Improbability of the Many-Worlds Interpretation?

[akvadrako]

No. Or at least, if you're going to allow for that possibility, then you are allowing for possibilities that invalidate our belief in past data, and that version of the MWI undermines itself, as I argued in post #24. The chance that enough of the molecules will happen to all have tunneled into the "can't fire" state, and none of them will have tunneled back into the "can fire" state, at the exact instant that you try to fire the bullet, is comparable to the chance that @DrChinese actually was president of the US 5 minutes ago, but then a quantum fluctuation happened that changed everything on Earth, including all of our memories, to the state we all perceive and remember now. And if you allow for possibilities like that, all bets are off and there's no point in doing science at all.

I don't think taking MWI literally requires the assumption that every massive tunneling event is realized. Incredibly unlikely things might not be stable enough to form recognizable branches, the interference effects might be too strong before they fully split, or they might not contain something that can be considered a future version of one's self, so must be ignored.

Looking at it backwards is also helpful. Maybe there is a very small contribution to my current state from almost-orthogonal past states where Dr. Chinese was president. But that past state is so incompatible with my current personal state (containing my memories) the contribution will be too small to notice.

I'm not suggesting these are solved problems, because I suspect one needs to really understand how people perceive the world and form their sense of self to fully connect objective unitary evolution to the subjective experience of life inside that universe.

 

[akvadrako]

"Everything" and "rules" meaning what exactly?

I also wouldn't connect a clarification request from me about what exactly you were referring to to be related in any way to what physicists think about or don't think about. I just wasn't sure precisely what you meant.

I see; sometimes I'm just surprised by what things I say turn out to be least clear :) I meant once you have a way to try every possible program, you have the power to do (almost) anything not ruled out by the laws of physics.

 

[Hans de Vries]

Perhaps you should read this first:
It might save you from tilting at straw men.

I know Sean Carrol's arguments but quote:

Everett, by contrast, says that the universe splits in two: in one the cat is awake, and in the other the cat is asleep. Once split, the universes go their own ways, never to interact with each other again.

I don't see how Sean Carrol's following arguments help in anyway:

1) All universes are in superposition and superposition is normal in QM
2) In any universe all particles are entangled so they can't interact with particles in other universes.
3) And because of decoherence particles in one universe do not interfere with particles in other universes.

- At the end you need the same amount of independent universes. Since the splitting started right at the big bang we can be assured that universes are totally different from each other.

- The entanglement claim does not hold. Only certain properties can be entangled and momentum is not one of them. You can reflect entangled photons on mirrors, guide them through glass fiber and so on. I don't see how entanglement justifies the claim that particles can not interact with each other anymore. It's just a subset of their properties that is entangled.

- Also the decoherence argument for non-interference runs counter to accepted physics. A particle in two worlds may obtain different momentum states in each world. In QED, and subsequently QFT, a particle in a superposition of 2 momentum states gives rise to interference currents which are the source of the bosons of the Standard model.

The rest of the article is rather denigrating and political. It goes about the skeptics emotional states: "angry", "denial" and finally "acceptance". The latter is of course to accept the Everettian MWI approach and to forget the "silly" objections.Finally: I do not choose sides with any of the quantum philosophical interpretations, simple because I'm highly skeptical to all of them

 

[PeroK]

I know Sean Carrol's arguments but quote:
I don't see how Sean Carrol's following arguments help in anyway:

1) All universes are in superposition and superposition is normal in QM
2) In any universe all particles are entangled so they can't interact with particles in other universes.
3) And because of decoherence particles in one universe do not interfere with particles in other universes.

I must confess, I find this post quite bizarre. I'm not an advocate of MWI, nor do I know the Carrol piece particularly well. But, my first reaction was "I didn't think he said any of that". So, I went back to his blog, and nothing you ascribe to him he actually says!

Those three points, as far as I can tell, are entirely your own invention!

My understanding of Carrol's argument (reading what he actually says) is:

Fundamentally, despite its name, in MWI there is only one universe. But, it contains ultimately a superposition of all (measurement) outcomes. Like orthodox QM does before you measure it. Unlike orthodox QM, the superposition is never resolved, but continues indefinitely.

