Hacker News new | comments | show | ask | jobs | submit login
Thermodynamic Asymmetry in Time (2016) (stanford.edu)
92 points by lainon 121 days ago | hide | past | web | 67 comments | favorite



IMHO, Julian Barbour and Gary Drescher have satisfactorily resolved this:

Memories[1] can only form in the increasing entropy direction.

Or, to be more precise, higher entropy states can contain memories of lower entropy states, but not vice versa. This remains true regardless of how the memory is represented.

So the arrow of time (and second law) are not facts about the universe, but about observers' ability to represent it.

Even if you wound back time past t=0 and kept the simulation going, you would see the same thing in the reverse direction, such that the negative time direction should now be considered futureward.

IOW, it's not that "time goes forward, entropy goes up, such coincidence". It's "if entropy were not higher, we could not regard it as the future."

[1] what Barbour calls "time capsules" and Drescher calls "[metaphorical] wakes"


I don't know about this because you can create memories using only reversible circuits, which will not increase the entropy of the system. you're more resource-limited if forced to make it reversible (you have to store additional information to make it so) but you can still do interesting things. I'm not sure i buy that only irreversible processes constitute "the future".


The "write readably to a storage medium" part of a(n otherwise) reversible circuit will still be reversible.


Oops, that should be "will still be irreversible".


What powers the reversible circuits?


There are two conceptually different arrow of time problems.

1) observed, macroscopic arrow of time

2) microscopic, fundamental particle physics level arrow of time.

Thermodynamic solution is satisfactory solution only for macroscopic arrow of time.

Time reversal in general is not symmetric. There are particles that are violate CP and T-symmetry called kaons. That's completely different arrow of time.


Reading the chapter about time in "Good and Real" by Drescher blew my mind. See http://commonsenseatheism.com/?p=11068 for a short version.


This is neat. I think there's a way around it tho. What if you can division the futures high entropy states into k, lower entropy states, and subdivide those, and so on. Substructure. Information about some of those substates can flow back from the future and be detected by observers in the present, IMO. It's not easy, but it's possible and it happens. There's still signal. The bandwidth is not nearly as much as the flow from past to present, but it's still more than any single observer can possibly hope to ingest, so some details of the future can be reconstructed by some observers in the now.


Here's a web app that gives a concrete example of an asymmetry in time arising from time-symmetric rules:

http://timmaxwell.org/pages/cellular-automaton/index.html

Each row of the grid represents the state of the universe at a certain "time". Given any two adjacent rows, we can compute the row above them or the row below them according to a predefined rule, which is symmetric in "time". So we randomly generate the two initial rows and then from there derive the rest of the pattern. However, by default the two initial rows are mostly empty, corresponding to a low-entropy initial state. From this initial state, applying the rule either forward or backward in time leads to states of higher and higher entropy. So the system exhibits "arrows of time" flowing from the low-entropy initial state forward and backwards in time to the high-entropy equilibrium states.


> Using Popper 1956’s famous mechanical wave example as an analogy, throwing a rock into a pond so that waves on the surface spread out into the future requires every bit the conspiracy that is needed for waves to converge on a point in order to eject a rock from the bottom. […] The main interesting difference is that Popper’s time-reversed pond seems approximately attainable […]

Indeed it is:

https://www.youtube.com/watch?v=WffR6HrEqTA#t=40

I wonder if the FloWave people ever considered Popper's argument and tried to eject an object from the bottom.


I imagine the turbulence caused by a rock falling through water is much more difficult to reverse than the waves caused by a rock impacting the surface of water.


>Does it account, for instance, for the fact that we know more about the past than the future?

Reminded me of a side remark from another context:

The past only exists in our memory, therefore in some sense we can't recall incorrectly.


That depends on what you mean. The past state of the universe is faithfully encoded in the current state of the universe. But that does not mean that a subset of that state (a single human, say, or even the entire population of a single planet) cannot have false memories.


What do you mean "faithfully"?

