Making the wave observable in the double-slit experiment

[Quantum Waver]

PS my mistake, it was Mermin who said it apparently.

In a 1989 article. Then he forgot he had written that phrase to characterize CI and had to do a web search in 2004 to make sure it wasn't Feynman.

But while “shut up and calculate” sounded dimly familiar to me as a characterization of a certain interpretive stance, I couldn’t recall where Feynman had written it. Mulling this over, a terrible thought began to dawn on me. Could it be that I myself had once used the phrase? If so, then it would appear that I had picked it up from something by Feynman, forgotten the source, and presented it as my own. Devastating! https://pubs.aip.org/physicstoday/article/57/5/10/412592/Could-Feynman-Have-Said-This#references-1

 

[WernerQH]

Instead, we can have a strong understanding of measurement without needing a primitive ontology of "what's going on". Rejecting a primitive ontology and adopting an instrumentalist approach does not mean abandoning the measurement problem.

Is there a measurement problem? "Measurement" appears to play an essential role in the formulation of quantum theory, but there seems to be no consensus on whether or not there is a measurement problem. Isn't this a peculiar situation for a theory that (after nearly a century!) can justifiably be called mature?

 

[Quantum Waver]

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.

I'll reference David Wallace's paper The Evertt Interpretation regarding entanglement and superposition.
http://philsci-archive.pitt.edu/8888/1/Wallace_chapter_in_Oxford_Handbook.pdf

How is this possible? Haven’t we just seen that the linearity of quantum mechanics commits us to macroscopic objects being in superpositions, in indefinite states? Actually, no. We have indeed seen that states like psi — a superposition of states representing macroscopically different objects — are generic in unitary quantum mechanics, but it is actually a non sequitur to go from this to the claim that macroscopic objects are in indefinite states. - S3, p4

And this matters, in turn, because it is interference phenomena which allow the different structures represented by a quantum state in a superposition from interacting with one another, so as influence each other and even to cancel out. If interference is suppressed with respect to a given basis, then evolving entangled superpositions of elements of that basis can be regarded as instantiating multiple independently evolving, independently-existing structures. Applying the analysis of emergence used in the previous section, we conclude that if macroscopic superpositions are decohered — as they inevitably will be — then such superpositions really should be taken to represent multiple macroscopic states of affairs. - S5, p10

What Wallace argues is that branches/worlds are emergent phenomena from the components of entangled environments, similar to how everyday objects are emergent from the microphysical. So while it's true the entire entangled state has no definitive values, classically emergent structures within appear to have definitive values, because the superposition isn't (feasibly) observable. That's what the classical world is understood to be in MWI.

 

[DrChinese]

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.

I don't believe you can call it "entanglement", as in the usual meaning given that. If that were true, monogamy of entanglement would be violated (since that same particle might have been entangled already). The implication of using the term "entanglement" in this context is that every quantum interaction results in entanglement.

There is an interaction I presume between each possible individual MWI branch when an observed particle interacts with the observer environment. I don't know what you would say is the entangled attribute/observable though. Or what the conserved quantity is.

 

[Quantum Waver]

Is there a measurement problem? "Measurement" appears to play an essential role in the formulation of quantum theory, but there seems to be no consensus on whether or not there is a measurement problem. Isn't this a peculiar situation for a theory that (after nearly a century!) can justifiably be called mature?

This is what Sean Carroll says about it in the prologue to his Something Deeply Hidden book:

There are basically two options. One is that the story we've been telling our students is woefully incomplete, and in order for quantum mechanics to qualify as a sensible theory we need to understand what a "measurement" or "observation" is, and why it seems so different from what the system does otherwise. The other option is that quantum mechanics represents a violent break form the way we have always though about physics before, shifting from a view where the world exists objectively and independently of how we perceive it, to one where the act of observation is somehow fundamental to the nature of reality.

David Wallace puts it this way:

So it seems that our standard approach to understanding the content of a scientific theory fails in the quantum case. That in turn suggests a dilemma: either that standard approach is wrong or incomplete, and we need to understand quantum mechanics in a quite different way; or that approach is just fine, but quantum mechanics itself is wrong or incomplete, and needs to be modified or augmented. Call these strategies “change the philosophy” and “change the physics”, respectively. http://philsci-archive.pitt.edu/8888/1/Wallace_chapter_in_Oxford_Handbook.pdf

Of course plenty of people disagree with them, and some of them think the measurement problem is solved/dissolved in their branch of QM interpretations. But the overall superposition remains undetermined.

