Quantum mechanics, many worlds, and its implications -- I have questions

[SDM88]

I don't have good references yet and am hoping you all can help me understand my pop-sci reading.

I have read that quantum mechanics implies that there is a very small probability that I can fall right through my chair, or suddenly appear on the moon among other crazy things. I subscribe to the many worlds theory, but I have a hard time accepting these things are possible. I'm curious to know if there are any theories that may accept many worlds, but not accept that things like falling through your chair is possible. Or maybe even if it is not forbidden by the laws of physics, it still does not happen in any universe.

I think it is possible that many worlds is true, but there are still an infinite number of seemingly possible universes do not happen. For example, people insist that if many worlds is true, there is a universe where instead of having toast for breakfast today, I actually had cereal. I do not accept that this is necessarily true. Are their theories that say many worlds is true, but not everything that seemingly has to happen does happen in another universe?

I would love to hear your thoughts!

 

[phinds]

even if it is not forbidden by the laws of physics, it still does not happen in any universe.

This

Also, since the various many worlds theories don't posit any testable conclusions I don't think they matter much.

 

[SDM88]

This

Also, since the various many worlds theories don't posit any testable conclusions I don't think they matter much.

Can you expand on this please? What is the reasoning in which things that are seemingly plausible might not happen in any universe?

 

[PeterDonis]

Moderator's note: Thread moved to the QM interpretations subforum.

 

[PeterDonis]

I have read

Where? Please give specific references. I realize that they will be pop sci references, and the simplest answer to that is to look at textbooks or peer-reviewed papers instead. But even leaving that aside, it will help us to understand your state of knowledge if we know which particular pop sci treatments you have read.

 

[PeterDonis]

I'm curious to know if there are any theories that may accept many worlds, but not accept that things like falling through your chair is possible.

Many worlds is an interpretation of quantum mechanics. So QM is the only "theory" under discussion if we are talking about many worlds.

I don't think there is a single consistent position within the many worlds interpretation on exactly what is possible, or in many worlds terms, what worlds are actually contained in the wave function of our actual universe. Just looking at the math, what is contained in the wave function now would depend on what was contained in it at the beginning of the universe, and it is not at all clear what that would have been. So I'm not sure it's possible to really answer questions along the lines you are asking. There are probably as many answers as there are many worlds advocates, if not more.

 

[SDM88]

Where? Please give specific references. I realize that they will be pop sci references, and the simplest answer to that is to look at textbooks or peer-reviewed papers instead. But even leaving that aside, it will help us to understand your state of knowledge if we know which particular pop sci treatments you have read.

Basically I have just watched a lot of different youtube videos over the years. I also have read Max Tegmark's Mathamatical Universe book. I understand the many worlds interpretation, I just don't have a great grasp of what kinds of worlds necessarily have to exist. I subscribe to many worlds, but I don't think we fall through our chair in any universe. I also question whether it is really possible to fall through our chair or if there maybe exist reasons unknown to us why that might not be possible.

 

[SDM88]

Many worlds is an interpretation of quantum mechanics. So QM is the only "theory" under discussion if we are talking about many worlds.

I don't think there is a single consistent position within the many worlds interpretation on exactly what is possible, or in many worlds terms, what worlds are actually contained in the wave function of our actual universe. Just looking at the math, what is contained in the wave function now would depend on what was contained in it at the beginning of the universe, and it is not at all clear what that would have been. So I'm not sure it's possible to really answer questions along the lines you are asking. There are probably as many answers as there are many worlds advocates, if not more.

Does this mean that their are scientists who disagree that QM implies we can fall through our chairs?

 

[PeterDonis]

Does this mean that their are scientists who disagree that QM implies we can fall through our chairs?

I think a better way to state it would be to ask what scientists, if any, have made such claims in actual peer-reviewed papers or textbooks. As far as I know, none have. So such claims are not "what science says". They are just particular scientists stating their personal opinions in a pop science context.

 

[Demystifier]

Are their theories that say many worlds is true, but not everything that seemingly has to happen does happen in another universe?

To my knowledge, there are no such theories.

 

[mitchell porter]

This discussion would be improved, if someone presented an actual calculation of the probability of "falling through one's chair" or something similar.

It would also be good if one looked at the situation, first from the perspective of the approximation that allows such a calculation, and then in a more realistic way. What I mean is that the easiest way to get a probability here, is to treat oneself as a point mass that will quantum tunnel through a potential barrier. But in reality, both human and chair consist of bazillions of atoms, and if we are going to think about tunneling events with vanishingly small probabilities, it might be worth remembering that tunneling events in which human and/or chair simply spontaneously disintegrate, will be far more numerous and probable (though still vanishingly unlikely), than the possibility under consideration (in which there is a macroscopic tunneling that leaves both human and chair intact).