For sure we can all agree that this encoding is irreversible - i.e. we can't reconstruct the past state from the present.

And due to the combination of chaos in macroscopic systems and quantum uncertainty, I think it's highly likely that we can conceive of two slightly different past states that give present states indistinguishable even to $deity_of_unlimited_power.

So how is it "faithful"?


> What do you mean "faithfully"?

A good question! I mean that future states are produced by past states according to physical laws.

> For sure we can all agree that this encoding is irreversible - i.e. we can't reconstruct the past state from the present.

Not with full accuracy, no. But past states are constrained by present states in useful and interesting ways.


Usually "encoded faithfully" is used to mean that the encoded thing can be recovered perfectly (mathematically, not necessarily physically). I thought you were saying that both the past and the future are functions of the present, but we can't calculate those functions ourselves with full accuracy.


> I thought you were saying that both the past and the future are functions of the present

Yes, that is exactly what I'm saying.

> but we can't calculate those functions ourselves with full accuracy.

Yes, that is also true. The universe as a whole is not constrained by the limits of what we humans can compute.


> Yes, that is exactly what I'm saying.

Sorry to be a stickler for detail, but earlier you defined "faithful" to mean the future is a function of the present, and now you're saying that "the past and future are functions of the present" is exactly what you are saying. Perhaps you mean that it's exactly what you intended to say?

I'm not intending to undermine anything with "gotchas." It just seems to me that more precision will help your arguments.

One thing I do not see, in your essay, is how reducing "memory" to "entanglement" means time is asymmetric. What is it about entanglement that is asymmetric that isn't just "that's how entanglement is defined"?

I also do not understand how the thought experiment implies time travel cannot happen. Has anyone proved that the wave equation has no solutions when there are closed timelike curves? (I assume not since there are papers studying quantum computations possible in the presence of closed timelike curves, for instance.)


All of those statements are consistent with the concept that I am attempting to communicate through the imprecise medium of natural language.

> What is it about entanglement that is asymmetric that isn't just "that's how entanglement is defined"?

Entanglement is symmetric. You can reverse an entanglement. But only by returning the entangled particles to the same physical location.

The reason that this symmetric quantum process gives rise to (what appears to us to be) a time-asymmetric classical universe is that what we classical entities actually are is massively entangled systems of vast numbers of quantum particles (or, to be as precise as I can, we are quantum systems with a vast number of mutually entangled degrees of freedom). All those entanglements can be reversed, but if you reverse them, the result is not "moving backwards in time" as humans commonly conceptualize it. The result is rewinding the whole universe to a previous state. That is actually possible in principle. As I note at the end of the essay, there is no way to distinguish a universe that is constantly being rewound and replayed from the universe we live in. But what most people think of as going backwards in time is rewinding the whole universe with the exception of themselves to a previous state. That's not possible.

I don't actually know what the consequences are of applying this idea to CTCs. I don't understand CTCs well enough to do it myself. There's probably a thesis or two in there somewhere. Mixing QM and GR is a rare skill.


> For sure we can all agree that this encoding is irreversible

Isn't the loss of information, i.e. the breaking of quantum determinism, at the centre of the black hole information paradox [1]? It's a paradox because quantum determinism and reversibility imply information can never be destroyed.

[1] https://en.wikipedia.org/wiki/Black_hole_information_paradox


The past state of the universe is encoded in the present state only in the same way, and to the same extent, that the future is.


only in the same way, and to the same extent

Yes, but entropy can make it asymetrical - in practice past usually have less legal states (a lower entropy point) than the future.

Past and future can be completely encoded by the direction of entropy change, if we start from, or end in one legal state.

(You can exactly tell the past of the Logo turtle (or something similar physical thing) by following its trajectory line. You can have an inverse turtle that follows and erase an existing line, then you can tell its future, but not its past by looking only its present state)

This kind of entropy increase is very common in human life - like forming memories, filling empty screens and white papers with signs, leaving footsteps in the snow etc... So the subjective feeling of asymetry is not completely ungrounded.