 

[hutchphd]

Isn't this a peculiar situation for a theory that (after nearly a century!) can justifiably be called mature?

Why? That supposes a great number of our (tacit) prejudices are true. Remember the parable of the drunk with the car keys

 

[Morbert]

My impression is that you are reading things into this that he has not actually said (or meant). All he does is trying to explain why interpretation of QM was off-topic for a long time in physics departments, and why this state of affairs has changed in recent years. He is not pushing a specific interpretation of QM in that video, nor is he emphasizing the measurement problem about everything else, or claiming that having a primitive ontology would be the only way to make progress in interpretation of QM.

I think my reading of Carroll is reasonable. I've been looking through his writings this evening and I'm trying to find an instance where he tackles instrumentalism/anti-realism/Copenhagen as distinct from shut up and calculate. At the same time, I regularly find him framing realism as antithetical to shut up and calculate. E.g from "Something Deeply Hidden"

"Einstein would have none of it. He was firmly convinced that the duty of physics was precisely to ask what was going on behind the scenes, and that the state of quantum mechanics in 1927 fell far short of providing a satisfactory account of nature. [...] While Einstein failed to put forward a complete and compelling generalization of quantum mechanics, his insistence that physics needs to do better than shut up and calculate was directly on point."

If he is not conflating the two, then I can only assume he has an unfortunate blind spot for this large school of thought.

 

[Quantum Waver]

I think my reading of Carroll is reasonable. I've been looking through his writings this evening and I'm trying to find an instance where he tackles instrumentalism/anti-realism/Copenhagen as distinct from shut up and calculate. At the same time, I regularly find him framing realism as antithetical to shut up and calculate.

I found this on Carroll's blog:

The most important point is that the underlying goal of science is not simply making predictions — it’s developing an understanding of the mechanisms underlying the operation of the natural world. This point is made very eloquently by David Deutsch in his book The Fabric of Reality. As I mention in the dialogue, Deutsch chooses this quote by Steven Weinberg as an exemplar of hard-boiled instrumentalism:

The important thing is to be able to make predictions about images on the astronomers’ photographic plates, frequencies of spectral lines, and so on, and it simply doesn’t matter whether we ascribe these predictions to the physical effects of gravitational fields on the motion of planets and photons or to a curvature of space and time.

That’s crazy, of course — the dynamics through which we derive those predictions matters enormously. https://www.preposterousuniverse.com/blog/2008/03/15/science-and-unobservable-things/comment-page-2/

Carroll goes on to mention how physicists keep trying to devise experiments to find cases where the Standard Model fails to make an accurate prediction so that they can figure out the underlying mechanism. Prediction isn't enough, science needs to explain how the world works.

 

[hutchphd]

Prediction isn't enough, science needs to explain how the world works.

P:rediction is exactly enough. That's the point.

Whatever fairy tale you choose to wrap it in is exactly irrelevant unless it somehow enhances predictive value. As humans we do love a good story.

 

[Quantum Waver]

P:rediction is exactly enough. That's the point.

Whatever fairy tale you choose to wrap it in is exactly irrelevant unless it somehow enhances predictive value. As humans we do love a good story.

Carroll's point is that if prediction were enough, there wouldn't have been continued experiments trying to make the Standard Model fail. But imagine applying this view to evolution. Darwin wasn't trying to explain the mechanism(s) for the diversity of life, he was only trying to come up with a model for paleontologists to make predictions about their dig sites, or biologists when they locate a new species. That doesn't work very well, since the mechanisms of evolution explain the past history of life after it first emerged on Earth.

Do you view cosmology as a fairy tale? What about dinosaurs? Just a story we tell ourselves about big bones we found in the ground?

 

[hutchphd]

Carroll's point is that if prediction were enough, there wouldn't have been continued experiments trying to make the Standard Model fail.

I doubt that is what he said. Science continuously tests models. Exact reference please.

