How badly does this supertechnology break thermodynamics?

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How badly does this supertechnology break thermodynamics?

Postby Robert'); DROP TABLE *; » Sat Sep 19, 2015 1:33 am UTC

(The entire following post is speculation about the counterintuitive physics surrounding an impossible device. I might've messed up at some point in the logic.)

I'm writing a mid-future sci-fi story that involves a computer that contains a small time machine, and works on self-consistent time-loop logic. (In the context of the story, "small" in this case means able to transport a ~1um volume ~1s into the past/future - enough volume to transmit a laser pulse, but not much in the way of material objects) As explained on that page, this effectively eats PSPACE problems for breakfast, which prompts everyone to add a few kilobits onto their private keys.

However, what I'm focusing on is that a machine like that isn't just an abstract computation oracle, it's a physical object subject to the laws of physics. Specifically, a "normal" time-loop computer sends messages to itself based on the results of computations, but it doesn't have to - it could send messages based on any state that it could measure. However, before it sends the message, it receives a message, which serves as an indication that, at least, that message will be sent a short amount of time in the future.

This has a really weird consequence if the machine receives a message it is programmed to only send under physically unlikely circumstances - for instance, a message indicating that the temperature detected by a sensor has radically changed. If the machine receives that message, then the self-consistency principle forces that message to be sent later on. The most obvious reason that such a message might get sent is that the program sends it as designed... because the temperature registered by the sensor has radically changed, and e.g. all of the gas molecules have spontaneously huddled away from the sensor. There are other scenarios (such as spontaneous corruptions in program memory, and such) that result in that message being sent even if that particular violation of thermodynamics doesn't happen, but they all work by the same mechanism: the omnipresent "noise" in the universe (from random thermal movement of molecules, the electrical noise in circuitry, etc) starts doing incredibly unlikely and organized things in order to bring about the circumstances that result in sending that message indicating the unlikely circumstance. This happens because the "normal" behaviour - random, incoherent noise that doesn't add up in any particular way - is suddenly disallowed, because it doesn't result in the messsage that has already been received being sent, which causes a paradox.

IOW, a time-loop computer becomes a finite improbability generator if you base the time-loop logic on physical, rather than logical, state.

However, while using this machine allows you to force very very unlikely events to spontaneously happen, it doesn't give you complete control over the what that leads up to those events. The likeliest thing that will result in the received message being sent will happen, and there's nothing that says that event can't be your machine breaking down in a very specific way such that it sends itself a spurious message. Therefore, if we want to use this as a general-purpose improbability generator, we need to consider what system will "break" first, and for practical purpose, we want it to be more unlikely that our computer system breaks down than whatever task we want to happen spontaneously does happen via quantum noise "conspiring." (This is why I feel you only need to add a few kilobits to a private key to defend it against this machine - each added bit makes it exponentially harder to pick the correct answer out of the entire solution space, meaning you need a more noise-resiliant machine to do sucessfully.) IOW, at the moment we receive a message saying, "The cup of tea will spontaneously get hot half a second from now," it needs to be more unlikely that thermal/quantum noise breaks our computer spontaneously, than it is that the same forces spontaneously warm up the cup of tea that we have connected the computer to.

Question: is it possible to use this machine to force the universe to reverse an arbitararily large amount of entropy/produce an arbitararily large amount of usable work? IOW, is there any known a priori reason (rather than engineering reasons) that the entropy expended in running the computation must necessarily be greater than the work gained?
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Re: How badly does this supertechnology break thermodynamics

Postby speising » Sat Sep 19, 2015 10:59 am UTC

I guess what would happen is just that the message will never be received.

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Re: How badly does this supertechnology break thermodynamics

Postby elasto » Sat Sep 19, 2015 12:10 pm UTC

Reminds me a lot of the Outcome Pump

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Re: How badly does this supertechnology break thermodynamics

Postby Robert'); DROP TABLE *; » Sat Sep 19, 2015 3:41 pm UTC

speising wrote:I guess what would happen is just that the message will never be received.

