Collapse Postulates

I suppose that suggesting 'other' amplitudes must collapse or cancel just because we don't remember them is like suggesting the spaceship disappears once it leaves our light cone because we've lost contact with it. You're adding an extra element of complexity for no apparent reason. Never thought of it that way really. Unless I've missed the point entirely....

Main thing I've learnt from this series: the human brain must be really badly suited to understanding how nature works on the lowest levels. How else to explain our most basic laws being split into 'interpretations'?

Question - is there absolutely no communication between one world and another? Does this rule out any testable predictions?

I distracted my proto-AGI for a moment and asked it to take a minute to explain this to me.

The reason for collapse, apparently, is quite simple: while most of the fundamental laws of physics are all nice, linear and elegant, keeping track of all these wave forms quickly becomes computationally intractable, even on the machine that's simulating our universe (PhD candidate Zirro's request to uses the department's new infinitely powerful super computer for his project was apparently turned down as they are still trying to simulate AIXI). Anyway, once the wave form starts to interact with too many things a subroutine kicks in and simply collapses the matrix representing the wave. Yeah, it's an ugly hack, but Zirro's A+ in epistemology means getting a B in universe simulation isn't too much of a problem for him.

or the hope of somehow explaining the Born statistics

That does seem to be the main legitimate reason for considering collapse theories. But I agree that avoiding splitting humans probably is an important driver.

Shane,

Did vit mention how the simulation goes about choosing which wavefunctions to collapse and which to continue processing? Is it based on how 'interesting' the resulting universe turns out? If so, should I be dancing on tabletops?

Also, is Zirro's own universe a simulation itself? How do the wavefunctions in the top-level universe decide what to do?

Ben: It's simulations all the way up.

It seems that many physicists are strongly biased to deterministic theories, and that this is a prime selling point for MWI. So we have a configuration space that comprises every possible state of the universe. And we have a wavefunction over that space which evolves deterministically. So game over: there is no novelty in the universe. There is no meaningful distinction between past, present or future; they are just points on the trajectory through the configuration space, any one of which is completely determined by any other along with the universal wave equation. How boring. I think this is more of a bug than a feature.

I've already said a little about what kind of interpretation I prefer. It's along the lines of Lande's theory. Realistic interpretation of the wavefunction; reality as a single point in configuration space, and random time evolution under the influence of the wave equation.

To me, science is bound to explain human experiences by explaining qualities of the objects that form the world (I hope it's not too far fetched, I just made it up). Some qualities can be observed, even if it takes an LHC, some can't, at least we don't have any idea yet how. If then the world splitting can't be observed at all and all we know is our single resulting world then I guess science's task is to explain this single world. At least, from inside the single world that may look like the main task of science. I may be wrong, that's my thoughts right now.

In entangled systems, those systems only keep being entangled because they're experimentally protected from outside influences. I always understood collapse as a result of special interactions of the wave with the surrounding, particularly interactions which expose particle-like features of the wave-particle. It has nothing to do with distance or size. And I think that can be shown really nice in the double-slit experiment. So right there, there's no possibility in collapse theory that our brain or consciousness could be the referee of wave collapses. Before it gets to the brain, the wave function obviously has to interact. That's also an argument against the Earth's being a wave function. Wave and collapsed wave, in my understanding, explicitly behave differently, so we can't say it was a wave all along, we just never knew it.

Finally, if you substitute collapse for world splitting, wouldn't then world splitting produce the same effects and fulfill your last list quite as well as the collapse interpretation?

Nice series, really like it!

@Ben: The communication exists but it's exponentially tiny. Not 20th decimal place, 10^20th decimal place.

Bob: It seems that many physicists are strongly biased to deterministic theories

No, physics is strongly biased toward deterministic phenomena. There is no known law in all of physics that is non-deterministic. I eliminate collapse fantasies because there is no observed phenomenon that cannot be explained as well without collapse as with it.