In the infamous cat experiment, there is only ever one cat. It's the state (of the particles that make up the cat) that is in superposition; not that an extra cat has been brought into existence. When you open the box, in orthodox QM the state resolves itself in one or the other. In MWI, the two possibilities continue to exist, in some sense - but, through decoherence, there is no subsequent mixing of the two possibilities

It's the branches of the wave function that decohere, so that they do not in general interfere with each other. Not that new universes of trillions of particles are continuously created.

PS the crux of Carrol's argument is here (direct quotation, with my underlines):

"All of this exposition is building up to the following point: in order to describe a quantum state that includes two non-interacting “worlds” as in (2), we didn’t have to add anything at all to our description of the universe, unlike the classical case. All of the ingredients were already there!"

 

[Hans de Vries]

I must confess, I find this post quite bizarre. I'm not an advocate of MWI, nor do I know the Carrol piece particularly well. But, my first reaction was "I didn't think he said any of that". So, I went back to his blog, and nothing you ascribe to him he actually says!

Those three points, as far as I can tell, are entirely your own invention!

I would urge you to read carefully through the text as accurate and painstakingly as I have done (and anybody can do in the link at the bottom), before you come out in the aggressive way you did. Let's carefully go through the 3 statements (as I ascribed them to Carrol) one by one:

1) All universes are in superposition and superposition is normal in QM

First Carrol comes up with the theory that both particle and observer (apparatus or human) are in a superposition state with different versions of them self:

But there is clearly another possibility. If the particle can be in a superposition of two states, then so can the apparatus...What would it be like to live in a world with the kind of quantum state we have written in (2)? It might seem a bit unrealistic at first glance; after all, when we observe real-world quantum systems it always feels like we see one outcome or the other. We never think that we ourselves are in a superposition of having achieved different measurement outcomes.

If the human being is already in superposition after the split then both human beings need their own versions of the universe because:

Everett, by contrast, says that the universe splits in two: in one the cat is awake, and in the other the cat is asleep. Once split, the universes go their own ways, never to interact with each other again.

2) In any universe all particles are entangled so they can't interact with particles in other universes.

But there is clearly another possibility. If the particle can be in a superposition of two states, then so can the apparatus.... There are more things in the universe than our particle and the measuring apparatus; there is the rest of the Earth, and for that matter everything in outer space. That stuff — group it all together and call it the “environment” ... We expect the apparatus to quickly become entangled with the environment, if only because photons and air molecules in the environment will keep bumping into the apparatus. As a result, even though a state of this form is in a superposition, the two different pieces (one with the particle spin-up, one with the particle spin-down) will never be able to interfere with each other

Here we see that the apparatus (or human observer) is expected by Carrol to become entangled with the environment which includes "everything in outer space". The second odd thing here is that, while Carrol mentions entanglement, A particle spin-up never interferes with particle spin-down because the two states are orthogonal. This is a very well known property of the Dirac field! Entanglement has nothing to do with this !

3) And because of decoherence particles in one universe do not interfere with particles in other universes.

This is where the magic of decoherence comes in... As a result, even though a state of this form is in a superposition, the two different pieces (one with the particle spin-up, one with the particle spin-down) will never be able to interfere with each other. Interference (different parts of the wave function canceling each other out) demands a precise alignment of the quantum states, and once we lose information into the environment that (interference) becomes impossible. That’s decoherence

Here Carrol blames decoherence for the loss of interference between the two states in superposition.

My advice would be (to Carrol as well) : Study at least QED.http://www.preposterousuniverse.com...ion-of-quantum-mechanics-is-probably-correct/

 

[PeterDonis]

I don't think taking MWI literally requires the assumption that every massive tunneling event is realized

Perhaps not, but many MWI proponents seem to talk as if it does.

 

[PeterDonis]

Only certain properties can be entangled and momentum is not one of them.

Where are you getting this from? Momentum can certainly be entangled. To give just two examples: in a Stern-Gerlach apparatus, the momentum of a particle like an electron is entangled with its spin; and in a process where two photons are created by particle-antiparticle pair annihilation, the momenta of the two photons are entangled since they must sum to zero in the center of mass frame.

