the rest frame. It
also depends if we model the plate elastically (ooh boy, is this
academic!). I don't think we have to: there are no rigid bodies in SR,
but as long as the rivet is elastic, I think we can get away with an
ideally fixed and rigid plate.

> Remember that a "dilational wave" merely describes the location and motion of
> atoms over time. Ditto for a "compressional wave". Since the times are different
> in the two frames, especially in the way they map onto spatially-separated
> events, it's no surprise that the locations and motions of atoms are different
> for the two interpretations of time.
>
> This is a non-problem -- it is wholly explained by the difference in
> simultaneity in the two frames. There is a sound wave inside the rivet in every
> frame; its direction and nature ("dilational"/"compressional") depends on which
> frame one uses to describe it.
>
> I use a directional horn to send a sound wave to the east.
> Relative to an eastward-moving supersonic jet that same sound
> wave moves to the west. Such motions are frame dependent.
>
> Tom Roberts

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