 

[Quantum Waver]

I doubt that is what he said. Science continuously tests models. Exact reference please.

It's a couple of paragraphs below the part I quoted.

If making predictions were all that mattered, we would have stopped doing particle physics some time around the early 1980’s. The problem with the Standard Model of particle physics, remember, is that (until we learned more about neutrino physics and dark matter) it kept making predictions that fit all of our experiments! We’ve been working very hard, and spending a lot of money, just to do experiments for which the Standard Model would be unable to make an accurate prediction. And we do so because we’re not satisfied with predicting the outcome of experiments; we want to understand the underlying mechanism, and the Standard Model (especially the breaking of electroweak symmetry) falls short on that score. https://www.preposterousuniverse.com/blog/2008/03/15/science-and-unobservable-things/comment-page-2/

That is very much in line with what Sean says on his podcast and in other talks regarding the interpretation of QM and the purpose of science.

 

[vanhees71]

Is there a measurement problem? "Measurement" appears to play an essential role in the formulation of quantum theory, but there seems to be no consensus on whether or not there is a measurement problem. Isn't this a peculiar situation for a theory that (after nearly a century!) can justifiably be called mature?

There is no measurement problem. To the contrary QT describes very accurately what's measured!

 

[gentzen]

I think my reading of Carroll is reasonable. I've been looking through his writings this evening and I'm trying to find an instance where he tackles instrumentalism/anti-realism/Copenhagen as distinct from shut up and calculate. At the same time, I regularly find him framing realism as antithetical to shut up and calculate. E.g from "Something Deeply Hidden"

So now you looked through his writings, and managed to find an instance where he at least used "shut up and calculate". But that instance shows no signs of any conflations with "instrumentalism/anti-realism/Copenhagen":

"Einstein would have none of it. He was firmly convinced that the duty of physics was precisely to ask what was going on behind the scenes, and that the state of quantum mechanics in 1927 fell far short of providing a satisfactory account of nature. [...] While Einstein failed to put forward a complete and compelling generalization of quantum mechanics, his insistence that physics needs to do better than shut up and calculate was directly on point."

The words "shut up and calculate" are unfriendly. (And that is why I protest if people claim Feynman or Carroll, or ... would embrace them.) I am an instrumentalist, and I would much prefer words like "let me calculate and explain". But in the quote passage, Sean skillfully used those unfriendly words in a friendly way, namely "physics need to do better than ..." where "..." is something very unfriendly. So he minimized the requirements on how physics "needs to improve".

If he is not conflating the two, then I can only assume he has an unfortunate blind spot for this large school of thought.

Which "two"? I count four notions in your post: "shut up and calculate", "instrumentalism", "anti-realism", and "Copenhagen".

All he does is trying to explain why interpretation of QM was off-topic for a long time in physics departments, and why this state of affairs has changed in recent years.

Where I could agree is that Sean conflates "shut up and calculate" and "interpretation of QM was off-topic for a long time in physics departments". If we look through his writings, we will probably find-out his thoughts and postions regarding "anti-realism" and "Copenhagen" (or we could ask him, if we really want to know). Regarding "instrumentalism," I guess Sean was careful not to say too much about it, because philosophers often use this denomination in a derogatory way, and Sean has enough contact with philosophers to be aware of this.

 

[Morbert]

Carroll goes on to mention how physicists keep trying to devise experiments to find cases where the Standard Model fails to make an accurate prediction so that they can figure out the underlying mechanism. Prediction isn't enough, science needs to explain how the world works.

He says

The most important point is that the underlying goal of science is not simply making predictions — it’s developing an understanding of the mechanisms underlying the operation of the natural world

Which sounds like shut up and calculate: "Who cares how the world works. All that matters is calculating predictions." At best it is an uncharitable reduction. The instrumentalist approach as exemplified by authors like Asher Peres is deeply concerned with how the microscopic world works at the fundamental level. It is deeply concerned with the ontological meaning of quantum theories. Instrumentalists maintain that the this deep understanding will be in terms of the impressions the microscopic world leaves on our instruments, and the dynamics between the microscopic world and these macroscopic tests and responses. Quoting Asher Peres in "Quantum Theory: Concepts and Methods"

There are many excellent books on quantum theory from which one can learn to compute energy levels, transistion rates, cross sections etc. The theoretical rules given in these books are routinely used by physicists to compute observable quantities. Their predictions can then be compared with the experimental data. There is no fundamental disagreement among physicists on how to use the theory for these practical purposes. However, there are profound differences in their opinions on the ontological meaning of quantum theory. The purpose of this book is to clarify the conceptual meaning of quantum theory.
[...]
The notion of "physical reality" thus acquires a new meaning with quantum phenomena, different from its meaning in classical physics. We therefore need a new language. We shall still use the same words as in everyday's life, such as "to measure", but the meaning of these words will be different.[...]