 

[Hans de Vries]

Where are you getting this from? Momentum can certainly be entangled. To give just two examples: in a Stern-Gerlach apparatus, the momentum of a particle like an electron is entangled with its spin;

and in a process where two photons are created by particle-antiparticle pair annihilation, the momenta of the two photons are entangled since they must sum to zero in the center of mass frame.

It's not as simple as just energy conservation. Do you have an example of a correlation experiment using momentum as an entangled quantum state?

 

[PeterDonis]

Do you have an example of a correlation experiment using momentum as an entangled quantum state?

The first example I gave is an experiment that has been done.

The second example I gave might not have been realized in precisely the form I gave it, but since it's just an example of momentum conservation (not energy conservation), and momentum conservation has been verified by countless experiments, I don't see what the issue is.

 

[Hans de Vries]

The first example I gave is an experiment that has been done.

The second example I gave might not have been realized in precisely the form I gave it, but since it's just an example of momentum conservation (not energy conservation), and momentum conservation has been verified by countless experiments, I don't see what the issue is.

Well yes, that is of course that's what I wanted to say: It's more than just momentum conservation.

One would expect at least some "action-at-a-distance" correlation effect in need for an explanation. For instance a higher probability that both green detectors go off or both red detectors go off because the entanglement relation maintains the momentum relation somehow at a distance, even after going through the mirrors. What is entanglement without "action-at-a-distance"? I'm sure if you do this experiment that you won't see this kind of correlation though. It is just some example.

Note that I made the remark to counter the claim suggesting there is no interaction possible when all particles in a superposition states are entangled. This clearly suggests an "action-on-a-distance" for momentum which I do not believe to be correct.

 

[PeroK]

I would urge you to read carefully through the text as accurate and painstakingly as I have done (and anybody can do in the link at the bottom), before you come out in the aggressive way you did. Let's carefully go through the 3 statements (as I ascribed them to Carrol) one by one:

1) All universes are in superposition and superposition is normal in QM

Carrol does not say this.

2) In any universe all particles are entangled so they can't interact with particles in other universes.

Carrol does not say this either. This is your interpretation of MWI.

3) And because of decoherence particles in one universe do not interfere with particles in other universes.

Carrol does not say this either.

I fail to see the connection between Carrol's text and your analysis of it. In fact, your analysis is precisely the misunderstanding of MWI that his blog was intended to address.

You are free to believe that all the advocates of MWI are either mad or ignorant. But, I don't buy that. I don't buy that you know so much more about QM that its professional advocates. Especially, as it seems quite clear to me you are tilting at a straw man of your own creation.

 

[PeterDonis]

One would expect at least some "action-at-a-distance" correlation effect in need for an explanation.

This is true of any experiment involving spacelike separated measurements on entangled particles, since any such experiment can produce correlations which violate the relevant Bell inequalities.

This clearly suggests an "action-on-a-distance" for momentum which I do not believe to be correct.

Then you evidently don't believe in conservation of momentum, since conservation of momentum plays the same role in an experiment involving momentum entanglement that conservation of angular momentum plays in an experiment involving spin entanglement. The "action at a distance" effect on correlations is the same in both cases.

 

[Hans de Vries]

Then you evidently don't believe in conservation of momentum, since conservation of momentum plays the same role in an experiment involving momentum entanglement that conservation of angular momentum plays in an experiment involving spin entanglement. The "action at a distance" effect on correlations is the same in both cases.

Conservation of momentum is maintained at all times, always. One of the most basic laws of nature. Who would ever make such a ridiculous claim?

- Momentum can also be absorbed by the silver mirrors.
- Angular momentum can be absorbed by Wollaston prisms.

So a loss of correlation at the detectors does not violate any conservation laws.

 

[PeterDonis]

For instance a higher probability that both green detectors go off or both red detectors go off because the entanglement relation maintains the momentum relation somehow at a distance, even after going through the mirrors

The photons can transfer momentum to the mirrors, so once they are involved the momentum of the two photons by themselves is not necessarily conserved.

