Quantum Entanglement Drives the Arrow of Time
simonsfoundation.org
simonsfoundation.org
“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.)
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
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 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...
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.
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.
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."
A quantum solution to the arrow-of-time dilemma—Lorenzo Maccone
The arrow of time dilemma: the laws of physics are
invariant for time inversion, whereas the familiar
phenomena we see everyday are not (i.e. entropy
increases). I show that, within a quantum mechanical
framework, all phenomena which leave a trail of
information behind (and hence can be studied by
physics) are those where entropy necessarily increases
or remains constant. All phenomena where the entropy
decreases must not leave any information of their
having happened. This situation is completely
indistinguishable from their not having happened at
all. In the light of this observation, the second law
of thermodynamics is reduced to a mere tautology:
physics cannot study those processes where entropy has
decreased, even if they were commonplace.
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.103... – http://arxiv.org/abs/0802.0438
"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.
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.
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.
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 ;)
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.
[1] http://www.phy.bris.ac.uk/people/Popescu_S/papers/sandu_othe...
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.
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).
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.
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?
One way that this result makes sense to me is by considering the properties of light speed and "spooky action at a distance." Particles become entangled with one another at the speed of light -- photons or fields carrying the information between the two. Looking at this from the perspective of light speed, there has been an instantaneous change between the two particles. State A has led directly to a more complicated, entangled State B. Still looking at this from light speed, there is no time between the transition from one state to the next and from that one to the next and so on. The universe has already worked itself out from the initial disentangled state to all the states that are increasingly more entangled.
Thanks to Einstein, we know that all objects try to move at light speed, but that the more massive they are the slower they become. Because we are massive objects, we don't experience time instantaneously like the photons do. We see the propagation of entanglement and see the state transitions. Our massiveness has given rise to a direction of time, the order that we understand the states of the universe to be proceeding in. Unlike light, we have to experience all the intermediate states in the order of less entangled -> more entangled. Thus an arrow of time.
This is already subtly bundled up in the classical explanations. Coffee cools off because it reaches equilibrium. Classical physics says this is because the particles in the coffee are hotter than the surrounding air, so it is more likely for those particles to break free of the coffee, thereby reducing its average kinetic motion. Consider though how those particles are interacting with one another. They don't just "know" the direction they're supposed to go, they bump into each other's fields and communicate at light speed. Each particle informs the next and as they become more entangled and learn more about where they are, they progress from state to state.
This doesn't just apply to physics, but the history of physics makes it easy to find case studies in this.
http://physics.stackexchange.com/questions/10068/on-the-natu...
and I thought it was all explained quite simply and now this?
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.
Is there something about entanglement that is irreversible? As the article says "it is the loss of information through quantum entanglement, rather than a subjective lack of human knowledge, that drives a cup of coffee into equilibrium with the surrounding room." Okay, but then why don't we ever see the reverse making coffee depart from equilibrium? Something like the acquisition of information through breaking entanglement drives a cup of coffee away from equilibrium.
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.
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.
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
So, you have independent physical system (say, a photon). Before it interacts it exists in quantum superposition. It has the potential to exist in any possible configuration and, in fact, seems to exist in all of them simultaneously. Almost like a variable of a certain type but this type is kind of special in that some possible values are more likely than others.
You can combine these 'probability types' systems with others and get useful information out of them in aggregate (example, wave interference patterns) very easily. They seem very well suited to treating them in aggregate in bulk calculations -- IOW, it is computationally cheaper to keep them in this state until the individual values of the variables must be extracted and used. Then the universe accesses the actual value of that individual variable that, so far, has only been needed as part of the aggregate if at all, through an interaction. Then, and only then, is the variable loaded with a concrete value chosen from its probability type through entanglement and it becomes useless as part of these aggregate calculations since it must be treated as an individual entity with a value.
(I am ignorant of quantum physics outside of pop science articles, so if I have something egregiously wrong, please let me know).
Let's say you've made a video game. It is a MMO set in the Stone Age based around massive battles with slings and swords. There are hundreds of thousands of players and computer controlled NPCs in the same world simultaneously. To conserve server resources many calculations are done on the client computer. The clients cannot be expected to do a full calculation for every projectile in the world so there is an algorithm that chooses to load state of only those players that are near enough to actually act on that particular client.
Let's say a player has come onto the battlefield out of range of everyone else but has a scrying spell that allows that player to see an overhead map showing dots of troop formations. This is the aggregate calculation. This player doesn't need to know every other player's full state, just their general density (because he only gets a dot for every ten or so players). As this player moves toward the battle, some NPC comes in range. Suddenly the player needs to know much more state so it is chosen from the possible values and now that NPC must act in a certain way -- only have certain state changes, because only certain transitions make sense now that he's been interacted with. The NPC can't go from fully armored with a spear to in a loin cloth with a sling, for example. And any NPCs in range of that NPC must also de-cohere into a fully defined state and so on. They all become entangled.
Does any of that make any sense whatsoever? I know these are imperfect analogies.
But that seems like an exponential process so it immediately makes me ask: Why isn't everything entangled at this point? Is there that much in the universe still in superposition that it just hasn't happened or can something that has previously been entangled become un-entagled and re-enter a state of superposition?
The new 'player character' on decoherence is, essentially, the many worlds interpretation. That is a valid interpretation, and while it matches the data (and may not be falsifiable), I have a hard time buying it (where does all that energy come from??).
1. http://www.amazon.com/Quantum-Enigma-Physics-Encounters-Cons...
Re: SoftwareMaven's "why is the 'player character' so important?", I don't think the player character we follow is necessarily any more important than the other player characters. You can say every individual character (or particle in the real-world side of the analogy) has an importance only within its own reference frame and I think it still works.
Just like you can have many players playing the MMO game and "collapsing the state" of different things from their own reference frames at different times, you can have the same be true for the particles in the real-world analogy. No one player of the game is more "important" than any others. The only requirement is that it all stays self-consistent in the backend and across everyone's individual points of view at all times.
But (for better or worse) I don't think what we're talking about now is science, really, unless there's some way to test it.
Maybe you could try to detect a "lag" by doing something that causes an especially large number of states to collapse across an especially large number of frames of references all at once, but I'm not sure if you could do anything that would detect this lag because all of our ways of detecting would be lagging too. (This goes along the same lines as trying to tell if the computer you're using is running within a VM or running natively.)
Any ideas?
I need to research more into what it means to have a collapse of state. Also whether a state of superposition is one that a system can return to or if once a system has collapsed if it stays that way. And if a system can return to superposition, what makes that happen?
And isn't the whole description of entanglement based on empirical observations anyway?
The rate of information increases.
Information wants to be free.
Only information explains its own existence.
The order and connection of ideas is the same as the order and connection of things.
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?).
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...
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.