How do “many worlds” theorists explain particle double-slit interference patterns?

Question

In the past couple of weeks I’ve re-watched Sidney Coleman’s wonderful 1994 lecture “Quantum Mechanics” in Your Face” and Sean Carroll’s 2019 Google talk “Something Deeply Hidden: Quantum Worlds & the Emergence of Spacetime”. They’re both fascinating and undergrad accessible, and I highly recommend treating yourself to both.

Coleman, 1994: https://www.youtube.com/watch?v=EtyNMlXN-sw

Carroll, 2019: https://www.youtube.com/watch?v=F6FR08VylO4

Both professors dismiss the Copenhagen Interpretation’s concept of wave collapse, treat the observer as a QM system, and set up the “many worlds” interpretation (MWI) of QM, although both express reservations about that name, which was coined by others.

My question is, how do professional physicists who subscribe to the MWI explain the electron double-slit interference pattern? If every quantum decision splits the wave function into branching histories, and we shoot 1000 electrons one-at-a-time at a double slit, then the wave function should split into 2^1000 "worlds" corresponding to every combination of which slit each electron passed through. But then none of the 2^1000 observers would ever see interference between electrons coming from the left AND right simultaneously. They would each just see two overlapping single slit patterns with no “dark” bands.

I’m not a professor, but the way I’ve explained it to myself is that those branching histories must actually come back together and even prune some branches off the "tree". When you shoot an electron through the slits and it hits a “bright” band of the double-slit pattern, its left and right histories come back together into one. If an electron hits a “dark” band, the two histories that got it there are incompatible, and so they prune each other off of the tree, and so no history that leads to an electron in the dark band will survive.

But again, that’s just me telling myself a story that makes sense to me. Have any professional physicists published theories about the branching “many worlds” recombining or pruning each other? If not, how else do they explain the double slit pattern?

OP EDIT: Some commenters said that even in the MWI, the electron passes through both slits and creates an interference patter. I’m skeptical of this claim about MWI, because it would still require that electron’s wave function to collapse—Copenhagen style—to a single point on the target, and getting rid of Copenhagen collapse was a major motivator of MWI.

I would also be clear that I’m asking what MWI supporters believe about this issue, not whether people think MWI is correct or not.

Also, yes I know that serious MWI proponents don't literally believe in "worlds" "splitting". It's just terminology, and both professors voiced this reservation about the name in the lectures I linked.

Answer 1

"Many worlds" is just a name, and not a very good one, since the theory that it refers to says nothing about worlds or splitting.

The closest thing to an explicit rule about splitting of histories in quantum mechanics is the Born rule (wavefunction collapse) which says that at a specific time the universe chooses one measurement outcome and commits to it permanently. The outcomes that it didn't choose are alternate histories of the universe (in the "alternate-history novel" sense), and while most people probably think that those alternate histories don't happen, that's only a philosophical position and not something that we could ever know for certain.

When you write

If every quantum decision splits the wave function into branching histories, and we shoot 1000 electrons one-at-a-time at a double slit, then the wave function should split into 2^1000 "worlds" corresponding to every combination of which slit each electron passed through.

you are essentially describing the situation when the Born rule is applied as each particle passes the slits.

The many worlds/relative state picture doesn't have the Born rule, it just has continuous evolution according to the Schrödinger equation. The prediction of the Schrödinger equation is that you do get an interference pattern in the basic double-slit experiment (the one with no detection apparatus at the slits). This is completely uncontroversial, so it isn't necessary for MWI proponents to convince anyone else that it's true.

those branching histories must actually come back together and even prune some branches off the "tree". When you shoot an electron through the slits and it hits a “bright” band of the double-slit pattern, its left and right histories come back together into one. If an electron hits a “dark” band, the two histories that got it there are incompatible, and so they prune each other off of the tree, and so no history that leads to an electron in the dark band will survive.

This is a pretty accurate description of the sum over histories formulation of quantum mechanics, and it's a valid way of understanding double-slit interference, but it isn't what people usually mean when they talk about "worlds" in the MWI.

David Deutsch and a few others in his camp do say that quantum computers exploit interference between different MWI worlds, and that a working quantum computer would prove MWI correct. But with a notion of "world" that broad, their "MWI" is just ordinary quantum mechanics and it's already strongly confirmed by experiment. Everyone else defines a world as a part of the wave function that is permanently prevented by thermodynamic irreversibility from interfering with other parts. These worlds are undetectable (and useless for quantum computation) essentially by definition.

Answer 2

The many worlds interpretation (MWI) and the Copenhagen interpretation (CI) are not different physical theories, because in all real-world experiments devised so far, they make the same predictions. The theory is quantum mechanics. MWI and CI are interpretations. Physicists therefore do not have to pick one or the other to believe in. These days, attention has shifted away from MWI/CI and toward decoherence.

