Quantum Theory and The Many Worlds Theory

[billl]

I'm not sure how to word this (I've already been sloppy by using the word "collapse" while describing MWI) but, to begin with, I'm pretty sure you already know the pattern we are expected to see. MWI explains the interference pattern in the double-slit experiment as a result of interference between "versions" of the particle(s) in different worlds. At least that's my shorthand way of thinking of it, I wouldn't be surprised if I'm somehow getting it wrong or being simple-minded about it, missing nuances, etc. Anyhow, by all accounts the MWI explains the results of the double-slit experiment, it is not undone by the results of the experiment.

I'm not sure if it can be fairly said that this would suggest the existence of a sort of interface between the worlds or not, perhaps there's some interesting stuff going on with the existence-as-a-wave portion of the model beyond just what we see in the experiment. There's a certain sense of arbitrariness about MWI, I think, yet it handles the situation very well, mathematically--and the arbitrariness of course is just coming from my everyday perspective, not the perspective of someone actually trained and capable to really try and understand advanced physics. Anyhow, in the end, I'm not sure the MWI is too much stranger than other respected interpretations.

[YesNo]

The question was somewhat rhetorical to focus on the problem.

With the double slit experiment, without measurements being performed, and with both holes open, one would see a wave interference-like pattern signalling a non-deterministic pattern and not a particle pattern signalling determinism. If one of the holes were closed one would get a particle pattern with all the electrons coming from the open hole in a deterministic manner.

A deterministic result would be a sum of the patterns with first one hole closed and then the other. Given a position P on the detector screen and P12 being the electrons coming from both holes 1 and 2 going to that position, the number of electrons one would expect to arrive at P would be P12 = P1 + P2. But that is not the wave interference pattern that is actually seen. The wave pattern would get results suggesting that P12 <> P1 + P2.

I think there are two alternatives:

1) Either MWI does not actually interpret QM since each world contributing to the superposition is assumed to be deterministic and should generate a particle pattern even though a wave pattern actually appears,

2) or, MWI is not deterministic, but uses enough of the Schrodinger wave function to get Heisenberg's uncertain principle in play prior to collapse or decoherence, to generate the wave interference pattern.

In the second case, MWI doesn't resolve any mystery of QM since the indeterminism is still present, but it does add the mystery of many worlds to the problem after the collapse or decoherence. In the first case, MWI is a false interpretation of QM since it would not account for actual experimental results.

[billl]

Well, I can just recommend that you maybe look over MWI a bit more, because your number 1) doesn't seem to be taking into account what MWI suggests (which I tried to point out in the previous post). I don't think we need to consider the second part of the either/or, I really can't see how it could apply to the MWI.

Again, I am all for skepticism in regards to MWI, but I'm not sure you're attacking what the MWI actually is.

[MorpheusSandman]

I'm not sure you're attacking what the MWI actually is.

He's not. I, like you, don't remember enough about my research/reading to correct him in detail with a high confidence level, but I'm pretty sure Cioran knows more than both of us combined and even he had no luck; so there you go.

[Cioran]

1. QM is only indeterministic IF YOU ACCEPT/TAKE FOR GRANTED THE WF COLLAPSE!

Laugh. Out. Loud. And there YesNo goes again. I mean, seriously? Has he read any of the material I linked? How stupid is this?

Hey, YesNo: QM IS ONLY INDETERMINISTIC ON THE ASSUMPTION OF WAVE FUNCTION COLLAPSE! Capice?

Jesus. Crackers.

[MorpheusSandman]

I'll take some Jesus crackers... so long as they're not the ones YesNo's been eating... and I can put some cheese whiz on them.

[Cioran]

Same could be said for any expert that disagrees with your prior beliefs. I'm seriously tiring of this game.

Yup, And that's all it is with him, a game. He has no interest in an honest and unbiased exploration of this issue. He has an agenda, which is that x cannot be right because he doesn't like x. Really, it's sickening.

[Cioran]

You can certainly put some Cheese Whiz on Jesus Crackers if you like, though it might piss Him off, since after all, it's His body. The Bible doesn't say whether Jesus approved of cheese or not (I don't think), so those of us who eat it do so at our own risk!

[YesNo]

Well, I can just recommend that you maybe look over MWI a bit more, because your number 1) doesn't seem to be taking into account what MWI suggests (which I tried to point out in the previous post). I don't think we need to consider the second part of the either/or, I really can't see how it could apply to the MWI.

Again, I am all for skepticism in regards to MWI, but I'm not sure you're attacking what the MWI actually is.

I'm aware that MWI claims that multiple versions of the world account for the indeterminacy, but I don't see how that is done. Any way one tries to put on the electron some deterministic way to tell which hole it will go through and where it will land on the detector will destroy the wave interference pattern.