It is this conceptual meaning outlined by authors like Peres, which centers preparations, tests, and responses, that I have never seen Carroll tackle. He only ever speaks of deeper understanding in the context of an instrument-independent account of quantum systems (hidden variables, many worlds, spontaneous collapse).

 

[WernerQH]

There is no measurement problem. To the contrary QT describes very accurately what's measured!

Of course! I agree with you. Luckily quantum theory can be applied while a solution to the "measurement problem" is still lacking.

But how do you explain that so many physicists think that there is a measurement problem? Haven't they understood quantum theory? Might it take another century for physicists to reach a consensus about its correct interpretation?

 

[vanhees71]

That's an engima, and I don't know any physicists around me, who think there is a measurement problem. They all just use Q(F)T to describe what's measured ;-).

 

[Lord Jestocost]

Of course! I agree with you. Luckily quantum theory can be applied while a solution to the "measurement problem" is still lacking.

But how do you explain that so many physicists think that there is a measurement problem? Haven't they understood quantum theory? Might it take another century for physicists to reach a consensus about its correct interpretation?

"It is enough for any argument against the suggestion of a measurement problem that Schrödinger’s equation does not give an objective description of the motion of the quantum system. As long as you are an instrumentalist concerning the wave function, no argument can get you to believe that there is a measurement problem. It does not matter what sort of probabilities you support. It can be a problem only in the case that you are a scientific realist and believe that our best scientific theories give us a true or approximately true description of the world."

Jan Faye in „Faye J. 2016 Darwinism in disguise? A comparison between Bohr’s view on quantum mechanics and QBism. Phil. Trans. R. Soc. A 374: 20150236”.

 

[Morbert]

The words "shut up and calculate" are unfriendly. (And that is why I protest if people claim Feynman or Carroll, or ... would embrace them.) I am an instrumentalist, and I would much prefer words like "let me calculate and explain". But in the quote passage, Sean skillfully used those unfriendly words in a friendly way, namely "physics need to do better than ..." where "..." is something very unfriendly. So he minimized the requirements on how physics "needs to improve".
[...]
Which "two"? I count four notions in your post: "shut up and calculate", "instrumentalism", "anti-realism", and "Copenhagen".

Claim A: We don't need to worry about the meaning of quantum mechanics, so long as we can compute probabilities for outcomes of experiment that follow from preparations.

Claim B: The properties of microscopic systems measured by our instruments cannot be removed from their measurement contexts. As such the scope of quantum mechanics is is the computation of probabilities for outcomes of experiment that follow from preparations .

Claim C: Quantum mechanics offers a measurement-independent ontology of the microscopic world, with thoroughgoing intelligibility.

You can see that claim A and B are closely related, but not identical. I have seen Sean Carroll discuss A. I have seen him contrast it with C. I have not seen him discuss B.

 

[Quantum Waver]

He says

Which sounds like shut up and calculate: "Who cares how the world works. All that matters is calculating predictions." At best it is an uncharitable reduction. The instrumentalist approach as exemplified by authors like Asher Peres is deeply concerned with how the microscopic world works at the fundamental level. It is deeply concerned with the ontological meaning of quantum theories. Instrumentalists maintain that the this deep understanding will be in terms of the impressions the microscopic world leaves on our instruments, and the dynamics between the microscopic world and these macroscopic tests and responses. Quoting Asher Peres in "Quantum Theory: Concepts and Methods"

It is this conceptual meaning outlined by authors like Peres, which centers preparations, tests, and responses, that I have never seen Carroll tackle. He only ever speaks of deeper understanding in the context of an instrument-independent account of quantum systems (hidden variables, many worlds, spontaneous collapse).

