**From:** Eliezer S. Yudkowsky (*sentience@pobox.com*)

**Date:** Sun Nov 26 2000 - 13:31:13 MST

**Next message:**Brian Atkins: "Re: dawn of neurohacks"**Previous message:**xgl: "Re: The mathematics of effective perfection"**In reply to:**Mitchell Porter: "Perpetual motion via entropy disposal (was Re: effective perfection)"**Next in thread:**Daniel E. Azzopardi: "Re: Perpetual motion via entropy disposal (was Re: effective perfection)"**Reply:**Daniel E. Azzopardi: "Re: Perpetual motion via entropy disposal (was Re: effective perfection)"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Mitchell Porter wrote:

*>
*

*> First, the mistakes:
*

*>
*

*> >The first law of thermodynamics states that "You can't win"; you cannot
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*> >decrease the amount of entropy in the Universe.
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*>
*

*> This is the second law. The first law is conservation of energy.
*

D'oh! I knew that. Actually, it would be more accurate to say that I've

*heard* that, but the version I keep on remembering is "You can't win, you

can't break even, and you can't get out of the game." Sorry.

*> And: Hamiltonian != phase space. The Hamiltonian is a function
*

*> on phase space, whose value is the total energy, and in terms
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*> of which you can write Hamilton's version of the laws of motion.
*

Double d'oh! I remember that too - or think I do; can't trust LTM.

Wasn't there a name for phase space, though? M-something? I can't find

it on the 'Net, though, and "phase space" is something for which it's

really convenient to have a single word.

Incidentally, one formulation I've run across online is that the

"Hamiltonian" refers to the (6N-1)D surface in (6N)D phase space with

constant energy, with the (as it turns out) first law of thermodynamics

referring to a constraint on the trajectory through phase space; i.e., any

individual point must move along the Hamiltonian hypersurface that has

constant energy. The memory I seem to remember having is that the

"Hamiltonian" is the (6N+1)D hypersurface that shows the energy as a

function of phase space and is used locally to describe potential energy

surfaces. Sigh... I either need to actually read my set of the Feynman

lectures, find a good physics encyclopedia, or give up physical science.

*> Now, some more substantive comments.
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*>
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*> - The negative-energy PMM
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*>
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*> Paul Davies talks about negative-energy perpetual motion
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*> machines at http://www.newscientist.com/ns/980321/features.html,
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*> along with the extra influences that would stop them working.
*

<RANT>

Paul Davies sez: "It is easy to dream up scenarios that produce

unphysical or paradoxical consequences--building perpetual motion

machines, or even travelling backwards in time. To physicists, these are

alarming notions."

Who knows, Davies may turn out to be right; but even so, this strikes me

as the sort of thing that future historians call a 'blind spot', like the

unbreakability of the sound barrier or the impossibility of

heavier-than-air flight. "Despite numerous demonstrations that their own

theories permitted the possibility of time travel / negative energy /

naked singularities etc., twentieth-century physicists still refused to

believe, calling them 'alarming notions'." This rant is more about time

travel then about thermodynamics, but real physical laws don't look like

they're about to be violated every second Tuesday. Sometimes physics

fights back, as when it turns out that the Alcubierre warp drive required

more energy than existed in the entire Universe, but sometimes the Cosmic

Censorship patches turn out to be equally flawed themselves - the

Alcubierre drive was replaced by the Van Den Broeck drive, and so on. The

original "Cosmic Censorship" hypothesis preventing naked singularities

also turned out to be flawed, as I recall.

Real physical laws, like conservation of mass and energy, are not

preserved by all these Cosmic Censorship patches; the global law is the

result of the absolute firmness of the local law. Paul Davies talks about

"permissible fluctuations in entropy", but did you ever hear of a

permissible fluctuation in mass-energy?

If current physical theory offends a physicist, so what? God does play

dice with the Universe, Einstein, get over it. Even the more imaginative

physicists, like David Deutsch, suffer from the same disease, confining

closed timelike curves to quantum universes and so on. Time travel,

*including* global causality violation, is explicitly permitted by General

Relativity. Physicists will just need to learn to deal with it.

Oh, never mind. I'm not a physicist. You can get personally annoyed with

physical theories, but you're supposed to buy the right to do so with a

physics doctorate. This system works so well generally that I would have

no real objection to being slapped down by it personally. Not my job.

