I MWI and path of single electron

[FallenApple]

So in MWI, the electron takes many paths through the double slit experiment and each path is in a different world.

So if electrons are fired one at a time, what makes an electron go on a certain path. Say it goes on some weird path that would have implied that a force exist when viewed classically. But in QM, there is no force. So does the MWI view the strange path as resulting from an electron in one world interacting with the same electron in the other world? Does that explain the various trajectories?

 

[newjerseyrunner]

So in MWI, the electron takes many paths through the double slit experiment and each path is in a different world.

So if electrons are fired one at a time, what makes an electron go on a certain path. Say it goes on some weird path that would have implied that a force exist when viewed classically. But in QM, there is no force. So does the MWI view the strange path as resulting from an electron in one world interacting with the same electron in the other world? Does that explain the various trajectories?

It doesn't require any more forces. Elementary particles don't move in straight lines, they follow Schrodinger's wave equations so all of them are a valid pathway. It just means that the result is not deterministic.

 

[PeterDonis]

in MWI, the electron takes many paths through the double slit experiment and each path is in a different world.

That's not quite what MWI says. What MWI says is that the electron can arrive at many different points on the screen, and each such point corresponds to a different world. The different "worlds" come about when a measurement is actually made, and in this case the "measurement" is the electron hitting the screen.

if electrons are fired one at a time, what makes an electron go on a certain path

The electron doesn't have a single path while it's passing through the experiment. See above.

 

[FallenApple]

That's not quite what MWI says. What MWI says is that the electron can arrive at many different points on the screen, and each such point corresponds to a different world. The different "worlds" come about when a measurement is actually made, and in this case the "measurement" is the electron hitting the screen.
The electron doesn't have a single path while it's passing through the experiment. See above.

Oh so the MWI is not about the actual paths, but about the end results. Only the different possible end results are in different worlds.

So then, even in the MWI, the electron while traveling is still in some sort of existential limbo, described only by the wavefunction.

 

[FallenApple]

It doesn't require any more forces. Elementary particles don't move in straight lines, they follow Schrodinger's wave equations so all of them are a valid pathway. It just means that the result is not deterministic.

I thought the MWI is deterministic. It's just that the probability is frequentist now.

 

[PeterDonis]

even in the MWI, the electron while traveling is still in some sort of existential limbo, described only by the wavefunction

In the MWI, the electron is always described by the wavefunction. So is everything else, including the measuring device--the screen in this case. The "different worlds" arise when the interaction between two systems, such as the electron and the screen, causes them to become entangled in such a way that the wave function branches--heuristically, different terms in the electron part of the wave function become coupled to different terms in the screen part of the wave function, and you can no longer separate things into an "electron" and a "screen" as independent systems, as you could before the interaction.

I thought the MWI is deterministic.

It is.

 

[Manyme]

So in MWI, the electron takes many paths through the double slit experiment and each path is in a different world.

So if electrons are fired one at a time, what makes an electron go on a certain path. Say it goes on some weird path that would have implied that a force exist when viewed classically. But in QM, there is no force. So does the MWI view the strange path as resulting from an electron in one world interacting with the same electron in the other world? Does that explain the various trajectories?

I'm currently trying and really struggling to understand that same thing. Problem is, it seems like the more I read, the less I understand. There's just so much conflicting and misleading information, and I thought that the basic double slit would be one of the easier cases...

First of all, there seems to be a number of different "multi world" theories, some going by slightly different names, some by the very same. Some say there really physically are multiple worlds and multiple copies of myself, whereas others say that's just a simplification or way to visualize what is really going on, and what is really going on is something very confusing with the wave functions. Which were supposed to be "real" in the MWI, it's just quite unclear what that actually means.

As for the double slit, some say the results have something to do with the worlds interacting, whereas others say the worlds never interact. Some say the worlds sometimes merge back, some say they never do. Some describe MWI as sort of an extension to superposition, as if the alternatives in the superposition are separate worlds already, whereas others describe them as more or less separate phenomena. And then there's a whole bunch of those who resort to Copenhagen style terms of probability waves and observers and so on, which are often quite misleading in terms of a deterministic interpretation.

For me personally some sort of simplistic idea of constantly branching multiple worlds, where particles actually follow clear trajectories, feels understandable, and not that odd, which is probably why those ideas are simplified that way when presented to us non-scientists. But it seems to me that at the same time the simplifications go too far, so that they rather mislead than help us really understand how experiments like the double slit, GHZ and DCQE can be explained with that interpretation.

What I'm really trying to find is clear understandable information on simple things like in what sense those multiple worlds are really separate worlds, do those particles really follow well defined trajectories, how the double slit (and others) are really explained in such simple terms etc. And since this is quantum mechanics, I understand that some things really are too complex or unknown to put in simple terms, and interpretations vary within one interpretation as well, but at least it would be nice to know which of those things belong to which category. I would really appreciate any pointers to such information.

 

[Strilanc]

You're probably just running into people with different ideas of what is meant by "world", since that's about as well defined a concept as "species" when you really dig into the details.

When some people say world, they mean (roughly) the transitive closure of "case A can still strongly interact with case B". This would put the two electron paths into the same world, and the "split" would only happen upon measurement. But when some other people say world, they would count the two paths as different worlds.

Regardless of which view you take, things branch into more and more cases over time. Which is probably why the name stuck, despite the many-worlds interpretation never defining what a world is. It was originally called the "universal wave function" interpretation or something like that. Nothing to do with "worlds". All MWI really does is drop the collapse postulate and take the remaining math seriously.

 

[Manyme]

You're probably just running into people with different ideas of what is meant by "world", since that's about as well defined a concept as "species" when you really dig into the details.

Boundaries between species are somewhat artificial and depend on definitions, but at least everyone agrees there are species with physical manifestations. I'm not quite sure if even that applies to these worlds.

When some people say world, they mean (roughly) the transitive closure of "case A can still strongly interact with case B". This would put the two electron paths into the same world, and the "split" would only happen upon measurement. But when some other people say world, they would count the two paths as different worlds.

I have had the impression that MWI advocates have criticized Copenhagians for vagueness on how and when the collapse actually happens, but MWI splits seem to be even less clear.

Regardless of which view you take, things branch into more and more cases over time.