Sounds similar to what Bohr argued for, to the extent I understand what Bohr was saying. There is some agreement with Dr. Carroll's realism, in that both agree there is a microscopic world which is responsible for experimental results. So Peres formulation of instrumentalism is still realist about the microphysical. The difference being that people of Carroll's persuasion don't think instruments and measurements belong in a fundamental theory of nature. They should rather emerge from the description of the microphysical.

Also Carroll's form of realism is structural, because all the structure emerges from Hilbert space.

 

[Quantum Waver]

You can see that claim A and B are closely related, but not identical. I have seen Sean Carroll discuss A. I have seen him contrast it with C. I have not seen him discuss B.

I'm fairly confident Carroll disagrees with B on the grounds that classical stuff like measuring devices emerge from the quantum, so it shouldn't be part of the QM formalism, if QM is a fundamental theory. Instead, measurement and experimental setups should all be understood in a quantum pseudo-classical manner. At least as I understand what the implication of MWI is for the macroscopic.

It turns the CI and instrumentalism on it's head, focusing on the quantum instead of the classical. Whereas Bohr (at least) thought classical concepts were essential for making scientific statements. Maybe modern instrumentalists have a more nuanced take about the quantum/classical divide.

 

[Morbert]

I'm fairly confident Carroll disagrees with B on the grounds that classical stuff like measuring devices emerge from the quantum, so it shouldn't be part of the QM formalism, if QM is a fundamental theory.

Asher Peres addresses this in the same book.

There should be no misunderstanding. Bohr never claimed that different physical laws applied to the microscopic and macroscopic systems. He only insisted on the necessity of using different modes of description for the two classes of objects. It must be recognized that this approach is not entirely satisfactory. [...] This raises a thorny issue. We may wish to extend the microscopic (supposedly exact) theory to objects of intermediate size. [...] Ultimately we must explain how a very large number of microscopic entities, described by an utterly complicated vector in many dimensions, combine to form a macroscopic object endowed with classical properties.
[...]
The hallmark of a measuring instrument, which distinguishes it from other physical objects, is this ambivalence: it must be treated as a quantum system while it interacts with the measured object, and as a classical system once the measurement is over. How can we "dequantize" the apparatus? Can this "dequantization" be done consistently?

He goes on to sketch out this dequantization: A quantum system $S$ coupled to an apparatus $A$ gives us a density matrix $\rho_{S+A}$ which gives us a reduced density matrix $\rho_A$ which gives us a Wigner function $W_A(\mathbf{q},\mathbf{p})$, which gives us a fuzzy Wigner function. which gives us a Liouville density $f_A(\mathbf{q},\mathbf{p})$ which gives us a probability distribution for the final classical state of the apparatus.

In short, instrumentalism does not demote quantum theory to something that only applies to a patch of the universe. It is universal and exact and fundamental. Classical physics only plays a role as a mode of description that we deploy to get our probabilities for the data we register, and an understanding continuous with Bohr, but nevertheless post-Bohr, consistently relates the two.

 

[Morbert]

So Peres formulation of instrumentalism is still realist about the microphysical.

Yes, where he departs from realism is the properties of the microphysical measured by our instruments, and characterised by quantum mechanics. A quantum system to him is "an equivalence class of preparations" and is not real, even if the microscopic world is.

 

[gentzen]

If we look through his writings, we will probably find-out his thoughts and positions regarding "anti-realism" and "Copenhagen" (or we could ask him, if we really want to know). Regarding "instrumentalism," I guess Sean was careful not to say too much about it,

I did that search now, and it seems I was right that it is easy to find material online where Sean writes/talks about "anti-realism" or "Copenhagen" (although never at the same time about both), but hard to find him talking about "instrumentalism". I didn't have enough patience to understand in detail what he writes about anti-realism, but his position regarding Copenhagen is easy to understand, therefore I quote it here:

https://www.preposterousuniverse.com/blog/2013/01/17/the-most-embarrassing-graph-in-modern-physics/

