I Making the wave observable in the double-slit experiment

[Morbert]

The discussion I was trying to start is the idea that the measurement problem could be the result of treating observation classically instead of quantum mechanically, which is how it's usually presented in the double slit experiment. If we think of particles as decohered waves, the problem goes away, although it does leave other implications to work through, depending on the interpretation.

Instrumentalists can have their cake and eat it. Quantum theory is mature enough that we can extend the theory to the relevant collective degrees of freedom of the measurement apparatus and establish the correlations between macroscopic properties of the apparatus and microscopic properties of the measured system (having the cake). We can also acknowledge that the measurement process produces irreversible, classical records registered by the experimenter (eating the cake).

 

[Nugatory]

The discussion I was trying to start is the idea that the measurement problem could be the result of treating observation classically instead of quantum mechanically, which is how it's usually presented in the double slit experiment. If we think of particles as decohered waves, the problem goes away, although it does leave other implications to work through, depending on the interpretation.

Although there was some early optimism along these lines, it is not at all clear that thinking in terms of decohered waves helps with the measurement problem. Yes, that line of thought explains why macroscopic measuring devices will only produce classical results (the cat is dead or alive and we don't know which until we look, but not in a coherent superposition of dead and alive before we look). How do we get from the quantum mechanical prediction of various probabilities of various outcomes to the post-measurement fact that we got this result rather than that? What physical process justifies discarding some components of the wave function in a collapse interpretation, or confining our attention to one branch of the wave function in MWI interpretations?

 

[PeroK]

Alright well I'm confused then as to why the wave equation gets treated as just a calculation tool in the minimal interpretation if you can observe the entire photon paths making interference? Other kinds of particles get treated the same in QM, so photons should be enough empirical evidence for there being a wave.

Let's replace light with electrons and look at the double-slit experiment from a purely QM viewpoint.

The electron initially is constrained by a narrow uncertainty. In the rest frame of the electron it is perhaps a narrow Gaussian.

When it reaches a single slit it is effectively in an infinite potential well. The Gaussian must then be decomposed into eigenstates of the potential well, each of which has a charteristic lateral momentum.

When it exits the slit it is in a superposition of these eigenstates and already has a superposition of quantized lateral momenta.

This is how the wave pattern immediately after the slits is explained.

Note that the usual heuristic explanation in terms of the uncertainty principle does not fully explain the single or double slit in terms of the quantized lateral momenta.

 

[PeterDonis]

The electron initially is constrained by a narrow uncertainty. In the rest frame of the electron it is perhaps a narrow Gaussian.

This is momentum uncertainty, or more precisely lateral momentum uncertainty, correct? In the usual idealized case the electron's state is a plane wave with zero lateral momentum.

 

[PeroK]

This is momentum uncertainty, or more precisely lateral momentum uncertainty, correct? In the usual idealized case the electron's state is a plane wave with zero lateral momentum.

Yes, effectively zero lateral momentum. The Gaussian would spread out only slowly laterally relative to the time to the slit.

PS and the breadth of the Gaussian must encompass both slits.

 

[Quantum Waver]

What physical process justifies discarding some components of the wave function in a collapse interpretation, or confining our attention to one branch of the wave function in MWI interpretations?

In GRW, it would be stochastic as I understand it. In MWI, it's because we're in this decohered branch.

 

[Nugatory]

In GRW, it would be stochastic as I understand it. In MWI, it's because we're in this decohered branch.

Right, and that's just restating the problem not resolving it. Why this decohered branch and not that one? Why are we only able to access one branch?

 

[Quantum Waver]

Right, and that's just restating the problem not resolving it. Why this decohered branch and not that one? Why are we only able to access one branch?

Entanglement with the environment causes the interference with different branches to be suppressed. As for why we're in one branch and not another, that's a philosophical question of indexicality that would apply the same in an infinite universe. Why here and not somewhere far away? Because we're here and our doppelgängers are elsewhere is the only answer i can give to that question.

