I Wigner's friend and quantum tunneling

[DDTG]

please keep it simple, im a physics layman...

when the friend inside the box keep looking at the electron, the electron is in a definite position and cannot tunnel outside the box. but in wigner's perspective, his wavefunction for the electron evolves according to schrodinger and has a non zero probability of being outside the box. if wigner repeats the experiment many times to try to measure the electron, he will never find it, but his wavefunction has a non 0 probability for the electron to be outside the box. this implies his wavefunction is wrong, how can that be?

if one views wavefunction as bayesian probability, everything is normal because wigner hasn't updated his beliefs. but i thought the wavefunction evolution as predicted by schrodinger is supposed to give the correct probabilities and isn't just bayesian probability, so wigner's wavefunction is supposed to be correct. it would be correct if his friend isn't inside the box looking at the electron, but he doesnt know that.

can someone please explain what's going on here? sorry if this sounds stupid, im a layman and very confused here.

 

[PeroK]

I'm not sure I understand the question. Do you have a reference for the scenario in question?

 

[Nugatory]

when the friend inside the box keep looking at the electron, the electron is in a definite position and cannot tunnel outside the box.

But it can, as long as the wave function has non-zero amplitude outside the box. Two consecutive position measurements will in general yield different positions, and there's no reason why both results must be inside (although if the measurement is performed by the insider, the result may present as "hey, it's not in here with me any more").

In the modern understanding of Quantum Mechanics, the Wigner's Friend thought experiment is generally considered to be a reductio ad absurdum showing that consciousness causing collapse is not a viable interpretation of the theory.

 

[Demystifier]

when the friend inside the box keep looking at the electron, the electron is in a definite position and cannot tunnel outside the box.

You seem to be talking about the quantum Zeno effect.

but in wigner's perspective, his wavefunction for the electron evolves according to schrodinger and has a non zero probability of being outside the box. if wigner repeats the experiment many times to try to measure the electron, he will never find it, but his wavefunction has a non 0 probability for the electron to be outside the box. this implies his wavefunction is wrong, how can that be?

If there is a measuring apparatus inside the box which causes the quantum Zeno effect, then this fact should be taken into account even by Wigner. The measuring apparatus affects the wave function, which is why the naive wave function without the measuring apparatus is wrong.

 

[Demystifier]

In the modern understanding of Quantum Mechanics, the Wigner's Friend thought experiment is generally considered to be a reductio ad absurdum showing that consciousness causing collapse is not a viable interpretation of the theory.

And in post-modern understanding of QM, it's considered to be a reductio ad absurdum showing that objective facts don't exist.

 

[PeterDonis]

And in post-modern understanding of QM, it's considered to be a reductio ad absurdum showing that objective facts don't exist.

This is because the scenario described in the Wigner's Friend thought experiment requires reversing decoherence. And if decoherence can be reversed, then yes, what we think of as objective facts don't exist.

Personally, I think it makes more sense to consider the thought experiment as a reductio ad absurdum of the idea that decoherence can be reversed, i.e., that some quantum operation can be done on a system in which a particular measurement result has been obtained, that "undoes" that result.

 

[Demystifier]

This is because the scenario described in the Wigner's Friend thought experiment requires reversing decoherence. And if decoherence can be reversed, then yes, what we think of as objective facts don't exist.

I don't think that's essential. As explained here
https://www.physicsforums.com/threads/the-extended-wigners-friend-scenarios.1078165/post-7239760
that's only a technicality, equivalent to a version of experiment in which one does not reverse decoherence, but instead performs quantum measurements in a complicated basis involving macroscopic states of the whole apparatus/observer. The reasons for interpreting it as non-existence of objective facts are instead of the same type as reasons for non-realistic interpretations of the Bell theorem (Bell theorem excludes local realism, so if locality is true, then realism isn't). This is particularly clear from the local friendliness version of the extended Wigner friend thought experiment, which is just a version of the Bell theorem.

