# B Improbability of the Many-Worlds Interpretation?

#### PeterDonis

Mentor
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

Mentor
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.

#### PeterDonis

Mentor
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

Mentor
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

Mentor
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

Mentor
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

Mentor
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

Mentor
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

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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 any one world if it is likely to occur in $10^{70}$ years then it occurs in some worlds splitting off right now.

#### PeroK

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In the gas in a chamber example, yes, in any one 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

Mentor
In the gas in a chamber example, yes, in any one 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

Mentor
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.

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