So if we assume split on measurement, that same instant would result in a random selection of possible choices in Copenhagen, throwing away the rest of the possibilities that could have branched. Is that basically all it takes to transform an indeterministic interpretation to a deterministic one?

It was originally called the "universal wave function" interpretation or something like that. Nothing to do with "worlds".

According to Wikipedia, Everett however believed in multiple quantum worlds more or less literally.

https://en.wikipedia.org/wiki/Many-worlds_interpretation#Reception

All MWI really does is drop the collapse postulate and take the remaining math seriously.

My understanding has been that pretty much all the interpretations take that math seriously and especially Copenhagen takes it a bit "too seriously", meaning they sort of replace reality with a purely mathematical construct. I have thought that MWI (as well as Bohmian mechanics) anchor the math to something that actually exists physically in a more concrete way. But now that I have tried to find out just how it does that, I'm not sure it does it at all.

 

[Strilanc]

Boundaries between species are somewhat artificial and depend on definitions, but at least everyone agrees there are species with physical manifestations. I'm not quite sure if even that applies to these worlds.

No, the analogy between "worlds" and species is actually really good. We're trying to make discrete groups out of a very fine-grained thing. There are some cases that are really obviously distinct, but for any useful rule you make there will be borderline cases that are hard to classify.

I have had the impression that MWI advocates have criticized Copenhagians for vagueness on how and when the collapse actually happens, but MWI splits seem to be even less clear.

So if we assume split on measurement, that same instant would result in a random selection of possible choices in Copenhagen, throwing away the rest of the possibilities that could have branched. Is that basically all it takes to transform an indeterministic interpretation to a deterministic one?

MWI doesn't assume there's a split on measurement. It doesn't say anything about splitting. You set up the state, you run the math, and that's it. There's no inherent need for the concept of a world, and no experiment ever depends on that categorization.

Analogously, at the lowest level, evolutionary theory doesn't say anything about species. Species and "worlds" are just high-level descriptions we use to simplify the respective underlying continuums of biology and physics.

The concepts of "is a world" and "is a species" and "is a planet" are useful tools we use to make thinking about things easier. They are not underlying ground truths. There's no experiment whose result depends on whether we consider the members of a ring species to all be of the same species or not, or on whether we call pluto a planet or not, or whether we call a particular bundle of states a "world" or not.

According to Wikipedia, Everett however believed in multiple quantum worlds more or less literally.

https://en.wikipedia.org/wiki/Many-worlds_interpretation#Reception

My understanding has been that pretty much all the interpretations take that math seriously and especially Copenhagen takes it a bit "too seriously", meaning they sort of replace reality with a purely mathematical construct. I have thought that MWI (as well as Bohmian mechanics) anchor the math to something that actually exists physically in a more concrete way. But now that I have tried to find out just how it does that, I'm not sure it does it at all.

I didn't mean to imply that other interpretations don't take the math seriously. I just meant that many-worlds says that the math without the collapse-turns-squared-amplitude-into-probabilities postulate is complete. In MWI, the Born rule is not postulated but derived (using concepts like indexical uncertainty, but of course this is controversial).

 

[Manyme]

Analogously, at the lowest level, evolutionary theory doesn't say anything about species. Species and "worlds" are just high-level descriptions we use to simplify the respective underlying continuums of biology and physics.

In biology there are plenty of pretty clearly separate individuals, so it is a matter of choosing which are similar enough in some way to belong to the same species, even if the borders are vague. But with these worlds, I don't have an understanding what the "individuals" are. Things seem to be interconnected in a different way.

Are you basically saying that you think this in terms of the all-encompassing universal wave function, and would you classify your thoughts belonging to the unreal camp of these:

"According to Martin Gardner, the "other" worlds of MWI have two different interpretations: real or unreal; he claims that Stephen Hawking and Steven Weinberg both favour the unreal interpretation.[83] Gardner also claims that the nonreal interpretation is favoured by the majority of physicists, whereas the "realist" view is only supported by MWI experts such as Deutsch and Bryce DeWitt."

https://en.wikipedia.org/wiki/Many-worlds_interpretation

 

[PeterDonis]

What I'm really trying to find is clear understandable information on simple things like in what sense those multiple worlds are really separate worlds, do those particles really follow well defined trajectories, how the double slit (and others) are really explained in such simple terms etc.

You won't, because all of these things are interpretations, and all of the different interpretations make exactly the same predictions for all experimental results, so there is no "right" answer to any of these kinds of questions.

You really need to start with what underlies all of the interpretations: the actual experimental results and the actual mathematical model that is used to make predictions that match those experimental results. In the case of the double slit, for example, the basics are (I'll describe them in terms of electrons, though the experiment could be run with any quantum particle):

(1) We have a source of electrons that can emit many of them, one at a time, all in the same state.

(2) We have a screen with two slits in it; electrons can only pass the screen through the slits.

(3) We have a detector on the other side of the screen from the source, which makes a little flash of light when an electron hits it.

(4) We have the source emit many electrons, one at a time; for each electron emitted, we see one and only one flash of light on the detector, similar to what we would expect from particles.

(5) When we look at the pattern of flashes on the detector after many electrons have been through the experiment, it is an interference pattern, similar to what we would expect from waves.

(6) The mathematical model we use to predict results that match the above is that each possible way an electron could go from the source to a particular point on the detector has an amplitude (a complex number) attached to it. There are a variety of mathematically equivalent ways of writing down the equations that determine this amplitude; they go by names like "Schrodinger equation", "matrix mechanics", "path integral", etc. The key point is that the amplitude is determined by properties of the electron like its mass and charge, and properties of the experiment like the distance from the source to the screen and from the screen to the detector (and also the fact that the detector gives a definite result for which point on it the electron arrives at, whereas there is no indication from the screen of which slit the electron went through), the energy of the electrons when they are emitted from the source, the spacing between the slits, etc.

(7) For each point on the detector, we add up all the amplitudes for the different possible ways the electron could get there (in the simplest approximation for this experiment, there are two of them, one for each slit), then take the squared modulus of the resulting complex number; that gives us the probability that the electron will arrive at that point on the detector. When we assign amplitudes we also have to make sure that the probabilities for all of the possible points on the detector add up to 1 (this is called "normalizing" the amplitudes in the literature; it's just a mathematical condition on them that has to be satisfied).

