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How Many Worlds?
How many universes "branch off" from a "quantum event", and in how many of them is the cat dead vs alive, and what about non-50/50 scenarios, and please answer so that a physics dummy can maybe kind of understand?
(Is it just 1 with the live cat and 1 with the dead one?)
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Comments (64)
How many ink blots are in this picture ?
For "many worlds", imagine that evolving in time, with fuzzy borders.
The Many Worlds Interpretation doesn't imply a countable number of worlds that suddenly branch, it's more like a fuzzy continuum; talking of branching worlds and timelines is just a high-level abstraction that makes things easier to discuss.
This is a really good analogy to explain what a wrong question is.
It rather seems to me an imprecise analogy which makes thinks harder to discuss. But I agree with the general sentiment.
Not countable many, but continuum many? Is that what you say?
Maybe - I'm not sure of what you mean by "continuum many" - you mean like real numbers? I was thinking more of something like "roughly countable, though the count will depend on which definition of "world" (or "blob") you use", or even better, "it doesn't really matter".
Yes, I mean as many as real numbers. Or maybe even more, I don't know. I am asking you, who is telling us that:
(Of course, MWI is popular, but I agree with those who say - it's just ridiculous.)
Thanks for answering!
I guess I was confused by this:
That is a somewhat useful analogy, but it can be taken too far. But it seems to me to be saying the same thing (though perhaps not as clearly) as the inkblot above:
Can you really count it? Not really!
I thought that when it said "At the beginning there is one blob, at the end there are two blobs" it was saying that the "worlds" did eventually become discrete, you just couldn't tell exactly when.
When you mix regions of stability and chaos, eventually things settle down into relatively discrete zones... along some directions... while being smeared out all over the place in others.
Edited to add: Are these downvotes from people who know quantum mechanics or dynamics in phase space, or is my comment just making people confused again (a bad thing to be sure), or what? I can probably fix it, but it'd be best to know what about it needs fixing.
No idea why whoever downvoted you did so, but here’s why I think I felt your comment was not useful to me, or much less useful of what it could have been if you happen to know what you’re talking about (I don’t so I can’t tell):
Your statement states a fact without any explanation, examples or pointers to such. If you had said something like “When you mix regions of stability and chaos, things never settle down into discrete zones... it’s all smeared out all over the place.” — then the effect of reading it would pretty much have been the same unless I already knew about the subject enough not to need your comment.
Imagine someone not having any education in astronomy saying something like “I thought the sun and stars turn around the Earth”, and you commenting “Actually, the Earth spins around itself, and it turns around the sun, while the other stars pretty much go every which way.” Unless the first person knew you were a good astronomer, they don’t really learn anything. And even if they did believe you knew you to be an expert on what you were talking about, they might learn it as a rote fact, but won’t really understand much.
Oi, if that's the problem I'll just call a halt. Chaos theory is kind of like quantum mechanics: done right, it's tough, and done easy, comes out horribly wrong.
So... your comment was an attempt at “done easy”, or was it “tough”?
(It occurs to me that the line above would be normally interpreted as snarky. My intent was half friendly joke, half “if you have that opinion about Chaos theory, what did you try to achieve in your earlier comment?” I just don’t know how to express that in written English...)
So the key idea is that of "Hilbert space," which is a way to describe the universe named after a guy called Hilbert.
So for example if I flip a fair quantum coin, it's 0.5 heads and 0.5 tails. "Heads" and "tails" here are actually dimensions, like x and y, in Hilbert space, and the universe is at the point (0.5, 0.5). If the coin wasn't fair, then the universe could be at the point (0.6, 0.4) or even (0.999, 0.001). The number of dimensions didn't change, because there's still just heads and tails, but the point that represents our universe changed.
When you look at the coin, the universe collapses to two possible points: (0,1) and (1,0). The coin is either heads or tails. This corresponds to two "worlds." It doesn't matter whether, previously, your description was fair or not - the coin is still either heads or tails, so there are two worlds. Though I suppose if your previous description was (1,0) - definitely heads - you wouldn't assign any probability to it being tails, so there would only one "world".
