The question of whether time is in fact directional is far from being closed, at least for quantum physicists. In fact, one of the physicists cited in the article is known for proposing a time-symmetric formulation of Quantum Mechanics [1].
This Google Talk https://www.youtube.com/watch?v=dEaecUuEqfc uses entanglement and quantum information theory in a clear and understandable way to explain 'spooky' quantum phenomena, like the quantum eraser, de-coherence, the aspect experiment, and the measurement problem. Even if you don't know any QM, just basic algebra and calculus, it's really approachable.
I used to be a fan of the Many Worlds interpretation, but after seeing this, I'm now a big fan of the Quantum Information Theory explanation. Starting about 43 minutes in, he goes into the QM Information Theory explanation, but I'd recommend watching the entire prezo.
I'm having a difficult time following his explanation. Here are a few of my stumbling points. Maybe you can help me out.
1) What does it mean that entangled particles are supercorrelated? How can S(A|B) = 2 or -1?
2) The formula for Von Neumann entropy is S = -Tr(p log(p)), where p is the density matrix. How do you take a log of a matrix?
3) Why does the interpretation rely on the density matrix? I've always thought of the density matrix as something that gives information about our ignorance rather than the system (this is why the density matrix mixes classical probabilities in alongside quantum amplitudes/probabilities - observer uncertainty is classical). Therefore, to me, any good interpretation of quantum mechanics ought to work without density matrices.
2. Tr (ρ log_2 ρ ) = Σ_k of λ_k log2 λ_k where λ_k is the k-th eigenvalue of ρ. Sometimes the log2 is instead ln.
3. Density matrix indicates degree of entanglement. You can measure L or R polarized light but you have an entanglement of the two. Mind you that detecting a bell state without loopholes has, to my knowledge, never been done. A systems density matrix for a system can be measured statistically (Quantum tomography?).
> 1) What does it mean that entangled particles are supercorrelated? How can S(A|B) = 2 or -1?
The density matrix does not have the same properties of a joint probability distribution, so quantum entropy doesn't really have the same properties of classical entropy. [1]
> 2) The formula for Von Neumann entropy is S = -Tr(p log(p)), where p is the density matrix. How do you take a log of a matrix?
The log of a matrix is defined as the inverse of the matrix exponential. The matrix exponential can be defined as the usual power series, only using matrices rather than scalars.
What one usually does is: diagonalize the matrix (if possible), take the log of the eigenvalues and rotate again. Obviously taking the log of a matrix is a little trickier than the exponential because if you have negative or complex-valued eigenvalues you have to be a bit more careful.
Good answers. Just a small comment: quantum entropy is a generalization of classical entropy. In particular, if A and B are classically correlated, then S(A|B) has all the properties of a classical entropy (Shannon's, in this case), for instance, it is non-negative.
>I used to be a fan of the Many Worlds interpretation, but after seeing this, I'm now a big fan of the Quantum Information Theory explanation.
I know that both MWI and QIT interpret entanglement differently but I am not sure if I understand why one precludes the other (Your g+ post didn't help me much). Can you please point out exactly where the conflict lies, as they still seem compatible to me (perhaps with minor adjustments)?
I must say, I'm not sure what he even means by this "zero universe" business. Sure, the classical illusion is bust, but the wave function itself, as far as we know, is real, is it not?
While we're at throwing quantum explanation links, here is the Quantum Physics Sequence on Lesswrong: http://lesswrong.com/lw/r5/the_quantum_physics_sequence/ I'd say the math is even simpler there, yet the explanation go deeper. It's a long read however.
Once in Hawaii, at a meeting of philosophers sitting around a table discussing reality, several days passed and Suzuki said nothing. And finally the chairman said, "You've been silent all this time. Would you say something about reality." And Suzuki didn't say anything. I think he may have looked up. Finally the man said, "Well, is this table real?" And Suzuki said, "Yes." And then the man said, "In what sense is it real?" And Suzuki said, "In every sense."
Recently, there was a paper talking about this aspect of quantum theory - http://xxx.lanl.gov/abs/1111.3328 ... well, it was "recently" and fresh in my mind, but it appears to be back in 2011 :)
Whether the wave function is real depends on your answer to the question: is momentum real? You can't directly measure or observe momentum, you can't point to it in the world, but you can definitely feel its impact and it's a convenient measure for certain properties of objects. In that sense the wave function is just as real.
But you can argue both those things are not as real as e.g. extension, force and energy, which are much more readily available to our senses.
Can't I just weigh Galileo's cannon ball, then based on T from when I dropped it know its momentum?
I think the difference comes on moving past the macroscopic world: say I drop a uranium atom into Shroedinger's box - I can't calculate at time T whether the cat is alive.
Yes, you can calculate the momentum it had anywhere along the path while it dropped. Does being able to calculate some property make it real? If I take the square root of the momentum and call it the 'squish' of an object, is my 'squish' property then real?
I like it too, because it's the first explanation of QM I've heard that isn't just about minuscule systems floating in a void.
I did the double slit experiment in uni, and it involved a real screen and a real divider with real slits, made out of 10^n atoms. Feynman's line integrals say that particles explore all possible paths. This would seem to include possibly interacting with all those atoms that are nearby. Yet we pretended none of that mattered and could just talk about the photons.
QIT seems entirely unsurprising to me. Especially the idea about measurement and two opposite interference patterns.
This also isn't the first time I've heard software guys take to it. I think it's because programmers deal with much larger scale than most occupations. We do not delegate to junior aides, we construct our own robot aides, and then deploy them on a massive scale.
It always surprises me when mathematicians and physicists are crappy programmers who fail at making basic complex systems work. If you can't handle complexity, how can you handle the universe?
There seems to be a growing understanding that our universe is actually made of three things, not two: matter, energy, and information. Informatics is joining with thermodynamics and matter physics / chemistry as a fundamental science of "stuff."
This was surprisingly beautiful. As a geek in programming/computers/information/mathematics, but only a physics admirer from afar, it is very suggestive, even natural, to explain the deepest physical reality in terms of information:
"It was as though particles gradually lost their individual autonomy and became pawns of the collective state. Eventually, the correlations contained all the information, and the individual particles contained none. At that point, Lloyd discovered, particles arrived at a state of equilibrium, and their states stopped changing, like coffee that has cooled to room temperature."
“What’s really going on is things are becoming more correlated with each other,” Lloyd recalls realizing. “The arrow of time is an arrow of increasing correlations.”
“The present can be defined by the process of becoming correlated with our surroundings.”
Makes me imagine anthropomorphized variables in a program having discovered the file system and the class definitions that they're instantiated from, but are still trying to figure out what RAM is...
Quantum mechanics is where physics became more like mathematics: common sense no longer provides much guidance. It is really cool that it provides the missing explanation for one of the most common sense ideas in classical physics: the arrow of time.
“Finally, we can understand why a cup of coffee equilibrates in a room,” said Tony Short, a quantum physicist at Bristol. “Entanglement builds up between the state of the coffee cup and the state of the room.”
I think you can understand coffee cooling quite well without any quantum stuff - the atoms in the coffee are moving faster than those in the room. There will be a tendency when one impacts with an atom of the air in the room for that to speed up and the coffee atom to be slowed.
Actual quantum entanglement is a strange and interesting thing. It's a shame people tag the term on things it is not really relevant to try to sound impressive for the most part.
I don't know why tim333 is being downvoted. The particular quote does sound iffy - Boltzmann did explain the cooling of coffee via purely classical processes.
The basic idea - the particle system moves throughout phase space. The vast majority of phase space consists of areas where thermal equilibrium is reached. If you compute the time it would take for the system to return to a non-equilibrium state, it's way larger than the age of the universe.
(Note: I'm not an amateur, though I did leave the field a few years back.)
