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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.

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  • $\begingroup$ Maybe my answer to a similar question helps physics.stackexchange.com/q/507858 $\endgroup$ – anna v Oct 20 '19 at 11:34
  • $\begingroup$ @annav Yes, your Answer to that other question is great, my thoughts exactly. But I've never heard any MW theorist talk about the worlds interfering with each other; in fact Carroll is pretty explicit in his lecture about them only branching. $\endgroup$ – Jerry Guern Oct 20 '19 at 11:50
  • $\begingroup$ Not an mwi fan or expert, but I don't think mwi interpretation of double slit experiment with interference of two slits taking place would assume that there is a world where the two slits don't interfere. The number of worlds which end up with screen dots with the usual interference pattern is immensely bigger than number of worlds where the dots are devoid of such interference. This by design of the manyworld, it has to obey the "psi squared" Born rule. $\endgroup$ – Ján Lalinský Oct 20 '19 at 11:59
  • $\begingroup$ In metaphysics you will find the worlds interfering :) ( example Jane Robert's Seth sayings) $\endgroup$ – anna v Oct 20 '19 at 12:08
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    $\begingroup$ Related: How many "many worlds" theorists does it take to get a straight answer about anything? $\endgroup$ – Mitchell Porter Oct 22 '19 at 10:54
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"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.

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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.

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  • $\begingroup$ If you watch the Carroll lecture, you'll find that what you've said here about MWI proponents is not true. In his example of a particle splitting into an entangled spin pair, branching occurs when the particles are emitted, not at the detector. $\endgroup$ – Jerry Guern Oct 20 '19 at 16:24
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    $\begingroup$ @JerryGuern: Not all MWI proponents agree on what it means for "worlds" to "split". Many of them think that the world doesn't split until the state "decoheres", which for an entangled spin pair happens at the detectors. $\endgroup$ – Peter Shor Oct 20 '19 at 17:33
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    $\begingroup$ @JerryGuern "Worlds" "splitting" is purely an illustrative device to help describe MWI to laypeople. The real theory is to just compute using the Schrodinger equation plus the idea of decoherence; the idea of separate "worlds" never enters into it. $\endgroup$ – knzhou Oct 21 '19 at 22:39
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    $\begingroup$ @JerryGuern Like every other analogy in popular physics, "world splitting" starts to make no sense if you push it too far -- which is why it's just an analogy to describe a theory, not the theory itself. $\endgroup$ – knzhou Oct 21 '19 at 22:39
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    $\begingroup$ @JerryGuern: that's what I'm saying. The world splits when the quantum state decoheres, which doesn't happen until the detectors. However, decoherence is a very complicated process, and my analysis is probably overly simplistic. $\endgroup$ – Peter Shor Oct 22 '19 at 1:41
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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.

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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.

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  • $\begingroup$ I didn't bypass interference, and I didn't ask whether MWI was meaningful. My question was specifically how interference is explained under MWI. $\endgroup$ – Jerry Guern Oct 20 '19 at 16:21
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    $\begingroup$ Upon closer reading, I agree. Still you assume that the electron passes through one slit or the other, which precludes interference. You asked how interference was explained in MWI. If interference cannot be explained than MWI is not meaningful. $\endgroup$ – my2cts Oct 20 '19 at 17:32
  • $\begingroup$ The term 'interference' is historical and misleading but it is still taught today in high school and in early university courses. The interference explanation does work mathematically in many situations (double slit approximation, thin film interference). Ultimately it falls short as in single photon experiments where we realize there are no photons or no energy in the dark areas. The interference explanation is convenient and as well was the norm in the early days of physics .... early 1900s. Interference violates conservation of energy for photons. $\endgroup$ – PhysicsDave Oct 22 '19 at 22:20
  • $\begingroup$ @PhysicsDave This is very wrong $\endgroup$ – my2cts Oct 23 '19 at 4:14
  • $\begingroup$ @my2cts What is taught at MIT for example is "The total instantaneous electric field E at the point P on the screen is equal to the vector sum of the two sources:E =E1 + E2 ." They do not add probability waves for the DS experiment in first year, that would likely be done at the PhD level. This classical approach works quite well to explain DS patterns and thin films. The probability wave for a photon (called photon wave function) is a difficult concept and the boundary conditions are required to calculate the probable paths, it is not as simple as saying the probability waves interfere. $\endgroup$ – PhysicsDave Oct 23 '19 at 12:59
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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.

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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.

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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.

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    $\begingroup$ No. Quantum mechanics requires that the difference of two path lengths that interfere must be a multiple of the wavelength. $\endgroup$ – Peter Shor Oct 22 '19 at 1:44
  • $\begingroup$ @PeterShor I think you are confusing QM with classical mechanics. P.S. if you use the word "interfere" then you are likely violating conservation of energy. Probability and wave function explanations are the way to go. $\endgroup$ – PhysicsDave Oct 22 '19 at 22:08
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    $\begingroup$ I don't think I'm confusing anything. In the double slit experiment, two paths constructively interfere if the length difference between them is an integral number of wavelengths, and destructively interfere if the difference between them is a half-integral number of wavelengths. How do you think it works? $\endgroup$ – Peter Shor Oct 22 '19 at 22:18
  • $\begingroup$ @PeterShor The term 'interference' is historical and misleading but it is still taught today in high school and in early university courses. The interference explanation does work mathematically in many situations (double slit approximation, thin film interference). Ultimately it falls short as in single photon experiments where we realize there are no photons or no energy in the dark areas. The interference explanation is convenient and as well was the norm in the early days of physics .... early 1900s. Interference violates conservation of energy for photons. $\endgroup$ – PhysicsDave Oct 22 '19 at 22:24

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