 

[PeterDonis]

a loss of correlation at the detectors does not violate any conservation laws

Indeed, as I just posted myself in response to you. Which simply means this experiment is not a good one for testing momentum entanglement. But if you take out the mirrors, and just use pairs of detectors in opposite directions, and do coincidence counting, it is.

 

[Michael Price]

It's not clear to me that Michael Price is saying Dr. Chinese is president right now. For me that doesn't make sense, since he clearly isn't president based on the information contained in this lab. I'm not even sure you can compare times between different worlds as they are casually disconnected from the point of branching.

Dr Chinese is President of the US in some parallel timelines right now, in the sense that those timelines use our dating system and show a date of 2019.

 

[Michael Price]

But I also think you can't just consider classical evolution since inflation. When people perform quantum measurements now, it forms new branches. This is most clearly true when people use quantum outcomes to make macroscopic decisions. It's not clear if you are suggesting an alternative view, where quantum outcomes are overwhelmed by classical evolution and the branch we are living in is actually deterministic.

I also think quantum branching and decoherence is ubiquitous, though it's more controversial. This is based on the only analysis I've seen on the topic, which I linked in the other linked thread, looking at how the average coin flip is an amplification of quantum uncertainty.

Yes, and this branching occurs not just at quantum measurements, but at every entropic event.
PS, nice article.

 

[Michael Price]

.
The point I'm making is that all this blithe talk about "multiple worlds" fails to pay attention to specifically how such multiple worlds get created, if the MWI is true. They don't get created by magic. They don't get created just because we humans can imagine them. They get created by having genuine quantum mechanical uncertainty, "

Of course these multiple worlds (or timelines, as I prefer) don't get created by magic. I am at a loss to see why you thought I said or implied otherwise.

 

[Quanundrum]

Of course these multiple worlds (or timelines, as I prefer) don't get created by magic. I am at a loss to see why you thought I said or implied otherwise.

So what you contend is essentially that at least one of the branches that branch from THIS exact universe at THIS exact moment will reconfigure all particles in our lightcone to put you in the white house and every citizen of Earth will have their brain (again just particle reconfiguration) filled with memories where Michael Price (or whoever else) as president make sense. Right?

 

[Mentz114]

Dr Chinese is President of the US in some parallel timelines right now, in the sense that those timelines use our dating system and show a date of 2019.

How can possibly claim that from the laws of physics ? Are you a clairvoyant now ?

Being so certain in your proclamations is not becoming in a scientist.

 

[PeterDonis]

Dr Chinese is President of the US in some parallel timelines right now, in the sense that those timelines use our dating system and show a date of 2019.

Sorry, but I've already made several posts explaining why this claim is extremely implausible. I can't prove it's wrong, but you can't prove it's correct either, because neither of us knows the universal wave function and what possibilities it includes.

Of course these multiple worlds (or timelines, as I prefer) don't get created by magic. I am at a loss to see why you thought I said or implied otherwise.

Because you keep helping yourself to extremely extravagant claims like the one quoted at the top of this post. If you want to avoid people thinking that you are making dubious claims, you should not make dubious claims.

 

[PeroK]

Sorry, but I've already made several posts explaining why this claim is extremely implausible. I can't prove it's wrong, but you can't prove it's correct either, because neither of us knows the universal wave function and what possibilities it includes.
Because you keep helping yourself to extremely extravagant claims like the one quoted at the top of this post. If you want to avoid people thinking that you are making dubious claims, you should not make dubious claims.

Just to be on the safe side, it might be worth PF putting in some software that plays "Hail to the Chief" everytime @DrChinese makes a post.

 

[PeterDonis]

this branching occurs not just at quantum measurements, but at every entropic event

First, "entropic event" is not well-defined.

Second, in order for this to justify your much more extravagant claim about there being a world in which @DrChinese is president right now, you have to claim that there is a possible sequence of "entropic events" that can generate, from some common starting point, both the world we are actually in, and an alternate world in which @DrChinese is president right now, but which is similar enough in all other respects to make that description a reasonable one. And you can't possibly justify such a claim; you're just waving your hands and helping yourself to it without any consideration of whether it's actually at all plausible.