Of course, it can get much more complicated. If you roll a quantum d20 instead of flipping a coin, you have to assign a point with 20 coordinates: (0.05,0.05,0.05,0.05,0.05,0.05, 0.05,0.05,0.05,0.05,0.05,0.05, 0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05). And if you throw a dart at a continuous dartboard, you have to assign a value to an infinite number of points! But don't worry - that's just the same as a function, like x^2 or sin(x). But if you throw a dart at a dartboard, does that mean you just split off an infinite number of worlds? If you flip a coin, and then throw the dart, is that 2*infinity = infinity?
So basically, when there are lots of possible outcomes the idea of "worlds" becomes not so useful.
Although this gives the correct answer as far as the number of worlds is concerned, it sounds strange within the MWI (which was supposedly assumed in the original question).
I think you can't do MWI justice without introducing the observer in the game: apart from the coin which lives in a two-dimensional universe, there is the observer whose mental state lives in a (at least) three-dimensional universe. The dimensions of the observer's mind are "think the coin landed heads (TH)", "think the coin landed tails (TT)" and "don't know (DN)". Together we have six dimensions, all combinations of coin and observer states:
In this space there are three planes defined by the observer's mental states: for example, the plane TT consists of vectors that have all coordinates except the second and fifth equal to zero. The observer's consciousness has a peculiar property of seeing only projections to these planes. Those projections are what is called worlds.
In the beginning, the observer doesn't know and the coin is 50% heads and 50% tails; this means the state vector of our model "universe" is (0, 0, 0.707, 0, 0, 0.707). (Have I mentioned that the probabilities aren't in fact the coordinates but their squares? Anyway, this is a technicality we don't really need now, but we should be consistent. The state vector must have lenght precisely 1.) At this moment, the projections to the aforementioned planes are
In a sense, three "worlds" already exist, but since two of them have zero length, they can be disregarded.
Now the observer measures (looks at) the coin. Measurements are mysterious processes which, over some time, get the observer into correlation with the coin. The universe state vector becomes (0.707, 0, 0, 0, 0.707, 0) and the projections are now
Now we have two non-zero projections and can speak about two worlds. But remember, there is still only one six-dimensional Hilbert space with one universe state vector. It is believed that under normal circumstances no processes can put the state vector back to the state where there are less non-zero projections than before. But in principle it could happen and if it does, the worlds would merge again.
Congratulations, you just earned yourself one "click." I've never really gotten quantum physics, not that I've tried much. But your description as a Hilbert space makes a lot of sense to me. It also helps me understand why "decomposing the wavefunction" is important or even necessary as a concept.
Here I predicted that a question like this one about quantum physics would get voted up, even though a similar question on classical physics got voted down. Currently I'm wrong, but only just.
Uncountably many. Consider that on the scale of the Omniverse (which contains only this one particular universe among uncountably many) the probability for any event is 1. It is also so, because it is absurd to suppose there is a universe in which something, if there be anything, does not exist. Furthermore, even if the probability for an event in our universe were 0 that would in no way serve as an impediment to its occurring in the long run.
I read your post in the other thread by Mitch_Porter, asking about why your post here got downvoted. As someone who would also have responded with the answer "uncountably many" and was in fact surprised to find that that wasn't quickly established as the obvious correct answer, I thought I might come take a look.
I would guess that the (mild) downvoting on this post comes from the fact that after your first sentence, you stop talking about specific instances of decoherence and start talking about omniverses and probabilities of 1 and 0. your language is more technical than it needs to be and grammatically odd.
all of these fragments make me cringe and have to parse what you're saying.
I hope this helps!
The answer is only true if the measured quantity has continuous spectrum, therefore not applying to the only explicitly mentioned example of the cat. Furthermore I don't follow your subsequent reasoning.
Taking the universe as a QM event most definitely implies there are uncountably many universes. The OP very clearly asked for non-standard instances of the question, and a generalization of the question most certainly applies thereto.
I certainly hope others do not continue to down-vote what they don't grasp, because LW will only be the worse off for it. (Not implying you down-voted, but if you weren't, then the one who did obviously hasn't the wherewithal to state an outright objection.)