If every quantum decision splits the wave function into branching histories, and we shoot 1000 electrons one-at-a-time at a double slit, then the wave function should split into 2^1000 "worlds" corresponding to every combination of which slit each electron passed through.

Despite the name MWI, the many-worlds interpretation does not have to involve branching of universes. The original name of the interpretation was the "relative state interpretation." The most austere versions of MWI do not have any branching at all.

You seem to be imagining that the electron randomly picks one slit or the other to travel through. That's not correct. The electron passes through both slits. There is still interference when the electron reaches the detector.

Even in versions of MWI that talk about branching, people would imagine the branching as occurring at the detector.

Answer 3

Decoherence only happens at the detector, if it is present. If the detector is absent, then decoherence can only take place at the wall. But if you were to shoot the electron one at a time, you would only see one spot on the wall. It's only when you start sending multiple electrons that the interference pattern emerges (if there is no initial detector). This is consistent with both MWI and the Copenhagen interpretations. For example, here are the results of a double-slit-experiment performed by Dr. Tonomura showing the build-up of an interference pattern of single electrons. Numbers of electrons are 11 (a), 200 (b), 6000 (c), 40000 (d), 140000 (e):

An understanding of the experiment helps better understand what it does and does not entail: https://en.wikipedia.org/wiki/Double-slit_experiment#Interference_of_individual_particles

For further details about the specific experiment by Dr. Tonomura, check out this link: https://web.archive.org/web/20110114170600/http://www.hitachi.com/rd/research/em/doubleslit.html

Answer 4

In this experiment a 1000 electrons land on a sensor that creates an image of their position distribution. The probability of an electron to land on a particular location is given by the square of the wave function. This squared wave function is the famous interference pattern. Assuming the detector has N pixels, it takes in principle $2^N$ worlds to describe the result. Of course, inside each pixel it may again take $2^M$ , with M something of the order of Avogadro's number. I leave it to the reader to make up his own opinion on how meaningful MWI is in this context. I am confident that it may be helpful to consider the ensemble interpretation instead.

Answer 5

Many explanations of the MWI are bad. The best explanations to read are those given by David Deutsch in "The Fabric of Reality" chapter 2 and "The Beginning of Infinity" chapter 11 and

https://www.daviddeutsch.org.uk/many-minds-interpretations-of-quantum-mechanics/

https://arxiv.org/abs/quant-ph/0104033

In the MWI each system exists in multiple versions and under some circumstances those different versions can interfere with one another. During those inteference experiments it is not a good approximation to say that the different versions are in parallel universes because you can't explain the result without taking both versions into consideration. If information about the state of a system is copied out of the system during interference then the interference is suppressed and it may be a good approximation to treat the two versions as being in different universes, see:

https://arxiv.org/abs/1212.3245

So when a system is measured at the end of an interference experiment, it is a good approximation to regard the different versions as being in parallel universes.

You wrote:

Some commenters said that even in the MWI, the electron passes through both slits and creates an interference patter. I’m skeptical of this claim about MWI, because it would still require that electron’s wave function to collapse—Copenhagen style—to a single point on the target, and getting rid of Copenhagen collapse was a major motivator of MWI.

The explanation for the fact that you see a particular interference pattern after the experiment is that there are multiple versions of the measuring results and you see only one of them because of there is one version of you for each outcome and interference between the different versions is suppressed by the copying of information.

Answer 6

It is difficult to give a definitive explanation of the MWI, since there seems to be so many variations of it. However, a logical common denominator is the assumption that the branching occurs at those points at which the Copenhagen interpretation would assume that the wave function had collapsed, which in the two slits experiment would be when the particle passing through the slits encounters the detector screen beyond it. If the branching occurs at the screen, then it will embody the interference effects.

Answer 7

First, to address your final comment, yes I know that serious MWI proponents don't literally believe in "worlds" "splitting". Actually MWI proponents do literally believe in worlds splitting, which can be defined in terms of entropy release and decoherence.

Second, how is the double slit experiment described in MWI? The crucial point is that in the Copenhagen Intepretation the wavefunction collapses when it hits the final detector where the interference bands form. In MWI it is the same, except that there is no collapse at the final detector, so each possible outcome, for each electron (or photon), causes a splitting of worlds. After you have passed multiple electrons though the system the usual interference pattern has built up in most of the worlds. In a minority of worlds the pattern does not form 'correctly' - and would probably be dismissed in those worlds as just a statistical abnormality or outlier.

Answer 8

Interference is the most poorly explained concept in physics, often it is based on older classical thinking which is OK for many problems. The modern method is the probability wave but it is complex to apply the correct boundary conditions for the double slit. One way to understand it is to see that the wave function requires that the photon or electron must travel n multiples of its wavelength, any path that that is too long or too short is not highly probable.

Dark areas after the double slit are where almost no photons land! Bright areas get almost all photons.

The electron does not go thru both slits, just one, but it had a chance to go either way.