# I MWI and path of single electron

1. Jan 19, 2017

### 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?

2. Jan 19, 2017

### newjerseyrunner

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.

3. Jan 19, 2017

### Staff: Mentor

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.

4. Jan 19, 2017

### FallenApple

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.

5. Jan 19, 2017

### FallenApple

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

6. Jan 19, 2017

### Staff: Mentor

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.

It is.

7. Jan 20, 2017

### Manyme

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.

8. Jan 20, 2017

### 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.

9. Jan 20, 2017

### Manyme

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.

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?

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.

10. Jan 20, 2017

### Strilanc

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.

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.

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).

11. Jan 20, 2017

### Manyme

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

12. Jan 20, 2017

### Staff: Mentor

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.

13. Jan 20, 2017

### Manyme

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.

14. Jan 20, 2017

### Strilanc

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.)

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.

15. Jan 20, 2017

### Staff: Mentor

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.

16. Jan 20, 2017

### Manyme

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.

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

17. Jan 20, 2017

### Staff: Mentor

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.

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.

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

18. Jan 20, 2017

### Manyme

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 :).

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

19. Jan 20, 2017

### Staff: Mentor

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.

20. Jan 21, 2017

### Manyme

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.

21. Jan 21, 2017

### PeroK

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

22. Jan 21, 2017

### Manyme

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.

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?

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.

23. Jan 21, 2017

### PeroK

Can you quote the post that says this?

They have no choice.

24. Jan 21, 2017

### Manyme

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.

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.

25. Jan 21, 2017

### PeroK

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.

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.