Only in a classical universe, not a quantum one. The past is encoded in a way that the future is not because our classical universe emerges from a quantum universe through the creation of entanglements, which is what defines the arrow of time.


Except classical physics doesn't really tackle causation, and you'll find that Newtonian mechanics is not deterministic: http://www.pitt.edu/~jdnorton/Goodies/Dome/


That's a very interesting example, but it doesn't contradict what I said. Let's recall how we got here:

> > The past state of the universe is encoded in the present state only in the same way, and to the same extent, that the future is.

> Only in a classical universe, not a quantum one.

In in Norton's dome, the indeterminacy extends equally into the past and the future: you can't tell when the ball will leave the dome, and you can't tell when it arrived.


That was bad physics. Even assuming poetical cow physics with perfect spheres, domes, no friction, no air, and no external forces, the sphere will simply never move. There is no underlying instability to trigger its motion.


Except Newtonian mechanics doesn't say anything about causation, it simply says which equations are valid solutions. Most people find it counter-intuitive, but it's totally possible for multiple solutions to exist in the Newtonian framework for some circumstances.


No what I'm saying is that the single Newtonian solution in this problem is no motion. The ball stays at the top of the dome. If there is a problem with multiple Newtonian solutions, this isn't it.


How did you determine that? There are infinitely many solutions that follow all laws of Newtonian mechanics. The burden of proof is yours to show uniqueness of a solution here, which I'm certain you cannot do with the canonical Newtonian laws alone.


Because moving in any direction down the dome requires epsilon momentum from an application of epsilon force, which is not present in the assumed setup.


There is an explanation in the article as to why a causative force is not required to obey Newtonian mechanics.

At every moment that the ball is moving, there is indeed an external force due to gravity.


Indeed. If you want to challenge the example, you need to argue that in reality things are never quite so finely balanced, and that we can thus assume what geometers call "general position". (https://en.wikipedia.org/wiki/General_position)


The ball is never moving at any time ever.


Why? The wave function evolves symmetrically and deterministically, doesn't it?


Yes, it does. But the classical universe emerges because sub-systems of the wave function become classically correlated as a result of entanglements [1]. These entanglements are what define the arrow of time in the (or perhaps it would be more accurate to say "a" instead of "the" here) classical universe [2]. Information about the past is the classical correlations that arise from entanglements. Entanglements can only arise in (sub-)systems that were initially co-located, so relativity insures that these propagate only from the past into the future.

[1] http://www.flownet.com/ron/QM.pdf

[2] http://blog.rongarret.info/2014/10/parallel-universes-and-ar...


Do we really understand quantum mechanics well enough to say how our classic approximation arises from it?

Edit: interesting paper on quantum information theory and measurement vs entanglement!


Read reference 1 (or watch the video: https://www.youtube.com/watch?v=dEaecUuEqfc) and decide for yourself.


Any idea what the scientific background of the author of [2] is?


Yes :-) The author is me. I have a Ph.D. in computer science. But I worked for 15 years at JPL so I learned my quantum physics from Caltech professors.


Thank you kindly for your reply!

I was impressed by the article, and it made a lot of sense to me -- but I've also found that, given sufficiently persuasive writing, I'm easily persuaded that something incorrect is correct in QM, and the only way to get the 'right' answer is to do actually the math. This is why I was curious about your background: if I could reasonably surmise that you had 'done the math' so I didn't have to! (:

(Note that I realise this is not how science is meant to work, but is a quite useful filter in practice)


The math is in reference [1], and also here:

https://arxiv.org/abs/quant-ph/9605002


You are incorrect. According to systems theory, the current state of a system holds the information you need to go forward, not necessarily backwards. Imagine a bouncing basketball: if you can only see its current state, you don't necessarily know when the ball started bouncing. It could be that it started years ago, bouncing all the way from the stratosphere. You can't know the initial conditions of a system just from it's current state. After the ball stops bouncing it can rest on the floor for a million years and you will never know if it stopped bouncing a million years ago or five seconds ago, that is because a real bouncing ball is a non-linear system. So no, the history of a system is not encoded on its current state. On the other hand, you can always predict the future state of a bouncing ball system if you know its current state.