Anything over and above what I have stated is interpretation. Notice that the above doesn't contain anything about "multiple worlds" or "well defined trajectories" or anything like that. So all that stuff is interpretation.

 

[Manyme]

You won't, because all of these things are interpretations, and all of the different interpretations make exactly the same predictions for all experimental results, so there is no "right" answer to any of these kinds of questions.

I'm not looking for a "right" answer, but that interpretation part, especially for the MWI at the moment.

I know that the math works, and is mostly shared between the interpretations, and that various experiments give results that are hard to understand. I also know that, at least at the moment, there's no way to find out which interpretation is actually correct, if any, especially since they make the same predictions. But nevertheless I would like to know what it would mean in some sort of physical terms if MWI was correct.

I understand there's at least that one major difference to Copenhagen that there's no collapse which means all alternatives happen and that removes the need for randomness and indeterminism in interpreting those results. But where do those alternatives happen? For some MWI advocates the answer is more or less literally in a separate world like ours, which is the sort of thing that in my view actually helps to interpret and understand those results. Similarly to having some actual physical Bohmian wave, whatever that exactly is. At least those are not just math that works, but something that relates to some sort of physical reality. And I find it pretty hard to believe that there wouldn't be any sort of physical reality underneath it all.

I have thought that those sort of links to physical reality (or not) are more or less the point of these interpretations, but it seems few of them actually go to that sort of details to the extent that it would actually give some sort of understandable potential explanation to those experimental results.

 

[Strilanc]

In biology there are plenty of pretty clearly separate individuals, so it is a matter of choosing which are similar enough in some way to belong to the same species, even if the borders are vague. But with these worlds, I don't have an understanding what the "individuals" are. Things seem to be interconnected in a different way.

The border between species is really really hazy when you dig into the details. There's a reason that, when I took a bioinformatics course in university, the first thing the professor told us was "Everything I tell you about biology is going to have exceptions. And those exceptions are going to have exceptions.".

For biology, the rule of thumb for species is that two groups are separate species when there can't be any more gene flow in between them.

For many worlds, the rule of thumb for worlds is that two clumps of configuration space are separate worlds when there can't be any more amplitude flow in between them. (But, again, some people aren't so strict.)

Are you basically saying that you think this in terms of the all-encompassing universal wave function, and would you classify your thoughts belonging to the unreal camp of these:

"According to Martin Gardner, the "other" worlds of MWI have two different interpretations: real or unreal; he claims that Stephen Hawking and Steven Weinberg both favour the unreal interpretation.[83] Gardner also claims that the nonreal interpretation is favoured by the majority of physicists, whereas the "realist" view is only supported by MWI experts such as Deutsch and Bryce DeWitt."

https://en.wikipedia.org/wiki/Many-worlds_interpretation

I've never understood what the hell people are thinking when they ask if the math is "real" or not. Clearly they don't mean "matches experiment". It's particularly bad in the Copenhagen interpretation, where people keep saying things aren't real until they're measured. As if being real was equivalent to not being in superposition with respect to some arbitrary basis...??

So I don't have any particular opinion about whether to call worlds "real" or "not real". All I can tell you about is the math and what that says. And the math doesn't say anything verifiable about whether parts of configuration space suddenly disappear when separated.

 

[PeterDonis]

I would like to know what it would mean in some sort of physical terms if MWI was correct.

And there's no way to answer this at present because the MWI makes the same physical predictions as every other interpretation. In order for this question to have an answer, we would have to have an actual different "many worlds" theory that made different predictions from other theories based on other interpretations of QM. Then we could look at the different physical predictions to see what it would mean in physical terms for one theory to be correct vs. another.

 

[Manyme]

I've never understood what the hell people are thinking when they ask if the math is "real" or not. Clearly they don't mean "matches experiment".

My understanding is that it's not about whether the math is real but whether there's some physical reality that exists and works according to that math. In this case whether there really is an actual physical world where one of my clones is currently writing something else and so on, not just some mathematical equation that could be interpreted like that. It may be that we will never have the means to verify if that is the case, but nevertheless to me that sort of possibility is already very interesting, even if it remains speculation and a philosophical issue.

It's particularly bad in the Copenhagen interpretation, where people keep saying things aren't real until they're measured. As if being real was equivalent to not being in superposition with respect to some arbitrary basis...??

Copenhagians say there is no physical particle at a precise position and Bohmians say there is, yet for the most part the math is the same. So the mathematical reality doesn't seem to be equivalent to that sort of physical reality.

So I don't have any particular opinion about whether to call worlds "real" or "not real". All I can tell you about is the math and what that says. And the math doesn't say anything verifiable about whether parts of configuration space suddenly disappear when separated.

So is that the "Shut up and calculate!" interpretation then? :)

 

[PeterDonis]

My understanding is that it's not about whether the math is real but whether there's some physical reality that exists and works according to that math.

The math for all the interpretations is the same. Yet different interpretations make different claims about "physical reality". So at our current state of knowledge, there is no one answer to what the "physical reality" is that "works according to that math". The questions you are asking simply do not have answers.

for the most part the math is the same

Not "for the most part". The math is the same, period. Even if it's written down in a different form, it's the same math; all of the interpretations are mathematically equivalent.

is that the "Shut up and calculate!" interpretation then? :)

It's the we don't know which, if any interpretation is the "really correct" interpretation, so there's no point in asking, interpretation.

 

[Manyme]

The math for all the interpretations is the same. Yet different interpretations make different claims about "physical reality".

And that's exactly what I would like to know, what those different claims are according to the MWI. For example what actually happens in "physical reality" according to MWI when the double slit experiment is performed.

Since there seems to be multiple many worlds interpretations or interpretations of those interpretations, it would be nice to have at least one that would provide something like that :).

So at our current state of knowledge, there is no one answer to what the "physical reality" is that "works according to that math". The questions you are asking simply do not have answers.

I'm not really asking that question but that above.

 

[PeterDonis]

what actually happens in "physical reality" according to MWI when the double slit experiment is performed.