I think the author pretty clearly explained the connection:
the arrow of time does not seem to follow from the underlying
laws of physics, which work the same going forward in time as in
reverse. By those laws, it seemed that if someone knew the paths
of all the particles in the universe and flipped them around,
energy would accumulate rather than disperse: Tepid coffee would
spontaneously heat up
What he's saying is a bit unclear: we know the how, which is even a kind of plausible explanation as to why. What the author says we couldn't explain before is the converse: why does the opposite never happen? So I interpret that quote more like "Finally, we can understand why a cup of coffee only equilibriates..."
Statistical mechanics doesn't say why a coffee cup never heats up spontaneously - rather, it says that the probability of that happening is incredibly small. You end up with probabilities like 10^-100000. This doesn't require quantum at all, and is effectively the same.
Two objects always attract under gravity, never repel under gravity. Why is this less mysterious than thermodynamic equilibrium, which is some sense just an opposite of gravity (repulsive instead of attractive)?
I think of the arrow of time like this. We started in an extremely exceptional state of very low entropy. The state space is very high dimensional. Therefore the entropy is much higher, pretty much everywhere we go. In this space we do a random walk.
Now, the mystery that remains to be solved is: Why did we start with such an exceptional (low entropy) state?
One possible answer is based on complexity: we were more likely to start in a low entropy state because it had a description with low Kolmogorov complexity, or something like that. (K-complexity induces a probability distribution on the state space that is very different from the uniform distribution.) If that reasoning works, it seems to reduce the question "why did we start in a low entropy state?" to the question "why do we often observe hypotheses with low complexity to be true?", which is pretty much the problem of induction. I'd love to know the answer to that.
Another possible answer is anthropic: you see an ordered universe because otherwise it wouldn't create an ordered mind like you. Unfortunately, the anthropic answer seems to predict that we're in a tiny ordered bubble that will be swallowed by chaos any moment now, so the complexity-based answer looks more promising to me.
>Another possible answer is anthropic: you see an ordered universe because otherwise it wouldn't create an ordered mind like you.
Well, DUH.
This, so called, "anthropic" answer is still a naive non-answer. It's as if those that use the anthropic priniple in this sense have a very shallow understanding of Epistemology and/or Philosophy of Science.
It's obvious that the question concerns at least one level deeper than what the "anthropic principle" attempts to answer. Now just "how come" (possibillity of it being observed by an ordered entity) but "why" (actual mechanism causing this).
I think the issue is that the quantum stuff is more real than the macroscopic systems.
Sure we can describe coffee cooling without quantum stuff, but the quantum stuff is the only part that is essential. Everything we experience aside from gravity must emerge from the quantum stuff. So the question wouldn't be "do we need the quantum stuff," it would be "do we understand why our macroscopic experience must emerge this way from the quantum stuff?"
I'm certainly no expert but I think the issue is that the rules of quantum mechanics work just as well in either direction of time.
I've always wanted to study quantum mechanics because of this very "entanglement". Can people please post recommendations on good resources/books on the topic for a person like me having no solid experience with physics(except college level courses)?
I'm extremely ignorant, but I've enjoyed Brian Greene's books and I'm currently reading The Fabric of the Cosmos.
I've no idea how accurate it is or if I'm even understanding it. He could literally flip around the explanation and I'd have no way of verifying. Yet I still find it very satisfying to read.
Which all, I think, intuitively follows from Spinozist/Cartesian "Conatus" principle. That is to say:
The order and connection of ideas is the same as the order and connection of things.
Some of us rave about this or that: "well, how many folk use X today" or "qualify as X" or "subscribe to X". But these expressions are all within the scope of multiply converging nexuses of increasing correlative potentia. The coffee cup is a simple example — so like Wittgenstein's point: "if a lion could speak, we could not understand him". The lion, like the cup, has restricted correlative powers: these laws apply, these others do not.
The laws of information are laws about the dimensions of proportionality, which give the arrow of time an aspect of curvature (needing to exhaust a universe for exponentially narrowing arrows, so the onion-skinning of properties of a thing "come way may" at "frozen" temporal localities — what happens when we "bend" time at certain family resemblance (physical) properties?).
I have the sense there is something you are trying to say, but I cannot know what the dimensions of proportionality can be. I can see why you assign frozen temporal localities to property assignment but I think there is some confusion in your argument between information as perceived and information as signaled.
The second law is an empirical statement. This entanglement based approach is an attempt to understand the underlying physical mechanism that controls the spread of entropy. If this picture is right, the next question is what is the physical process behind entanglement.
Do we need entanglement to explain the Arrow of Time? Even though in classical mechanics, the past and the future are both equally observable, we remember the past and not the future because the future does not contain certain information yet -- the information to be introduced into the universe in the form of quantum fluctuations. One could even argue that all information in the universe was created at some point in time due to one quantum event or other.
I may have misunderstood though (I'm not a physicist). Entanglement does however, explain why systems tend to equilibrium rather than any other type of state as it evolves forward in time.
On a related note, I found this quote interesting. It reminds me of how HN comments about quantum information theory has a tendency to get downvoted:
> The idea, presented in his 1988 doctoral thesis, fell on deaf ears. When he submitted it to a journal, he was told that there was “no physics in this paper.” Quantum information theory “was profoundly unpopular” at the time, Lloyd said, and questions about time’s arrow “were for crackpots and Nobel laureates who have gone soft in the head.” he remembers one physicist telling him.
Information is produced in the course of a system evolving and information is destroyed (the past is forgotten).
The tendency of a system to move towards greater entropy could be said to give an explanation for the difference between past and future. But how does that work in an open system like the planet earth, where entropy hasn't increased, where the system has self-organized over time.
The ability of a system to store information in only one direction of movement could be the explanation - if we could define that more exactly. But since information is constantly being "created", destroyed and transformed, defining this is a difficult task.
Seeing this article is rather bittersweet. I came to a similar conclusion in my college years but I never pursuit it further.
Taking Quantum Physics in college was a life changing experience and it reshaped how I viewed the world. I was always obsessed by time and one afternoon it became clear.
I explained my variation not as a cup of coffee but a handful of dice. Essentially every tick of time is rolling these dice. And the variation of dice from one combination to the next is the arrow of time.
Like one of the authors in this article, I got the most amount of resistance from physics major. For most part they had a dogmatic view of anything that they had not studied yet. If it wasn't in their books then it didn't exist.
I also came to the conclusion time travel as depicted in the movies will never happen. It can happen randomly in a smaller body but for anything large the arrow of time is almost impossible to reverse.
There's good reason you got the most amount of resistance from physics majors. Intuition won't help you with theoretical physics. The only understanding is that achieved through studying the math in depth. Unless you've developed the formalism (in which case you'd be the subject of this article), you haven't reached any conclusions.
Hate to break it to you. There's no such thing as pedagogical theoretical physics- no shortcut to understanding physics.
How did you assume I took quantum chemistry in college and was asked by my prof to join his lab without having any math background, or to be the #1 student in my physics class of 300, or was a member of 3 person team that won our state math championship. Not to mention scoring high enough to make it to the chemistry Olympiad, but ultimately being rejected once realizing US citizenship was required....
> variation of dice from one combination to the next is the arrow of time
How can a sequence of random numbers introduce a preferred direction? Randomness has the same properties backwards and forwards, and random numbers are not dependent on one another.
You are presupposing the arrow of time to explain the arrow of time. You say you roll the dice every tick of time, but what makes the tick? Why does it tick in the direction it does? The dice do not explain such things.
I have a question. I just went to a source of physical (quantum) randomness http://www.randomnumbers.info/ and I'm giving you a random number between 0 and 10,000 which I've just generated there. Here it goes: 6296.
Ok. Now that light cone had finally reached you. And you (neurons in your brain to be precise) are thoughtfully entangled with that random event (outcome), now in your past.
