[ExI] Interstellar FedEx

Anders Sandberg asa at nada.kth.se
Wed Sep 30 00:36:01 UTC 2009

spike wrote:
>> ...Hmm, so what is the most entropic kind of stable matter?
> Anders, I need to review my thermo books to be sure, but I think the
> answer
> to that question is molecular hydrogen in the form of a cloud in
> interstellar space.  It might depend on how you define stable matter.: the
> answer might be atomic hydrogen.

Hmm, I don't want to lose my precious matter, so I would like to keep it
bottled as heat reservoirs. Hydrogen does indeed look like it got a great
specific heat capacity - I was surprised how much better it was than water
gram for gram.

> I have been thinking about the original question of how to derive the
> equation for inherent entropy production in moving mass.  I have a thought
> experiment for you.

Cool! Yes, this seems to show that there is an energy loss. The spring, if
it is compressed x meters beyond its resting length, will let go off the
mass M payload when it passes the rest length (because the spring will
start to deaccelerate, but not the payload). I get an estimate of
kmx^2/2(m+M) J of kinetic energy left in the mass m spring at that point.
Hmm, if we can let m approach zero then the loss goes to zero

Presumably the moral is that the tube becomes perfectly reversible if the
springs have zero mass, but you need some mass to store the compression
energy in the first place. At the very least the spring will have
kx^2/2c^2 mass-energy just from the compression, which would give a
minimal loss of
k^2 x^4/(2kx^2+4Mc^2) J. You can still get zero loss if x=0, but then the
payload never arrives. The velocity of the payload will be
sqrt(kx^2/(M+kx^2/2c^2)) - the bigger kx^2, the closer it will get to
sqrt(2)c??? In the non-relativistic case I guess one could look at the
heating of the spring.

[Caveat: after midnight calculation, correctness may vary]

Doing this with an electromagnetic launch would probably produce some
similar loss: opening a superconductive box hiding a magnet to repel a
magnetic payload would at the very least produce radiation from the
accelerated magnet and likely also from the act of opening the box (I
think the closed box is a bit like a coiled spring). Ditto for the
electric field version.

> In that particular thought experiment, you demonstrate that moving a mass
> cannot be made perfectly reversible.  The third law is called a law for a
> reason.  It isn't just a suggestion.  It means business.

"Nice heat engine you have here... look at those nice cycles. Lots of
pressures and volumes changing. It would be *such* a shame if something
bad happened to it, wouldn't it? Whaddya say,  wouldn't you want to pay a
bit of entropy insurance?"

Anders Sandberg,
Future of Humanity Institute
Philosophy Faculty of Oxford University

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