 

[DrChinese]

That would be Bohr's complementarity. Bohmian mechanics would say the wave guides the particles. MWI would say particle-behavior emerges from decoherence.

The decoherence from the smoke isn't destroying the interference pattern of the beam. The core issue here is that the double slit experiment is presented as classical-looking particles forming an interference pattern until their path to the screen is detected. But that doesn't explain cancellation unless the particles are waving on their way to the screen.

Sure that the unobserved particle isn't a wave. The two videos are making a case for particles being waves, and only particle-like in a non-classical way.

You are mixing metaphors with you commentary. First, as @PeterDonis explained, the experiment with a laser and smoke has no useful connection to the quantum description of light in a double slit setup. That would be obvious if you reduced the intensity so that one photon at a time was present in the apparatus. Then you would notice that the addition of smoke merely causes some photons to be absorbed by the smoke and some others to have which slit information present.

As to whether the wave function is "real" i.e. "ontic": An important paper on that exact debate came out in 2012 (of course there have been many on the subject). Known as "PBR", the authors conclude that with a couple of reasonable assumptions, the quantum state is a description of reality - and not a description of our knowledge (or lack thereof). Not everyone accepts their result, and not all interpretations need be modified if you do accept it. But generally, quantum interpretations featuring "epistemic" descriptions are excluded. Those include Bayesian-type interpretations, though those followers typically deny the PBR result. I would label the PBR paper otherwise as generally accepted.

https://arxiv.org/abs/1111.3328

"Here we present a no-go theorem: if the quantum state merely represents information about the real physical state of a system, then experimental predictions are obtained which contradict those of quantum theory. The argument depends on few assumptions. One is that a system has a “real physical state” – not necessarily completely described by quantum theory, but objective and independent of the observer."

 

[Quantum Waver]

As to whether the wave function is "real" i.e. "ontic": An important paper on that exact debate came out in 2012 (of course there have been many on the subject). Known as "PBR", the authors conclude that with a couple of reasonable assumptions, the quantum state is a description of reality - and not a description of our knowledge (or lack thereof). Not everyone accepts their result, and not all interpretations need be modified if you do accept it. But generally, quantum interpretations featuring "epistemic" descriptions are excluded. Those include Bayesian-type interpretations, though those followers typically deny the PBR result. I would label the PBR paper otherwise as generally accepted.

https://arxiv.org/abs/1111.3328

"Here we present a no-go theorem: if the quantum state merely represents information about the real physical state of a system, then experimental predictions are obtained which contradict those of quantum theory. The argument depends on few assumptions. One is that a system has a “real physical state” – not necessarily completely described by quantum theory, but objective and independent of the observer."

I've seen that paper mentioned on here, but haven't read it. Thanks for the link.

 

[PeterDonis]

Why this decohered branch and not that one? Why are we only able to access one branch?

Let me try to restate this in a way that might help make the problem clearer.

Normally in QM, when a system is entangled with another system, we don't describe it as there being multiple "copies" or "branches" of each system, each in a different state. We say that neither system by itself has any definite state at all: only the joint system comprising both of them does. For example, if we have two electrons in the singlet state, we say that neither electron has a definite spin by itself; we say that only the joint two-electron system has a definite state.

The MWI, however, changes this for the case of a measuring device being entangled with a measured system. In this case, according to the MWI, we do describe it as there being multiple "copies" or "branches", each in a different state. (Everett's original thesis used the term "relative state", but that doesn't change anything.) The question is, why is this justified? Why does it suddenly become OK to describe this case of entanglement in a way that we don't describe any other case of entanglement (i.e., any case that doesn't involve a measurement)?

"Decoherence" by itself doesn't solve this problem, because the way we normally describe ordinary entangled systems makes no mention of quantum coherence. The two entangled electrons in my example above could just as well fly off into space in opposite directions and never interact again, and it wouldn't make any difference.

 

[Quantum Waver]

When it reaches a single slit it is effectively in an infinite potential well. The Gaussian must then be decomposed into eigenstates of the potential well, each of which has a charteristic lateral momentum.