Now imagine the following. A few days passes. And you forget that number. A few years passes. Connections between the neurons which were storing this information are now gone. Molecules and atoms which were part of these neurons are gone from your body. There are no entanglements any more which link you to that event. Is that event in your future now? Again?
> There are no entanglements any more which link you to that event.
Not directly, but the information has spread out from your neurons into the surrounding matter ad nauseum. It's just we can't interpret the information anymore.
The event still happened in your past, you just can't see it through your limited human view of reality.
And what if you would move away from that surrounding matter? Or, say launch it away with near light speed, so it would get behind the horizon at some point. How is that situation different from the one in which I've just generated the number and the light cone haven't reached you yet?
Can't I? What if the state of these poor remaining neurons and the body is scanned, encoded as polarization of a bunch of photons and sent to a receiver far far away? In that case good old environment would definitely end up behind the cosmic horizon.
Just replace a person [that gets entangled with a particular outcome of a random event (have measured it)] with a simpler organism, say a dog. Or a hamster. Or with a roomba vacuum cleaner ;). Or even with a computer. And we definitely know that a state of a computer can be represented as a bit string encoded on any media. Including polarization of a bunch of photons.
1. When you tell me the result 6296, my brain becomes only classically correlated with it, not entangled. The source of randomness (whether you got it through a quantum experiment or not) does not matter here, as I am only receiving the classical information.
2. After I forget it completely, all I can say is that I (my current body) am not correlated with the event --- but there is no reason to think of the event as being in my future. It's simply not correlated to me any longer. The process of forgetting means dumping all correlations with an event in the environment. For instance, neurons interact with blood stream that interacts with lungs, passing along those correlations to some air particles. So for my current body, the event never happened, although you might have written the number down and will always remember it. In other words, the past is relative.
> So for my current body, the event never happened, although you might have written the number down and will always remember it. In other words, the past is relative.
So where this event would be for you? In the future? Again?
Yes. Past is definitely relative. Special relativity is very specific about that ;)
The event is neither in my causal past (it has no influence over the current state of my body) nor in my causal future (I have no influence on it). It's simply uncorrelated with me. If now you remind me of the number again, it becomes part of the causal past of my (new) body. Analogy: if a dwarf dies in a fortress far far away and you don't hear about it, her death is neither in your past nor in your future. You know nothing about her state: in QM, you would say that your brain and her are in an uncorrelated, product state, something like |dunno><dunno| x (|dead><dead| + |alive><alive|)/2 .
The x stands for \otimes, tensor product.
When you say you receive classical information as the outcome of that experiment, what's an example situation in real life when you receive quantum information and do indeed get entangled with it (I mean if at all such a situation ever arises)?
"real life" as in "they can do it for real in a lab": Alice has two photons, applies a quantum operation to them so that they become entangled, and gives one to Bob. Bob received "quantum information" from Alice. They can use this resource (entanglement between the photons they own) to perform several tasks now, like "teleportation" of the state of a particle, or secure key distribution.
i recall learning that time "flows" both ways at the quantum scale, but i admit is has been a while since i've attended any lectures. has there been any new discoveries to say otherwise? i think i've read about research of both time reversal violations and time-invariance at the quantum scale.
also, what are peoples' thoughts on time being an emergent property at the macro scale and that down at the quantum level, everything is described by time independent equations, like the Wheeler-DeWitt equation? http://en.wikipedia.org/wiki/Wheeler%E2%80%93DeWitt_equation
Is this really new? IANAP, but I clearly remember being taught about the Arrow of Time as a probabilistic/thermodynamical phenomenon even in high school and I also read similar explanations that involved causality and probability theory without refering to quantum entanglement. Is the "quantum" bit even needed there for anything?
Probability theory is how we model the arrow of time, but it's not a physical mechanism by which the arrow of time occurs. The article covers this distinction.
Isn't the classical definition of Arrow of time is from the system with less entropy to a system with more entropy? What is lacking in this definition of Arrow of time that we need to take it to Quantum level?
Again, probability is just a model that can predict something, but not explain how it works. Take a pseudorandom number generator and do rand() > 0.5. Your probability is 50%, and that is a pretty good model to predict how the subroutine will behave, but it may also be useful to understand what algorithm the PRNG is using.
In physics, a "model" is the same as "how something works", unless and until you can uncover details (like the precise order of generated numbers) that the old model can't express.
> After some time, most of the particles in the coffee are correlated with air particles; the coffee has reached thermal equilibrium.
No doubt this is some way oversimplified explanation, but it still makes no sense.
Say I have hot coffee and lukewarm coffee. The lukewarm coffee will equilibrate faster. Does it interact with the air faster? What if I bring in coffee that's the same temperature as the air, so that it's instantly at equilibrium. Does it interact with the air instantly?
There's also the question of heating up the coffee. Are you disentangling it from the air and entangling it with the hot particles below? It does not make sense to equate equilibrium with entanglement.
We have two systems that have been isolated from each other. Then they get together and get entangled. The number of states in which they have come to thermal equilibrium while entangled is far greater than the number in which they do not.
They are being entangled, but that is just the process of putting the systems together, a necessary step in removing their isolationist tendencies, I would imagine. So entanglement is part of the process, but the classical notion of the evolution going to "more states" is still there.
But going towards equilibrium is more general than isolationist --> entangled. Whatever your state psi is of the system, it is likely to evolve, if it can, into a state that belongs to a more numerous class.
> Say I have hot coffee and lukewarm coffee. The lukewarm coffee will equilibrate faster.
It won't (all else being equal). :) Because of Newton's law of cooling, hot coffee will cool down faster (precisely, the rate of change of temperature of a solid body is proportional to the difference in temperature between the body and the environment).
At or very near the Big Bang, the Universe was in a state of minimum Entropy i.e. minimum entanglement i.e. maximum order (in some sense).
Post Big bang the cosmological arrow of time is in the direction of increasing disorder i.e. increasing Entanglement i.e. decreasing order
On a smaller closed system, Before is when the system is more pure, less entangled, more ordered After is when it has become less ordered, more entangled.
From a Bohmian perspective, quantum mechanics consists of a wave function psi(q) that guides all the particles Q. The wave function is distinct from the particles. The particles are in equilibrium, relative to the wave function. It is the wave function that is not in equilibrium in its realm of states.
As it turns out, the usual psi^2 probability distribution of the particles is a reflection that the particles are in quantum equilibrium, that is, psi^2 is the natural measure in quantum mechanics for what equilibrium ought to be since it is the only measure preserved by the dynamics. And so if the particles start that way, they stay that way. And they are likely to start that way using psi^2 as the distribution.
But what it implies is that the wave function is responsible for the arrow of time. It is a special state that evolves into a less special state. Presumably this is what their research is pointing at.
I would also comment that their description is exactly the classical explanation transferred to the quantum world (which it needs to be since our world is quantum). That is, we start in a special state and it evolves into a less special state because the less special states are more numerous and so more likely to be, all things being equal. And by more likely, we are talking 10^100 kind of more likely.
They still have the problem that the fundamental evolution of the wave function is time reversible. So if that bothered someone (it shouldn't), then their argument does not actually resolve that problem.
So I take from their work that what they are doing is getting the classical thermodynamic explanation (which is about volumes in phase space, not human ignorance) and translating it to the quantum theory. Neither wrong nor revolutionary.
One aspect of time’s arrow remains unsolved.
“There is nothing in these works to say why you
started at the gate,” Popescu said, referring to
the park analogy. “In other words, they don’t
explain why the initial state of the universe was
far from equilibrium.” He said this is a question
about the nature of the Big Bang.
Could it be that expansion, which proceeded much faster than light, therefore didn't allow entanglement to take place, delaying the heat death of the universe until everything is fully entangled?
