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From: Edward Green on 13 Jun 2010 17:46
On Jun 13, 11:06 am, "Inertial" <relativ...(a)rest.com> wrote:
> "Edward Green" <spamspamsp...(a)netzero.com> wrote in message
<...>
> > In the frame of the plate, the impacting rivet is too short to hit the
> > bottom initially. Hence we must see a region of dilating rivet
> > traveling from the impact of the head until the impact of the foot.
>
> Yeup .. the foot keeps going for a while after the head stops .. as the
> information from the head that it has stopped cannot travel to the foot
> faster than c
>
> > Part of this is the rivet coming to a stop in the plate's frame, hence
> > assuming its normal length. However, the dilation must go beyond that,
> > since by assumption the rivet at rest wrt the plate was too short to
> > reach the bottom of the hole.
>
> Is it?  As I recall it fits perfectly when at rest, but due to length
> contraction the bug thinks (its a clever bug) that the rivet is now too
> short to reach it.  But the rivet thinks (or at least some observer moving
> with it thinks) that the hold is contracted, and so the bug will surely die.

Well, follow the link I first posted: in this version, the rivet is .8
cm long at rest, and the hole is 1.0 cm deep. This adds piquancy to
the problem, because we know that the rivet is going to bottom out
anyway when moving at .9 c -- no signal can travel down the rivet fast
enough to stop the end.

> > What we have is a version of "no rigid
> > bodies" in SR -- the rivet _must_ stretch.
>
> So why is that a problem?

Not a problem. As I said, my puzzlement was over description of the
intermediate states when comparing the story in the rivet's rest frame
vs. the plate's rest frame.
From: Inertial on 13 Jun 2010 20:42
"Edward Green" <spamspamspam3(a)netzero.com> wrote in message
news:d1a6d86d-f844-4531-8fff-dcd3e4272581(a)18g2000vbe.googlegroups.com...
> On Jun 13, 11:06 am, "Inertial" <relativ...(a)rest.com> wrote:
>> "Edward Green" <spamspamsp...(a)netzero.com> wrote in message
> <...>
>> > In the frame of the plate, the impacting rivet is too short to hit the
>> > bottom initially. Hence we must see a region of dilating rivet
>> > traveling from the impact of the head until the impact of the foot.
>>
>> Yeup .. the foot keeps going for a while after the head stops .. as the
>> information from the head that it has stopped cannot travel to the foot
>> faster than c
>>
>> > Part of this is the rivet coming to a stop in the plate's frame, hence
>> > assuming its normal length. However, the dilation must go beyond that,
>> > since by assumption the rivet at rest wrt the plate was too short to
>> > reach the bottom of the hole.
>>
>> Is it? As I recall it fits perfectly when at rest, but due to length
>> contraction the bug thinks (its a clever bug) that the rivet is now too
>> short to reach it. But the rivet thinks (or at least some observer
>> moving
>> with it thinks) that the hold is contracted, and so the bug will surely
>> die.
>
> Well, follow the link I first posted: in this version, the rivet is .8
> cm long at rest, and the hole is 1.0 cm deep. This adds piquancy to
> the problem, because we know that the rivet is going to bottom out
> anyway when moving at .9 c -- no signal can travel down the rivet fast
> enough to stop the end.

Sorry .. don't have your original post handy on my server. But there are
obviously a few variations.

>> > What we have is a version of "no rigid
>> > bodies" in SR -- the rivet _must_ stretch.
>>
>> So why is that a problem?
>
> Not a problem. As I said, my puzzlement was over description of the
> intermediate states when comparing the story in the rivet's rest frame
> vs. the plate's rest frame.

It is a trickier scenario then most due to the sudden stopping of the rivet
(relative to the hole) .. and having to worry about how fast the information
about that travels though the rivet. It reality any rivet slamming into a
hole at the sort of speed would result in a bit of a mess for the hole and
the rivet :):)

From: Tom Roberts on 14 Jun 2010 15:40
Edward Green wrote:
> What I'm puzzled about is the intermediate descriptions: in the rivet
> frame, a compressional wave travels up the shaft of the rivet until
> the plate hits the head. In the plate frame, a _dilational_ wave seems
> to travel down the rivet from the opposite direction until the foot of
> the rivet hits the backstop. How to reconcile these descriptions?