According to the MWI, the physical reality is the wave function; that's it. So whatever happens to the wave function is what happens in physical reality. In the double slit experiment, each time an electron goes through the experiment, the wave function ends up with one term for each possible position on the detector that the electron could end up at: each such term is just the piece of the electron wave function that ends up at that position, multiplied by the piece of the detector wave function that describes an electron being detected at that position. Each such term is multiplied by the amplitude for the electron to end up at that position.

But, as I said before, there is no way to show that physical reality actually works this way, because the MWI makes the same predictions as all the other interpretations, which have very different descriptions of what is happening in physical reality.

 

[Manyme]

According to the MWI, the physical reality is the wave function; that's it. So whatever happens to the wave function is what happens in physical reality. In the double slit experiment, each time an electron goes through the experiment, the wave function ends up with one term for each possible position on the detector that the electron could end up at: each such term is just the piece of the electron wave function that ends up at that position, multiplied by the piece of the detector wave function that describes an electron being detected at that position. Each such term is multiplied by the amplitude for the electron to end up at that position.

So the math tells that even for a single particle all possibilities happen in the corresponding physical reality. Based on that alone, I could expect to see the full interference pattern after just one particle, if I perform the actual experiment, but instead I see just a single point in a seemingly random position.

So one needs to go beyond the math and add the actual many worlds interpretation story to make the experiment actually understandable in the observable world, right? Similarly how Copenhagen needs to add that collapse part.

That's what I'm looking for, the sort of explanations that make it clear that all those possibilities actually happen somewhere but you can only observe one of them because of this, and so on.

 

[PeroK]

So the math tells that even for a single particle all possibilities happen in the corresponding physical reality. Based on that alone, I could expect to see the full interference pattern after just one particle, if I perform the actual experiment, but instead I see just a single point in a seemingly random position.

So one needs to go beyond the math and add the actual many worlds interpretation story to make the experiment actually understandable in the observable world, right? Similarly how Copenhagen needs to add that collapse part.

That's what I'm looking for, the sort of explanations that make it clear that all those possibilities actually happen somewhere but you can only observe one of them because of this, and so on.

I think you have misinterpreted the MWI. To take a simpler example of a coin toss. MWI says (roughly) that each time you toss a coin two universes are "produced": one universe in which you threw a head and one universe in which you threw a tail. But, definitely not a universe in which the coin was both heads and tails.

Copenhagen says (roughly) that by tossing the coin you force it to take a stand and come up heads or tails, through a random process.

In QM the maths tells you how likely any event is (a particle hitting a a screen at point $x$ at time $t$). No one disagrees about the probability, in the same way that no one disagrees that heads and tails are 50-50.

Also, one further point about probabilities and probability amplitudes. If you think of QM in terms of probabilities, it doesn't work. For example:

The particle can go through slit 1 and hit a certain point $x$ on the screen with probability $p_1$ and through slit two and hit the same point $x$ with probability $p_2$. But, however you do the maths, there's no way that a combination of $p_1$ and $p_2$ can possibly be 0. In other words, there's no way to get destructive interference.

The key is that we are dealing with probability amplitudes. In a way, it's not the particle that takes every possible path, it's the particle's wave function (representing the probability amplitude) that is subjected to every possible path. And probability amplitudes can be positive or negative (in fact, they are complex numbers). And the sum of two amplitudes can, therefore, be 0, representing destructive interference. (Done probabilistically, rather than through a physical wave motion.)

One slightly facetious way out of the dilemma is to say that there is nothing to stop a probability amplitude function "moving" faster than light! And, in fact, a particle cannot reasonably in any physical sense try out an infinite number of paths in any case. But, a mathematical object (wave function) can be subjected to a sum over infinite paths, where the limit can be taken mathematically. This limit can be 0 where the complex probability amplitudes cancel. That's why a particle may have 0 chance of hitting the screen at a point which it could quite happily hit through slit 1, slit 2 or both.

PS re understanding the difference between probabilities and probability amplitudes try:

http://www.scottaaronson.com/democritus/lec9.html

 

[Manyme]

I think you have misinterpreted the MWI.

I'm sure I have in many, many ways, which is the very reason I'm trying to ask for understandable explanations according to some interpretation. However, in this case my understanding seems to match what you said.

Problem is, some others are contradicting what you just said, for example by saying that heads and tails DO happen in the same universe, but just within different "worlds" inside it. At least for the most part such differences likely just reflect different ways to define words and such. Nevertheless the end result is pretty confusing mixture of contradicting texts.

In a way, it's not the particle that takes every possible path, it's the particle's wave function (representing the probability amplitude) that is subjected to every possible path. And probability amplitudes can be positive or negative (in fact, they are complex numbers). And the sum of two amplitudes can, therefore, be 0, representing destructive interference. (Done probabilistically, rather than through a physical wave motion.)

I understand it's the wave that interferes and how waves can result interference patterns, but I'm having a problem with it being just something mathematical and non-physical. To me that part is quite clearly something that lacks physical interpretation, and I don't quite get it why most physicists seem so happy to live with something so abstract. I can accept some physical things just act according to some equation without deeper physical explanation, but this wave like interference doesn't feel like something that would make sense without any.

In Bohmian mechanics this interference is explained by an actual real wave and in MIW it's some repulsive force between particles in alternative worlds. Those are the sort of details I would expect to see in an interpretation, as they provide a physical understandable explanation to that behavior, even though it's more than unclear on what sort of pixie dust those waves and forces are based on. But with MWI it seems I'm supposed to just accept the universe performs somewhat magical calculations on virtual waves or something?

PS re understanding the difference between probabilities and probability amplitudes try:

http://www.scottaaronson.com/democritus/lec9.html

Thank you, that was quite clarifying on where this math comes from (though on some level I already knew the difference between probabilities and amplitudes). As a side note, I didn't quite understand why Aaronson seemed to represent determinism and QM as if they were mutually exclusive, but maybe that was just a simplification.

 

[PeroK]

Problem is, some others are contradicting what you just said, for example by saying that heads and tails DO happen in the same universe, but just within different "worlds" inside it.

Can you quote the post that says this?

and I don't quite get it why most physicists seem so happy to live with something so abstract.

They have no choice.

 

[Manyme]

Can you quote the post that says this?

Sorry I should have been clearer on that. I didn't mean others on this forum but elsewhere. For example here's one along those lines:

"The Many-Worlds Interpretation (MWI) of quantum mechanics holds that there are many worlds which exist in parallel at the same space and time as our own."