I think you can get around that if you program the machine to send the message if it both hasn't received it in the past and the horribly unlikely thing hasn't happened, but then change the condition when it receives the message so that it only sends it if the horribly unlikely thing happens. That might result in the message never being received because the machine breaks down trying to send it, but I think that'd only happen in the same sorts of conditions that'd result in the machine sending a spurious message that doesn't reflect the thing actually happening.

elasto wrote:Reminds me a lot of the Outcome Pump

...yeah, it's essentially an outcome pump by a different mechanism. (Although in the context of the story I'm using it for, there's a definitive way around the issue of actually telling the machine what you want.)
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Re: How badly does this supertechnology break thermodynamics

Postby Neil_Boekend » Sat Sep 19, 2015 4:28 pm UTC

I still fail to see why this machine would break anything except causality (as can be expected from any such device).
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Re: How badly does this supertechnology break thermodynamics

Postby elasto » Sun Sep 20, 2015 12:15 pm UTC

Neil_Boekend wrote:I still fail to see why this machine would break anything except causality (as can be expected from any such device).

One of the base assumptions is that causality can't be broken (see the link in the OP), which is where the machine gains its superpowers. Without that assumption it would be pretty boring*.

(*For certain definitions of boring)

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Re: How badly does this supertechnology break thermodynamics

Postby peregrine_crow » Tue Sep 22, 2015 11:53 am UTC

I don't think I entirely understand how this device forces arbitrary unlikely outcomes to happen (sure, if you get an unlikely message, then an unlikely outcome is guarantee to happen, but you only get that unlikely message if that outcome was already going to happen), but if you just want to use this device to reverse entropy, couldn't you use it to play Maxwell's demon?

1) Have room that can be split along arbitrary angles into two separate rooms that have some kind of very good thermal isolation between them.
2) Receive a message with a room number and an angle. Split the along the given angle. If the room number is -1 go to the next step, if not, you're done.
3) Measure whether one room is colder (by some pre-specified amount) than the other.
3a) If yes, send a message to the past with the angle you used and the room that is colder.
3b) If no, send a message to the past with the next angle to check and room number -1.

By venting the warmer room you can iteratively use this trick to get the cold room to arbitrarily cold temperatures (though it may take a lot of steps).

Note: I only have a vague idea of why Maxwells demon doesn't work in the real world, but I think this trick should work because the increase in entropy (from measuring and computing) that would normally break it is happening in a future that never comes to pass.
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Re: How badly does this supertechnology break thermodynamics

Postby douglasm » Tue Sep 29, 2015 9:11 am UTC

peregrine_crow wrote:I don't think I entirely understand how this device forces arbitrary unlikely outcomes to happen (sure, if you get an unlikely message, then an unlikely outcome is guarantee to happen, but you only get that unlikely message if that outcome was already going to happen)

The program logic works as follows:
1) If no message received, then send message.
2) If message received and <unlikely event X> did not happen, then do not send message.
3) If message received and <unlikely event X> did happen, then send message.

The universe forces a consistent outcome to happen. If you don't receive the message, condition 1 produces a contradiction. Therefore, you will always receive the message. Given that you do receive the message, if your designated event doesn't happen then condition 2 produces a contradiction. The only consistent outcome that satisfies these rules is that you receive the message, the designated event happens, and in response to that event you send the message.

The problem is that the implementation as a physical device rather than pure logic introduces a multitude of possible failure modes that produce consistency by making the device malfunction instead of causing the unlikely event to happen. Thus, you can only reliably use this machine to produce events that are much more likely than the machine malfunctioning. The odds involved in any but the most microscopic of violations of thermodynamics are... extreme. Very very extreme. Producing a macroscopic reduction in entropy by this method would require reliability that makes "fails once in a googolplex" seem like chump change. Good luck with that.

Short answer to the thread title: It doesn't, at least not on a scale anyone cares about. If you tried to use it that way, I suspect it would be more likely for the mechanism to spontaneously break by mass baryon decay than for the desired entropy reduction to happen.

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Re: How badly does this supertechnology break thermodynamics

Postby peregrine_crow » Tue Sep 29, 2015 12:55 pm UTC

douglasm wrote:
peregrine_crow wrote:I don't think I entirely understand how this device forces arbitrary unlikely outcomes to happen (sure, if you get an unlikely message, then an unlikely outcome is guarantee to happen, but you only get that unlikely message if that outcome was already going to happen)

The program logic works as follows:
1) If no message received, then send message.
2) If message received and <unlikely event X> did not happen, then do not send message.
3) If message received and <unlikely event X> did happen, then send message.


