From: bhoughto@sedona.intel.com (Blair P. Houghton)
Newsgroups: rec.arts.sf.written,rec.arts.sf.science,sci.physics,sci.skeptic
Subject: Re: Davis Mechanics (was Re: John Woods Campbell)
Date: 9 Jan 1993 20:29:28 GMT
Organization: Intel Corp., Chandler, Arizona
Distribution: world
NNTP-Posting-Host: stealth.intel.com

In article <1k3Nw2#B7S83O9Nz5dF4k9Qpy9KcjGV=esr@snark.thyrsus.com> esr@snark.thyrsus.com (Eric S. Raymond) writes:
>In <18342@bcars664.bnr.ca> Henry Troup wrote:
>> This is one I can't figure out.  Consider a steel bar, in free space, a
>> long way from anywhere, one light-year long.  place a large rocket
>> against one end, and turn it on.  Let it run for 364 days.  Turn it off.
>> What has happened?  Try it again with an incompressible rod - if the rod
>> moves, the message reached the far end faster than light.  If the rod
>> doesn't move, where'd the momentum go?

Someone mentioned "compression waves," and I think
everyone's explained that "incompressibility" is
impossible.  What I'd like to remind everyone of is that
solid materials of supraatomic extent are mechanically
connected by electromagnetic forces (the rigid equilibrium
of systems of nuclei bonded by molecular electron clouds
and intertwined by metallurgy, crystallization, etc.).

In the absence of dispersion, the best you can do is to
line up atoms and whack one with a scanning-tunnelling
microscope to see how fast the electromagnetic disturbance
takes to get to the other end.

Any mechanical (acoustical, momentum) disturbance will take
far longer, since it involves the motion of the nuclei.

Assume though that you can create a theoretically
"incompressible" rod (what's a good gedankenexperiment
without an assumption to be countervened?).

The frontier of impulse from the disturbance at one
end would propagate with the frontier of relativistic
energy (which moves at c).

The rod's elements of mass can not be accelerated if the
elements further down the rod will not move (this is the
definition of incompressible rigidity), so they will not
move until the frontier of impulse reaches the last element.

So, slice the rod into a line of short, incompressible
cylinders, and throw one at one end.  After the
relativistically correct time the last will pop off the
other end.  If they're suspended on strings it will swing
back, causing the reverse reaction, and we can be
mesmerized by it for centuries.

During the time between visible motions of the two
cylinders at the end, where is the momentum?  It is
somewhere in the rod, existing as pure momentum without
displacement (in the real version of this toy it exists as
minute deformations in the hanging balls, propagating as an
acoustical wave; is it correct then that incompressible
balls could not move because they could not propagate a
real impulse from one end to the other?).  The cylinders
between the ends act as though they have infinite mass.

But if the impulse is constant at one end, then the
frontiers of impulse are constant accross the length of the
rod behind the initial frontier.  When the initial frontier
reaches the end, the final cylinder moves in response to
it.  Once it is out of the way, the next frontier of
impulse accelerates the penultimate cylinder.

This produces a backward-propagating frontier of
acceleration.

If the rod is whole, we have simply a frontier of impulse
that propagates, reaches the other end, and is reflected,
because the end can not move since it is tied to the rest
of the rod, which is not moving.

If the impulse is constant, then it reaches the end,
reflects, and propagates backward, cancelling the forward
moving frontiers of impulse.  When it reaches the beginning,
it cancels the impulse generated by the external force, or
reflects again and doubles the frontier of impulse the external
force continues to generate.

It seems that relativity prevents an incompressible object
from accelerating when acted on by point forces.  (A field
of force acting all along the length of the rod should
accelerate it, still).

This should work on any scale, so even our incompressible
cylinders should not have moved.

"Where does the momentum go?" It goes into the effectively
infinite mass of the incompressible object, which accelerates
at an effectively infinitesimal rate, and dp/dt = f = ma = oo * 0
can be anything you want it to be.  No energy is transferred
between the rocket and the rod, apparently.

[This also spannerworks our ideas about incompressible
fluids, btw.]

So how does any real, "rigid" object accelerate when it's
pushed?  (Someone already mentioned compression waves;
that's all this is.) Each atom in turn pushes on the
successive atom, propagating the frontier of momentum at
the speed given by Young.  Frontiers of momentum continue
to arrive if the force is continuous, and the object moves
all in one direction.  If the force is momentary, the
object moves only a little bit and vibrates a lot.  How can
a unit (dirac-like) impulse make the entire object move?
Like a snake.  When the compression reaches the end, the
last atom moves outward into space and pulls on the one
before it.  The frontier of momentum is reflected and
propagates backward, but is now a frontier of negative
momentum, since the atoms are pulling.

This is different from the reflected frontiers of momentum
in the incompressible rod, which were reflected like a ball
off a wall, causing the frontier to reverse direction but
remain a pushing force (I have a really bad analogy
involving ornery drivers at a long stoplight, here, but
I'll omit it), cancelling the forward push.

>Thank you, Mr. Troup.  This is a better way of making the point I'd been
>driving at than I'd thought of.

What point is that?  It seems to depend on a fallacious
assumption.  To wit, that incompressible objects *can* be
accelerated by point forces.

>> But Davis didn't really account for the Dean Drive - partly because the
>> device Dean demo'd wasn't the one in the patent drawings, and he
>> wouldn't let anyone closely examine his model.  Dean was a classic
>> crackpot, as Harry Stine admits.  Stine did a followup article on Davis
>> mechanics and some actual experiments that did have unexpected results. 
>> Like a simple mechanical system with an unexplained 3 degree phase shift.
>
>Yup.  This is the article I read, I think; that's where I got the bit
>about the artillery shells.
>
>There is real physics here that no one is following up.  It's sad.

Que es que c'est, "Dean Drive?"

				--Blair
				  "And here I always thought I
				   was an irresistable force..."
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