"The fundamental idea of the MWI, going back to Everett 1957, is that there are myriads of worlds in the Universe in addition to the world we are aware of."

https://plato.stanford.edu/entries/qm-manyworlds/

There's more about various approaches and confusing terminology in chapter 6.

They have no choice.

Maybe so, or they just don't think these things are that important or interesting, at the moment at least, since they can't be experimentally tested and such.

Nevertheless, in my view, those pilot waves and repulsive forces I mentioned above are at least plausible physical explanations for the underlying mechanisms for those interpretations. Whereas for Copenhagen in particular, similar explanations have been more or less mystical. I don't know if too many take those concepts seriously anymore, but there has been special roles for consciousness and free will and the universe has been described in terms that seem to make it some sort of intelligent entity and so on. Basically stuff that you would expect to find in a religion, not so much in physics.

As far as I understand it, when you have e.g. some experiment that contains beam-splitters and mirrors and so on, finding out the end result either requires some pretty complex calculations on what will happen, or actually performing the experiment. To me the universe is not the sort of entity I would expect to perform the former. I would expect there to be some sort of actual physical chain of events that determines the outcome. And even if the results would indicate something very weird happened, like reversal of time or causality, at least that would be some sort of physical weirdness, and not something mystical :).

That's the sort of reasoning why I would expect to see some kind of possible physical explanations in these interpretations, instead of just math. Even if those cannot be tested, but having at least some realistic possibility is better than having none, right? At least there would be some idea how it could work.

Because of that, I would say Bohmian mechanics to be the strongest contender as an interpretation, in my layman opinion, as despite its shortcomings and issues with relativity and so on, at least it seems to be physical, and the weirdnesses it has are more or less physical.

 

[PeroK]

Sorry I should have been clearer on that. I didn't mean others on this forum but elsewhere. For example here's one along those lines:

"The Many-Worlds Interpretation (MWI) of quantum mechanics holds that there are many worlds which exist in parallel at the same space and time as our own."

"The fundamental idea of the MWI, going back to Everett 1957, is that there are myriads of worlds in the Universe in addition to the world we are aware of."

https://plato.stanford.edu/entries/qm-manyworlds/

There's more about various approaches and confusing terminology in chapter 6.

I started to read that and I thought to myself, "wait a minute, this is more philosophy than physics". Then I noticed the at the top of the page "Standford Encyclopedia of Philosophy". Whatever you think of philosophy, it isn't physics and, strictly speaking, it isn't allowed on these forums. For good reason, IMHO.

Perhaps you need to make up your mind whether you want to learn Physics, or the Philosophy of Physics.

Maybe so, or they just don't think these things are that important or interesting, at the moment at least, since they can't be experimentally tested and such.

Nevertheless, in my view, those pilot waves and repulsive forces I mentioned above are at least plausible physical explanations for the underlying mechanisms for those interpretations. Whereas for Copenhagen in particular, similar explanations have been more or less mystical. I don't know if too many take those concepts seriously anymore, but there has been special roles for consciousness and free will and the universe has been described in terms that seem to make it some sort of intelligent entity and so on. Basically stuff that you would expect to find in a religion, not so much in physics.

As far as I understand it, when you have e.g. some experiment that contains beam-splitters and mirrors and so on, finding out the end result either requires some pretty complex calculations ["nature laughs at the compexities of integration" - Laplace] on what will happen, or actually performing the experiment. To me the universe is not the sort of entity I would expect to perform the former. I would expect there to be some sort of actual physical chain of events that determines the outcome. And even if the results would indicate something very weird happened, like reversal of time or causality, at least that would be some sort of physical weirdness, and not something mystical :).

That's the sort of reasoning why I would expect to see some kind of possible physical explanations in these interpretations, instead of just math. Even if those cannot be tested, but having at least some realistic possibility is better than having none, right? At least there would be some idea how it could work.

Because of that, I would say Bohmian mechanics to be the strongest contender as an interpretation, in my layman opinion, as despite its shortcomings and issues with relativity and so on, at least it seems to be physical, and the weirdnesses it has are more or less physical.

I've highlighted the key points which show your philosophical approach. And inserted a quotation from Laplace, who wrote that long before QM was even dreamed of.

I have a different experience of QM from you. I've never read a pop-science book on QM, and have learned the relatively little I know from Griffiths and Sakurai. Neither of whom filled my head with any philosophical misgivings.

Nature is what she is and cares not for what you, I, Einstein or Everett thinks about it. That's my philosophy anyway.

 

[Manyme]

I started to read that and I thought to myself, "wait a minute, this is more philosophy than physics". Then I noticed the at the top of the page "Standford Encyclopedia of Philosophy". Whatever you think of philosophy, it isn't physics

The author of that page seems to be professor Lev Vaidman, a well known physicist with many publications about MWI. So does he speak rubbish about one of his areas of expertise just because the page is titled like that?

Nature is what she is and cares not for what you, I, Einstein or Everett thinks about it. That's my philosophy anyway.

Which IMHO isn't really an excuse for not having an explanation.

 

[PeroK]

The author of that page seems to be professor Lev Vaidman, a well known physicist with many publications about MWI. So does he speak rubbish about one of his areas of expertise just because the page is titled like that?

I never said philosophy was rubbish, just that it's not physics and isn't what we concern ourselves with on this forum.

 

[Manyme]

I never said philosophy was rubbish

I didn't say you did.

just that it's not physics and isn't what we concern ourselves with on this forum.

You asked where I saw the idea that MWI has a single universe with multiple worlds in it, and I replied with those quotes by a well known expert of MWI. That's what it was about, not about philosophy in general or what the title or other contents of that page are.

So if a noted physicist said that, is it somehow less about physics than you saying there are multiple universes before?

Also bear in mind, my original point was only about confusing terminology.

 

[fresh_42]

Please try to stay within physics. Quoting Lev Vaidman doesn't automatically mean to discuss his work in physics. The links above are clearly philosophy, which we don't discuss on PF. The reason basically is, that it cannot be confined to philosophical science and therefore leads to nowhere.

 

[PeterDonis]

So the math tells that even for a single particle all possibilities happen in the corresponding physical reality.

No, the math tells us nothing about "physical reality" since it is consistent with various different interpretations.