</RANT>

*> I would take issue with the description of phase space
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*> here. Suppose you have a world in which particles can be
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*> created and destroyed. This doesn't mean that phase
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*> space changes in size each time that happens, it means that
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*> phase space is the union of zero-particle phase space,
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*> one-particle phase space, two-particle phase space, etc.;
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*> and when a particle is created, you move from the N-particle
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*> region to the (N+1)-particle region.
*

This is an interesting way of looking at it. It looks to me like

particles being created and destroyed - in particular, negative-energy and

positive-energy particles annihilating, as opposed to matter-antimatter

interactions which give rise to gamma rays or other new particles - are

intrinsically many-to-one or one-to-many rather than one-to-one. As I

understand it, there is no way to predict, from the current state of the

Universe, where a negative and positive particle pair will come into

existence; thus the current phase-space point of the Universe can give

rise to multiple points at the next instant - one possible alternate point

for each place a virtual particle pair can pop up. Similarly, a virtual

pair ("virtual pair" in the negative-positive, not matter-antimatter,

sense) can annihilate either over *here* or over *there*, and the state of

the Universe will be same either way, since neither particle exists any

more - a many-to-one interaction. It's an interesting question whether

this same objection applies to Feynman diagrams; that is, whether a

positron and electron can collide in two different ways and give rise to

precisely the same gamma particle. I myself don't know.

(As Hal Finney from "Extropians" put it:

*> However I'm not sure it makes sense to explain that the whole idea works
*

*> because of increasing the volume of phase space due to adding particles.
*

*> If all it took to violate thermodynamic laws were to change the number
*

*> of particles, it would happen all the time. Chemical reactions change
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*> the number of molecules, which is often what we count in thermodynamics,
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*> and nuclear reactions can change the number of subatomic particles.
*

)

Anyway.

There are two possible ways that entropy could be conserved; either the

method of manufacturing negative matter could intrinsically create as much

additional entropy (through one-to-many interactions) as could be

destroyed by annihilating the matter (through many-to-one interactions);

or, it could be demonstrated that phase space really is unified and all

interactions involved are one-to-one; that is, no two different

annihilations will give rise to the same state of post-annihilation

Universe.

It's hard to tell which theory is represented by Paul Davies's Censorship

objections, but I would guess the former, since he does talk about

"permissible fluctuations in entropy". Paul Davies's objections seem to

show that if you try and take a beam of negative energy and use it to cool

something off, or if you try to go somewhere where there's a lot of

negative energy, you'll get hit by at least as much positive energy as

negative. This is not too surprising - conservation of mass-energy says

that positive energy has to show up somewhere. My specific suggestion

relied on actually manufacturing negative *matter*, not just beams or

regions of negative energy - which, confessably, is a much less analyzable

proposal since there's much more real analysis of negative *energy* than

negative *matter*. Nonetheless, physicists do make proposals relying on

negative matter, not just negative energy, and I recall that some

manufacturing proposals have been made. The lynchpin of my proposal is

not to just cool down matter with a negative-energy beam; it is to use the

negative and positive matter as actual heat sinks for the entropy of your

laced positive-matter and negative-matter Solar-System-sized computer,

then throw the matter away. In particular, it would be interesting to see

what Paul Davies would make of a proposal to transfer entropy to the

negative energy or positive energy itself before it annihilated, rather

than directing negative energy at an external target.

*> - The quantum collapse PMM
*

*>
*

*> The proposal here is pretty vague. It's just, 'what if
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*> entropy-increasing processes somehow acquired very low
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*> probability'.
*

*>
*

*> There is a 'quantum thermodynamics', it's called statistical
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*> mechanics, and entropy still increases there. There's interesting
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*> recent work in quantum information theory which suggests that
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*> entropy and entanglement are related, and maybe there will be
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*> distinctively quantum ways to *locally* decrease entropy ... but
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*> there's no inkling of a global violation of the second law.
*

*>
*

*> Once again on phase space ... You can conceive of a
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*> quantum state as a wavefunction on a classical state space,
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*> or as a point in Hilbert space, but in neither case does
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*> 'phase space'(*) itself change size when a wavefunction collapses.
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*> In the first case, the wavefunction is suddenly restricted to
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*> a small region of state space; in the second case, the state
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*> vector jumps to a different point in Hilbert space.
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*> (*) Technically, I'd rather say 'configuration space', since
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*> phase space refers to a space which has a position *and*
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*> a momentum coordinate for each degree of freedom, and neither
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*> Hilbert space nor the space upon which a wavefunction is based
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*> is like that.
*

The key feature of the proposal is not that the phase space changes sizes;

that is simply one way of looking at the underlying "problem", which is

that multiple points in phase space move to single points in phase space.