They are a natural consequence of the relativity of simultaneity. In the plate
frame the head hits first, and in the rivet frame the foot hits first.

The whole point of such paradoxes is to teach the student about the
non-intuitive aspects of relativity. The difference in simultaneity between
inertial frames is a major departure from Newtonian mechanics and our everyday
experience. It is, however, an essential aspect of SR.


Tom Roberts
From: Edward Green on 14 Jun 2010 18:41
On Jun 13, 8:42 pm, "Inertial" <relativ...(a)rest.com> wrote:
> "Edward Green" <spamspamsp...(a)netzero.com> wrote in message
>
> news:d1a6d86d-f844-4531-8fff-dcd3e4272581(a)18g2000vbe.googlegroups.com...
>
>
>
> > On Jun 13, 11:06 am, "Inertial" <relativ...(a)rest.com> wrote:
> >> "Edward Green" <spamspamsp...(a)netzero.com> wrote in message
> > <...>
> >> > In the frame of the plate, the impacting rivet is too short to hit the
> >> > bottom initially. Hence we must see a region of dilating rivet
> >> > traveling from the impact of the head until the impact of the foot.
>
> >> Yeup .. the foot keeps going for a while after the head stops .. as the
> >> information from the head that it has stopped cannot travel to the foot
> >> faster than c
>
> >> > Part of this is the rivet coming to a stop in the plate's frame, hence
> >> > assuming its normal length. However, the dilation must go beyond that,
> >> > since by assumption the rivet at rest wrt the plate was too short to
> >> > reach the bottom of the hole.
>
> >> Is it?  As I recall it fits perfectly when at rest, but due to length
> >> contraction the bug thinks (its a clever bug) that the rivet is now too
> >> short to reach it.  But the rivet thinks (or at least some observer
> >> moving
> >> with it thinks) that the hold is contracted, and so the bug will surely
> >> die.
>
> > Well, follow the link I first posted: in this version, the rivet is .8
> > cm long at rest, and the hole is 1.0 cm deep. This adds piquancy to
> > the problem, because we know that the rivet is going to bottom out
> > anyway when moving at .9 c -- no signal can travel down the rivet fast
> > enough to stop the end.
>
> Sorry .. don't have your original post handy on my server.  But there are
> obviously a few variations.
>
> >> > What we have is a version of "no rigid
> >> > bodies" in SR -- the rivet _must_ stretch.
>
> >> So why is that a problem?
>
> > Not a problem. As I said, my puzzlement was over description of the
> > intermediate states when comparing the story in the rivet's rest frame
> > vs. the plate's rest frame.
>
> It is a trickier scenario then most due to the sudden stopping of the rivet
> (relative to the hole) .. and having to worry about how fast the information
> about that travels though the rivet.  It reality any rivet slamming into a
> hole at the sort of speed would result in a bit of a mess for the hole and
> the rivet :):)

Yes. The bug, rivet and a large part of the plate vanish in a
fireball! I'm not sure if that answer gets full credit, though. :-)
From: Edward Green on 14 Jun 2010 21:02
On Jun 14, 3:40 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
> Edward Green wrote:
> > What I'm puzzled about is the intermediate descriptions: in the rivet
> > frame, a compressional wave travels up the shaft of the rivet until
> > the plate hits the head. In the plate frame, a _dilational_ wave seems
> > to travel down the rivet from the opposite direction until the foot of
> > the rivet hits the backstop. How to reconcile these descriptions?
>
> They are a natural consequence of the relativity of simultaneity. In the plate
> frame the head hits first, and in the rivet frame the foot hits first.
>
> The whole point of such paradoxes is to teach the student about the
> non-intuitive aspects of relativity. The difference in simultaneity between
> inertial frames is a major departure from Newtonian mechanics and our everyday
> experience. It is, however, an essential aspect of SR.

Yes. Got all that. The devil is in the details.

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. :)
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