Nope. The laws of classical mechanics are fully time-reversible. All you have to do to go backwards is invert the sign on all the velocities.


Right, but that was not my point. I said two things: you can't always know the initial conditions and you can't transpose non-linearities. Yes, you can invert the sign of all velocities and trace the path of a particle in reverse, but can you tell where it started moving if its current velocity is constant? What if that particle hits a wall and stays there? How can you know when in the past it stopped moving?


> you can't always know the initial conditions

Just because you can't know them doesn't mean they aren't physical. God can know the initial conditions. In a classical world, that's good enough.

> and you can't transpose non-linearities

So? Classical mechanics is linear.

> can you tell where it started moving if its current velocity is constant?

Yes, of course. Just as easily -- and by the exact same method -- as you can tell where it will stop moving.

> What if that particle hits a wall and stays there? How can you know when in the past it stopped moving?

That's a question that is answered in a first-year physics course, but the TL;DR is that any collision must conserve both momentum and energy. If a ball hits a wall and "sticks" then some of its energy must be dissipated as heat. That is the thermodynamic arrow of time, which is exactly what the original post was about.


Even a high school level equation of motion has a t squared term in it. Classical mechanics is not linear. And even if it were, the real world is obviously not. The basket ball will stop bouncing at some point, even though the model for the bouncing movement is an infinite exponentially decaying curve. After it stops bouncing it will stay there, resting, for ever. Good luck trying to determine when and if it moved at all. The fact that you have to invoke God to reverse a system back into its initial conditions proves my initial point. Remember, my whole point was the current state of a system does not necessarily encode its past.

You cannot know where or when a particle with constant velocity started or will stop moving. Unless you are God, of course. And you cannot know when a particle hit a wall. All you can know is that it happened some time in the past.

What did I say that made you think that initial conditions are not "physical" and what does that even mean? I feel like we are talking about different things...


You don't understand what a linear theory means. It does not mean that higher order polynomials don't exist in the theory, it means that the dynamics of the system are described by linear differential equations. And your bouncing basketball example is dissipative (look it up).

> Remember, my whole point was the current state of a system does not necessarily encode its past.

Yes, I know. You're wrong about that. The state of a bouncing basketball is not described by the position and velocity of the basketball, it's described in classical mechanics by the position and velocity of every elementary particle that the basketball comprises, and in quantum mechanics by the wave function of every such particle. That information, together with the same information about the environment, encodes the basketball's past and its future.


I feel like we are not gaining anything from this discussion. Here are some references to back my point:

"Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system."

https://en.wikipedia.org/wiki/State_variable

"State functions do not depend on the path by which the system arrived at its present state."

https://en.wikipedia.org/wiki/State_function

MIT lecture on state representation of linear systems: http://web.mit.edu/2.14/www/Handouts/StateSpace.pdf - see Section 1.1.

I got my "Linear Systems and Signals" B.P. Lathi 2nd ed from my shelf and found similar information. See section 10.1 if you have access to that book.

> The state of a bouncing basketball is not described by the position and velocity of the basketball, it's described in classical mechanics by the position and velocity of every elementary particle that the basketball comprises

I'm no physicist, but I think you might run into problems with the Heisenberg uncertainty principle when you try to determine the state of your system. Even if you are just mentioning that as a mental exercise and we assume that we can in fact determine everything there is to know about every particle in a basketball, your theory still won't hold. When your system reaches an equilibrium state (i.e., minimal energy state) it will rest there forever and you will lose the ability to reverse it. In other words:

"The science of thermodynamics is able to capture these generalizations as consequences of its claim that systems spontaneously evolve to future equilibrium states but do not spontaneously evolve away from equilibrium states."