The interpretation of the MWI tells us that all possibilities happen in one physical reality, where "physical reality" here means "the wave function". That includes all possibilities for measuring devices and conscious beings like you and I.

Based on that alone, I could expect to see the full interference pattern after just one particle

No. That's not what the math predicts. The math predicts that you will see one particle striking in a random position on the detector. But collapse vs. no collapse interpretations describe what is going on "behind the scenes" of this math very differently, and that leads to the word "you" in the sentence quoted above having very different referents:

On a collapse interpretation, such as Copenhagen, when the particle strikes the detector, all terms in the wave function except the one describing it striking at that point vanish--this is the collapse. Conscious observers like you and me then just observe the detector showing a particle striking at that point. So the referent of "you" in the sentence quoted above is the observer, who is described classically.

On a no collapse interpretation, such as MWI, all terms in the wave function are there, but each one describes not just the particle striking a different point on the detector, but the detector showing the particle striking at that point (different for each term), and conscious observers like you and me observing the detector showing a flash at that point (different for each term). So in this case the referent of "you" in the sentence quoted above is one particular term in the wave function describing a conscious observer, the term that has the observer's state corresponding to the detector and particle states for the particle striking at one point. And that "you" observes the particle striking at one random point on the detector (a different point for each different "you" corresponding to a different term in the wave function). There is no "you" that corresponds to the wave function as a whole, or even to the part of the wave function describing the observer as a whole (i.e., taking into account all the different possible observations).

That's what I'm looking for, the sort of explanations that make it clear that all those possibilities actually happen somewhere but you can only observe one of them because of this, and so on.

See above.

 

[PeterDonis]

MWI says (roughly) that each time you toss a coin two universes are "produced": one universe in which you threw a head and one universe in which you threw a tail. But, definitely not a universe in which the coin was both heads and tails.

The word "universe" can be confusing here. That's why I specifically used the term "wave function" in my previous post. The math plus the MWI interpretation of the math can be described as "different terms in the wave function are different copies of the universe", or as "the wave function is the universe, different terms are just different parts of the same universe"; both of these are just different ways of trying to convey in words something that doesn't really fit into the categories embedded in our language. (The same applies if you substitute "world" for "universe".) The first set of words would make your statement quoted above true; but the second set of words would make it false. But it's the same math and the same basic interpretation (no collapse) in both cases; so the apparent difference is not there in the math (or the physics), it's a confusion due to the limitations of our words. The only way to avoid this kind of confusion is to taboo the words and go back to the math.

 

[PeroK]

The only way to avoid this kind of confusion is to taboo the words and go back to the math.

Reading the Lev Vaidman piece in more detail, it seems to me that the MWI walks a fine line between a rigorous all-encompasing view of the universe based on QM and a philosophical investigation that (IMHO) defies rigorous analysis using QM. To take an example of the cat. Vaidman makes the point himself that a cat is not well-defined. But, also, is the state of the cat in terms of any macroscopic property really an observable in any QM sense?

In particular, do we have an observable with the two outcomes of alive and dead? Or, do the terms "cat" "alive" and "dead" simply make no sense within QM? Forensic science can tell how long an animal has been dead, so do you have a "dead for time t" outcome? Clearly the state of a cat that has just died is very different from the state of a cat that has been dead for a week!

I know that Vaidman is an expert in his field, but I personally can't help feeling his whole edifice is based on a potentially false premise: that everything can be understood directly from the laws of particle physics.

As a contrast, I was watching one of the Feyman lectures recently and he said:

"The understanding [of the real world] is not prima facie available by knowing about the laws ... The laws of physics do not have a direct relevance to the experience, but the laws are abstract from the experience to varying degrees ... There are often great distances between the detailed laws and the main aspects of real phenomema ... One does not by knowing all the fundamental laws as we know them today immediately obtain an understanding of anything much."

Brilliant stuff! and I could quote more. My interpretation of this is that in order to understand a cat, you need QM to explain the behaviour of the atomic nucleii, chemistry to understand the bonding of molecules, cell biology to understand the organic processes within the cat, a medical understanding of the cat's organs etc,, which eventually leads to an understanding of the cat and a method of ascribing "alive" or "just died" or "dead for a week" to a cat.

But, IMHO, as soon as one writes down $\Psi_{cat}$ for the wave-function of a cat, one is potentially misapplying the laws of particle physics and the concept of the wave-function for a cat is on very shaky ground.

That's not to say that the alternatives do not have their flaws, but I find the MWI presented by Vaidman to be based on the unsatisfactory premise that the laws of particle physics explain everything.

 

[PeterDonis]

do we have an observable with the two outcomes of alive and dead?

As long as one can partition the cat's state space into two disjoint subspaces, an "alive" one and a "dead" one, then there must be some observable that has those two subspaces as eigensubspaces. In other words, as long as "alive" and "dead" name two mutually exclusive conditions on the cat, there must be an "alive/dead" observable, which gives the output "yes" (or 1 or whatever) if the cat is "alive" (i.e., if its state is in the "alive" subspace) or "no" (or 0 or whatever) if the cat is "dead" (i.e., if its state is in the "dead" subspace).

Whether one can actually partition the cat's state space in this way is really a question about definitions, not physics: how do we want to define the terms "alive" and "dead"? There are certainly cat states which are unproblematically described by one of these two terms; the question becomes where in the state space we want to draw the boundary between them. But any such boundary will be arbitrary, so we can just pick one that meets our intuitions reasonably well.

Clearly the state of a cat that has just died is very different from the state of a cat that has been dead for a week!

That just means you have to draw the boundary in the cat's state space so that both of these states are in the "dead" subspace.

You could also observe that the state of a live cat today is very different from the state of the live kitten that grew into the cat. The same response applies.

 

[FallenApple]

Also, though the distinction may be philosophical, the differences in ideas may affect how future theories turn out. Feynman explains it very well here.

 

[bubsir]

I'm currently trying and really struggling to understand that same thing. Problem is, it seems like the more I read, the less I understand.