If expansion had been slower, would entropy maybe have kept up with it, leaving us as just a single black hole instead of a dispersed, interesting, unentangled, things-are-still-happening universe 13 billion years later?
This is nonsense; entropy and the arrow of time are essentially a many-body effects and require no quantum effects to occur. A simplest way to see it is to make small simulation of a, say, 1000 gas particles with only classical bouncing in a one side of a box partitioned in half with a barrier, obviously with a time-reversible numerical method -- after the removal of the barrier the gas will evenly spread over the box without any entanglement.
For any combined system, i.e. a situation where you've combined two systems such as the hot cup of coffee and the cool room, the number of "dispersed" states is far greater than the number of non-dispersed states. So any change of state is far more likely to be in the dispersed direction.
The article didn't make it clear what role entanglement plays in this.
yet, once the particles are spread, if you somehow reverse their velocities, they will concentrate back to one half.
Yet we can never do that. Why do you think?
The obvious answer in a classical universe is that we simply don't know the velocity and position of each particle, so we can't just reverse them. To pull such a feat, we'd have to be incredibly lucky, as in "winning every lottery for a century" lucky.
With entanglement and de-coherence however, such reversal becomes impossible even in principle: see, when the universe splits through de-coherence, you no longer have access to the other half. Even if you manage to reverse your half of the universe, you need the other half to be reversed too, or they'll never merge back together.
And not just the other half, since de-coherence happens all the time. You need all the Everett branches to be reversed. No. Way. So it does look like a better candidate for the arrow of time.
(Of course, a better candidate still would be collapse interpretation, since that one is not time reversible in the first place. But this interpretation is ridiculous to begin with, so let's ignore it.)
> So it does look like a better candidate for the arrow of time.
I don't fully agree. You seem to agree that even in a fully classical world, you would experience physics as irreversible on a macro level. So we cannot dismiss subjective uncertainty (lack of knowledge that could in principle be known) a priori as an explanation for the apparent irreversibility of physics. Certainly quantum uncertainty is an additional component of uncertainty, but most likely it's not only quantum uncertainty that causes our experience of irreversibility. For instance if we create a gas of very heavy particles, we would still experience irreversibility, but the quantum effects would be negligible. It seems to me therefore that it would be a good idea to try to investigate to which extent our experience of irreversibility is due to quantum uncertainty and to which extent it is due to subjective uncertainty.
Assuming that we can breaks nothing; particles will concentrate, but without the barrier they will spread again and this would be a disturbance that simply averages out.
> The obvious answer in a classical universe is ...
Since there is an obvious answer in classical physics, it's a bit disingenuous to claim that this solves a long-standing problem in classical physics, no?
> With entanglement and de-coherence however, such reversal becomes impossible even in principle [...] So it does look like a better candidate for the arrow of time.
That would be true if you could demonstrate by experiment that a broken egg springing back up onto the table and reforming is physically impossible instead of just unfathomably unlikely. Can you demonstrate that?
At one point a breeze did blow two pieces of shell closer to one another, but beyond that entropy has appeared to increase quite a bit. At this point my highest hopes are that the mold growing on it will evolve into an intelligent species capable of manually reconstructing the egg.
You go on a space ship, on your way to the edges of the universe. Your buddy goes on a space ship, on his way to the other side of the universe. You will soon be outside each other's observable universe.
Now, if you drop something in your ship (it spins, so you have gravity), you can "reverse time", and pull it back up. Can you do the same to you buddy's ship, should something ever fall there?
The simple answer is no. You can't. He's on his own.
Now there _is_ a way I haven't spoken of: non-causal interaction. You and your buddy could agree on some things before you depart. For instance, you could agree to pull back up whatever falls.
With Everett branches, it's even easier: you pre-commit to reversing your own Everett branch, whatever it is, so all your selves do it. If successful, the worlds should merge back together, at least locally. Just one catch: all your other selves must successfully reverse time locally. It only takes one failure for the plan to fail.
But if you want to reverse time after the fact, say because you happen to be in an Everett branch you don't like (you lost a bet about which way the photon will go), you won't be able to reverse time here, because your other self certainly will not (he won the bet, so…). Maybe, just maybe, you could use the vanishingly small entanglement left with the other Everett Branch to directly communicate with your other self. I'm not even sure it can be done in principle. For practical purposes, it should be forever beyond reach, even if you have a super-intelligent AI to help you.
> Maybe, just maybe, you could use the vanishingly small entanglement left with the other Everett Branch to directly communicate with your other self. I'm not even sure it can be done in principle.
My understanding is that this would violate a physical law that we still believe to hold.
You're right though, that I don't understand. At least I thought I understood your last post. With this one, I don't follow the connection to the OP.
I was replying mainly to mbq: https://news.ycombinator.com/item?id=7602812 My understanding is, with QM, is is even harder or even impossible to reverse time, even with perfect knowledge of your reachable surroundings.
In a classical universe however, it looks much easier, so in such a universe, the explanation for time is less satisfactory.
Here's a crazy thought... the really stonking smart physics PhDs who have spent their whole lives working on this problem are perfectly aware of the classical 18th-century physics you are referencing, and they've found it an unsatisfactory explanation. Perhaps you might like to dig in a bit further before being so dismissive.
(As a bit of a hint, your argument circularly assumes the existence of a forward arrow of time to demonstrate the forward arrow of time. Your "simulation" snuck a forward arrow of time into its definition, then proceeded to prove it exists. This is not satisfactory.)
Then again, if one is going to argue from authority, could one not equally well cite the equally stonking smart physics PhD's who dismissed the argument with "there is no physics in this paper"? And does the argument about quantum entanglement not also circularly assume the existence of a forward arrow of time?
'dismissed the argument with "there is no physics in this paper"?'
Since retracted by essentially the same authorities and it's now a bustling field, so that doesn't work very well as an argument.
And I'm pretty sure the entire point here is that the arrow falls out of the entanglement process itself, not that we first assume temporal ordering in the physics. Remember that we do get to assume the existence of time in general in this argument; the article may not have spelled it out as clearly as it could have but it did in fact observe this still doesn't solve "time" in general. It's a big result, though.
Is the entanglement "process" theoretically reversible in the same way that classical physics is theoretically reversible? Is it possible to describe the idea without using words that implicitly include the arrow of time?
It's possible that I'm simply not understanding the concepts well enough, but I don't see how the "process" of entanglement is any less dependent on temporal ordering. Why wouldn't running it backwards make physical sense as a "disentanglement" phenomenon?
For that matter, why is it right to conclude that the coffee cup has only become entangled with its exterior after it has cooled down? Is this only because the matter in the cup is supposedly the result of disentangled quantum fluctuations from the distant past? I realize that the coffee cup example is an imperfect one, but can someone explain why the process of entanglement is special in this regard where the process of increasing entropy is not?
I'm sure that many smart people have been thinking about these questions, but the interpretations of QM still seem to be stuck in the realm of philosophy.
Classical physics does not presume time arrow either. The equations are all symmetric if you reverse time. Classical physics adequately explains time arrow through entropy. What is missing is decoherence or resolution of the classic/quantum dichotomy.
It depends which point of view. If I made a movie of the simulation and then played it backwards, the gas would go into the box.
There is nothing in your experiment that says this is wrong. In your experiment, you must wait, and therein lies the problem. You've implicitly put a forward arrow in there.
This implies that atoms behave like little billiard balls, but nearly a century of quantum physics has shown us very clearly that belief is false. Unless you are looking at it, atoms exist as their wave function (and recent experiments have shown that a collapse won't occur while you are watching so e.g. a radioactive isotope will not decay while being observed), so any description of behavior needs to use their wave function to describe it.
The problem is that doesn't distinguish the positive time direction, since flipping the direction and running it back past zero would produce the same evenly spread gas.