I would also say that the phenomenon of outlandish things being logically possible, albeit extremely unlikely, already exists in deterministic classical theories. For example, it is logically possible that most of the atoms in the room will happen to head for one corner, and you will suffocate to death in the vacuum thereby created. But the odds of this are vanishingly low.

 

[PeroK]

I don't have good references yet and am hoping you all can help me understand my pop-sci reading.

I have read that quantum mechanics implies that there is a very small probability that I can fall right through my chair, or suddenly appear on the moon among other crazy things. I subscribe to the many worlds theory, but I have a hard time accepting these things are possible. I'm curious to know if there are any theories that may accept many worlds, but not accept that things like falling through your chair is possible. Or maybe even if it is not forbidden by the laws of physics, it still does not happen in any universe.

I think it is possible that many worlds is true, but there are still an infinite number of seemingly possible universes do not happen. For example, people insist that if many worlds is true, there is a universe where instead of having toast for breakfast today, I actually had cereal. I do not accept that this is necessarily true. Are their theories that say many worlds is true, but not everything that seemingly has to happen does happen in another universe?

I would love to hear your thoughts!

Ironically, there is no explanation for why you and your chair are solid in classical physics. It's QM that explains the solid state of matter in the first place.

You will eventually fall your chair. I've seen it myself once or twice where someone sits on a chair and it immediately collapses. That's nothing to do with QM, per se. That's because the chair must have previously been weakened to the point of collapse.

The real problem with your question is the idea that this question someone defines QM. And that we should judge QM not by the accuracy by which it predicts natural phenomena that can be shown by repeated experiments, but instead by bizarre coincidences with vanishingly low probability that will never be observed.

To take an analogy. In a democratic election it's possible that everyone forgets to vote. Or decides not to or gets distracted on the day. Do you judge democracy in this way? By the small probability that no-one votes?

This probability in fact is extraordinarily greater than the nonsensical ideas that get thrown at QM - like falling though a chair. Such events in either case are not worth thinking about - let alone making them your primary concern.

If you have a popular science book that emphasises such nonsensically rare events, you should throw it away.

 

[gentzen]

Both Sean Carroll and David Wallace are many worlds proponents. In their discussion, there are many places where it becomes clearer how they interpret „existence“, for example when talking about coarse grained descriptions which just work, independent of our „knowledge“ of the microstate:
https://www.preposterousuniverse.com/podcast/2021/08/02/158-david-wallace-on-the-arrow-of-time/

Basically their position is close to what you wish for, in many ways. Let‘s hope that I find time later to quote explicit parts from that transcript, and explain how this is related to your question.

 

[SDM88]

Ironically, there is no explanation for why you and your chair are solid in classical physics. It's QM that explains the solid state of matter in the first place.

You will eventually fall your chair. I've seen it myself once or twice where someone sits on a chair and it immediately collapses. That's nothing to do with QM, per se. That's because the chair must have previously been weakened to the point of collapse.

The real problem with your question is the idea that this question someone defines QM. And that we should judge QM not by the accuracy by which it predicts natural phenomena that can be shown by repeated experiments, but instead by bizarre coincidences with vanishingly low probability that will never be observed.

To take an analogy. In a democratic election it's possible that everyone forgets to vote. Or decides not to or gets distracted on the day. Do you judge democracy in this way? By the small probability that no-one votes?

This probability in fact is extraordinarily greater than the nonsensical ideas that get thrown at QM - like falling though a chair. Such events in either case are not worth thinking about - let alone making them your primary concern.

If you have a popular science book that emphasises such nonsensically rare events, you should throw it away.

Just to be clear, when I say fall through my chair, I mean pass through my chair... As if it were a gas.

 

[haushofer]

As a side question: Does anyone know a reference where a reasonable analysis is given of the probability of such 'macroscopic tunneling', like tunneling through a wall as a person?

 

[gentzen]

Both Sean Carroll and David Wallace are many worlds proponents. In their discussion, there are many places where it becomes clearer how they interpret „existence“, for example when talking about coarse grained descriptions which just work, independent of our „knowledge“ of the microstate:
https://www.preposterousuniverse.com/podcast/2021/08/02/158-david-wallace-on-the-arrow-of-time/

Basically their position is close to what you wish for, in many ways. Let‘s hope that I find time later to quote explicit parts from that transcript, and explain how this is related to your question.