Obtained from the first paragraph of the original article.


> I feel like we are not gaining anything from this discussion

Sorry about that. I'm frustrated, but I really am trying to be constructive here.

> "Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system."

Right. So if your state describes the whole universe, that provides enough information to determine its future behavior because there is nothing external to the universe (by definition!)

> "State functions do not depend on the path by which the system arrived at its present state."

Right. However, because the dynamics of both classical and quantum mechanics are reversible, you can determine the past states of a closed system (like the universe) in exactly the same way you can determine its future states. (That's how we know, for example, that the big bang happened.)

> I think you might run into problems with the Heisenberg uncertainty principle when you try to determine the state of your system.

Right. That's why it's important to distinguish between classical and quantum mechanics. In classical mechanics there is a mystery about where the arrow of time comes from because the fundamental equations are all time-symmetric. Quantum mechanics (and more specifically QIT - quantum information theory) solves that mystery.

> "The science of thermodynamics is able to capture these generalizations as consequences of its claim that systems spontaneously evolve to future equilibrium states but do not spontaneously evolve away from equilibrium states."

This is not a solution to the mystery because it has to introduce this extra axiom about equilibrium states, which does not follow from Newton's equations. QIT is a better solution because the (practical) irreversibility of measurements can be derived from the basic axioms of QM. It doesn't have to be assumed.



This is a great link, thank you for the reference. @lisper, check this out.


You cannot necessarily climb down a mountain the same way you climbed up.

Or swim backwards.


I agree, but I don't understand what your point is.


I am working on understanding the paper itself. I am reflecting, that's all:)


Me too! Sorry about that.


"The past ..." — If there is only one.


So you didn't post this message three hours ago?


The arrow of time can be explained by information-theoretical interpretation of quantum mechanics:

http://blog.rongarret.info/2014/10/parallel-universes-and-ar...

TL;DR: the decoherence process by which the classical world emerges from the quantum is necessarily asymmetric with respect to time.


I don't think your theory holds water.

Quantum mechanics can be formulated to be time symmetric. With time symmetric quantum mechanics decoherence happens symmetrically in both directions in time.

If you use many-worlds interpretation as illustrative as metaphor for decoherence, reality splits also backwards from the current moment in time symmetric quantum mechanics. In fact I think Stephen hawking uses QM backwards in his quantum cosmology theories. Calculating every possible history of the that leads to next event might tell us something about early universe.

As a final point. Quantum decoherence cant' explain existing CP-violations that are not time symmetric.


Did you actually read the essay? Because the whole point was to address this exact issue. In fact, the second sentence of the piece is, "All measurements are in principle reversible."


You did not adress the issue, you mentioned it without solving the complications it brings to your theory.

Quantum mechanics and entanglements have nothing to do with the thing you are trying to explain. It's all thermodynamics and entropy. Memories can formed only by increasing entropy. Thus personal time flows from lower entropy to higher entropy.


> the complications it brings to your theory

Like what?

> Memories can formed only by increasing entropy

That's right. So? Once again you seem not to have read what I wrote at all (or you did not read the background material that I link to).


Sorry if I can't understand what you are writing. Your writing is extremely difficult to read. You should concentrate to the point you are making and not try to lecture other things you know on the side.

Answer to this question:

If you can explain whole stuff using thermodynamics, why you bring QM and entanglement into the picture at all? Time would work exactly same in classical universe.


Nota bene: it appears you're talking to a crackpot.


Who are you talking to here, me or nokinside?


Did you write the essay? Because I feel your tl;dr doesn't reflect it accurately.


> Did you write the essay?

Yes.

> Because I feel your tl;dr doesn't reflect it accurately.

Could be. It's really hard to sum this up into a pithy slogan.




Guidelines | FAQ | Support | API | Security | Lists | Bookmarklet | DMCA | Apply to YC | Contact

Search: