[ExI] Interstellar FedEx
Anders Sandberg
asa at nada.kth.se
Mon Sep 28 00:03:41 UTC 2009
Is there a fundamental energy or entropy cost of moving matter around? If
I want to send a mass M from point A to point B within time T, how much
would that cost? Obviously there are concerns of friction in terrestrial
environments, but I am mostly concerned here with interstellar distances.
To get a distance d within time T requires a speed greater than d/T, which
implies a kinetic energy of at least [-1 + 1/sqrt(1-(d/Tc)^2)]Mc^2. I need
to do this much work to get it moving, but I can also get the work back by
catching the object in a skillfull manner. The drawback is of course that
now I have also moved the energy from A to B too. Worse, the system
launching the mass at A and the system receiving it at B will now have
acquired a slight velocity away from each other due to momentum
conservation.
To me this looks a bit like some kind of entropy effect: to restore the
systems to their original rest positions and velocities a further
2d/[T sqrt(1-(d/Tc)^2)] Joules have to be spent in station-keeping to get
rid of the momentum, losing that energy as "waste momentum". Is there
something akin to thermodynamics here suggesting we must always pay this
price?
As always, GR complicates things:
Jack Wisdom has shown that it is possible to move without expending energy
permanently by "swimming" in a curved spacetime:
http://dspace.mit.edu/handle/1721.1/6706
In Schwartzschild geometry the amount of motion you get per stroke scales
as 1/r^3 and is pretty microscopic: for meter-sized objects on the Earth's
surface the displacement is on the order of 1e-23 meters. So this is
pretty useless over larger distances or when T is short. Further work has
produced glider models that appear more efficient,
http://arxiv.org/abs/gr-qc/0612131
although the effect is still pretty tame. The glider, if it oscillates its
parts at 10% of c, manages to move itself 10^-4 of the distance it falls
in a gravity field.
Are there any other ways of moving from A to B, and what would their costs
be?
--
Anders Sandberg,
Future of Humanity Institute
Philosophy Faculty of Oxford University
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