Here is a relevant explicit quote of a part of that transcript:

0:38:20.1 SC: .... There’s the idea of a macro state, which we sort of glossed over, and people want to make a big deal about this, and I think it’s proper to make a big deal about this. So one of Boltzmann’s genius moves was to say, look, there’s atoms and molecules, they’re moving around, but I can’t see what the atoms and molecules are, so I’m going to group them, all the atoms and molecules that look similar, into a single group that I’ll call a macro state. I don’t know if he used those words, but that’s what we do. And so people have been asking, so I will ask you, what’s the license to do that? Is that okay, is that objective or is human agency sneaking its way in here, something subjective?

0:39:02.3 DW: Good. Yeah, I mean, the words get used in two kind of different ways, and I think one of them should worry reductionists, naturalists. So one of them basically shouldn’t, and the one that should worry people is the one that defines macroscopic in terms of our own abilities to distinguish them. So you want to say, well, the reason why we treat two different configurations of gas in the room as being the same macro state is something like, “We can’t distinguish between them with our eyes,” or sometimes even like, “We’re only interested in the gas at the level of a course graining,” like a macroscopic description.

0:39:42.0 DW: But #EmbarrassingConfessions, I don’t actually care about the gas at all. Beyond the minimal requirements of being able to breathe, I didn’t really mind where the air in my room is. It’s still true that thermodynamics describes it really well, even though I’m not curious about it. And similarly, we use statistical mechanics to describe even things like the way galaxies, stars in the galaxy develop, and we can obviously just… Our telescopes can tell us where the damn stars are, and yet we still want to dump various clearly visibly distinct arrangements of stars into the same macro state and say, “What we care about is the average distribution of the stars,” or something.

0:40:19.9 DW: So I think the good notion of macro state, the one that the naturalists can be relaxed about, is something like, “This is a level of description at which you can get some kind of robust, autonomous, in the philosophers’ jargon sense, self-contained dynamical story.” So, if I want to know how the air in the room is going to evolve over the next five minutes, at a certain coarse grained description, it turns out that all I need to know about the air now is, again, at a certain… Well, modulo these worries about thermodynamics it’s just that empirically, it’s true that I can make reliable predictions about what the air will do at a certain coarse level, provided I know what the air is doing now at a certain coarse level.

0:41:10.8 DW: And you know, we have equations to say what water does that don’t require us to say where all the individual molecules are. We can do higher-level science, and the macro states are the way of breaking up the lower-level stuff into higher-level stuff such that you can do higher-level science. That’s the robust version, I think, that we shouldn’t be suspicious about.

 

[pines-demon]

As a side question: Does anyone know a reference where a reasonable analysis is given of the probability of such 'macroscopic tunneling', like tunneling through a wall as a person?

As this is in the realm of macroscopic stuff, you can use semi-classics, using WKB approximation for a rectangular barrier, you have a transmission for a single particle of
$$T\approx \exp\left[\frac{-2}{\hbar} a \sqrt{2 m V} \right]$$
where $m$ is the mass, $V$ is the energy barrier with length $a$. For a gravitational barrier of 1cm in height and thickness of 1 mm, a fly has a chance in $1/10^{10^{24}}$ to go through.

 

[DaveC426913]

Does this mean that their are scientists who disagree that QM implies we can fall through our chairs?

It behooves us to remember that this concept was born into a classical world, where things never ever passed through other things - i.e. the chance of one particle passing through a sheet of atoms was exactly zero. The very idea was preposterous.

HUP, not only showed that it was possible for particles to tunnel but that there was no theoretical upper limit on how large those particle/systems could be.

People ran with the idea that 'cosmically-close-to-zero' is not 'zero'. They took it to outrageous extremes, making 'particle' into 'chair', and 'eventually' into 'imminently'.

 

[phinds]

People ran with the idea that 'cosmically-close-to-zero' is not 'zero'. They took it to outrageous extremes, making 'particle' into 'chair', and 'eventually' into 'imminently'.

this

 

[PeroK]

Just to be clear, when I say fall through my chair, I mean pass through my chair... As if it were a gas.

That's not going to happen. Also, you would be unable to demonstrate anything remotely like it.

Note that we cannot experimentally distinguish between MWI having an infinite number of branches and a large finite number of branches. For the latter, there may be no likelihood of these events in any branch.