I’ll go out on a limb to suggest that the results of this poll should be very embarrassing to physicists. Not, I hasten to add, because Copenhagen came in first, although that’s also a perspective I might want to defend (I think Copenhagen is completely ill-defined, and shouldn’t be the favorite anything of any thoughtful person). The embarrassing thing is that we don’t have agreement.
...
I’m sitting in a bistro at the University of Nottingham, where I gave a talk yesterday about quantum mechanics. I put it this way: here in 2013, we don’t really know whether objective “wave function collapse” is part of reality (as the poll above demonstrates). We also don’t know whether, for example, supersymmetry is part of reality. Wave function collapse has been a looming problem for much longer, and is of much wider applicability, than the existence of supersymmetry. Yet the effort that is put into investigating the two questions is extremely disproportionate.

https://www.preposterousuniverse.com/eternitytohere/quantum/

The Copenhagen interpretation of quantum mechanics is as easy to state as it is hard to swallow: when a quantum system is subjected to a measurement, its wave function collapses. That is, the wave function goes instantaneously from describing a superposition of various possible observational outcomes to a completely different wave function, one that assigns 100 percent probability to the outcome that was actually measured, and 0 percent to anything else. That kind of wave function, concentrated entirely on a single possible observational outcome, is known as an “eigenstate.” Once the system is in that eigenstate, you can keep making the same kind of observation, and you’ll keep getting the same answer (unless something kicks the system out of the eigenstate into another superposition). We can’t say with certainty which eigenstate the system will fall into when an observation is made; it’s an inherently stochastic process, and the best we can do is assign a probability to different outcomes.

He says

The most important point is that the underlying goal of science is not simply making predictions — it’s developing an understanding of ... the natural world

Which sounds like shut up and calculate: "Who cares how the world works. All that matters is calculating predictions." At best it is an uncharitable reduction. The instrumentalist approach as exemplified by authors like Asher Peres ...

My reply are the "..." above. Hope it demonstrates how we both read our own "interpretation" of Sean into his writings. But at least his position regarding Copenhagen quoted above is pretty straightforward and "immune" to different interpretations. That was my main reason to write this comment, and I will stop here.

 

[Quantum Waver]

Going back to the first video, I have a naive question about measurement. Both the screen and the smoke act as measurements, but they don't destroy interference, even if one photon were emitted at a time. So why does using a detector cause decoherence? Is it because it's detecting photons in one specific location, or is it because the detector is a complex macroscopic object?

Debates around measurement, collapse and decoherence seem to confuse the issue as to exactly when and why a measurement destroys the interference pattern. If the environment is causing decoherence, then why does the smoke and screen still allow for an interference pattern?

 

[Morbert]

Going back to the first video, I have a naive question about measurement. Both the screen and the smoke act as measurements, but they don't destroy interference, even if one photon were emitted at a time. So why does using a detector cause decoherence? Is it because it's detecting photons in one specific location, or is it because the detector is a complex macroscopic object?

Debates around measurement, collapse and decoherence seem to confuse the issue as to exactly when and why a measurement destroys the interference pattern. If the environment is causing decoherence, then why does the smoke and screen still allow for an interference pattern?

The smoke doesn't detect which slit the photon went through, which is what would destroy interference.

 

[Quantum Waver]

The smoke doesn't detect which slit the photon went through, which is what would destroy interference.

But if you just block off one of the slits, you get a single slit diffraction pattern. So would attaching a tube to the one open slit long enough to fill just the tube with smoke count as a detector?

 

[Morbert]

But if you just block off one of the slits, you get a single slit diffraction pattern. So would attaching a tube to the one open slit long enough to fill just the tube with smoke count as a detector?

The smoke isn't analogous to the detector behind the slits in the conventional double-slit experiment. A photon detected by smoke is destroyed. As such, it is more like the 2D detector screen in the conventional experiment. It registers whether or not there is an interference pattern. It does not register which slit the photons went through.

 

[PeterDonis]

I don't believe you can call it "entanglement", as in the usual meaning

But that's what the equations say. It's not just pulled out of thin air, it is literally what the math (without collapse) tells you happens during any interaction. Measurement is just a type of interaction.

If that were true, monogamy of entanglement would be violated

No, it wouldn't. The entanglement created by an interaction does not have to be maximal. Non-maximal entanglements can be spread out among an arbitrary number of degrees of freedom. That is the basis of decoherence theory.