Oh wow, that is a fantastic piece of lateral thinking :D . Thanks for the explanation.
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Re: How badly does this supertechnology break thermodynamics

Postby Xanthir » Sat Oct 03, 2015 7:19 pm UTC

Just remember the rest of douglasm's post, which boils down to:

4) If no message received, intend to send message, but something prevents the message from being sent
5) If message received, and <unlikely event X> did not happen, then don't intend to send message, but something accidentally sends the message anyway.

These are the two bits that people usually forget about when considering this as a thought experiment, and they can easily become far more likely than event X.
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Re: How badly does this supertechnology break thermodynamics

Postby Robert'); DROP TABLE *; » Sun Oct 11, 2015 7:18 pm UTC

douglasm wrote:The program logic works as follows:
1) If no message received, then send message.
2) If message received and <unlikely event X> did not happen, then do not send message.
3) If message received and <unlikely event X> did happen, then send message.

The universe forces a consistent outcome to happen. If you don't receive the message, condition 1 produces a contradiction. Therefore, you will always receive the message. Given that you do receive the message, if your designated event doesn't happen then condition 2 produces a contradiction. The only consistent outcome that satisfies these rules is that you receive the message, the designated event happens, and in response to that event you send the message.

Thanks for explaining that better than I did.

The problem is that the implementation as a physical device rather than pure logic introduces a multitude of possible failure modes that produce consistency by making the device malfunction instead of causing the unlikely event to happen. Thus, you can only reliably use this machine to produce events that are much more likely than the machine malfunctioning. The odds involved in any but the most microscopic of violations of thermodynamics are... extreme. Very very extreme. Producing a macroscopic reduction in entropy by this method would require reliability that makes "fails once in a googolplex" seem like chump change. Good luck with that.

Using the formula on this page, I found that the entropy change in a mole of hydrogen gas going from 19C to 20C was roughly ~1022, or 266. (i.e. I understood that there are 1022 times as many ways to arrange 1M of hydrogen at 20C than at 19C) That seems unreasonably low, since it means you could only use the machine to atack problems of 66 bits or fewer before you potentially start causing macroscopically visible changes. Have I missed an exponential somewhere or something?
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Re: How badly does this supertechnology break thermodynamics

Postby douglasm » Mon Oct 12, 2015 6:59 pm UTC

Robert'); DROP TABLE *; wrote:Using the formula on this page, I found that the entropy change in a mole of hydrogen gas going from 19C to 20C was roughly ~1022, or 266. (i.e. I understood that there are 1022 times as many ways to arrange 1M of hydrogen at 20C than at 19C) That seems unreasonably low, since it means you could only use the machine to atack problems of 66 bits or fewer before you potentially start causing macroscopically visible changes. Have I missed an exponential somewhere or something?

Judging by the portions of that page that I understand, I'd guess that even if you got all your math right (which is far from certain) there may be a units problem that makes the number you got mean something very different. I'm pretty sure the units in the formula at the top of the page come out to S being in Joules, the standard unit of energy, which a) is macroscopic and b) is used in chemistry and physics, not information theory.

Even if both your math and your understanding of its meaning are correct, I'd expect the message contents to be many orders of magnitude easier for the message to influence than anything else. The original "force something unrelated to happen" scheme depends on quantum fluctuations to somehow randomly conspire to do what you want, with the message serving only as a way to reroll until it happens. When you provide a mechanism for the message to directly cause what you want, using that mechanism is a much more natural path to fulfillment and much more likely to happen.

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Re: How badly does this supertechnology break thermodynamics

Postby Robert'); DROP TABLE *; » Wed Oct 14, 2015 12:36 am UTC

douglasm wrote:Judging by the portions of that page that I understand, I'd guess that even if you got all your math right (which is far from certain) there may be a units problem that makes the number you got mean something very different. I'm pretty sure the units in the formula at the top of the page come out to S being in Joules, the standard unit of energy, which a) is macroscopic and b) is used in chemistry and physics, not information theory.