 

[Michael Price]

How can [you] possibly claim that from the laws of physics ? Are you a clairvoyant now ?

Being so certain in your proclamations is not becoming in a scientist.

This claim, in the context of MWI, is no more extravagant than the claim that such occurrence is possible from a spontaneous random rearrangement of molecules in the Copenhagen interpretation. How this any different from saying that all the gas molecules in a chamber could suddenly bunch up in one small portion of the chamber? Such claims are often made in textbooks and seen as quite unremarkable.

 

[Michael Price]

So what you contend is essentially that at least one of the branches that branch from THIS exact universe at THIS exact moment will reconfigure all particles in our lightcone to put you in the white house and every citizen of Earth will have their brain (again just particle reconfiguration) filled with memories where Michael Price (or whoever else) as president make sense. Right?

Sounds about right. In the context of MWI...

 

[PeterDonis]

How this any different from saying that all the gas molecules in a chamber could suddenly bunch up in one small portion of the chamber?

Saying that this could happen once in $10^{70}$ years or something is not the same as saying there's a world right now in which it is happening.

 

[PeterDonis]

Sounds about right. In the context of MWI...

Which, as I've already pointed out, means that the MWI undermines itself, since allowing for the possibility of quantum fluctuations like this means we cannot trust our memories and records of past data, and if we can't trust our memories and records of past data, we have no reason to accept that QM is true in the first place, let alone the MWI interpretation of it.

 

[Michael Price]

Saying that this could happen once in $10^{70}$ years or something is not the same as saying there's a world right now in which it is happening.

We shall have to agree to disagree about this.

 

[PeterDonis]

We shall have to agree to disagree about this.

I don't see why. Saying that it could happen once in $10^{70}$ years or something is different from saying it is happening at every instant. Your claim is equivalent to saying it is happening at every instant, because your claim is that, for anything that has a nonzero quantum amplitude, there is some world at every instant in which it is happening. Can you seriously not see the difference between that claim and the (much, much, much less extravagant) claim that it could happen once in $10^{70}$ years or so?

 

[charters]

I don't see why. Saying that it could happen once in $10^{70}$ years or something is different from saying it is happening at every instant. Your claim is equivalent to saying it is happening at every instant, because your claim is that, for anything that has a nonzero quantum amplitude, there is some world at every instant in which it is happening. Can you seriously not see the difference between that claim and the (much, much, much less extravagant) claim that it could happen once in $10^{70}$ years or so?

What about the issue that in a single world which is an infinite flat or open universe, there will, with unit probability, be some planet somewhere on which such fluctuations occur much more often? I think even in a single world interpretation, saying an event happens once in $10^{70}$ years requires a typicality assumption for your observer. But in a (fairly generic) cosmology that admits infinite observers, you can't guarantee this for every observer, just as MWI can't guarantee typicality for all branches.

 

[Quanundrum]

What about the issue that in a single world which is an infinite flat or open universe, there will, with unit probability, be some planet somewhere on which such fluctuations occur much more often? I think even in a single world interpretation, saying an event happens once in $10^{70}$ years requires a typicality assumption for your observer. But in a (fairly generic) cosmology that admits infinite observers, you can't guarantee this for every observer, just as MWI can't guarantee typicality for all branches.

I, personally, think this is a fallacy. In an infinite spacious universe (flat topology + inflation) these events would indeed occur. Guaranteed. In fact they would not only occur, but do so INFINITELY times over. However, as it pertains to MWI the question boils down to whether you can justify this claim based solely on the wavefunction evolution in Hilbert Space or 3D space (as the numero uno leading candidate: David Wallace is in favor of). It's not a matter of human psychology and preference, but a very ontological one that has never been addressed to any serious philosophers degree...

 

[PeterDonis]

What about the issue that in a single world which is an infinite flat or open universe, there will, with unit probability, be some planet somewhere on which such fluctuations occur much more often?

Why?

