QM Many Worlds Interpretation

Well OK, maybe the thread doesn't have to die an excruciating death, ... yet.

Help me understand something. I think of an object as a combination of bezillions of wave functions related to its particle composition, and as any movement occurs involving the object, those bezillions of wave functions are multiplied many times over each instant. Is that a faulty picture?

Now I think of the wave function as a set of possible, I guess we say the set of probable combinations of location/momentum of the particles.

So how many worlds are we talking about just to represent all of the possible combinations. For each instant, whatever an instant is, we have the bezillions of wave functions times all the possible location/momentum combinations of all the particles.

In MWI does each of the bezillions to the bezillionth power of possibilities of location/momentum combinations have a separate time line.

If so, then the following instant will present an impossible set of possibilities because the amount of energy in a given space is limited and the space occupied by the object at that instant is finite. This assumes that there must be enough energy in each time line to accommodate the presence of the object.

Or on the other hand are the MWI advocates saying that is not the case because each time line shares the energy and doesn't need to have incremental energy for multiple time lines even though the different time lines would diverge?
 
You bring up another problem (IMO) with MWI, and it's worse than you think. Think about atom decay - it's a quantum process but it isn't discrete at all. It can happen at any time along the continuum. This in itself would "produce" an infinite number of worlds based upon this single event. A system with 2 decaying atoms squares the number of worlds required to represent all possibilities. Very quickly you are presented with a number of worlds that is equal to infinity raised to the power of infinity or some such absurdity. On this point alone I would say MWI fails on economical grounds.
 
Yes, that is my response. The law of economy applies to the theory, not to its consequences.
 
...the principle recommends selecting the hypothesis that introduces the fewest assumptions and postulates the fewest entities
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Some would consider an infininite number raised to the infinite power as a significant number of entities required to represent reality in MWI.
 
RJBeery said:
Some would consider an infinite number raised to the infinite power as a significant number of entities required to represent reality in MWI.
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I consider that number a consequence, not a postulate.
 
And, I think that each "universe" isn't an entity in that context... like each individual atom isn't an entity in atomic theory.
 
I see it as a variable, but ok. Do you agree that we as conscious observers are capable of only experiencing a single "version" of reality? If you agree that each conscious "path" that our various Many World's conciousness takes represents a unique reality, then each reality can be expressed in terms of matter + energy from each conscious observer's perspective, agreed? Because these infinite worlds are created via the forward "arrow of time" in MWI (in other words, they did not all "always" exist), from whence does this infinite source of energy originate to generate these infinite new worlds? It's frankly hard for me to believe that you subscribe to the theory of MWI, Pete. :bugeye:
 
RJBeery said:
It's frankly hard for me to believe that you subscribe to the theory of MWI, Pete. :bugeye:
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I consider it an interesting possibility.
I don't understand the field enough to be able to either subscribe to or discount any interpretation of quantum weirdness.

I see it as a variable, but ok. Do you agree that we as conscious observers are capable of only experiencing a single "version" of reality? If you agree that each conscious "path" that our various Many World's conciousness takes represents a unique reality, then each reality can be expressed in terms of matter + energy from each conscious observer's perspective, agreed? Because these infinite worlds are created via the forward "arrow of time" in MWI (in other words, they did not all "always" exist), from whence does this infinite source of energy originate to generate these infinite new worlds?
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You're asking the wrong guy.
Where does any energy come from?
Why is mass energy conserved in any given interaction?
What does MWI imply about the global conservation of mass/energy?

Before you can answer those, you might need to consider...
How do we describe mass/energy in a universal wavefunction/superposition of states?
What did this wavefunction look like initially, and how does it evolve over time?



I suspect consciousness is probably irrelevant to MWI, but again, I don't know enough to have a strong opinion.
 
Yes, MWI is definitely thought provoking just as your questions are. What I was trying to get at last night has come to me in a more succinct description:

In a world with a single quantum event (let's stick with the half-silvered mirror), the photon is describable as a wavefunction. At the measurement event which would traditionally be called the "wavefunction collapse", we now have two completely divergent worlds - there is no wavefunction that describes the two together, and there is absolutely no correlation between the two. I think you and a couple of others may be under the impression that this "wavefunction" continues to describe ALL possible Universes, but the theory of MWI can only claim to describe multiple Universes while the quantum particle is in its state of superposition.

That isn't to say that a chair in the lab, for example, is indescribable as a wavefunction. But that wavefunction is distinct from the chair sitting in the lab that experienced a divergent wavefunction collapse measurement of the photon moving through the half-silvered mirror.

The point is that where we once had one chair, now we have two. Assuming that there is only a single chair existing across all possible Universes does not work. Therefore, as I see it MWI requires an infinite, constant source of new energy which just doesn't ring true.
 
RJBeery said:
Some would consider an infininite number raised to the infinite power as a significant number of entities required to represent reality in MWI.
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An infinite number is an infinite number. Raising it to a large power doesn't change that fact.

Special relativity predicts an infinite number of reference frames, for example.