Edit: if you don't "follow", at least state in what exactly you don't follow so that I can actually provide something to your explicit satisfaction.
I was the first person to downvote. Not because I don't grasp, but because I believe your explanation is in the best too brief to be generally intelligible. My negative opinion can be, of course, due to my stupidity, but as for my downvoting strategy, my own judgment is all I can rely upon. (My judgment also tells me that you appear a bit oversensitive to downvoting.)
From the former comment:
I don't see how it is relevant. Quantum branching doesn't require Omniverse. That alone makes your argument seemingly irrelevant. But let's proceed.
I have no clear idea what a probability of event happening in the Omniverse means. Could you elaborate? (Possible issues: From an observer-independent point of view, the event either happens or not. The observers are restricted to their own universes, how do they construct probabilities over events in different universes? If the generic word "event" is replaced by the actual specification of the event, is the number of universe included - i.e. do you replace it by "two protons collide at given x,y,z,t" or rather "two protons collide at given x,y,z,t in universe #554215"? How do you solve the apparent problem that the given definition of the event may not have sense in some universes, e.g. if the universe happens to be one-dimensional and have no protons in it for the example given above? If you simply mean "for any event, we can imagine a universe that contain it", why did you start speaking about probabilities?)
Is this supposed to justify the previous claim, i.e. that the probability of any event in Omniverse is 1? If so, I don't regard "each universe contains something, therefore any event has probability 1 in the Omniverse" a valid inference, whatever interpretation of both the premise and the conclusion I can imagine.
What is "long run"? Does it mean "in other universes" (that would make sense, but the choice of words "long run" to denote that seems bizarre) or does it mean "sometimes later in this universe" (that would be the natural interpretation of "long run", but then the statement says "p(the event happens) = 0 and the event can happen", which is a contradiction).
And of all that, how does anything imply, or even relate to, the "uncountably many" answer you gave at the beginning?
From the immediate parent:
This is an assertion without explanation. I even don't understand what do you mean by "taking the universe as a QM event".
From the single sentence the OP consists of, could you quote the section where it very clearly asks for non-standard instances of the (which?) question?
In fact there are many continuous outcomes in quantum mechanics. The overved velocity or momentum of an electron or any other mass. In fact the number of stated problems where the results are broken down in to discrete states is small compared to the ones with continua. In fact, the heisenberg cat example, there are not just two states of outcome, either alive or dead. Rather there are a myriad of state outcomes where the cat is alive, and another myriad of outcomes where the cat is dead.
I personally think the many worlds hypothesis is ludicrous, failing Occams Razor by such an astonishing margin that it might as well just grow a long beard. Admittedly, I have not read any respected physicists argument for it (or at least I didn't respect the arguments I did already read). I think the many worlds hypothesis is just a very dopey hack for people who have decided ahead of time that the universe "just HAS to be" deterministic. I say if you observe indeterminism in the universe, then it is your theory that is broken, not the universe.
You don't agree that Decoherence is Simple? (Not that I'm qualified to have any opinion on the matter.)
I'm glad you gave me that link, thanks. I had seen that article a while ago and it was good to refresh.
The problem with the Many Worlds Hypothesis is that it solves no problem, in my opinion.
In simplest terms, the problem with the "standard" interpretation is that you have probabilistic outcomes from some experiments. Some people hate that.
The "solution" offered by MWI is that at every instance where a wave function would have collapsed to some probabilistically determined valuewe have the universe split into as mny choices as there are possible wave function collapses, even when that number is infinity because the wave function collapses into a continuum of position or velocity values. And this happens over and over and over so you have an efflorescense of zillions and 3^^^^^^3 and googleplexes of universes.
What problem did this solve? Oh yeah, the arbitrariness of the probabilistic result predicted in quantum mechanics.