The real issue is whether we can treat macroscopic systems the same way we treat the quantum microscopic ones. This includes quantum unitary operations (time inversion is only one of them), quantum projective measurements, and quantum interpretations. The logic is the following: If we can treat them so operationally (unitary operations and projective measurements), then we must also treat them so interpretationally. So any interpretation that denies objective existence of microscopic properties such as particle spins or positions will translate into an interpretation that denies objective existence of analogous macroscopic properties as well.

 

[PeterDonis]

quantum measurements in a complicated basis involving macroscopic states of the whole apparatus/observer

In such cases, there is no decoherence, so even according to standard QM, there are no objective measurement results; it's no different than typical quantum computing operations with small numbers of qubits passing through gates, with no result ever being read off.

But then the thought experiment requires that systems containing $10^{30}$ qubits or more can be kept in a state of quantum coherence for a long enough time to run the experiment at all, which is at least as outlandish a claim as the claim that decoherence can be reversed.

 

[FactChecker]

But then the thought experiment requires that systems containing $10^{30}$ qubits or more can be kept in a state of quantum coherence for a long enough time to run the experiment at all, which is at least as outlandish a claim as the claim that decoherence can be reversed.

That's a lot of qubits. But there are an estimated $10^{50}$ atoms in the Earth, so with luck it could happen. ;-)

 

[PeterDonis]

That's a lot of qubits. But there are an estimated $10^{50}$ atoms in the Earth, so with luck it could happen. ;-)

Call me when they run a double slit experiment with the Earth as the "particle".

 

[Demystifier]

In such cases, there is no decoherence, so even according to standard QM, there are no objective measurement results;

Of course there is decoherence. The measured quantum system is the friend and her laboratory, but this is measured by Wigner and his laboratory, which serves as an environment for the measured quantum system.

 

[PeterDonis]

Of course there is decoherence.

Not of the friend and her laboratory. See below.

The measured quantum system is the friend and her laboratory, but this is measured by Wigner and his laboratory, which serves as an environment for the measured quantum system.

Yes, and the way you described the measurement Wigner makes on the friend and her laboratory was: "quantum measurements in a complicated basis involving macroscopic states of the whole apparatus/observer". That's just another way of saying that Wigner is treating the whole friend/laboratory system as if it were a qubit, where the friend makes her measurement in the analogue of the "spin-z" basis, but then Wigner makes his measurement in the analogue of the "spin-x" basis. But in order for Wigner to do that as you're describing it, quantum coherence has to be maintained over the entire friend/laboratory system for long enough for Wigner to make his measurement, since he's undoing the result of the "spin-z" measurement, which is equivalent to making use of interference between spin-z-up and spin-z-down. But there's no interference if decoherence has taken place in the friend/laboratory system before Wigner makes his measurement.

In short, you can't have it both ways. If the friend/laboratory measurement was an actual measurement, with decoherence in the friend/laboratory system, then Wigner would have to reverse decoherence to make his measurement. If you claim that Wigner doesn't have to reverse decoherence to make his measurement, then you're saying the friend/laboratory measurement wasn't a real measurement in the first place--there was no decoherence, because quantum coherence had to be maintained over that system for Wigner to make his measurement. Either way, you're claiming something outlandish--the difference is only in the details of which outlandish thing you claim. There is no innocuous way to realize what the thought experiment requires Wigner to do. Macroscopic systems are not qubits.

 

[Demystifier]

Not of the friend and her laboratory. See below.


Yes, and the way you described the measurement Wigner makes on the friend and her laboratory was: "quantum measurements in a complicated basis involving macroscopic states of the whole apparatus/observer". That's just another way of saying that Wigner is treating the whole friend/laboratory system as if it were a qubit, where the friend makes her measurement in the analogue of the "spin-z" basis, but then Wigner makes his measurement in the analogue of the "spin-x" basis. But in order for Wigner to do that as you're describing it, quantum coherence has to be maintained over the entire friend/laboratory system for long enough for Wigner to make his measurement, since he's undoing the result of the "spin-z" measurement, which is equivalent to making use of interference between spin-z-up and spin-z-down. But there's no interference if decoherence has taken place in the friend/laboratory system before Wigner makes his measurement.