MWI runs into mathematical "paradoxes" of the infinite. Which is one reason to suppose that branching is finite, even though we have an infinite model.

Whatever the resolution, none of this affects the reality of quantum tunneling by electrons in modern electronics etc. Which is what you should be learning about instead of filling your head with nonsense about falling through your chair.

 

[DaveC426913]

Yet another way to intuit this is the following:
For every event where a person on a chair falls though the floor, there would probabilistically be ten times as many events where only one tenth of a chairperson tunneled. And million times more events where only a millionth of a chairperson tunneled.

There are on the order or 10^27 Atoms in a chair person. Probabilistically, before any perceptible amount of chairperson tunnels, we should actually be observing all those bits of that chairperson appearing to have tunneled trillions and trillions of times already.

And don't forget that not all tunnelings are equal. We will see trillions of atoms tunneling atomic scale distance before we are likely to see on tunnel miscroscopically, and trillions will tunnel microscopically before we see anyvtinnel macrcoscopically.

If it takes a trillion years for a single nonagrom of chair person to tunnel one nanometer, imagine how many times we will expect actually witness this happening before even one microgram tunnels one micrometer.

We have yet to see that happen even once, which puts a lower limit on how long we might have to wait for each event.

You can bet it will take far, far longer than the universe will exist.

Think about billion monkeys typing up the works of Shakespeare. Before we see it, we should expect millions of outputs that are perfect - but for a single typo. And trillions more before that of outputs with only two typos. And even more of outputs that are perfect but for a single word. Ov the right stanza but out of order.

Work that back as far as you want. How long did it take for the monkeys to get a single stanza correct? Now multiply by the possible combinations. It too will take longer than the life of the universe.

If you prefer the multiuniverse model, substitute universe for time. Thre are trillions of universe where not acdingle monkeys has typed cause single stanza, or a single microgram of chairperson has tunneled more than an atom-width.

And we haven't even started counting th vanishingly small cases where ALL the atoms happen to tunnel in the SAME direction - let alone SIMULTANEOUSLY.
Again, start with just TWO atoms tunneling in the same direction at the same time.

 

[SDM88]

Here is a relevant explicit quote of a part of that transcript:

Thanks! So I read it and listened to some of the podcast. Can you help me understand how this might cast doubt on macro tunneling for example? I think I understand that he is saying something like the macro world is an abstraction, but I don't see what it tells us about what can or can not happen to macro objects.

 

[SDM88]

Yet another way to intuit this is the following:
For every event where a person on a chair falls though the floor, there would probabilistically be ten times as many events where only one tenth of a chairperson tunneled. And million times more events where only a millionth of a chairperson tunneled.

There are on the order or 10^27 Atoms in a chair person. Probabilistically, before any perceptible amount of chairperson tunnels, we should actually be observing all those bits of that chairperson appearing to have tunneled trillions and trillions of times already.

And don't forget that not all tunnelings are equal. We will see trillions of atoms tunneling atomic scale distance before we are likely to see on tunnel miscroscopically, and trillions will tunnel microscopically before we see anyvtinnel macrcoscopically.

If it takes a trillion years for a single nonagrom of chair person to tunnel one nanometer, imagine how many times we will expect actually witness this happening before even one microgram tunnels one micrometer.

We have yet to see that happen even once, which puts a lower limit on how long we might have to wait for each event.

You can bet it will take far, far longer than the universe will exist.

Think about billion monkeys typing up the works of Shakespeare. Before we see it, we should expect millions of outputs that are perfect - but for a single typo. And trillions more before that of outputs with only two typos. And even more of outputs that are perfect but for a single word. Ov the right stanza but out of order.

Work that back as far as you want. How long did it take for the monkeys to get a single stanza correct? Now multiply by the possible combinations. It too will take longer than the life of the universe.

I like this example. Some people will argue that all you demonstrated is that the probability of falling through the floor is vanishingly small. If it is true that there are an infinite number of universes, they will argue that it is a certainty that people will fall through the floor in some universes. They will argue anything with a greater than 0 probability happens. What do you say to this?

 

[DaveC426913]

"Vanishingly small" is a severe understatement. It doesn't do infinity justice.

I say people have a tough time grappling with infinities.

I mean, so what if it might happen in a universe infinitely far away. It is still a infinitely small chance of it happening to ours, here, now.

 

[PeroK]

I like this example. Some people will argue that all you demonstrated is that the probability of falling through the floor is vanishingly small. If it is true that there are an infinite number of universes, they will argue that it is a certainty that people will fall through the floor in some universes. They will argue anything with a greater than 0 probability happens. What do you say to this?