What problem did it not solve? That I wound up in this particular universe, no physics to explain that. "Oh, but you wound up in ALL the universes!" I got cloned a zillionplex times with the universe. So did everybody else. In fact you got cloned a zillionplex times when a wave function collapsed because I observed something, and then your zillionplex clones got cloned another zillionplex times when you observed something, and then a zillionplex more splittings of each of you for each wavefunction collapse for each of the billions of humans on the planet. Do ants have enough "observer status" to collapse wave functions? Probably, if not ants than certainly frogs.
So we wind up with a near meaningless explosion of universes that is constantly going on, and indeed is in important senses accelerating constantly.
And of course every one of these overwhelmingly zillionplexes of zillionplexes of universes is unobservable to us, will never have the slightest affect on us, once they split off from us!
Its almost as though they don't exist!
Except things like quantum computers. It's almost like those worlds do exist and that we can even use their transistors to parallel process stuff.
Well that is definitely a fun thing to say. It doesn't seem to be consistent with what is currently thought about quantum computers and Many Worlds, though.
Your link to the wikipedia article on the MWI does not clarify your objection to the statement made above.
The wikipedia article states
If a quantum computer could correctly be characterized as a computer which utilized the transistors in other branches of the multiverse to speed up calculations in this one, then it would merely require the operation of any quantum computer at all to provide strong evidence for the multiverse. However, the article states that a test for MWI requires a particular special operation of a particular special quantum computer, that the multiverse is not a conclusion we reach merely by seeing a quantum computer work.
Sorry I didn't make that connection clearer before.
I'm pretty confident that that paper is in error. Or rather, it assumes that the Copenhagen Interpretation is implemented so that it deviates from pure Quantum Mechanics in a particular, testable, way (or category of ways) - and that renders his version of CI distinguishable from MWI, and less useful for quantum computing. When I get academic library access again, I'll take a closer look at it.
Upon returning and rereading... no. Branches in MWI aren't said to have 'split off' until they are mutually decoherent. That renders them unsuitable for quantum computing.
The chief virtue of decoherence and MWI (as I understand it) is that it avoids 'the measurement problem' or the necessity of a natural observer. If you go back far enough in the history of the universe, there were no natural observers.
Well the beauty of the actual system is that you don't need a "natural observer" until you have one. You calculate the time-evolution of the system with non-collapsing wave functions, then you collapse the wave function only when an observer finally shows up to make the observation.
It doesn't matter if the wave functions were waiting billions of years to finally be collapsed, you are not missing anything by not having collapses before you have natural observers.
meaning the standard QM interpretation?
But consider the first natural observer, composed of matter. At what point do the wave functions associated with that matter collapse? Before or after its first observation?
With decoherence & MWI, this question presents no problem.
Irrespective of my below comment where i get more empathetic wiht the motivation for MWI, I do want to point out some of the reasons why I think MWI may be a "bridge too far" to solve any problems.
The universe as we know it has proven to be gigantically "conservative" in the sense of having a bunch of conservation laws that it simply never violates. Conservation of mass-energy being among the deepest and most powerful. In this universe, at this epoch, stuff is neither created nor destroyed: it is converted from one kind of stuff into another with strict conservation. Even particle pairs that arise from random vacuum fluctuations all soon "realize" if they are violating conservation of energy and disappear before you can say within the uncertainty principle that they were ever there.
So now we come along, have a subtle issue with wavefunction collapse and what really causes it and what does it all mean, and the solution is: the universe may be strictly conservative, but the multiverse is growing in total mass and energy about as fast as any growth fuction that you can conceive, and THAT is what makes the direction of time so strong?
Yes, of course this COULD wind up being right and being the simplest. I await proposed experimental verifications, without them I can NEVER pick a non-conservative multiverse.
But thanks for making it clearer what some of the things that are gained are.
That's not how MWI works. These worlds are not being created. The wavefunction of the universe is being split up between them.
Are there more of these worlds now than there were 15 billion years ago?
If so, you can call it anything you want, but I vote that "created" is a pretty good term for explaining something that exists now that didn't used to.
I failed to mention one major additional point. Decoherence and MWI also account for the observed fine-tuning of the universe to support life, including key details of the inflation hypothesis. The standard interpretation doesn't.
