MadSci Network: Physics

Re: Is BEC perfectly rigid?

Date: Fri Jan 27 15:57:51 2006
Posted By: Calvin Cole, Faculty, Engineering Physics, Northeastern State University
Area of science: Physics
ID: 1136064975.Ph

    Your question brings up in a new way one of the main difficulties we
have in dealing with the world of quantum mechanics.  We have a very real
lack of good descriptive terms that make any sense in an every day sort of
way or allow us to make analogies that aren't more wrong than they are
right for what goes on at the quantum level.  Many people have noted this
over the years and probably most agree that it is in large part because we
just don't see behavior for the common physical objects about us that in
terms of energy, momentum or position obeys rules much at all like those
for things the size of atoms and smaller.  Lacking this everyday experience
we not only don't have good unambiguous words for it but have trouble even
imaging it even though we can describe it in exquisite detail
mathematically.  That being said, here we go:
    What do we mean by rigid?  In our everyday world nothing is perfectly
rigid.  There is always a delay between pushing on one side of an object
and the vibration caused making it to the other side.  We usually interpret
this to be something like the speed of sound in that material.  It happens
because molecules take time to either bump into one another or for the
distortion of an atomic or molecular bond to be noticed by a neighboring
atom or molecule, much liked a wave in a spring.  In fact if something were
perfectly rigid any disturbance of one part would cause instantaneous
motion of all parts.  It's the word "instantaneous" that gets us in trouble
here since that would imply knowledge of what was going on in one place to
travel infinitely fast (much more rapidly than even the speed of light!) to
some other place.  If you check what we know of BEC you find that it is a
group of "indistinguishable" (you can't tell which is which) atoms all in
the same energy state in the same volume of space.  Saying it's now all
"one big atom" is perhaps a bit misleading but even if true would make it
no more rigid than any other ordinary atom.  It's probably not a good idea
to talk of "all the atoms moving in unison" either since this implies in
our ordinary view of the world that they all go the same way at the same
time instantly. It certainly sounds that way and as you correctly point out
if that's what happened it would be perfectly rigid.  Rather what happens
is that the energy of the group is disturbed as a whole but in fact we
don't really know where any one atom of the group is any more precisely
than any other and for none of them any better than Heisenberg's
Uncertainty Principle allows.  This is why we say, (and experimentally see)
all the atoms "condensed" into the same volume of space with the same
energy or quantum state.  If you haven�t already been there check out the
entire site at
Especially their interactive energy level diagram.  I hope this is helpful
Chris.  Keep on asking good questions.

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