The resolution that Gary Drescher gives in Good and Real is to stop thinking in terms of a positive and negative time direction, but instead define an away-from-order direction. This is the same direction in which memories (like "wakes" that follow a moving object in the ocean) form, so we will only have memories of things in a pastward, higher-order state. This holds true whether you record the memory in a brain, wake, hard drive, film, or notches on a log: they are all entropy increasing processes, and so all observations will align with the increase in entropy.
However, I agree that you don't need quantum-specific effects for the explanation; the same thing happens in a classical world. The article and the one linked in the above comment, are wrong in this respect, as you say. Even so, decoherence can be regarded as a special case of entropy increasing.
This is an interesting step, but doesn't actually explain why time is asymmetrical. Ok, so things equilibrate as time moves forwards because they entangle as time moves forwards. But this just shifts the question – why is entanglement asymmetrical when time, when the underlying laws are not?
You still have the same problem: if you reverse time, the states become untangled and the coffee heats up.
It's nice to be able to model this from a quantum perspective, but make no mistake – no philosophical issues have been resolved here, and we don't "finally" understand anything we didn't before.
It basically shows that observation (measurement) and entanglement are the same things.
Think about it: particles are not magically going out of superposition as we observe (measure) them. We (our atoms) become entangled with those particles, we become superposition. It's just propagation of entangled state.
Why we don't perceive ourselves as in superposition? "It turns out that this result generalizes to any number of mutually entangled particles. If we ignore any one particle, the entropy diagram of the remaining particles looks like a system of N-1 particles in a classically correlated state with a non-zero entropy.". That means each atom of our bodies perceives other atoms entangled with it as they were not in any superposition (though as a whole, the system is still in superposition). We (atoms) are constantly entangled and in superposition with our environment, but we perceive it as classical state.
In what state each atom "sees" every other? According to probability. That's why in double slit experiment we see only one of most probable outcomes, not a random one.
Time could be rate of entanglement propagation. Entanglement propagates with speed of light (speed of particles), so we seem live in same timeline. But if something moves away from us with speed of light, the time for this object goes slower, but only relative to us.
Until two particles interact with any way, they live in totally different timelines. After they "observe" each other (entangle with each other), also their time becomes entangled. That's why after we see a cup begin dropped, it becomes part of our reality, and the cup becomes broken in our time.
We live in spacetime. As mentioned in article "“Spooky action at a distance” ought to be no more and no less) mysterious than the “spooky action across time” which makes the universe consistent with itself from one moment to the next.".
Why arrow of time? The article says: "Under QIT, a measurement is just the propagation of a mutually entangled state to a large number of particles. To reverse this process we would have to "disentagngle" these quantum states. In principle this is possible. In practice it is not.". I think differently though.
I have a question: What does being in a superposition mean exactly here? I only know the term from classical mechanics, e.g. that an acceleration vector in R^3 can be seen as a superposition of three accelerations along the base vectors (a linear combination).
Superposition in sense of linear combination of quantum states. For example 2-state superposition is qubit.
If you think about systems can be in superposition only relative to one another. For example in double slit experiment light is in superposition relative to us, but not relative to photon from other slit. Or maybe photon in one slit does not exist in timeline of photon from other slit? I don't know :)
It's kind of like that. The state of a particle in classical mechanics is a linear combination of some basis vectors which are not it's states as such. But the superposition in QM is the superpositions of states. The phase space in classical mechanics is not a vector space, but in QM it is. This is a fundamental difference because in QM you can take any number of states, make a linear combination a it will result in another perfectly valid state. Not so in classical mechanics. For example, consider a particle orbiting a point. If you take some position vectors as it moves and make a linear combination, the resulting vector will not be a possible position of a particle in this system. In QM, it would necessary be another possible state. This is a slightly sloppy example, but I hope you get the gist.
Just a thought that I've been thinking about. Time has a direction because of causation. State1 causes state2 which causes state3 and so on. You get weird paradoxes if you allow causation to work in both directions. The universe would also have to magically align everything perfectly so that everything is consistent.
Another observation is that even with reversible laws of physics that can work in both directions, if you have a single starting state, all other states will causally propagate from it. In a single dimension of time/causation.
Yes, reversible laws of physics are possible. State1 can cause state2, and state2 can cause state1.
Here is the question: Do you pick a state for state1 and then figure out what state2 should be from it (that is, cause state2)? Or do you pick a state for state2 and figure out what state1 should be (causing state1)?
If you have a "starting state", it doesn't matter if the time is reversible. All states will be caused by the starting state propagating forward in one direction. This is exactly what we seem to observe in the real universe. The big bang starts the universe and everything appears to be a chain of cause and effect from it. We never observe events that are caused by things in the future. Glasses do not spontaneously assemble themselves out of shards and fly on top of tables. Photons do not just spontaneously fly from all directions in space to form sensible images on Earth.
Now you might say "what if the universe somehow decided on all the states at once". Well that isn't what appears to be true in our universe for one (or you'd have things spontaneously happening in the future and then rippling effects back in time, rather than the other way around.) Second it might not even be possible. In order to do that you'd have to try every possible combination of states and see which ones are valid. Does writing down every possible combination of bits create universes? Even if you apply some rule to them to check if they are "valid" universes?
I think that "real" universes like ours have to have a chain of causation like that.
In the article the author describes the notion of a "pure state" which is something that has independently evolving probability. Individual 'units' lose their pure state and become part of an entangled ensemble--move to equilibrium.
How is the evolution of biological organisms and technological systems explained in this sense? Played backwards, evolution would fit this and traditional notions of thermodynamic entropy. Is evolution a kind of de-entangling?
>How is the evolution of biological organisms and technological systems explained in this sense? Played backwards, evolution would fit this and traditional notions of thermodynamic entropy. Is evolution a kind of de-entangling?
Evolution and technological change are completely different from the physical arrow of time. Optimization processes (evolution, technology) cannot, as far as we know, actually disentangle themselves on-net. What they can do is move the waste-heat/entropy/entanglement into concepts they don't care about, or entangle themselves with some radiating source of "fuel".
(Shout-outs to everyone who thinks the concept of an "optimization process" is total hokum, as I'd like to hear alternate explanations for the apparently similar behavior of so many things that seem to share no purely physical properties at all, and yet all seem to function to shift entropy from some things into other things according to a computable ordering.)
Or in other words, yes, all Earthly life actually lives by converting sunlight into a combination of life and waste, with the "waste entropy" often being radiated off as waste-photons into space, which we don't care about.
An interesting question, I conjecture, is how this conception of entropy/entanglement ties into energy, which apparently remains necessary for the whole process to occur, and yet is conserved in all physical processes.
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[ 2.8 ms ] story [ 238 ms ] thread[1] http://www.phy.bris.ac.uk/people/Popescu_S/papers/sandu_othe...
I used to be a fan of the Many Worlds interpretation, but after seeing this, I'm now a big fan of the Quantum Information Theory explanation. Starting about 43 minutes in, he goes into the QM Information Theory explanation, but I'd recommend watching the entire prezo.
Link to my original post on the subject: https://plus.google.com/110412141990454266397/posts/HC49S9ip...
http://www.flownet.com/ron/QM.pdf
1) What does it mean that entangled particles are supercorrelated? How can S(A|B) = 2 or -1?
2) The formula for Von Neumann entropy is S = -Tr(p log(p)), where p is the density matrix. How do you take a log of a matrix?
3) Why does the interpretation rely on the density matrix? I've always thought of the density matrix as something that gives information about our ignorance rather than the system (this is why the density matrix mixes classical probabilities in alongside quantum amplitudes/probabilities - observer uncertainty is classical). Therefore, to me, any good interpretation of quantum mechanics ought to work without density matrices.
Unfortunately his paper here (http://www.flownet.com/ron/QM.pdf) doens't seem to have significantly more information than his talk.