As to conservation of mass-energy, this seems to be something that conflicts with your intuition that if there were decoherence, mass-energy would be divided up into the various branches and thus diminished in each branch. If you did accept the superiority of decoherence & MWI over the standard interpretation, you'd have to set this intuition aside.
You are free to select the version of Occam's Razor that appeals to you. I like the one that chooses a complete explanation (that also explains fine-tuning) over an incomplete explanation that also requires an exogenous wave-collapse for the first natural observer.
Yes I see the motivation there. MWI may seem like an OK alternative to wave functions actually changing in the presence of consciousnesses, but not in their absence.
I guess I've never really believed the consciousness was an important part of it. Take for example setting up a two-slit experiment with a slow stream of electrons launched at it and a recording electron detector array beyond the slits. One would have a time series of locations the electrons hit the array which would probabilistically over time build a two-slit diffraction pattern, but in which each electron particle was identified with where on the array it ended up. Suppose you set this up in a room. In one version you send an observer in 3 days later to look at what happened, and you see all those evidences of each electron wavefunction collapse into a position eigenstate on the array detector. In the other version you don't send someone in to the room until 10 years later, at that point the observer sees the historical record of all those wave function collapses. Finally there is a version where you never send someone in to the room.
It has always been my opinion that whatever collapses happened actually happened at the time recorded for each electron wave function hitting the screen. The version of the Copenhagen interpretation used here seems to go with the idea that the entire room including the detector array and the equipment used to record its results exist in a quantum superposition of all the wavefunctions UNTIL the observer finally goes in to the room, at which point they collapse in to a state with all the data stored showing one allowed version of the historical record of electron collapses.
Very intriguing. There is literally no way in this experiment to distinguish between "the wave functions collapsed as the electron hit the detector, that I came along later to see the record of it isn't what caused the collapse" and "all possible histories of that room were swirling around in a quantum superposition until I finally came along and my peaking in the door caused it to collapse on to one possible outcome."
I've never fully understood Bell's theorem and EPR, but I suppose I am stating a version of the same question. How do I design an experiment that distinguishes between that room being in a quantum superposition until I finally get there, and that room being a dry tomb of the records of wave functions that collapsed long ago? Bells theorem, if I am right and it applies here, says you can distinguish and that the room does exist in a quantum superposition until you get there, that there are certain subtle statistics of correlations that are true but not possible in a room which is merely the tomb of old dead wave functions.
I realize as I participate in this discussion that for me, the collapse has been a result of the wave function and the observing EQUIPMENT, not a function of my consciousness. It is possible that Bells theorem test results mean I am just wrong about this, but maybe not and bear with me.
I did work for years on the quantum treatment of one example of "measuring equipment," a linear amplifier for radio waves. The quantum uncertainty in radio waves is manfested as "photon counting noise." You think you have a pure sine wave, but it has some randomnesses due to quantum uncertainty, and a variety of bookkeeping methods for characterizing that uncertainty show it is equivalent to one-photon's worth of noise power in the system even at absolute zero of temperature when all removable noise has been removed. THe linear amplifier, we see, amplifies those fluctuations so at the output of the amplifer those quantum fluctuations are now large, comprised of the energy of a million photons each (for an amplifier with gain one-million) and therefore, essentially, treatable as a classical phenomenon. My interpretation is: the linear amplifier collapsed the original input wavefunction, and turned its quantum noise into solidly instantiated classical noise.
But I have a feeling if I understood EPR and Bells theorem that I would see it is not the amplification that collapses it. Hmmm.
This is the hypothesis that was tested, and failed, in the 2007 implementation of Wheeler's delayed choice experiment.
Thanks for the link to Wheeler's experiment. This experiment doesn't address what I was addressing.
In wheeler's experiment, the detector is put in place or taken away after the photons would have had to have passed through the slits. Even though the choice of detector (difraction pattern vs which slit) is made after the photons pass through, the photons are not "fooled" by this and behave at whichever detector is there when they get to it exactly as they should according to QM.