 

[PeterDonis]

What Wallace argues is that branches/worlds are emergent phenomena from the components of entangled environments

Yes, I understand all this. I'm just pointing out that it is not how any physicists, including MWI proponents, talk about ordinary entangled systems. The "branches/worlds" talk is an extra element that has to be added in for some particular kinds of entanglements. The only basis in the math for making any such distinction is decoherence, but decoherence is not a sharp distinction, it's gradual, whereas the "branches/worlds" distinction is sharp--either the individual terms in an entangled state represent "branches/worlds" or they don't. But nobody, AFAIK, has given any kind of criterion for where the boundary is--where "branches/worlds" come into being.

 

[PeterDonis]

There is an interaction I presume between each possible individual MWI branch when an observed particle interacts with the observer environment.

No. There is no interaction between branches. The branches are the outcome of the interaction.

For example, consider a single electron passing through a Stern-Gerlach device. Say the electron starts in the z-spin up state, and the Stern-Gerlach device is oriented in the x direction. Then the state before the interaction is

$$
\ket{z+} \ket{\text{input beam}}
$$

and the state after the interaction is

$$
\frac{1}{\sqrt{2}} \left( \ket{x+} \ket{\text{x-spin up beam}} + \ket{x-} \ket{\text{x-spin down beam}} \right)
$$

The former state is a product state, but the latter state is an entangled state; the entanglement is produced by the interaction between the electron and the Stern-Gerlach apparatus.

This interaction by itself does not necessarily produce decoherence, since the beams can in principle be recombined; to complete a spin measurement one needs to put detectors in each output beam and observe which one fires. But the entangled state produced by that further interaction looks simliar to the above, just with an additional ket for the detector system.

I don't know what you would say is the entangled attribute/observable though.

In the Stern-Gerlach case, the entanglement is between the spin and the momentum of the electron. The specific degrees of freedom that are entangled will depend on the particular interaction.

Or what the conserved quantity is.

I'm not sure why a conserved quantity would be relevant.

 

[vanhees71]

But that's what the equations say. It's not just pulled out of thin air, it is literally what the math (without collapse) tells you happens during any interaction. Measurement is just a type of interaction.No, it wouldn't. The entanglement created by an interaction does not have to be maximal. Non-maximal entanglements can be spread out among an arbitrary number of degrees of freedom. That is the basis of decoherence theory.

That's of course right: In an ideal von Neumann filter measurement the measurement appartus's "pointer state" gets maximally entangled with the system's state. That's the definition of a von Neumann filter measurement.

Take the ideal Stern Gerlach experiment: You measure a spin component by letting the Ag atoms through an appropriate magnetic field (large constant part in direction of the spin component to be measured and some inhomogeneous part) to entangle the spin component with the position of the particle. Then measurement of the position is 100% correlated with measuring the spin component.

 

[vanhees71]

This interaction by itself does not necessarily produce decoherence, since the beams can in principle be recombined; to complete a spin measurement one needs to put detectors in each output beam and observe which one fires. But the entangled state produced by that further interaction looks simliar to the above, just with an additional ket for the detector system.

Indeed, the time evolution of a closed system is always unitary and (in principle) reversible. Decoherence occurs when looking at a sub system of a larger system. The effective description of the state evolution of the subsystem, i.e., its reduced statistical operator is described in terms of some non-unitary master equation, which involves decoherence through the interaction of the "system" with "the environment".

By chance, there's just a nice Nature paper about the issue, how the 2nd law of thermodynamics (H-theorem) for subsystems is compatible with the unitary evolution of the closed system:

https://doi.org/10.1038/s41467-023-38413-9 (open access!)

 

[kered rettop]

TL;DR Summary: Physicist becomes convinced Schrodinger's equation describes real waves, because they can be made visible in the double-slit experiment using a laser and smoke machine.

I don't see how the smoke makes the wave visible. Each photon is scattered by the smoke at a different point, so it's equivalent to having the screen at that point. You are not watching the evolution of a single photon's wave function, you're just seeing its final state (where it's scattered). You can assume that they all behave the same way, but that just begs the question.

 

[vanhees71]

Obviously Youtube has not only very good explanations of QT. Very likely a good textbook is the better choice for learning it!