Kamenin: Finally, if you substitute collapse for world splitting, wouldn't then world splitting produce the same effects and fulfill your last list quite as well as the collapse interpretation?

NO, DAMN IT!

Many-worlds does not involve a special, extra, 'splitting' postulate. It is simply the pure, unaltered result of applying the same equations that are known to govern microscopic phenomena, which equations happen to result in superpositions (experimentally verified) and would logically result in macroscopic superpositions (experimental verification in progress).

So, #1, above all, the fundamental physics of many-worlds is experimentally nailed-down. It consists simply in supposing that the same rules govern at all levels. We know quantitatively what those rules are for microscopic cases. There is no theoretical doubt as to when and under what circumstances decoherence should happen - it's all in the equations already, though in practice we may have trouble doing the math.

With that said,

Macroscopic decoherence is linear, unitary, differentiable, local, CPT symmetric, probability-current conserving, deterministic, and relativistic JUST LIKE ALL THE REST OF PHYSICS, DAMNIT!

@ E.Y. O.K., no need to damn something or someone -- I think I'm almost there. I still have a blockade at this point: The splitting world describes the world from a all-knowing top-down perspective from where everything looks linear, unitary etc. But from our encapsulated one-world perspective we see this as a series of nonlinear accidents: particles hit at one point, only one point, given by the probabilities governed by the wave function. Entanglement breaks when we measure it. So what I meant was, the splitting produces the illusion for us that the world is non-linear. Wouldn't you say that from our perspective we would never be able to discriminate between both positions, if the non-linearity is true or if it's just an illusion of an superordinate process? I cannot see how you could get experimental verification from within this one world. Or as long as we just want to describe our one world, how we could get better results than by calling the non-linearity 'collapse' and go on with our maths.

If I missed something along the line, I'm really willing to learn.

So to preserve the illusion of determinism, which is not observed, you concoct the illusion of multiple worlds, which are also not observed. (feel free to imagine the preceding in all caps, to reflect my righteous indignation).

4 points:

If collapse actually worked the way its adherents say it does, it would be:

1. The only non-linear evolution in all of quantum mechanics.
2. The only non-unitary evolution in all of quantum mechanics. 3.... WHAT DOES THE GOD-DAMNED COLLAPSE POSTULATE HAVE TO DO FOR PHYSICISTS TO REJECT IT? KILL A GOD-DAMNED PUPPY?

Not a valid argument. The physics of the universe are what they are, at the microscopic and macroscopic levels. If it so happens that there is some non-GR-violating non-locality going on (don't complain, just cause you can't imagine it, doesn't mean it's not possible), then your list above simply would be wrong, and there would be no violation of "traditional physics" to complain about.

In any case, since from the perspective of each world we have non-determinism, and the only world we are acting on is our own, why is it necessary to explain many worlds for the purposes of AGI?

Well, first: Does any collapse theory have any experimental support? No.

Neither does MW, they are both interpretations.

I'm going out on a limb on this one, but since the whole universe includes separate branching “worlds”, and over time this means we have more worlds now than 1 second ago, and since the worlds can interact with each other, how does this not violate conservation of mass and energy?

Bob: But multiple worlds are observed, in subatomic phenomena. That's what superposition is. There is experimental evidence for multiple worlds.

Determinism is also observed, at the subatomic level.

So the alternative is: (1) It's exactly the same at the macroscopic level (= decoherence), or else (2) Something new, with no experimental evidence, must be happening at the macroscopic level (= collapse).

Wiseman, re: conservation of mass/energy. What's your answer for the simple cases, like the double-slit experiment? When you start, you have a single photon. When "it" passes through the slit(s), apparently there are at least two "things", one going through each slit. Does this mean the single photon became two photons, and violated conservation of energy?

Probably not...

Bob: But multiple worlds are observed, in subatomic phenomena. That's what superposition is. There is experimental evidence for multiple worlds.