In my experiment, the detector and a recording device are locked in a room with no observer. The detector is never changed, the experiment just takes place without a human observer. It isn't till sometime later that th room is opened and some human comes in to see the results of the experiment. The human does indeed see a time series of recorded electron hits on the detector which when summed up show the famous diffraction pattern. The question I address is: * Did the wavefunction for the whole room including the detection apparatus not collapse on to one of its allowed outcomes until the human finally went in to the room to see the result or * Did each electronic wavefunction collapse at the time the computer records the detector saw that electron?
My intuition has always been that it is not so much a consciousness seeing the result of the experiment that causes the collapse, as it is something about the apparatus for detecting the outcome of the experiment that causes the collapse. That the wavefunction is spread out across the detector array and then BAM it all gets sucked down somehow to only a single element of the detector array which is triggered.
In this view, wavefunction collapse is much more mechanical than in the way Copenhagen gets talked of around here.
Also, I think that whether the WF collapses when you go in the door, or whether pieces of it collapse each time an electron is recorded at the array are possibly experimentally indistinguishable. However, it may be that Bell's Theorem EPR experiments do speak to this situation, that there would be experiments in closed rooms that could be done where an earlier collapse vs a later collapse when the observer finally arrives could be distinguished from some subtlety in how results are distributed (which is how I see EPR).
You have my condolences. I have waged this battle here for some time, without much success. If you press EY on the matter, all he says is something along the lines of "MWI is decoherence, decoherence is MWI", which renders the MWI a redundant concept. Unfortunately, nearly all non-experts here fall into the password-guessing trap, while furiously denying it. Probably because the MWI seems so cute and even intuitive, even if bereft of substance.
The number of possible outcomes you are able to distinguish. For the cat, if the only information you get is dead/alive, two. If the probabilities aren't 50/50, you can think of one of those branches as stronger.
(Edited several times, this is the final version, I hope.)
I'm surprised that this has not been said, so I'll present the way I think about branching, though it will be a bit heavy on the mathematics and I apologize for that. Perhaps someone else can pare it down a bit. Also, I am not a physicist, I am a mathematician, so my model is probably more optimized for making me feel like quantum mechanics describes a world in the abstract, and less optimized for describing the specific world we live in.
In the Schrodinger's cat experiment, we have a vast number of elementary objects, which are essentially all wave functions. If we consider the reduced density matrices, the set of all possible reduced density matrices is... well naively I might guess that it is the n^2-fold product of the unit interval, where n is the dimension of the matrix, but it's also possible that the space of reduced density matrices is some other lie group (if it turns out the space is NOT a lie group, this interpretation is in serious trouble!). Either way, there is a Haar measure on it; which is to say we can, in some sense, have a continuous space of all the elements of that group. Now conceptually I'll consider each of the coefficients of these matrices as sort of like a probability. Now I construct one universe for every member of the direct product (maybe direct sum?) of the group, indexed by the set of wave functions in my experiment, and I call this set of universes the "branches which causally descend from my circumstance" because that sentence makes me feel warm and fuzzy. In each of those universes, each wave function expresses itself as though it collapsed in one direction if the coefficients of the matrix indexed by that wave function are greater than the reduced density matrix of that wave function, and the other if they are less. The fact that I don't know what should happen if the coefficients are equal bothers me, but this isn't really a good expression of the "directions" that a matrix can "collapse in" so I will guess that there is a better formulation that a physicist could make that resolves this issue, and if I am convinced there isn't, I'll start reading up on quantum physics for the purpose of sleeping better at night.
The naive picture that I had that I tried to comb out into a real model here is that there are a bunch of continuous probabilities (intervals [0,1]) which resolve as either 0 or 1. So the number of universes coming out should be indexed by intervals [0,1] for every probability in the situation, with that universe coming out with a 0 if the value in the index is less than the probability and a 1 if it is greater. I suppose, since the big deal here is measure, that you could arbitrarily assign the equality case here to either side and it would never make a difference.
I'll reiterate at this point that I'm a mathematician, not a physicist. This is what's gone on in my head as an explanation for what it REALLY MEANS to have many worlds. I would love to hear a physicist's perspective on why this is all complete nonsense.
See section 6 of this David Wallace paper.