🚀 go-pugleaf

In article <1992Dec15.013620.24161@galois.mit.edu> jbaez@riesz.mit.edu (John C.  
Baez) writes:
Disclaimer deleted. 
> Imagine an extremely (although not infinitely) rigid crystal.  It takes
> a huge amount of energy to deform the crystal lattice ever so slightly.
> Thus if this crystal is placed in the earth's gravitational field at sea
> level, the curvature of space due to the gravity prevents the
> lattice from being perfectly regular, at the cost of a large amount of
> energy.  The crystal would have much less energy if it were far away
> from the earth where the curvature of space is less.  If we make the
> crystal rigid enough it will actually be energetically favorable for the
> crystal to float upwards - since the decrease in its internal energy
> will more than compensate for the increase in gravitational potential
> energy.
> 
> Now, I *know* that this material would have to be insanely rigid for
> this effect to be noticeable at all -- far more rigid than any actual
> stuff.  However, we're talking questions of principle here.  Is there
> any reason *in principle* why a sufficiently rigid material wouldn't
> levitate to get out of the earth's gravitational field - that's what I'm
> asking.  

On the general principle that the universe conspires to prevent
such useful things as antigravity or faster than light communication,
I say it won't work.  I think the results of a detailed calculation
would have the following results:

To levitate the material would have to be rigid enough that the
vertical derivative of deformation energy/unit mass would exceed 
the gradient in gravitational potential energy/unit mass.  Mass 
cancels out, and as is usual in eleasticity, rigidity with mass
factored out gives a velocity - the speed of sound in the material.
Now nature will have so arranged things that a levitational material
(calorite? what did H.G.Wells call it?) would have a speed of sound
greater than c.  Therefore such a material is impossible!?

--
Thomas Clarke
Institute for Simulation and Training, University of Central FL
12424 Research Parkway, Suite 300, Orlando, FL 32826
(407)658-5030, FAX: (407)658-5059, clarke@acme.ucf.edu