How does the experimental evidence favor MW over a possible collapse function with non-GR-violating non-locality?

Wiseman: How does the experimental evidence favor MW over a possible collapse function with non-GR-violating non-locality?

Because, at the subatomic level, no "collapse" is ever seen. At the subatomic level, there is always a distributed amplitude of position and momentum throughout all space, and it evolves deterministicly. When a photon hits a half-silvered mirror, it both gets reflected and also gets transmitted at the same time. That's basically what a "multiple world" is.

If you just put a detector in the paths, you'll never realize that the multiple worlds exist. You'll only either (apparently) detect a reflection or a transmission. You'll never detect both. But there's no question that the single photon is both transmitted and reflected.

How can you tell? By recombining the paths, causing constructive and destructive interference between "identical" particles and/or configurations.

At the subatomic level, these "multiple worlds" do exist.

At the macroscopic level, decoherence says "the exact same thing is happening to the humans; nothing different". But notice that even in the subatomic realm, you can't notice the multiple worlds until you recombine paths with identical configurations. The "problem" is that, in the macroscopic world, you never get identical configurations, so you never see constructive and destructive interference from the "multiple worlds".

MW in subatomic experiments really shouldn't be controversial. You just follow the equations. Evolve the waveform. There is always superposition between multiple outcomes. Collapse never happens. Surely you realize the theory/model for the subatomic quantum case?

The MW "interpretation" merely says that nothing changes in the macroscopic case. It's exactly the same as the quantum case. (Remaining to be explained: the Born probabilities.)

Don Geddis: I don't agree that "multiple worlds are observed, in subatomic phenomena. That's what superposition is." That is your preferred interpretation. I prefer to think that the wavefunction is real, but it is a function over potential configurations, only one of which is real. Superposition reflects the influence of other physically equivalent configurations. I would not call my interpretation a "collapse" interpretation. The wavefunction is always there, in the sense that nature "knows" the probability amplitude for points in configuration space other than the that represented by the real state of the universe.

I am also puzzled by your statement that "determinism is observed". It most certainly is not. When an atom is in an excited state, the time and direction of the photon emitted is essentially random. Isn't it more satisfactory to just acknowledge this than to postulate an infinity of other worlds being spawned for every possible direction and time of emission?

Bob, what makes you think there's a difference?

Caledonian: There is no difference at the level of predictions, because I'm not calling for any new laws of physics beyond QM. It's a matter of what makes sense as interpretation.

'Interpretation' is irrelevant, Bob. If they have identical consequences, they're equivalent no matter what you choose to call them.

Caledonian, two current theories may have identical consequences and yet suggest very different directions for refinement. For example, a theory which postulates a fundamentally deterministic universe suggests that we look for causes of observable events, whereas a theory which postulates a fundamentally random universe includes events for which it would be fruitless to search for a cause.

The theories are not equivalent, because they have different implications about the next sensible step in understanding the universe.

'Interpretation' is irrelevant, Bob. If they have identical consequences, they're equivalent no matter what you choose to call them.

You're confusing metaphysics with epistemology AGAIN.

Quantum suicide might allow for subjective checking of MWI.

There is no difference at the level of predictions, because I'm not calling for any new laws of physics beyond QM. It's a matter of what makes sense as interpretation.

Attaching an empty concept to a thing doesn't differentiate between them. The idea of 'metaphysical reality' is meaningless.

The various interpretations don't just make the same predictions for the phenomena we know about, but they have no known implications that vary between them. They are equivalent. The descriptions of the mathematical processes differ, but the function they implement are the same. They're precisely the same thing with a different superficial appearance. That's all.

Something that looks like a duck, and walks like a duck, and sounds like a duck, and behaves in all ways like a duck, IS A DUCK. It's the function of a thing within the set of interactions with the universe that determine identity. Talking about something that behaves in all ways like a duck, but is somehow metaphysically different, is not only wrong-headed but silly.