Thanks for any help you can offer.
1. Super-correlation is entanglement.
2. Tr (ρ log_2 ρ ) = Σ_k of λ_k log2 λ_k where λ_k is the k-th eigenvalue of ρ. Sometimes the log2 is instead ln.
3. Density matrix indicates degree of entanglement. You can measure L or R polarized light but you have an entanglement of the two. Mind you that detecting a bell state without loopholes has, to my knowledge, never been done. A systems density matrix for a system can be measured statistically (Quantum tomography?).
> 1) What does it mean that entangled particles are supercorrelated? How can S(A|B) = 2 or -1?
The density matrix does not have the same properties of a joint probability distribution, so quantum entropy doesn't really have the same properties of classical entropy. [1]
> 2) The formula for Von Neumann entropy is S = -Tr(p log(p)), where p is the density matrix. How do you take a log of a matrix?
The log of a matrix is defined as the inverse of the matrix exponential. The matrix exponential can be defined as the usual power series, only using matrices rather than scalars.
What one usually does is: diagonalize the matrix (if possible), take the log of the eigenvalues and rotate again. Obviously taking the log of a matrix is a little trickier than the exponential because if you have negative or complex-valued eigenvalues you have to be a bit more careful.
[1] http://arxiv.org/abs/quant-ph/9610005
I know that both MWI and QIT interpret entanglement differently but I am not sure if I understand why one precludes the other (Your g+ post didn't help me much). Can you please point out exactly where the conflict lies, as they still seem compatible to me (perhaps with minor adjustments)?
While we're at throwing quantum explanation links, here is the Quantum Physics Sequence on Lesswrong: http://lesswrong.com/lw/r5/the_quantum_physics_sequence/ I'd say the math is even simpler there, yet the explanation go deeper. It's a long read however.
For instance, apples are real, and gravity is real. So when you drop an apple, what happens? It falls. Now what really, ultimately happens? It falls.
But you can argue both those things are not as real as e.g. extension, force and energy, which are much more readily available to our senses.
I think the difference comes on moving past the macroscopic world: say I drop a uranium atom into Shroedinger's box - I can't calculate at time T whether the cat is alive.
[1] http://lesswrong.com/lw/pp/decoherence/
I did the double slit experiment in uni, and it involved a real screen and a real divider with real slits, made out of 10^n atoms. Feynman's line integrals say that particles explore all possible paths. This would seem to include possibly interacting with all those atoms that are nearby. Yet we pretended none of that mattered and could just talk about the photons.
QIT seems entirely unsurprising to me. Especially the idea about measurement and two opposite interference patterns.
This also isn't the first time I've heard software guys take to it. I think it's because programmers deal with much larger scale than most occupations. We do not delegate to junior aides, we construct our own robot aides, and then deploy them on a massive scale.
It always surprises me when mathematicians and physicists are crappy programmers who fail at making basic complex systems work. If you can't handle complexity, how can you handle the universe?
http://www.reddit.com/r/science/comments/236ap1/science_ama_...
There seems to be a growing understanding that our universe is actually made of three things, not two: matter, energy, and information. Informatics is joining with thermodynamics and matter physics / chemistry as a fundamental science of "stuff."
http://en.wikipedia.org/wiki/Alain_Aspect
"It was as though particles gradually lost their individual autonomy and became pawns of the collective state. Eventually, the correlations contained all the information, and the individual particles contained none. At that point, Lloyd discovered, particles arrived at a state of equilibrium, and their states stopped changing, like coffee that has cooled to room temperature."
“What’s really going on is things are becoming more correlated with each other,” Lloyd recalls realizing. “The arrow of time is an arrow of increasing correlations.”
“The present can be defined by the process of becoming correlated with our surroundings.”
this and all other reformulations of it can be said simply - increasing entropy.
“Finally, we can understand why a cup of coffee equilibrates in a room,” said Tony Short, a quantum physicist at Bristol. “Entanglement builds up between the state of the coffee cup and the state of the room.”
I think you can understand coffee cooling quite well without any quantum stuff - the atoms in the coffee are moving faster than those in the room. There will be a tendency when one impacts with an atom of the air in the room for that to speed up and the coffee atom to be slowed.
Actual quantum entanglement is a strange and interesting thing. It's a shame people tag the term on things it is not really relevant to try to sound impressive for the most part.
The basic idea - the particle system moves throughout phase space. The vast majority of phase space consists of areas where thermal equilibrium is reached. If you compute the time it would take for the system to return to a non-equilibrium state, it's way larger than the age of the universe.
(Note: I'm not an amateur, though I did leave the field a few years back.)
Now, the mystery that remains to be solved is: Why did we start with such an exceptional (low entropy) state?
Another possible answer is anthropic: you see an ordered universe because otherwise it wouldn't create an ordered mind like you. Unfortunately, the anthropic answer seems to predict that we're in a tiny ordered bubble that will be swallowed by chaos any moment now, so the complexity-based answer looks more promising to me.
Well, DUH.
This, so called, "anthropic" answer is still a naive non-answer. It's as if those that use the anthropic priniple in this sense have a very shallow understanding of Epistemology and/or Philosophy of Science.
It's obvious that the question concerns at least one level deeper than what the "anthropic principle" attempts to answer. Now just "how come" (possibillity of it being observed by an ordered entity) but "why" (actual mechanism causing this).
Sure we can describe coffee cooling without quantum stuff, but the quantum stuff is the only part that is essential. Everything we experience aside from gravity must emerge from the quantum stuff. So the question wouldn't be "do we need the quantum stuff," it would be "do we understand why our macroscopic experience must emerge this way from the quantum stuff?"
I'm certainly no expert but I think the issue is that the rules of quantum mechanics work just as well in either direction of time.
I've no idea how accurate it is or if I'm even understanding it. He could literally flip around the explanation and I'd have no way of verifying. Yet I still find it very satisfying to read.
http://physics.stackexchange.com/questions/10068/on-the-natu...
and I thought it was all explained quite simply and now this?
The laws of information are laws about the dimensions of proportionality, which give the arrow of time an aspect of curvature (needing to exhaust a universe for exponentially narrowing arrows, so the onion-skinning of properties of a thing "come way may" at "frozen" temporal localities — what happens when we "bend" time at certain family resemblance (physical) properties?).
And isn't the whole description of entanglement based on empirical observations anyway?
I may have misunderstood though (I'm not a physicist). Entanglement does however, explain why systems tend to equilibrium rather than any other type of state as it evolves forward in time.
On a related note, I found this quote interesting. It reminds me of how HN comments about quantum information theory has a tendency to get downvoted:
> The idea, presented in his 1988 doctoral thesis, fell on deaf ears. When he submitted it to a journal, he was told that there was “no physics in this paper.” Quantum information theory “was profoundly unpopular” at the time, Lloyd said, and questions about time’s arrow “were for crackpots and Nobel laureates who have gone soft in the head.” he remembers one physicist telling him.
Information is produced in the course of a system evolving and information is destroyed (the past is forgotten).
The tendency of a system to move towards greater entropy could be said to give an explanation for the difference between past and future. But how does that work in an open system like the planet earth, where entropy hasn't increased, where the system has self-organized over time.
The ability of a system to store information in only one direction of movement could be the explanation - if we could define that more exactly. But since information is constantly being "created", destroyed and transformed, defining this is a difficult task.
Which is to say the problem as a whole is hard.
Taking Quantum Physics in college was a life changing experience and it reshaped how I viewed the world. I was always obsessed by time and one afternoon it became clear.
I explained my variation not as a cup of coffee but a handful of dice. Essentially every tick of time is rolling these dice. And the variation of dice from one combination to the next is the arrow of time.