I think even in a single world interpretation, saying an event happens once in $10^{70}$ years requires a typicality assumption for your observer.

No, it doesn't, it just requires that the probability of the event is very low. In an infinite universe, yes, there will be somewhere (roughly one in $10^{70}$ places, with the specific number I gave) which experiences a fluctuation of this sort. But in any given place, it will still only occur once in $10^{70}$ years, roughly. There won't be any single place where it occurs much more often.

Also, even in a single world infinite universe, saying "everything occurs someplace" is still misleading, because it's still a single universe which is evolving, and there are lots of other things that will happen with much, much higher probabilities than one in $10^{70}$ years that will prevent things like the gas all bunching up in one corner from ever happening. So even with an infinite number of places for things to happen, it's still not guaranteed that everything happens somewhere; for example, on average, in every place it still takes $10^{70}$ years for gas to bunch up in one corner, and the gas simply won't remain undisturbed in the same container for that long, by many, many orders of magnitude. Too many other things will happen to it first.

 

[PeterDonis]

In an infinite spacious universe (flat topology + inflation) these events would indeed occur. Guaranteed. In fact they would not only occur, but do so INFINITELY times over.

Not necessarily; see my previous post just now in response to @charters.

Basically, the argument you are making here has an implicit assumption: that the universe overall remains the same, or close enough to being the same, for a long enough time. But that assumption is false for our universe; our universe is evolving and will simply not remain the same long enough for lots of these low probability events to ever happen, even though it is (according to our best current models) spatially infinite.

 

[charters]

But in any given place, it will still only occur once in 1070107010^{70} years, roughly. There won't be any single place where it occurs much more often.

I think there will be places where it occurs more often. In an infinite universe, there will be some place where an arbitrarily long string of very low Born weight events happen in close succession, and observers there come to different inductive conclusions. It is the same as how there is some unlucky planet where every Stern Gerlach experiment they ever do comes back spin-up (except prepared spin-down particles of course), and they never get experimental confirmation of basic QM.

But also, what you say above is true in MWI too. There will be a vanishingly small number of MWI branches where any observer sees a freak macroscopic fluctuations happen once, let alone twice, so an MWI expects to never actually see this happen, same as a Copenhagen observer. So I don't think these fluctuations in MWI necessarily undermine the trustworthiness of quantum theory any *more* than other interpretations.

 

[PeterDonis]

In an infinite universe, there will be some place where an arbitrarily long string of very low Born weight events happen in close succession

According to the MWI, or at least an extravagant enough version of it, yes, this will be true. But not in a single world. In a single world infinite universe, there will be some place where low probability events happen (assuming that no other higher probability events make them impossible--see my previous posts), but there will not be any place where lots of low probability events happen in succession.

There will be a vanishingly small number of MWI branches where any observer sees a freak macroscopic fluctuations happen once, let alone twice, so an MWI expects to never actually see this happen

No, this is not the same. In the MWI, all possible branches from a given quantum uncertainty point happen, so it makes no sense to say that an MWI observer "expects" to see only the high probability ones. If the MWI observer can rationally expect anything, it is to be split into multiple decoherent copies, each of which will experience one of the possible results. And if there are, say, twenty branch points in succession (say Stern-Gerlach measurements on twenty successive electrons), then the MWI observer expects to split into $2^{20}$ copies, each of which will experience one of the $2^{20}$ possible sequences of measurement results. One of the key issues with the MWI is how to make sense of the concept of "probability" and the Born rule at all given that every measurement outcome happens.

 

[PeterDonis]

There will be a vanishingly small number of MWI branches

Another way of putting my objection to this is: no observer in the MWI knows the weight of his branch relative to all the other branches. So the "vanishingly small" here can never be measured. The weights have to be put in by hand by assuming the initial quantum state and evolving it by unitary evolution; but since we have no way of measuring the weights in the MWI, we have no way of actually knowing that our assumptions about initial quantum states are valid.