...wait, the collapse postulate doesn't suggest different results? In order for collapse to occur, the amplitude-summing effect we see at the level of particles would have to vanish at some point. Which implies that above that point, "interference" effects will vanish.

We might have a hard time running the experiment, but that sounds like a different result to me.

You aren't paying attention. Theories make predictions, interpretations of theories do not. In any case, suppose we grant you your little maxim. Then, if we can't tell the difference between an interpretation which claims that wavefunctions and their collapses are real and one which explicitly claims that they are not real by experiment, they're equivalent. Your maxim has just given us that wavefunctions are metaphysically real if and only if they are not.

And, in any case, someone who reacts against metaphysical realism should also take the brain in the vat hypothesis seriously, and you have no grounds for saying that something which is measured in all ways to be like a duck is, metaphysically, a duck. And that's fine. I'd agree. But if you don't want to play metaphysics, don't. Don't claim that two different ontologies are equivalent when they clearly aren't. Just don't reify the physical model. Tell anyone who purports to have a reification of a physical theory that they're committing a fallacy of reification and be done with it. You can't have it both ways.

Theories make predictions, interpretations of theories do not.

That's precisely the point!

Arguing over the 'interpretations' is pointless. Even if we could identify a difference in the implications, we don't have any relevant data that would permit us to distinguish them. So there are no grounds for rejecting or accepting any one of them - doing so is departing from rational skepticism.

We don't even have a difference of implication between the interpretations. So there isn't even a theoretical distinction between them.

Are you a professional philosopher by any chance, Dustin?

Bob wrote: I prefer to think that the wavefunction is real, but it is a function over potential configurations, only one of which is real. Superposition reflects the influence of other physically equivalent configurations. I would not call my interpretation a "collapse" interpretation. The wavefunction is always there, in the sense that nature "knows" the probability amplitude for points in configuration space other than the that represented by the real state of the universe.

Bob, I'm having a hard time assigning semantics to your words. What does it even mean, in general, for a mere "potential" non-real thing (like your configurations), to influence the "real" world? What is reality, other than things that affect the real world? How can a "potential" thing cause real effects in the real world?

What does it mean for there to be a "probability amplitude" for non-real things? If they are non-real, wouldn't their probability (of "being real", presumably) be zero? What is that a probability of, if it isn't of reality?

I know the meanings of the individual words you've written, but the way you put them together sounds like nonsense. "Colorless green ideas sleep furiously", that sort of thing. Your theory doesn't seem "wrong" to me, so much as not even meaningful.

If I'm mistaken, perhaps you can help me out by explaining what it might mean for something to not be "real", and yet to affect "reality". That seems to be an inherent contradiction to me.

So there isn't even a theoretical distinction between them.

By the way, you still have a contradiction to explain away.

"Theories make predictions, interpretations of theories do not. In any case, suppose we grant you your little maxim. Then, if we can't tell the difference between an interpretation which claims that wavefunctions and their collapses are real and one which explicitly claims that they are not real by experiment, they're equivalent. Your maxim has just given us that wavefunctions are metaphysically real if and only if they are not."

I'm sympathetic to caledonians position at least for non-theoretical physicists (one position might be better than the other for trying to find better theories). My way out is that, "real" is not a predicate that can be attached to "collapse".

The Koan of Master Foo

It is recorded that once, when Master Foo was iterating along a beach, he came upon two of his disciples arguing by a computer processor. "It is subtracting positive 1", declared the first. "No; it is adding negative 1", asserted the other. Master Foo answered them thus: "Not incrementing, not decrementing — Equalizing!" whereupon both were enlightened.

Ben Jones, the spaceship DOES disappear once it leaves our light cone. What do you imagine dis-appear means, that you think it's not what the spaceship does?

Our universe has an edge. Throw something over that edge, and it ceases to be. You might as well say that it doesn't disappear if we break the First Law of Thermodynamics and utterly unmake it - which is what we're doing, as it happens.