Like one of the authors in this article, I got the most amount of resistance from physics major. For most part they had a dogmatic view of anything that they had not studied yet. If it wasn't in their books then it didn't exist.
I also came to the conclusion time travel as depicted in the movies will never happen. It can happen randomly in a smaller body but for anything large the arrow of time is almost impossible to reverse.
Hate to break it to you. There's no such thing as pedagogical theoretical physics- no shortcut to understanding physics.
How can a sequence of random numbers introduce a preferred direction? Randomness has the same properties backwards and forwards, and random numbers are not dependent on one another.
You are presupposing the arrow of time to explain the arrow of time. You say you roll the dice every tick of time, but what makes the tick? Why does it tick in the direction it does? The dice do not explain such things.
Ok. Now that light cone had finally reached you. And you (neurons in your brain to be precise) are thoughtfully entangled with that random event (outcome), now in your past.
Now imagine the following. A few days passes. And you forget that number. A few years passes. Connections between the neurons which were storing this information are now gone. Molecules and atoms which were part of these neurons are gone from your body. There are no entanglements any more which link you to that event. Is that event in your future now? Again?
Not directly, but the information has spread out from your neurons into the surrounding matter ad nauseum. It's just we can't interpret the information anymore.
The event still happened in your past, you just can't see it through your limited human view of reality.
You can't :)
By surrounding matter I meant the rest of your body that isn't neurons, as well as the environment outside your body.
Just replace a person [that gets entangled with a particular outcome of a random event (have measured it)] with a simpler organism, say a dog. Or a hamster. Or with a roomba vacuum cleaner ;). Or even with a computer. And we definitely know that a state of a computer can be represented as a bit string encoded on any media. Including polarization of a bunch of photons.
So where this event would be for you? In the future? Again?
Yes. Past is definitely relative. Special relativity is very specific about that ;)
also, what are peoples' thoughts on time being an emergent property at the macro scale and that down at the quantum level, everything is described by time independent equations, like the Wheeler-DeWitt equation? http://en.wikipedia.org/wiki/Wheeler%E2%80%93DeWitt_equation
No doubt this is some way oversimplified explanation, but it still makes no sense.
Say I have hot coffee and lukewarm coffee. The lukewarm coffee will equilibrate faster. Does it interact with the air faster? What if I bring in coffee that's the same temperature as the air, so that it's instantly at equilibrium. Does it interact with the air instantly?
We have two systems that have been isolated from each other. Then they get together and get entangled. The number of states in which they have come to thermal equilibrium while entangled is far greater than the number in which they do not.
They are being entangled, but that is just the process of putting the systems together, a necessary step in removing their isolationist tendencies, I would imagine. So entanglement is part of the process, but the classical notion of the evolution going to "more states" is still there.
But going towards equilibrium is more general than isolationist --> entangled. Whatever your state psi is of the system, it is likely to evolve, if it can, into a state that belongs to a more numerous class.
It won't (all else being equal). :) Because of Newton's law of cooling, hot coffee will cool down faster (precisely, the rate of change of temperature of a solid body is proportional to the difference in temperature between the body and the environment).
Post Big bang the cosmological arrow of time is in the direction of increasing disorder i.e. increasing Entanglement i.e. decreasing order
On a smaller closed system, Before is when the system is more pure, less entangled, more ordered After is when it has become less ordered, more entangled.
Obvious really...
As it turns out, the usual psi^2 probability distribution of the particles is a reflection that the particles are in quantum equilibrium, that is, psi^2 is the natural measure in quantum mechanics for what equilibrium ought to be since it is the only measure preserved by the dynamics. And so if the particles start that way, they stay that way. And they are likely to start that way using psi^2 as the distribution.
There is actually a lot of subtlety involved in accepting that argument; I recommend http://plato.stanford.edu/entries/qm-bohm/#qr and an actual paper: http://www.ge.infn.it/~zanghi/BMQE.pdf
But what it implies is that the wave function is responsible for the arrow of time. It is a special state that evolves into a less special state. Presumably this is what their research is pointing at.
I would also comment that their description is exactly the classical explanation transferred to the quantum world (which it needs to be since our world is quantum). That is, we start in a special state and it evolves into a less special state because the less special states are more numerous and so more likely to be, all things being equal. And by more likely, we are talking 10^100 kind of more likely.
They still have the problem that the fundamental evolution of the wave function is time reversible. So if that bothered someone (it shouldn't), then their argument does not actually resolve that problem.
So I take from their work that what they are doing is getting the classical thermodynamic explanation (which is about volumes in phase space, not human ignorance) and translating it to the quantum theory. Neither wrong nor revolutionary.
If expansion had been slower, would entropy maybe have kept up with it, leaving us as just a single black hole instead of a dispersed, interesting, unentangled, things-are-still-happening universe 13 billion years later?
For any combined system, i.e. a situation where you've combined two systems such as the hot cup of coffee and the cool room, the number of "dispersed" states is far greater than the number of non-dispersed states. So any change of state is far more likely to be in the dispersed direction.
The article didn't make it clear what role entanglement plays in this.
Yet we can never do that. Why do you think?
The obvious answer in a classical universe is that we simply don't know the velocity and position of each particle, so we can't just reverse them. To pull such a feat, we'd have to be incredibly lucky, as in "winning every lottery for a century" lucky.
With entanglement and de-coherence however, such reversal becomes impossible even in principle: see, when the universe splits through de-coherence, you no longer have access to the other half. Even if you manage to reverse your half of the universe, you need the other half to be reversed too, or they'll never merge back together.
And not just the other half, since de-coherence happens all the time. You need all the Everett branches to be reversed. No. Way. So it does look like a better candidate for the arrow of time.
(Of course, a better candidate still would be collapse interpretation, since that one is not time reversible in the first place. But this interpretation is ridiculous to begin with, so let's ignore it.)
---
Read this to have an idea of how time could work in a timeless universe: http://lesswrong.com/lw/qr/timeless_causality/
I don't fully agree. You seem to agree that even in a fully classical world, you would experience physics as irreversible on a macro level. So we cannot dismiss subjective uncertainty (lack of knowledge that could in principle be known) a priori as an explanation for the apparent irreversibility of physics. Certainly quantum uncertainty is an additional component of uncertainty, but most likely it's not only quantum uncertainty that causes our experience of irreversibility. For instance if we create a gas of very heavy particles, we would still experience irreversibility, but the quantum effects would be negligible. It seems to me therefore that it would be a good idea to try to investigate to which extent our experience of irreversibility is due to quantum uncertainty and to which extent it is due to subjective uncertainty.
Since there is an obvious answer in classical physics, it's a bit disingenuous to claim that this solves a long-standing problem in classical physics, no?
> With entanglement and de-coherence however, such reversal becomes impossible even in principle [...] So it does look like a better candidate for the arrow of time.
That would be true if you could demonstrate by experiment that a broken egg springing back up onto the table and reforming is physically impossible instead of just unfathomably unlikely. Can you demonstrate that?
:)
You go on a space ship, on your way to the edges of the universe. Your buddy goes on a space ship, on his way to the other side of the universe. You will soon be outside each other's observable universe.
Now, if you drop something in your ship (it spins, so you have gravity), you can "reverse time", and pull it back up. Can you do the same to you buddy's ship, should something ever fall there?
The simple answer is no. You can't. He's on his own.
Now there _is_ a way I haven't spoken of: non-causal interaction. You and your buddy could agree on some things before you depart. For instance, you could agree to pull back up whatever falls.
With Everett branches, it's even easier: you pre-commit to reversing your own Everett branch, whatever it is, so all your selves do it. If successful, the worlds should merge back together, at least locally. Just one catch: all your other selves must successfully reverse time locally. It only takes one failure for the plan to fail.