When it exits the slit it is in a superposition of these eigenstates and already has a superposition of quantized lateral momenta.

This is how the wave pattern immediately after the slits is explained.

As a side note, Sean Carroll maintains (or is exploring the idea) that fundamental reality is best described by a list of energy eigenvalues and the components of a vector in Hilbert space. Everything else emerges from that structure. But that's way too abstract for me to make sense of.

 

[Quantum Waver]

"Decoherence" by itself doesn't solve this problem, because the way we normally describe ordinary entangled systems makes no mention of quantum coherence. The two entangled electrons in my example above could just as well fly off into space in opposite directions and never interact again, and it wouldn't make any difference.

Does entanglement with many different systems make the difference? A detector being many particles, plus everything else nearby.

 

[PeterDonis]

Does entanglement with many different systems make the difference?

What I have said about the normal way entanglement is described is the same regardless of how many systems/degrees of freedom are involved in the entanglement.

 

[PeroK]

As a side note, Sean Carroll maintains (or is exploring the idea) that fundamental reality is best described by a list of energy eigenvalues and the components of a vector in Hilbert space. Everything else emerges from that structure. But that's way too abstract for me to make sense of.

Sounds like orthodox QM to me!

 

[Quantum Waver]

What I have said about the normal way entanglement is described is the same regardless of how many systems/degrees of freedom are involved in the entanglement.

Branches would be the classical appearance of the world for observers. Decoherence would explain why the world looks classical for an observe relative to that part of the entangled system.

 

[PeterDonis]

Branches would be the classical appearance of the world for observers. Decoherence would explain why the world looks classical for an observe relative to that part of the entangled system.

Not according to the way we normally describe entanglement. "Branches" don't correspond to anything observable the way we normally describe entanglement. Decoherence does nothing to change that.

The MWI has to change this normal way of describing entanglement in order to make claims like the ones you make in the quote above.

 

[Quantum Waver]

Not according to the way we normally describe entanglement. "Branches" don't correspond to anything observable the way we normally describe entanglement. Decoherence does nothing to change that.

The MWI has to change this normal way of describing entanglement in order to make claims like the ones you make in the quote above.

I understand MWI to be a critique of the way QM is normally described because of its insistence on classical notions of observation, going back to Bohr and Heisenberg. That was my motivation for this thread, inspired by the two videos in the first post.

 

[PeterDonis]

I understand MWI to be a critique of the way QM is normally described because of its insistence on classical notions of observation

But MWI still has a classical notion of observation: it says each branch contains a definite observation of a measurement result, based on the fact that, if we restrict attention to that branch only, we have a "state" that corresponds to the same classical notion of observation that is used in collapse interpretations. The only difference is that in collapse interpretations, that state is the only one physically present; whereas in the MWI, all of the branches are physically present, we just ascribe a different classical observation to each branch and use decoherence to explain why they can't interfere with or interact with each other.

That was my motivation for this thread, inspired by the two videos in the first post.

The experiments in those videos say nothing about any QM interpretation vs. any other. All QM interpretations make the same predictions for experimental results.

 

[DrChinese]

1. Entanglement with the environment causes the interference with different branches to be suppressed.

2. Because we're here and our doppelgängers are elsewhere is the only answer i can give to that question.

1. This is a word salad that has no meaning in physics. Entanglement is not present and has no impact on the predictions of QM vis a vis MWI branches. There is no "suppression" of branches, in standard MWI all branches are equally probable.

2. There are no "doppelgängers" in our universe, although I guess it is possible they exist in some other universe (branch). There could also be magic unicorns there, that's about equally likely from my perspective.

This is getting pretty far afield of the original post.

 

[PeterDonis]

Entanglement is not present and has no impact on the predictions of QM vis a vis MWI branches

I'm not sure what you mean by this. In the MWI, the fact that measurement entangles the measuring device with the measured system is taken literally: that's what actually, physically happens. Since there is no collapse in the MWI, the entanglement created by measurement never goes away.