“Young man, in mathematics you don't understand things. You just get used to them.”
―John von Neumann

 

[Blue Scallop]

According to the MWI, the physical reality is the wave function; that's it. So whatever happens to the wave function is what happens in physical reality. In the double slit experiment, each time an electron goes through the experiment, the wave function ends up with one term for each possible position on the detector that the electron could end up at: each such term is just the piece of the electron wave function that ends up at that position, multiplied by the piece of the detector wave function that describes an electron being detected at that position. Each such term is multiplied by the amplitude for the electron to end up at that position.

But, as I said before, there is no way to show that physical reality actually works this way, because the MWI makes the same predictions as all the other interpretations, which have very different descriptions of what is happening in physical reality.

I've searched your previous statements. Let's tackle the issue head one. In the above you yourself stated that : "According to the MWI, the physical reality is the wave function; that's it." So you admit that the physical particle is the wave function. But elsewhere you stated that "No. Physical objects are physical objects. State vectors are mathematical objects that appear in mathematical models. They are not the same.". But in MWI, you admit they are the same? Please clarify.

Now to distinguish or test if MWI is correct. Then if we can change the wave function, and we can change the reality... then MWI is the right one. This is logically right and reasonable argument, right? Why not?

 

[PeterDonis]

Let's tackle the issue head on

That's not what you're doing. What you're doing is trying to give a precise interpretation to vague ordinary language. That doesn't work. Yes, the descriptions I've tried to give in different discussions, in ordinary language, might seem contradictory to you when put alongside each other. That's because they were different descriptions given in different contexts for different purposes, none of which were the purpose you're trying to put them to here. Trying to fit all those ordinary language descriptions, as they stand, into a single consistent picture is a fool's errand; there isn't one if the only tool you have to reason with is ordinary language.

If you really want to understand what the MWI, or any other interpretation of QM, says, you first have to learn the basic underlying math that all of the interpretations are based on. You have to learn the math of wave functions, state vectors, operators, Hamiltonians, Schrodinger picture vs. Heisenberg picture, etc., etc. (And if you really want to do it right, you then have to unlearn a good chunk of all that in order to learn quantum field theory, which you need to do in order to be relativistically correct.) Then you have to learn how all this math relates to what we actually observe in experiments, free of any interpretation. (Some physicists call what I am describing the "shut up and calculate" interpretation, but it's not really an "interpretation", it's just a description of the mathematical model and how it makes predictions and how those predictions are compared with experimental results.) If you don't understand all that, you won't even understand the questions that the various interpretations are trying to answer.

Actually learning all that stuff takes years, but if you want to take one small step, go back and read my post #12 in this thread. Notice that I don't use the words "physical reality" once. Nor do I make any of the claims that are apparently confusing you.

Then read my post #15 in this thread, and note carefully the statement of Manyme's that I quoted in that post and responded to. That's what I'm going to fall back on any time it looks like someone is misinterpreting my ordinary language attempts to explain claims that the various interpretations make.

 

[bhobba]

I never said philosophy was rubbish, just that it's not physics and isn't what we concern ourselves with on this forum.

Philosophy isn't rubbbish - its a perfectly legit disipine of much academic value.

The trouble with philosophy however is it never really resolves anything. Science has a resolving mechanism built right into its foundations:


That's the key difference. The reason we don't discuss it here is it leads to threads that go on and on but get nowhere. We actually want to help people understand science not be confused.

That said, since this is about MW there is a good textbook available on it by David Wallace who just happens to have a PhD is both philosophy and particle physics:
https://www.amazon.com/dp/0198707541/?tag=pfamazon01-20

Its not for the beginner though. But it does give the modern version of MW, which is basically the same as Consistent Histories, but it doesn't have the many worlds. In Consistent Histories QM is the stochastic theory about histories. In MW each history is a world.

Thanks
Bill

 

[bhobba]

“Young man, in mathematics you don't understand things. You just get used to them.”
―John von Neumann

Von Neumann, a man of great mathematical ability, was speaking from his rather lofty perspective as likely one of the 10 greatest mathematicians of all time. He was also a polymath - one of the greatest ever. What he saw easily the rest of us have to work very hard at - and yes through that work you do gain understanding.

Thanks
Bill

 

[bhobba]

But, also, is the state of the cat in terms of any macroscopic property really an observable in any QM sense?

Its a difficult issue, that, without going into the details (start a new thread if interested) is part of the Schrodenger Cat resolution, its very difficult to decide where the cat ends and environment begins. Feynman somewhere in the early chapters of his famous lectures looks at the issue from the viewpoint of what the surface of a table is. Look at deciding where it starts and ends is - well not even possible. Again this is part of the explanation of why things like tables etc have classical properties via decoherence.

Thanks
Bill

 

[bhobba]

I understand it's the wave that interferes and how waves can result interference patterns, but I'm having a problem with it being just something mathematical and non-physical.

This is the diffference betweeen pure and applied math.

A good example to understand this is good old probability theory which is based on the Kolmogorov axioms. These axioms speak of events. Pure mathematics doesn't worry what events are. Applied math, as you gradually learn how to use it, builds up the concept of what an event is in practice.

The best book for doing that in QM I know is - Ballentine - QM - A Modern Development
https://www.amazon.com/dp/9814578584/?tag=pfamazon01-20

Contrast this with a pure math appproach:
https://www.amazon.com/dp/0387493859/?tag=pfamazon01-20

Glance through both and you will see the difference.

Thanks
Bill

 

[mieral]

About quantum suicide or sorta..

Say your state is entangled with the system. If the electron is spin up.. you survive.. if the electron is spin down.. you commit suicide. After the experiment.. will you be alive or dead if it's MWI? It is emphasized the there is only one quantum system and there is only entanglement. I understand this and I know nothing gets duplicated in MWI. But is it not after the experiment.. one of you will come up dead and one alive? If nothing gets duplicated. Where did the alive version of you go and the dead version of you go?

 

[PeterDonis]

After the experiment.. will you be alive or dead if it's MWI?

In the MWI this question is not well-defined; "you" do not have a definite state after the experiment. Your state is entangled with the state of the electron. It's no different from two electrons being entangled--neither electron by itself has a definite state, only the system consisting of both of them does. Here instead of one electron, there's you: so neither you nor the electron have a definite state, only the system consisting of both you and the electron does.

is it not after the experiment.. one of you will come up dead and one alive?

No.

Where did the alive version of you go and the dead version of you go?

There are no such "versions" of you in the MWI. So this question is also not well-defined.