To put it in stark terms: suppose I measure a sequence of, say, a million qubits, and obtain a million "up" results in a row. In standard QM, that tells me that the source is producing pure spin up qubits. Under the MWI, however, I cannot deduce that; all I can deduce is that the source is not producing pure spin down qubits. But since I can't measure the weights of the other MWI branches, the source could be producing qubits in any state that is not pure spin down, i.e., any state that is not exactly orthogonal to spin up. So all of our experimental protocols for determining what quantum states are produced by various sources go out the window.

 

[charters]

One of the key issues with the MWI is how to make sense of the concept of "probability" and the Born rule at all given that every measurement outcome happens.

That's fair, but I think this is distinct from what I took to be the topic above, namely: if MWI allows a sensible notion of probability, as is necessary to take it seriously, do very low probability "record-changing fluctuations" constitute a bigger problem in MWI than elsewhere? I'm not convinced they do.

In a single world infinite universe, there will be some place where low probability events happen (assuming that no other higher probability events make them impossible--see my previous posts), but there will not be any place where lots of low probability events happen in succession.

I don't know about this. I think in a truly infinite universe, you can always find a patch where an arbitrarily long string of measurements or quantum events has deviated arbitrarily far from the expectation value. Seems like gambler's fallacy to claim otherwise.

 

[PeterDonis]

if MWI allows a sensible notion of probability, as is necessary to take it seriously, do very low probability "record-changing fluctuations" constitute a bigger problem in MWI than elsewhere? I'm not convinced they do.

I think they do because the MWI does not support the common sense notion of probability that comes into play in the single world case.

I think in a truly infinite universe, you can always find a patch where an arbitrarily long string of measurements or quantum events has deviated arbitrarily far from the expectation value.

Again, this assumes that all other conditions stay the same while all this is going on. But in our universe, they don't. Our universe evolves.

 

[PeroK]

I, personally, think this is a fallacy. In an infinite spacious universe (flat topology + inflation) these events would indeed occur. Guaranteed. In fact they would not only occur, but do so INFINITELY times over. However, as it pertains to MWI the question boils down to whether you can justify this claim based solely on the wavefunction evolution in Hilbert Space or 3D space (as the numero uno leading candidate: David Wallace is in favor of). It's not a matter of human psychology and preference, but a very ontological one that has never been addressed to any serious philosophers degree...

I don't think this is necessarily true. There are, in my opinion, problems with this argument, as follows:

If we take an infinite sequence of random 0's and 1's (equal probability), then (mathematically) it's true that for any $n$ there is a run of $n$ successive 1's. But, that is a mathematical statement. It's not physically possible to generate an infinite sequence.

But, of course, if $n = 100$, say, then in theory you could run a computer program for a certain time and have a probability of $0.99$, say, of getting $100$ 1's in a row. Note, in passing, that using a conventional coin and let's say 1 toss per second, when the universe expires, the probability of getting 100 heads in a road at some point is vanishingly small. I.e. for all practial purposes it can only be done on a computer simulation.

But, $100$ heads in a row is small scale compared to the random events talked about in this thread. For example, if we want all the air molecules in a room to occupy only on half of the room for an hour (or, perhaps only a minute or even a second), then the probability is much smaller.

In this case, if you run a computer simulation, let's say doing one calculation per Planck unit of time, then when the universe expires, the probability of the simulation having generated the required result is still vanishingly small.

To get to the point:

We have random quantum events that we have no realistic hope of ever actually seeing. And, in fact, we have no realistic hope of ever generating them in any computer simulation.

Now, the trick is, of course, to postulate an infinite universe, with an infinite number of trials being carried out simultaneously. Apparently, therefore, it is possible to physically generate an infinite sequence. An infinite universe is doing this all the time.

The issue I want to raise is the validity of this as an application of probability theory and processing this information in a physical context.

Let's assume we have an infinite number of planets in the universe. Let's say we just want one piece of data - mass to the nearest $kg$, say. But, that's an infinite amount of information. We cannot process that data. You might say there are "an infinite number of planets with the same mass as the Earth". And, in some mathematical sense that might be true, but we cannot confirm that in the data. All we can do with the data is look at a finite subset and find a finite number of planets with the same mass as the Earth.