But if you want to reverse time after the fact, say because you happen to be in an Everett branch you don't like (you lost a bet about which way the photon will go), you won't be able to reverse time here, because your other self certainly will not (he won the bet, so…). Maybe, just maybe, you could use the vanishingly small entanglement left with the other Everett Branch to directly communicate with your other self. I'm not even sure it can be done in principle. For practical purposes, it should be forever beyond reach, even if you have a super-intelligent AI to help you.
My understanding is that this would violate a physical law that we still believe to hold.
You're right though, that I don't understand. At least I thought I understood your last post. With this one, I don't follow the connection to the OP.
I was replying mainly to mbq: https://news.ycombinator.com/item?id=7602812 My understanding is, with QM, is is even harder or even impossible to reverse time, even with perfect knowledge of your reachable surroundings.
In a classical universe however, it looks much easier, so in such a universe, the explanation for time is less satisfactory.
(As a bit of a hint, your argument circularly assumes the existence of a forward arrow of time to demonstrate the forward arrow of time. Your "simulation" snuck a forward arrow of time into its definition, then proceeded to prove it exists. This is not satisfactory.)
Since retracted by essentially the same authorities and it's now a bustling field, so that doesn't work very well as an argument.
And I'm pretty sure the entire point here is that the arrow falls out of the entanglement process itself, not that we first assume temporal ordering in the physics. Remember that we do get to assume the existence of time in general in this argument; the article may not have spelled it out as clearly as it could have but it did in fact observe this still doesn't solve "time" in general. It's a big result, though.
It's possible that I'm simply not understanding the concepts well enough, but I don't see how the "process" of entanglement is any less dependent on temporal ordering. Why wouldn't running it backwards make physical sense as a "disentanglement" phenomenon?
For that matter, why is it right to conclude that the coffee cup has only become entangled with its exterior after it has cooled down? Is this only because the matter in the cup is supposedly the result of disentangled quantum fluctuations from the distant past? I realize that the coffee cup example is an imperfect one, but can someone explain why the process of entanglement is special in this regard where the process of increasing entropy is not?
I'm sure that many smart people have been thinking about these questions, but the interpretations of QM still seem to be stuck in the realm of philosophy.
There is nothing in your experiment that says this is wrong. In your experiment, you must wait, and therein lies the problem. You've implicitly put a forward arrow in there.
The resolution that Gary Drescher gives in Good and Real is to stop thinking in terms of a positive and negative time direction, but instead define an away-from-order direction. This is the same direction in which memories (like "wakes" that follow a moving object in the ocean) form, so we will only have memories of things in a pastward, higher-order state. This holds true whether you record the memory in a brain, wake, hard drive, film, or notches on a log: they are all entropy increasing processes, and so all observations will align with the increase in entropy.
It's very similar to the resolution linked in this comment https://news.ycombinator.com/item?id=7605595
However, I agree that you don't need quantum-specific effects for the explanation; the same thing happens in a classical world. The article and the one linked in the above comment, are wrong in this respect, as you say. Even so, decoherence can be regarded as a special case of entropy increasing.
You still have the same problem: if you reverse time, the states become untangled and the coffee heats up.
It's nice to be able to model this from a quantum perspective, but make no mistake – no philosophical issues have been resolved here, and we don't "finally" understand anything we didn't before.
It basically shows that observation (measurement) and entanglement are the same things.
Think about it: particles are not magically going out of superposition as we observe (measure) them. We (our atoms) become entangled with those particles, we become superposition. It's just propagation of entangled state.
Why we don't perceive ourselves as in superposition? "It turns out that this result generalizes to any number of mutually entangled particles. If we ignore any one particle, the entropy diagram of the remaining particles looks like a system of N-1 particles in a classically correlated state with a non-zero entropy.". That means each atom of our bodies perceives other atoms entangled with it as they were not in any superposition (though as a whole, the system is still in superposition). We (atoms) are constantly entangled and in superposition with our environment, but we perceive it as classical state.
In what state each atom "sees" every other? According to probability. That's why in double slit experiment we see only one of most probable outcomes, not a random one.
Time could be rate of entanglement propagation. Entanglement propagates with speed of light (speed of particles), so we seem live in same timeline. But if something moves away from us with speed of light, the time for this object goes slower, but only relative to us.
Until two particles interact with any way, they live in totally different timelines. After they "observe" each other (entangle with each other), also their time becomes entangled. That's why after we see a cup begin dropped, it becomes part of our reality, and the cup becomes broken in our time.
We live in spacetime. As mentioned in article "“Spooky action at a distance” ought to be no more and no less) mysterious than the “spooky action across time” which makes the universe consistent with itself from one moment to the next.".
Why arrow of time? The article says: "Under QIT, a measurement is just the propagation of a mutually entangled state to a large number of particles. To reverse this process we would have to "disentagngle" these quantum states. In principle this is possible. In practice it is not.". I think differently though.
That are my thoughts. Please don't judge :)
If you think about systems can be in superposition only relative to one another. For example in double slit experiment light is in superposition relative to us, but not relative to photon from other slit. Or maybe photon in one slit does not exist in timeline of photon from other slit? I don't know :)
Hmm, never heard of this one before. "Entanglement" is a mathematical concept, why does it have anything to do with speed of light?
I'm sorry, but I'm programmer, not physician or mathematician, so I can't reliably answer.
Another observation is that even with reversible laws of physics that can work in both directions, if you have a single starting state, all other states will causally propagate from it. In a single dimension of time/causation.
For example, suppose you have two billiard balls, A and B. In our world, A travels from left to right, strikes B, and then B flies off to the right.
We would say A striking B caused it to fly off.
But an observer moving through time in the opposite direction would be no less justified to claim:
B travelled from right to left, struck A, and caused A to fly off to the left!
Here is the question: Do you pick a state for state1 and then figure out what state2 should be from it (that is, cause state2)? Or do you pick a state for state2 and figure out what state1 should be (causing state1)?
If you have a "starting state", it doesn't matter if the time is reversible. All states will be caused by the starting state propagating forward in one direction. This is exactly what we seem to observe in the real universe. The big bang starts the universe and everything appears to be a chain of cause and effect from it. We never observe events that are caused by things in the future. Glasses do not spontaneously assemble themselves out of shards and fly on top of tables. Photons do not just spontaneously fly from all directions in space to form sensible images on Earth.
Now you might say "what if the universe somehow decided on all the states at once". Well that isn't what appears to be true in our universe for one (or you'd have things spontaneously happening in the future and then rippling effects back in time, rather than the other way around.) Second it might not even be possible. In order to do that you'd have to try every possible combination of states and see which ones are valid. Does writing down every possible combination of bits create universes? Even if you apply some rule to them to check if they are "valid" universes?
I think that "real" universes like ours have to have a chain of causation like that.
Here is a better description of this line of thought than mine: http://lesswrong.com/lw/fok/causal_universes/
How is the evolution of biological organisms and technological systems explained in this sense? Played backwards, evolution would fit this and traditional notions of thermodynamic entropy. Is evolution a kind of de-entangling?
Evolution and technological change are completely different from the physical arrow of time. Optimization processes (evolution, technology) cannot, as far as we know, actually disentangle themselves on-net. What they can do is move the waste-heat/entropy/entanglement into concepts they don't care about, or entangle themselves with some radiating source of "fuel".
(Shout-outs to everyone who thinks the concept of an "optimization process" is total hokum, as I'd like to hear alternate explanations for the apparently similar behavior of so many things that seem to share no purely physical properties at all, and yet all seem to function to shift entropy from some things into other things according to a computable ordering.)
Or in other words, yes, all Earthly life actually lives by converting sunlight into a combination of life and waste, with the "waste entropy" often being radiated off as waste-photons into space, which we don't care about.
An interesting question, I conjecture, is how this conception of entropy/entanglement ties into energy, which apparently remains necessary for the whole process to occur, and yet is conserved in all physical processes.