 

[mieral]

In the MWI this question is not well-defined; "you" do not have a definite state after the experiment. Your state is entangled with the state of the electron. It's no different from two electrons being entangled--neither electron by itself has a definite state, only the system consisting of both of them does. Here instead of one electron, there's you: so neither you nor the electron have a definite state, only the system consisting of both you and the electron does.
No.
There are no such "versions" of you in the MWI. So this question is also not well-defined.

But in the double slit experiment. The electron passes thru both slits in different branches/worlds. So they explain that we saw it hits one location in the screen in this world.. But in other worlds.. they hit different parts of the screen.. so how can you say the other worlds aren't there and actually duplicated? If someone else knows the answer to this. Please let us know because Peterdonis wil be back after 12 hours at this time and it is too long to wait for the answer. Thanks.

 

[PeterDonis]

in the double slit experiment. The electron passes thru both slits in different branches/worlds

No, it doesn't. The "branching" in the MWI--entanglement of a system with a measuring device--doesn't happen until a measurement is made. In the double slit experiment, that happens when the electron hits the detector screen and the position where it arrives is recorded. So according to the MWI, one run of the double slit experiment, with one electron, creates an entangled state with many terms (many more than two--how many depends on how accurately the detector screen detects position), each of which consists of the electron hitting the detector at a particular position and the detector showing a bright spot at that position.

how can you say the other worlds aren't there and actually duplicated?

The answer to this question is the same as all the previous times you asked it. What is going on is not a duplication of anything. It's just entanglement: the state of the system (electron in this case) gets entangled with the state of the measuring device (detector screen in this case). That's it. Do not ask this question again.

 

[mieral]

No, it doesn't. The "branching" in the MWI--entanglement of a system with a measuring device--doesn't happen until a measurement is made. In the double slit experiment, that happens when the electron hits the detector screen and the position where it arrives is recorded. So according to the MWI, one run of the double slit experiment, with one electron, creates an entangled state with many terms (many more than two--how many depends on how accurately the detector screen detects position), each of which consists of the electron hitting the detector at a particular position and the detector showing a bright spot at that position.
The answer to this question is the same as all the previous times you asked it. What is going on is not a duplication of anything. It's just entanglement: the state of the system (electron in this case) gets entangled with the state of the measuring device (detector screen in this case). That's it. Do not ask this question again.

Oh you are still awake.
But why do we only see one hit in the screen, what happens to the other hits.. do they just vanish. I can wait for the answer many hours later.
Meantime. Hope others can confirm if this is what orthodox Many World actually says in MWI.. because for many years.. I thought otherwise.

 

[PeterDonis]

why do we only see one hit in the screen, what happens to the other hits

According to the MWI, if we look at the screen, our state becomes entangled with the screen's state, just as the screen's state became entangled with the electron's state. So the state of the system as a whole--electron + screen + us--now includes multiple terms, each of which is a product of an eigenstate of electron position (corresponding to some location on the screen), an eigenstate of screen measurement of position (corresponding to the screen showing a spot at some location), and an eigenstate of us observing the screen (corresponding to us seeing the spot at some location on the screen). So now we, like the electron and the screen, no longer have a definite state: only the total system does.

This is how the MWI deals with any kind of interaction, so no matter what experiment or scenario you ask about, the answer will look the same.

 

[mieral]

According to the MWI, if we look at the screen, our state becomes entangled with the screen's state, just as the screen's state became entangled with the electron's state. So the state of the system as a whole--electron + screen + us--now includes multiple terms, each of which is a product of an eigenstate of electron position (corresponding to some location on the screen), an eigenstate of screen measurement of position (corresponding to the screen showing a spot at some location), and an eigenstate of us observing the screen (corresponding to us seeing the spot at some location on the screen). So now we, like the electron and the screen, no longer have a definite state: only the total system does.

This is how the MWI deals with any kind of interaction, so no matter what experiment or scenario you ask about, the answer will look the same.

Thanks. For me I had hard time believing in Many worlds before because I thought the excess baggage was multiplicities of worlds where at the end of the day.. I have many me in other worlds and I can't believe this. But with the context of what you describe. Then I think Many world is really elegant and possible and I may just become a many worlder now. Thanks again for explaining something that removes many years of wrong thinking!

 

[PeterDonis]

Then I think Many world is really elegant and possible

Bear in mind that, when we talk about conscious observers like ourselves, the MWI is making an assumption (IMO a very big one): that each term in the entangled state I described has a separate consciousness associated with it.

(Note that, at least as I understand it, Schrodinger's original motivation in constructing his cat thought experiment was to produce a reductio ad absurdum of this idea--he expected that people would recognize as obvious nonsense the claim that a sentient being like a cat could end up in an entangled state where one branch was "alive" and the other was "dead". But for the MWI to work, this has to actually be the case.)

 

[bhobba]

Schrodinger's original motivation in constructing his cat thought experiment was to produce a reductio ad absurdum of this idea--he expected that people would recognize as obvious nonsense the claim that a sentient being like a cat could end up in an entangled state where one branch was "alive" and the other was "dead". But for the MWI to work, this has to actually be the case.)

True

But he went further and claimed an actual superposition of alive and dead states which a little thought shows it utterly impossible.

Without going into why, but we know it's an observed fact here in the macro world (we do know why but its not really relevant here here) the cats constituent parts have definite position. The position of those parts of alive and dead cats are totally different eg alive cats breathe and their heart beats - dead cats do not. Since cats actually have definite position, like virtually all objects here in the macro world, you can't have a superposition of position - this is from the very foundations of QM. So you can't have a macro object like a live and a dead cat in superposition. Yes I know the great Dirac states in principle you can have a superposition of any two states - but what is, for theoretical convenience considered true, in principle (it's given a name BTW the strong superposition principle and is used a lot in the the foundations of QM) is not always true in practice for various reasons like the above.

Thus the issue is exactly as Peter said - one branch is alive - the other dead - an actual superposition is not possible.

Personally my view is MW is just the consistent histories interpretation where QM is the stochastic theory of histories with the twist each history happens in its own world. In that way we just have an evolving state for the whole universe - or maybe multiverse if some cosmological theories are correct. Which is better - it's purely a matter of taste.

Thanks
Bill