In short, "there are an infinite number of planets with the same mass as the Earth" is a statement about a mathematical model of the universe that is not physically verifiable (even theoretically there is no way to verify this claim).

To get to my second point. Now we consider one of these rare quantum events. And we want to find a planet where this has happened. We reach the same problem as before. If we go out into the universe in all directions at near the speed of light checking planets, then that is a hopeless task. When the universe expires we will almost certainly have found nothing unusual, let alone anything resembling the extravagently rare event that we are looking for.

We can even move to computer simulation of doing this. We don't need to find it in reality, all we need is our computer simulation (which can only proceed planet by planet) to generate the event somewhere. But, we have the same problem as before. The universe expires and we still have simulated nothing resembling these rare events.

Let me summarise as follows:

There are clearly mathematical models that are not physically realisable. For example, Hilbert's Hotel and Gambler's Hell. You can do stuff mathematically that does not represent stuff you can do physically and, in that sense, these models do not represent a reality in our universe.

The question in my mind is whether the naive model of an infinite universe in which "everything happens" (and the model of an infinitely branching wave function in which "everything happens") are purely mathematical in nature and do not represent reality in our universe.

This may turn out to be a philosophical question, but I think it is worth challenging the application of probability theory and data processing in both these cases.

 

[Michael Price]

I don't see why. Saying that it could happen once in $10^{70}$ years or something is different from saying it is happening at every instant. Your claim is equivalent to saying it is happening at every instant, because your claim is that, for anything that has a nonzero quantum amplitude, there is some world at every instant in which it is happening. Can you seriously not see the difference between that claim and the (much, much, much less extravagant) claim that it could happen once in $10^{70}$ years or so?

In the gas in a chamber example, yes, in anyone world if it is likely to occur in $10^{70}$ years then it occurs in some worlds splitting off right now.

 

[PeroK]

In the gas in a chamber example, yes, in anyone world if it is likely to occur in $10^{70}$ years then it occurs in some worlds splitting off right now.

Although it may or may not be relevant to the debate, if we are talking about the probability that all the air molecules in a room occupy one half of the room for a second, then the probability is more of the order of once every $2^{10^{28}}$ seconds, as an absolute maximum.

The other question is whether the split is into a) a large but finite number of worlds; b) a countable infinity of worlds; c) an uncountable infinity of worlds (which would be consistent with position being a continuous variable).

On the face of it a) implies that there are only finitely many possibilities, which undermines (in my view) the claim that "everything happens".

And, b) and c) may run into issues in mapping the mathematics to a verifiable reality. See above and compare a mathematical idea like Hilbert's Hotel with an infinitely splitting set of worlds.

 

[Michael Price]

Although it may or may not be relevant to the debate, if we are talking about the probability that all the air molecules in a room occupy one half of the room for a second, then the probability is more of the order of once every $2^{10^{28}}$ seconds, as an absolute maximum.

The other question is whether the split is into a) a large but finite number of worlds; b) a countable infinity of worlds; c) an uncountable infinity of worlds (which would be consistent with position being a continuous variable).

On the face of it a) implies that there are only finitely many possibilities, which undermines (in my view) the claim that "everything happens".

And, b) and c) may run into issues in mapping the mathematics to a verifiable reality. See above and compare a mathematical idea like Hilbert's Hotel with an infinitely splitting set of worlds.

Everett's position was c), expressed at a conference, 1962, at Xavier University.

 

[PeterDonis]

In the gas in a chamber example, yes, in anyone world if it is likely to occur in $10^{70}$ years then it occurs in some worlds splitting off right now.

Only if you allow the possibility of this happening by a fantastically improbable quantum fluctuation, which, as I have already argued, makes the MWI undermine itself.

 

[Michael Price]

Only if you allow the possibility of this happening by a fantastically improbable quantum fluctuation, which, as I have already argued, makes the MWI undermine itself.

I responded to that argument but it got incomprehensibly moderated out.

 

[PeterDonis]

I responded to that argument but it got incomprehensibly moderated out.

That's because the moderators did not consider it an actual response but something approaching a troll. As far as further discussion in this thread is concerned, we'll just need to consider that subtopic closed.