So what? It doesn't make it any more significant. It doesn't make the probability any greater.

PS if there are infinitely many branches is a big if.

 

[SDM88]

"Vanishingly small" is a severe understatement. It doesn't do infinity justice.

I say people have a tough time grappling with infinities.

I mean, so what if it might happen in a universe infinitely far away. It is still a infinitely small chance of it happening to ours, here, now.

I understand it doesn't matter practically speaking, but my goal is to find out if it can technically happen or not. I suspect that it can't happen in any universe, perhaps due to hidden variables or some other mechanism. Do you think it has a greater than 0 probability of occurring? Same question to @PeroK

 

[gentzen]

Thanks! So I read it and listened to some of the podcast. Can you help me understand how this might cast doubt on macro tunneling for example? I think I understand that he is saying something like the macro world is an abstraction, but I don't see what it tells us about what can or can not happen to macro objects.

This macroscopic description is something which "exists" for them, independent of humans forming that abstraction. And in a similar way, a world "exists" for David Wallace, if it is a similarly working description.

The macro tunneling example doesn't work in a similar way, and hence those worlds effectively don't exist for David Wallace. Sean Carroll (normally) argues a bit differently, namely that you should "act as if" those worlds would not exist. But the bottom line is the same for both, namely that those unphysical worlds are unwanted, and are not what the "worlds" in MWI are supposed to describe.

 

[gentzen]

This macroscopic description is something which "exists" for them, independent of humans forming that abstraction. And in a similar way, a world "exists" for David Wallace, if it is a similarly working description.

..., namely that those unphysical worlds are unwanted, and are not what the "worlds" in MWI are supposed to describe.

In fact, the "worlds" in MWI are actually supposed to be descriptions of "macroscopic worlds" for David Wallace and Lev Vaidman. I think Sean Carroll is a bit less committal at that point, and instead a bit more committal on the "only pure unitary QM" a la Schrödinger equation with initial state and Hamiltonian (i.e. without using any other implicit mathematical structures like a tensor product environment structure).

 

[PeterDonis]

my goal is to find out if it can technically happen or not.

You are thinking of it wrong. QM is a scientific model, and the many worlds interpretation is an interpretation of a scientific model. Scientific models are not "how it is", or even "what science says about how it is". Scientific models are tools we use to make predictions. In areas where the predictions have issues, like infinities, particularly if there is no conceivable way to test them now or in the foreseeable future, it is pointless to even ask whether some particular outlandish thing the model predicts can "technically happen". The best we can say is that the model is being pushed well beyond the domain where we can trust, or even take seriously, what it says, and it's all speculation and opinion beyond that point, not science.

 

[phinds]

You can bet it will take far, far longer than the universe will exist.

Do you mean after all the matter has devolved to radiation or do you have some inside scoop on the universe actually ENDING some day?

 

[PeterDonis]

do you have some inside scoop on the universe actually ENDING some day?

Maybe he's been to The Restaurant at the End of the Universe.

 

[Nugatory]

They will argue anything with a greater than 0 probability happens. What do you say to this?

No matter what we think about the ontological status of the universes that we aren’t in, we can only observe the universe that we’re in. And QM does just fine with the prediction that we will not observe someone tunneling through a chair.

 

[marcusl]

As this is in the realm of macroscopic stuff, you can use semi-classics, using WKB approximation for a rectangular barrier, you have a transmission for a single particle of
$$T\approx \exp\left[\frac{-2}{\hbar} a \sqrt{2 m V} \right]$$
where $m$ is the mass, $V$ is the energy barrier with length $a$. For a gravitational barrier of 1cm in height and thickness of 1 mm, a fly has a chance in $1/10^{10^{24}}$ to go through.

Don’t you have to estimate the probability of 7x10^4 g person x 6x10^23 atoms/g tunneling through a 0.02 m barrier simultaneously? If that isn’t close to 1/infinity, I don’t know what is.

 

[DaveC426913]

my goal is to find out if it can technically happen or not.

In a truly infinite universe or infinite multiverses or in an eternal universe, technically, yes it can happen - sort of by definition.

 

[Username34]

I have read that quantum mechanics implies that there is a very small probability that I can fall right through my chair,

Not the case.

"collapse is something that happens in our description of the system, not to the system itself".[1

/Fuchs and Peres

https://pubs.aip.org/physicstoday/article/53/3/70/411209/Quantum-Theory-Needs-No-Interpretation