Throw something over that edge, and it ceases to be.

And by the way, Zen master, you still have a contradiction to explain away.

Dustin, Caledonian is the local troll. Don't bother.

There is no such thing as "metaphysical reality", the concept is empty, and it's meaningless to question whether things possess the property.

The different 'interpretations' give the same results for everything we can observe, and the same predictions for the things we can't yet observe. They are logically equivalent. They are the same thing with different appearances. It is nonsensical to say that one is true, or that another is not true. They are all equally true.

If someone can locate a prediction that one makes that another does not, THEN we will recognize them as logically distinguishable. If someone can produce evidence compatible with some but incompatible with others, THEN we can begin to speak about some being or and untrue.

As it stands, asking about such matters is like asking whether the ice cream is 'metaphysically 'atop the pie, or the pie 'metaphysically' beneath the ice cream. The phrases are different - surely the things they describe must be different, too!

NO. Metaphysics is nonsense, and the question incoherent.

The different 'interpretations' give the same results for everything we can observe, and the same predictions for the things we can't yet observe. They are logically equivalent. They are the same thing with different appearances. It is nonsensical to say that one is true, or that another is not true. They are all equally true.

I never thought I'd see Caledonian affirm the existence of angels, even if all they do is use Maxwell's equations to figure out how to push on charged particles, but there it is in black and white. Wow.

I never thought I'd see Caledonian affirm the existence of angels,

You seem to have misunderstood. Having an invisible, intangible, etc. etc. dragon in your garage IS having no dragon in your garage. Having quantum collapses IS having Many Worlds... unless and until you can demonstrate that the two are different in some way. And it cannot simply be noting that you use different phrases to refer to them, because that's not a property of the phenomena, just how you choose to talk about them.

When it can be shown that they have different, operational implications, then they will be distinguishable. Until that time, they aren't. Arguing over which of two indistinguishable things is correct is fundamentally wrong - they both are.

Having quantum collapses IS having Many Worlds... unless and until you can demonstrate that the two are different in some way.

...

I do not believe that word means what you think it means.

Caledonian, my position is that the claim that there is no dragon in my garage and the claim that there is an undetectable dragon in my garage are logically inconsistent, not logically equivalent. From my perspective, the logical equivalence you are insisting on really does require you to ascribe Maxwell's equations + angels the same credence you ascribe to the bare Maxwell's equations. Kooky.

Having quantum collapses IS having Many Worlds

Cyan, the 'angels' are a completely empty concept with no meaning and no implications. Saying that your model has Maxwell's Laws plus angels is just a fancier way of saying it has Maxwell's Laws - it's like putting leading zeros on a number, or double negatives in sentences. It doesn't change the value of anything, it's just a somewhat silly elaboration. As ridiculous as such behaviors are, I don't see any reason to prohibit them.

It's when people insist that the dragon-without-actual-properties is somehow 'metaphysically distinct' from simply not having a dragon that they fall into error, as opposed to mere silliness.

People may use whichever 'interpretation' they prefer, because they're all the same. It's the people who insist that one of the interpretations is fundamentally better than the others, without producing new evidence that shows there is actually a difference, who are wrong.

Look at it this way: if I show you a given pattern in Conway's Game of Life, and ask you what the grid looked like one step earlier, how would you respond? (To simplify the thought experiment, let's restrict the size of the grid to something finite.)

Dustin: "Good God, he's even making up his own contradictions now."

That is a meaningless comment, and adds nothing to this discussion. The whole point I believe, of Caledonian's argument is that the statement "MWI -is- collapse" is not a contradiction, so long as the differences in the theories/interpretations of QM can never be substantiated with experimental evidence, ever, because the theories themselves don't allow for it, rather than we just haven't seen those experiments yet.