Again, I will emphasize the point that Pete made: any interpretation of quantum mechanics has to do with how we try to understand the results, not with what the results are. In this sense, interpretations of quantum mechanics are very hard to test, and can never be proven right. (Wrong interpretations can be proven wrong, however.) In this sense, any quantum theory you write down has the ``problem'' that you point out, namely that a measurement can give (say) P different results, and N such measurements mean that there are P^N different outcomes.

The MWI (as I understand it) doesn't draw a line between classical and quantum. The cat becomes entangled with the atom, and we become entangled with the cat when we observe it, and so on. This is what I meant by ``The universe exists in some disgusting superposition of staes''. Sometimes the cat is alive, and sometimes it is not. The mystery is why we never see the cat in a superposition of ``alive'' and ``dead''---this state surely exists in the Hilbert space, but we never observe it.

Presumably, decoherence solves this problem, but I don't know anything about that interpretation.
 
And, Occam's Razor is more of a loose guideline, not a rule---usually, it is only invoked ex post facto. For example, we make a measurement that we don't understand, and lots of people build models to try and understand the experiment. Every model is different, and every model builder declares that their model is the ``minimal'' one needed to fit the data.

One only need to look at development of the Standard Model to see how Occam's Razor failed on so many attempts. You have to fit the data first, then you can bitch about minimalism.
 
Well there is certainly more than one type of infinity. It is true, though, that a minimal "countably" infinite number of required worlds required by MWI would be enough for me to reject it.
 
RJBeery said:
Well there is certainly more than one type of infinity.
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I'm pretty sure that it's irrelevant for this discussion.

And you're missing the point. There are not an infinite number of "worlds", there are an infinite number of possibilities.
 
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Well in posts 29 and 31 I was trying to make the case that IF a given conscious being in a particular "probability Universe" perceives a complete and real world (which they would by measurement), then that world exists; that world is distinct from other Universes and is no longer related to them by any Schrodinger wavefunction; ergo, there are an infinite number of Universes. The only time the multiple Universes are related by a wavefunction is before the split which occurs at the the quantum measurement. After the measurement, the two (or more) Universes go on about their business in a very divergent manner and are not related by a wavefunction.
 
That's not the many worlds interpretation works. Also your argument relies on consciousness, which has its own problems. You haven't defined the term, nor have you defined "probability Universe" nor have you defined "complete and real", (...) And your argument is based on an incomplete understanding of many worlds.
 
I don't need to define consciousness for my point to hold. Any measuring apparatus will create the "split" between two Universes which are initially related by the wavefunction of a quantum particle. "Complete and real" means that any aspect of the Universe is measurable (without giving a superpositional answer).

Why don't you give me your specific definition of MWI so I may consider it? I feel like the ball is being moved a bit because I was originally refuting the interpretation defined in this thread in post #3 which states that "every possible outcome to every event defines or exists in its own 'history' or 'world.'" Then you claimed that they weren't actually separate histories, but rather the whole mess is represented by some uberwavefunction. To say that two (or infinite) Universes are "related by an uberwavefunction" seems contradictory to their definition of being discrete possibilities of the results of quantum measurements.
 
RJBeery said:
I was originally refuting the interpretation defined in this thread in post #3 which states that "every possible outcome to every event defines or exists in its own 'history' or 'world.'"
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Ahh I see. Let me guess...this is what wikipedia says?

Then you claimed that they weren't actually separate histories, but rather the whole mess is represented by some uberwavefunction. To say that two (or infinite) Universes are "related by an uberwavefunction" seems contradictory to their definition of being discrete possibilities of the results of quantum measurements.
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From Everett's paper (Reviews of Modern Physics, vol. 29, 1957, p. 459)

Everett said:
We thus arrive at the following picture: Throughout all of a sequence of observation processes there is only one physical system representing the observer, yet there is no single unique state of the observer... Nevertheless, there is a representation in terms of a superposition, each element of which contains a definite observer state and a corresponding system state.
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The interpretation SHOULD be that the universe exists in a HUGE superposition of states, as I said when I first commented in this thread, here.

The next sentence, I'm sure, is the source of a lot of confusion:

Everett said:
Thus with each succeeding observation (or interaction), the observer state ``branches'' into a number of different states
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The interpretaiton is this: you put the cat in the box, there is a state in which you open the box and find the cat dead, and there is a state which you open the box and find the cat as alive. That's it.
 
BenTheMan said:
An infinite number is an infinite number. Raising it to a large power doesn't change that fact.

Special relativity predicts an infinite number of reference frames, for example.
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Having read Einstein's pronouncements concerning Special Relativity ad nauseum, I am totally perplexed to try to remember where, in all his illustrious texts, he predicted that Special Relativity predicts an infinite number of reference frames.

I am sure that you will be so gracious and so patient as to explain exactly where , in all the extant Einstein literature, Einstein stated that, as you say, Special Relativity predicts an infinite number of reference frames.

I am prepared to grant that Special Relativity allows any and every observer to have his very own personal reference frame. But, where does Special Relativity say, as you claim it does, that there are an infinite number of reference frame? Thereby implying, of course, that Special Relativity proves that the universe is infinite rather than bounded. Where in Special Relativity, according to your understanding of it, does it claim to prove that the universe is infinite rather than finite?
 
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