However, something occurred to me yesterday. Rather than the two alternatives between MWI either being (1) incorrect, or (2) non-deterministic itself, I think it is actually both.

I assume that MWI still uses the Schrodinger wave function. If that is the case, then Heisenberg's uncertainty principle is a mathematical derivation from the wave function itself. The proof was first given by Earle Hesse Kennard and is displayed in the Wikipedia article on the Uncertainty Principle: http://en.wikipedia.org/wiki/Uncertainty_principle

As far as the mathematics goes, unless MWI uses something different than the wave function, MWI has not resolved Heisenberg's uncertainty principle. Non-determinism will remain there as long as MWI continues to use a wave function. That is why I think MWI is still non-deterministic even though it claims that it is not. This is also why it can say that everything that the QM experimentally observes it agrees with. They both use the same wave function. They are both non-deterministic.

I am aware that MWI tries to get around the non-determinism in the wave function itself by claiming that an electron can be split into various versions, superpositions or worlds, or whatever, each of which is deterministic. But if that were the case, then each of these individual versions would know which hole its component went through and where it landed in a deterministic manner. If there were a way for that to occur, according to Feynman that I quoted earlier, the wave interference pattern would not occur. That would make MWI not only non-deterministic, but also incorrrect.

I am aware that Cioran has claimed things like "QM IS ONLY INDETERMINISTIC ON THE ASSUMPTION OF WAVE FUNCTION COLLAPSE!", but that is not the case. As long as you have a wave function, you have indeterminism. The only time you get determinism is if the wave function collapses.

Consider it in this manner. Prior to the collapse, the wave function might say the electron has a 40% chance of going through hole 1 and a 60% chance of going through hole 2. Suppose you measured which hole the election went through and found it was hole 1. At that point the probability distribution of the wave function collapses to a deterministic situation and you have the chance of going through hole 1 as 100% and the chance of going through hole 2 as 0%. The indeterminism leaves only with a wave function collapse.

[Calidore]

What you're asking is more about epistemology (philosophical study of knowledge) than anything. Again, I'm more or less in agreement with Yudkowsky's views on this subject, Bayes' Theory applied on a more intuitive level. When you're relying on experts, one can put one's level of confidence in any proposition in alignment with the ratio of opinions on the matter. Eg, if 60% of experts believe in MWI, then put your confidence level at 60% that MWI is true. One doesn't have to split all beliefs into binary/boolean true/false, 0/1. Bayes itself says that there can be levels, and it's more about being "less wrong" than guessing the right answer. If I want to be less wrong then I'm going to favor what the leading experts tend to favor. Of course it can't guarantee truth, but the need for such certainty is in itself a cognitive trap. However, I do find what YesNo's doing, essentially "investigating" QM and trying to make it fit his preconceived beliefs, very counter-productive, if not dishonest. I myself have admitted I don't know enough to confidently answer many of his questions, so I've simply tried to point him (like Cioran) to those that do (or seem to).

As far as belief branching off from knowledge, this happens most strongly when beliefs stop being thought of as maps and start being confused for the territory itself. If one thinks of beliefs as a map then, like with any map, there is a way to compare it with reality. If I believe there's a mountain in Colorado, I should be able to go to Colorado and see a mountain, so my belief, my map, is confirmed by seeing the mountain. People's beliefs tend to get out of whack with reality when they stop making this map/territory connection, when beliefs become disconnected from verifiable, predictable sense experience. A lot has been said against positivism and verificationism in 20th century philosophy, and Popper's notion of falsifiability could be said to be an even better way to think of it than either, but I tend to find that when you get away from either then that's where quackery and pseudo-science flourishes.

I'm afraid I'm not sure how we got from science to philosophy, unless there's so little basis for these various quantum-related theories that that's the only option. I'm also not asking for the "truth" since the massive debate and number of books published promoting different positions indicates that nobody has a clue. I'm simply wondering where the tree trunk of science ends and the branches of speculation begin. Again, on this subject, what has been proven by experimentation and what hasn't been (yet)?

I can see the need for certainty being a trap when certainty cannot be found, but isn't science about trying to create certainty about things we were previously uncertain about?

[billl]

For the record, it's been years since I even looked over a popularization-type paperback on these subjects, and I don't want to sound like I think I'm an authority or anything. I've clicked here and there over the past two days, and I'm sure I will fail here to completely accurately get across what I've been reviewing. But I'll try.

Like a few posts ago, the key thing to keep in mind here is the difference between "subjective determinism" and "objective determinism", I think. In the MWI, things seem indeterminate because we are taking the measurements in one particular world. We can't inhabit/experience all of the worlds, only one. Since the worlds are different, we subjectively experience "random"/indeterminate measurements over time, our world is unique in comparison to the others, and the particulars are revealed to us as we check on them. From the perspective of the theory, though, all of the branches occur and represent a deterministic unfolding of events. It is all there, from the perspective of the MWI--however the particular world in which this particular version of you and I occur is just one out of many, and for us, with our limited perspective, events are subjectively indeterminate.