That said, I don't think that's the case with MWI. If you are saying something about reality that supposedly is true, and has an effect on the rest of reality, I find it unlikely that if it were true, it wouldn't eventually result in experimental evidence that proved that.

But if it can not be shown that MWI would result in experiments that explicitly differentiated it from non-local collapse, than Caledonian's point remains valid, or at least valid enough that there's no reason to be nasty about it (Eliezer, Dustin).

The problem here seems to be a deliberate conflation of "logically equivalent claims" (which are two sets of claims entailing precisely the same set of statements entirely independently of whether those statements are a good or even testable model for a physical pheonomenon) and "physically equivalent states" (which are two ostensibly different states which are the same at every level of examination), or a deliberate conflation of the model of a phenomenon with the phenomenon itself. This conflation is, in either case, completely solipsistic, and arguing with solipsists is futile.

I'll leave the two of you to congratulate yourselves on being both brains in vats and not brains in vats at the same time.

Caledonian, it's not that I don't understand what you're saying, it's just that I don't agree. I think I'll have to leave it there since I want to avoid fruitless arguments over the meanings of words.

Even if there is a difference between a completely undetectable dragon and no dragon, does anybody care? I can see ethical implications MWI (multiverse theories in general, really) might have even if they're not testable, analogous to the ethical implications of things not disappearing when they cross the cosmological horizon; but in the absence of any mention of practical reason, so much focus on interpretations seems unjustified.

Re: MWI (!)= Collapse.

But isn't this easy? They don't actually have the same logical implications. It's simple to find (theoretical) experiments that would distinguish them.

MWI implies that you'll see inteference phenomena at all scales, and without humans involved. It's hard to set up the experiment, but you can imagine a double-slit experiment with a macroscopic baseball, for example. According to MWI, if the configuations are the same, there will be interference.

Collapse implies some transition point, based on something. There are different versions of it. One of the originals said that it was consciousness, which has implications for humans being part of the experimental setup, and also suggests that AI will fail. AI (someday) succeeding is probably an observation that contradicts the consciousness-causes-collapse theory.

Even the more modern collapse theories suggest something about scale. So a baseball double-slit experiment would distinguish MWI from that collapse theory.

This isn't invisible dragons in a garage (except insofar as the collapse folks keep changing the goalposts every time their current theory is invalidated). Nor even the spaceship-over-the-horizon problem. This is really a case where the two interpretations agree on the subatomic consequences, but disagree on extending them to macroscopic scales.

There are testable differences between the theories.

You're actually somewhat mistaken in your view of many worlds. Many worlds can be seen as a kind of non-local theory, as the nature of the theory assumes a specific time line of "simultaneity" along which the universe can "split" at an instant.

But special relativity allows no one such objective simultaneous moment in time, and from the perspective of time lines at different angles, then the split could happen at different "spatial points" depending on their perspective. Thus, its split would not have one specific set of spacial locations unless one were to assume a privileged basis, which relativity denies. And if one were to assume such a privileged basis (which relativity denies), then some other basis would be forced to see a sort of faster then light communication as a moment that appears to be in the future would create at that moment a causal split to a different universe

Now, whether that's non-local in the same way, maybe you can argue, but the main reason locality is important in physics is through its status as an axiom of relativity, and many worlds violates special relativity just as much as collapse does.

The research to demonstrate quantum superposition at 50-micrometer that Eliezer was mentioning has been published in March 2010 :D

What about treating the collapse as the Bayesian probabilities update in light of the measurement (new evidence)?

Consciousness doesn't collapse the wave function per se.  Consciousness collapses an image of the wave function.  The collapse is not a necessary function of the universe, it is a necessary function of consciousness of the universe. As a result, consciousness is always necessatrily slightly out of phase with physical reality. 

Actual reality is not necessarily the same as what is needed to construct a comprehensible picture of reality. The inherent lack of one-to-one correspondence is most likely exactly what is neccessary for consciousness to exist. 

A unified theory is an oxymoron.