E.g., an electron with a .8 probability amplitude of being at A and a .6i

amplitude of being at B, and an electron with a .9 amplitude of being at A

and a .4i amplitude of being at B, can both collapse to having a 1

amplitude of being at A.

Hal Finney's objection in the parallel Universe of "Extropians" is quoted

here:

*> If you think of a many worlds model, any such attempt would not actually
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*> blip any other universes out of existence, but rather it simply allows
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*> you to learn where you are in the multiverse. Learning where you are
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*> can't change the overall statistics of what happens. So I think this
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*> blipping-out is a bad model and misleading about what could happen.
*

The problem is, of course, that the many-worlds model just isn't true. If

quantum collapse were an observational-effect illusion, it would make no

difference what the probability amplitudes were; we would have the same

observed chance of winding up in a .2 probability Universe as a .8

probability Universe. In this case, of course, my proposed method for

entropy disposal would totally fail.

Hal Finney's objection could be resurrected by pointing out that

decreasing the probability of high-entropy Universes, or increasing the

probability of low-entropy Universes, could require that a superposed

state learn how much entropy it has, which - in turn - could turn out to

generate more entropy than could be disposed of. After all, getting

particular states to add up or cancel out has to happen *before* the

quantum collapse. That would be a classic Censorship patch. It might be

possible, however, to generate all the self-observation entropy in the

high-entropy superposed states that are cancelling themselves out, thus

getting around that objection as well.

My mental visualization here is not a Maxwell's demon situation, but

something more "emergent" - some way of ensuring, e.g., that electrons

which all happen to be moving in the same direction, have amplitudes that

build up, while electrons which happen to be moving in different

directions have amplitudes that cancel out. From the internal,

pre-collapse perspective, no entropy violation has occurred. Let's say

there are two electrons. There are four superposed states where the

electrons are moving in the same direction, and four superposed states

where the electrons are moving in opposite directions. It's just that the

first four superposed states all have amplitudes of .8i, while the second

four superposed states have amplitudes of .8i, -.8, -.8i, and .8

respectively, cancelling each other out. In which case you could create a

crystal in which quantum effects turned heat directly into electricity,

although it might not be direct current, or at least not direct current of

a predictable direction, as that would violate CPT.

*> - The time-travelling Maxwell's-demon PMM
*

*>
*

*> This I haven't quite heard before, although I daresay someone
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*> who studies wormholes has thought about thermodynamics in
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*> wormhole spacetimes.
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*>
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*> But there's a hidden energy cost in waiting for the low-entropy
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*> states to come along. It takes energy to register the current
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*> state and decide whether it's low entropy. So entropy will be
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*> generated by the selection process. This is the parable of
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*> Maxwell's demon.
*

Maxwell's demon applies to individual particles, rather than whole

systems. Different rules might apply if you're willing to wait a

"decillion" years to get your low-entropy state. In other words, it could

be that the entropy cost of Maxwell's demon making one "selection" is

constant, and that it's performing the repeated discrimination on each and

every particle that defeats the process. Of course, it's just as possible

that constructing a demon which will actually last for a "decillion" -

I'll just say "zillion" - years would cost far more than any useful work

that could be gained from the system.

But your objection is probably correct; e.g., performing a discrimination,

or continually checking for one, on an entire physical system, could

easily turn out to have entropy costs far in excess of entropy gained.

A more interesting idea is this: Perform the Maxwell's Demon

discrimination, extract the information, send the information backwards in

time, and then don't perform the costly process that got you the

information in the first place. This throws away entropy into a future

that gets wiped out of existence by tampering with the past.

*> As for phase space here ... the Hamiltonian framework describes
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*> the state of the universe by a point in phase space, and the
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*> history of the universe by a path in phase space. A universe
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*> with time travel is probably better described in some other
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*> way, since it likely can't be divided up into a simple series
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*> of 'spacelike surfaces', it will have some more complicated
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*> topology.
*

Yes, that's what I see as a possible opportunity for violating the usual

"conservation of phase space volume" rules.

-- -- -- -- --

Eliezer S. Yudkowsky http://intelligence.org/

Research Fellow, Singularity Institute for Artificial Intelligence

**Next message:**Brian Atkins: "Re: dawn of neurohacks"**Previous message:**xgl: "Re: The mathematics of effective perfection"**In reply to:**Mitchell Porter: "Perpetual motion via entropy disposal (was Re: effective perfection)"**Next in thread:**Daniel E. Azzopardi: "Re: Perpetual motion via entropy disposal (was Re: effective perfection)"**Reply:**Daniel E. Azzopardi: "Re: Perpetual motion via entropy disposal (was Re: effective perfection)"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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