Yeah, as far as I can tell, S is actually in Joules/Kelvin, so I borrowed the statement from this page that S=k lnW and worked backwards to find the ratio of W that corresponds to the difference in S I'd found earlier. (Since a difference in S amounts to a difference of two logs once you take out the common factor, which is the ratio of the things inside the logs, i.e. the ratio of number of microstates... right?) Having wound up with what I think are the right units this time, I've found that there are around ~2(10^45) times more microstates for a 19C -> 20C increase. IMO, that's a much more reasonable answer, as much as any value with stacked exponents can be considered reasonable.

Even if both your math and your understanding of its meaning are correct, I'd expect the message contents to be many orders of magnitude easier for the message to influence than anything else. The original "force something unrelated to happen" scheme depends on quantum fluctuations to somehow randomly conspire to do what you want, with the message serving only as a way to reroll until it happens. When you provide a mechanism for the message to directly cause what you want, using that mechanism is a much more natural path to fulfillment and much more likely to happen.

I can't quite tell if you're meaning that using the machine to solve logic problems is easier than using it to break thermodynamics because generating answers to useful logic problems is a priori much easier than inducing useful thermodynamic effects, or that the fact that the stopping condition is embedded in the message itself somehow makes solving the logic problems easier when they wouldn't have been previously.
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Re: How badly does this supertechnology break thermodynamics

Postby douglasm » Wed Oct 14, 2015 2:21 am UTC

Robert'); DROP TABLE *; wrote:I can't quite tell if you're meaning that using the machine to solve logic problems is easier than using it to break thermodynamics because generating answers to useful logic problems is a priori much easier than inducing useful thermodynamic effects, or that the fact that the stopping condition is embedded in the message itself somehow makes solving the logic problems easier when they wouldn't have been previously.

I'm saying that producing a cause and effect chain is easier, even if that chain is circular, than producing an effect without a cause. The critical difference, I think, is that the former does not require depending on chance while the latter does.

Solving logic problems through time loop guess and check is done by creating a circular cause and effect chain. The universe does cause and effect all the time, it's the dominant paradigm on every scale except quantum mechanics. Give the universe a way for cause and effect to be the resolution on a macro scale, and it will nearly always take it.

Generating thermodynamic miracles is done by insisting that the universe rig the quantum dice for you, and that's dominant only on the microscopic scales that quantum mechanics deals with. Getting an effect of this type above that scale requires that you insist exceedingly strongly.

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Re: How badly does this supertechnology break thermodynamics

Postby jseah » Sat Nov 07, 2015 5:19 am UTC

The thing is that the message itself doesn't control an external factor, especially directly. That makes things difficult.
If instead of sending information only, you could send a small object, that would make it much easier to break entropy.

The reason why all the air in a room doesn't spontaneously stuff itself into a corner isn't because it is extremely unlikely to. We think of it in likelihood because it is easier to do so that way but imagine the following scenario:

In a vacuum chamber, you pop a highly pressurized balloon . The air starts out compressed into one corner of the chamber...
Run time forwards and the air is all over the place. Now take the current state of the room and reverse all the motions exactly. Run time forwards for the same amount and viola! All the air is stuffed back into the balloon.

(it's a spherical cow forcefield balloon that only confines the air and doesn't interact with it otherwise)
(the walls are also 'perfect' walls in the same way as the balloon)

The difference between a 'normal' room full of air and one that will stuff itself into a corner after some time is that the arrangement of air in the self-stuffing version is very exactly arranged even if it doesn't appear superficially different. Making said 'exact arrangement' is obviously non-trivial in the extreme.


Enter time loop logic.

Given a small block of material with sufficient degrees of freedom for the entropically-impossible task at hand, an "exact arrangement" of that material could conceivably generate the "exact arrangement" conditions for said task to spontaneously solve itself. The addition of the constraint that the machine has to return the same arrangement is comparatively tiny next to most useful tasks.

The task of getting this block of material is (to my untrained mathematical sense) of the same order as the NPHard problems that time loop logic is so good at solving, just with an incalculable number of degrees of freedom. Good that Time Loop Logic never actually needs any calculations, since generating such 'exact arrangements' are probably beyond the total computing power of the entire universe...
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Re: How badly does this supertechnology break thermodynamics

Postby ijuin » Fri Dec 11, 2015 5:37 am UTC

The simplest resolution to the issue is that the device simply fails to function properly. Under the "send message if the message was not received in the past" condition, the device could attempt to send the message but some malfunction prevents the command from being carried out completely.


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