 

[Quantum Waver]

I was paraphrasing the SEP article on MWI and Carroll makes similar statements about branch suppression and duplicate observers in his talks.

 

[PeterDonis]

I was paraphrasing the SEP article on MWI and Carroll makes similar statements about branch suppression and duplicate observers in his talks.

Please give specific references.

 

[Quantum Waver]

The experiments in those videos say nothing about any QM interpretation vs. any other. All QM interpretations make the same predictions for experimental results.

The videos are about how those two experiments changed Dr. Yoganathan’s understanding of QM.

 

[Quantum Waver]

Please give specific references.

The concept of a “world” in the MWI belongs to part (ii) of the theory, i.e., it is not a rigorously defined mathematical entity, but a term defined by us (sentient beings) to describe our experience. When we refer to the “definite classically described state” of, say, a cat, it means that the position and the state (alive, dead, smiling, etc.) of the cat is specified according to our ability to distinguish between the alternatives, and that this specification corresponds to a classical picture, e.g., no superpositions of dead and alive cats are allowed in a single world. https://plato.stanford.edu/entries/qm-manyworlds/#WhatWorl

The identity section is below that. On my phone, best I can do right now.

 

[PeterDonis]

The videos are about how those two experiments changed Dr. Yoganathan’s understanding of QM.

Which does not contradict what I said.

 

[PeterDonis]

The identity section is below that.

While the section you quote appears to disclaim any specific mathematical representation of a "world", sections 3.2 and 3.3 make clear that (a) each "world" is assigned a definite state (equation 1), which represents a classical state ("definite macroscopic state") for all "objects", and (b) the full quantum state of the universe (equation 2) is an entangled state, since it is a sum of terms and the same degrees of freedom appear in each term (i.e., in the "state" assigned to each "world"). Which is what I said earlier.

 

[PeroK]

The videos are about how those two experiments changed Dr. Yoganathan’s understanding of QM.

These videos are aimed at a general audience and attract thousands of comments. It's not clear the extent to which she has discussed this experiment with her peers. Occasionally, you see another physicist commenting on them, but the expert comment gets drowned out. In my experience, the people who post on YouTube tend to ignore expert comment. In any case, you shouldn't take such videos as peer-reviewed physics.

In a previous post I gave an explanation for the detection pattern after the slits. I would say it shouldn't have been a surprise. Although, she admits in the video that she'd hadn't thought much about what happens between the slits and the screen before.

If you could get Dr Yoganathan to post on here that would be great. Then we can have a serious discussion about this.

 

[PeroK]

PS this is why we shouldn't be discussing material in such videos. No matter how expert the poster. The videos are designed to spark an interest in QM and not be the definitive word on the subject.

 

[vanhees71]

Let's replace light with electrons and look at the double-slit experiment from a purely QM viewpoint.

The electron initially is constrained by a narrow uncertainty. In the rest frame of the electron it is perhaps a narrow Gaussian.

Well, the incoming wave function must be wide enough in position space to cover at least both slits! You can't see interference effects/wave properties with wave packets too narrow in space. They are then necessarily broad in momentum, and it's thus a priori hard to see intereference patterns, because the broad spectrum of the wave blurs the intereference patterns which you would when using an (almost) monochromatic wave.

When it reaches a single slit it is effectively in an infinite potential well. The Gaussian must then be decomposed into eigenstates of the potential well, each of which has a charteristic lateral momentum.

When it exits the slit it is in a superposition of these eigenstates and already has a superposition of quantized lateral momenta.

This is how the wave pattern immediately after the slits is explained.

Note that the usual heuristic explanation in terms of the uncertainty principle does not fully explain the single or double slit in terms of the quantized lateral momenta.

One simpler but still pretty good approximation is to use Kirchhoff's theory of diffraction, which applies here as in electrodynamics, because all you solve is the Helmholtz equation with the appropriate boundary conditions imposed by the grating. Then you get the diffraction pattern for an arbitray wave by superposition (Fourier transform).