For a different, but I think analogous, example: Imagine we had an enormous mansion with thousands of rooms. In each room we have a table and an unstarted game of checkers set-up on a table, as well as an (undoubtedly patient) observer in each room. I think there are six possible moves for the first player to make, and so we could go to each room, performing one of the six different moves in each room after the other--moves 1 to 6 each in the appropriately numbered rooms 1 to 6--and then repeated them for the next six rooms and so on for some time. Then we could try out the next possible move on the board, and distribute the possibilities across the games just underway in the succeeding rooms. For us, it would be a systematic way to play-out the early moves of each possible checkers game (each room being a slight variation from some other room), but for the observers the game taking place before them in their particular room would appear random. In that enormous Checkers Mansion, we have arranged things so that the games are objectively deterministic, but subjectively indeterministic to observers in particular rooms.

Regarding the double-slit experiment:

1) the strange behavior of particles being sent individually at the double-slit, yet ultimately forming the interference pattern is explained in the MWI by saying that different versions of the particle interfered with itself. Perhaps important to remember is that the arrival of the particle against the plotting surface indicates its existence in "our" world, and the "other" particle would be somewhere else on such a plotting surface in "another" world. Prior to that, the two worlds were the same, in complete overlap, with the wave function equation providing explanation of the interference (I think this is close enough of an explanation). The measurement itself (the arrival of the photon on the plotting surface) means a separate and distinct world. Rather than a "collapse" we have a "split". So ends my rudimentary effort at explaining "decoherence"--perhaps other sources can help patch up my failures to explain sufficiently.

Before moving on, I want to mention that my understanding of when the splitting occurs is not firm, but I think the basic idea is that the measurement marks a difference in the two worlds, "causing" the split (I need quotes around "causing" though...). Of course this is strange, but the flavor of it might come out a bit more if we take into account the theoretical (though not yet tested, I don't think?) notion of worlds returning to the exact same state. In theory, erasing all trace and memory of a measurement might allow two recently separated worlds to recohere or become "one" again (or something like that), but this is just a very specific and theoretical consideration. It isn't something that's normally going to happen, it's hard to imagine how we could measure such an event, and it is generally completely out of the question. (And I've probably "explained" this theoretical side-note inaccurately, while attempting to get the jist.)

2) The strange behavior of individual particles getting measured at one of two slits is also explained by this decoherence idea in the MWI. The measurement is performed (and we learn which world we are in--left-slit-world, or right-slit-world, which is a a subjectively indeterminate result...) and as the particle proceeds to the plotting surface, the "split" has occurred (the measurement makes "this" world distinct), and the particle is no longer interfered with by the other particle (which provided a different measurement result in a separate world).

Again, I'm not so sure how this is any less or more arbitrary than other interpretations. My suspicion is that a more thorough understanding of decoherence might help in envisioning the MWI, but it looks to me like some people find it satisfying, and others don't.

[MorpheusSandman]

I'm afraid I'm not sure how we got from science to philosophy, unless there's so little basis for these various quantum-related theories that that's the only option.

Perhaps I misunderstood, but your questions seemed more philosophical in nature than purely scientific. At least, the whole question of "who do we believe/how do we choose is more likely right" is a philosophical issue that transcends science itself. The distinction to made is that MW and Copenhagen are "interpretations" of QP and not "theories." They're all looking at the same experimental data and offering explanations that are consistent, but, AFAIK, there are still no valid testing methods to choose between them. There was even a joke about this on The Big Bang Theory:

Penny: So, what's new in the world of physics?
Leonard: Nothing.
Penny: Really, nothing?
Leonard: Well, with the exception of string theory, not much has happened since the 1930s and you can't prove string theory. At best you can, "Hey, look, my idea has an internal logical consistency."
Penny: Well, I'm sure things will pick up.

Now, I do know of the idea of quantum computing, which may be able to eventually provide a basis for testing MW. However, I think the reason that MW is becoming favored is because, at the core, it's a far simpler theory that removes a lot of mysteries by simply not taking the WF collapse for granted. Merely assuming that the WF is real, is an object itself, rather than something that's indeterminate until we measure it (making our mere observation the force behind every quantum event observed; which is horribly anthropomorphic thinking), makes all of the other aspects of MW a consequence. People don't like/don't get the consequences, so that's why I think there's so much enmity towards it. Plus, most of the classical theories were quite well entrenched before MW came along, and science is like any other discipline in that it can be slow to shift its paradigms even when clearly better answers are first presented--but that's especially true with something like MW and QP where we don't yet have adequate testing means.

[YesNo]

Like a few posts ago, the key thing to keep in mind here is the difference between "subjective determinism" and "objective determinism", I think. In the MWI, things seem indeterminate because we are taking the measurements in one particular world. We can't inhabit/experience all of the worlds, only one. Since the worlds are different, we subjectively experience "random"/indeterminate measurements over time, our world is unique in comparison to the others, and the particulars are revealed to us as we check on them. From the perspective of the theory, though, all of the branches occur and represent a deterministic unfolding of events. It is all there, from the perspective of the MWI--however the particular world in which this particular version of you and I occur is just one out of many, and for us, with our limited perspective, events are subjectively indeterminate.

The "subjective" adjective makes me think of something that is not-real or that is an illusion. I do think that is what MWI is trying to say: The indeterminacy evidence in the double slit experiment is an illusion; if we could only see the real, objective reality, we would see it as determinate.

However, the use of the wave function makes me think this is misguided, at least the way MWI is approaching it. The Heisenberg uncertainty principle is mathematically derived from the Schrodinger wave function. So, if anyone, including MWI, uses a wave function to mathematically describe reality, the reality that they describe is indeterminate. It cannot be determinate. It is part of the mathematics of the formalism. For MWI to be correct there must be some non-wave mathematical formalism that simulates the illusion of the mathematical wave formalism. I don't think such a formalism is possible. If it were, we would have it by now.

Now I don't see MWI providing an alternate mathematical formulation. They even claim there is a universal wave function or that the wave function splits because of its linear nature, but in either case they still have a wave function either at the universal level or at the split component level.

They have not formulated their interpretation to avoid indeterminacy. They only claim they have.

For a different, but I think analogous, example: Imagine we had an enormous mansion with thousands of rooms. In each room we have a table and an unstarted game of checkers set-up on a table, as well as an (undoubtedly patient) observer in each room. I think there are six possible moves for the first player to make, and so we could go to each room, performing one of the six different moves in each room after the other--moves 1 to 6 each in the appropriately numbered rooms 1 to 6--and then repeated them for the next six rooms and so on for some time. Then we could try out the next possible move on the board, and distribute the possibilities across the games just underway in the succeeding rooms. For us, it would be a systematic way to play-out the early moves of each possible checkers game (each room being a slight variation from some other room), but for the observers the game taking place before them in their particular room would appear random. In that enormous Checkers Mansion, we have arranged things so that the games are objectively deterministic, but subjectively indeterministic to observers in particular rooms.

This is a good example of the problem that I have with MWI. Consider all these checker games. They represent discrete outcomes and behave much as particles do. I agree that they can be represented in a deterministic way.

Now ask yourself, how would these checker games interfere with each other? In the case of the checker games, they really don't interfere at all. But if they were particles, such as bullets going through a double hole experiment, one could see them interfering with each other as particles would. That is, they would bounce off each other and in general create a scattered pattern on the detector wall. As particles they would not create a wave pattern which is more orderly than the scattered pattern of particles bouncing off each other.

In order to get the subjective indeterministic wave pattern it takes more than many particles interacting deterministically. That is why MWI is an incorrect interpretation of QM and to the extent that it continues to use wave functions is not even deterministic.

[mal4mac]

However, the use of the wave function makes me think this is misguided, at least the way MWI is approaching it. The Heisenberg uncertainty principle is mathematically derived from the Schrodinger wave function. So, if anyone, including MWI, uses a wave function to mathematically describe reality, the reality that they describe is indeterminate. It cannot be determinate. It is part of the mathematics of the formalism. For MWI to be correct there must be some non-wave mathematical formalism that simulates the illusion of the mathematical wave formalism. I don't think such a formalism is possible. If it were, we would have it by now.

Now I don't see MWI providing an alternate mathematical formulation. They even claim there is a universal wave function or that the wave function splits because of its linear nature, but in either case they still have a wave function either at the universal level or at the split component level.

Have a glance at a few MWI papers. Of course there is mathematical formalism! If there isn't it's just not physics...

Actually, can't you just use the wave equation? In one universe its indeterministic, but if there are many universes then *all* solutions are instantiated, i.e. determined.

[billl]

Anyhow, Yes/No, I tried. I don't think I can do much better. It should be obvious that Everett was never at all sheepish about involving the wave function in the MWI--it is an absolutely essential and core part of MWI and part and parcel of his inspiration in formulating it. The interference between versions of a particle might be strange/mysterious (it obviously is), and you might not see reason to consider it as a reasonable interpretation, but for many people it is preferable to other strange/mysterious interpretations. If you believe that the MWI is not determinate, I don't know what more to do to help get you past that, but it is obviously an indication that you're still struggling with this.