In short, you can't have it both ways. If the friend/laboratory measurement was an actual measurement, with decoherence in the friend/laboratory system, then Wigner would have to reverse decoherence to make his measurement. If you claim that Wigner doesn't have to reverse decoherence to make his measurement, then you're saying the friend/laboratory measurement wasn't a real measurement in the first place--there was no decoherence, because quantum coherence had to be maintained over that system for Wigner to make his measurement. Either way, you're claiming something outlandish--the difference is only in the details of which outlandish thing you claim. There is no innocuous way to realize what the thought experiment requires Wigner to do. Macroscopic systems are not qubits.

I can have it both ways, to understand it one just has to be a little bit more precise. First let me define 3 systems I am talking about:
system A: the measured particle
system B: the friend and her apparatus
system C: Wigner and his apparatus
Now the story is this. Initially A is in a pure state, i.e., in a state with a quantum coherence. But later, when B measures A, then A gets entangled with B, so B serves as an environment of A, i.e., the state of A gets decohered by B. And yet, A+B still retains coherence. Hence C, before performing his measurement, sees A+B as a pure state with a quantum coherence. (Finally, when C performs his measurement, then A+B gets entangled with C, i.e., the state of A+B gets decohered by C, but I think that's not an issue here.) The point is that, after the measurement by B but before the measurement by C, we simultaneously have both decoherence (because the state of A decohered) and coherence (because the state of A+B has not decohered).

 

[PeterDonis]

And yet, A+B still retains coherence.

Only if you isolate it from the rest of the universe. Which you can't. If nothing else, A+B are at finite temperature and are emitting photons, and there's no way for Wigner to capture all of them in a coherent way, not if B is a human and her laboratory. Maybe if B is a system with a small number of degrees of freedom, as has been the case in so-called "Wigner's friend" experiments actually realized, you can do it for long enough for Wigner to make his measurement--but in such cases, B isn't a system that can irreversibly record a measurement result anyway. All that in no way justifies extrapolating to the case where B is a human and her laboratory.

 

[Demystifier]

Only if you isolate it from the rest of the universe. Which you can't.

The thought experiment assumes that you can. At least approximately, if not exactly.

 

[PeroK]

Only if you isolate it from the rest of the universe. Which you can't. If nothing else, A+B are at finite temperature and are emitting photons, and there's no way for Wigner to capture all of them in a coherent way, not if B is a human and her laboratory. Maybe if B is a system with a small number of degrees of freedom, as has been the case in so-called "Wigner's friend" experiments actually realized, you can do it for long enough for Wigner to make his measurement--but in such cases, B isn't a system that can irreversibly record a measurement result anyway. All that in no way justifies extrapolating to the case where B is a human and her laboratory.

Would that apply to Schrodinger's cat as well? You cannot isolate the cat and the decoherence must leak out to the laboratory?

 

[Demystifier]

Would that apply to Schrodinger's cat as well? You cannot isolate the cat and the decoherence must leak out to the laboratory?

Exactly. And yet, Schrodinger "cat" experiments are done in the laboratory. Not with animal cats, but with relatively big systems cooled down to low temperatures, so that decoherence by thermal radiation is sufficiently small (though not exactly zero).

 

[PeterDonis]

The thought experiment assumes that you can.

Which, to me, means that the thought experiment is a reductio ad absurdum of that assumption.

But apart from that, the assumption seems to me to be outlandish, so drawing conclusions from it seems to me to be, at the very least, ill advised.

 

[PeterDonis]

relatively big systems

Compared to a cat, all of the systems this has been done to are miniscule. As in, "18 or more orders of magnitude fewer degrees of freedom" miniscule. Extrapolating anything observed in these experiments to cats (or humans) is, IMO, grossly premature at best.

 

[PeterDonis]

Would that apply to Schrodinger's cat as well? You cannot isolate the cat and the decoherence must leak out to the laboratory?

For a cat, yes. (Or a human, for that matter.) See my response to @Demystifier in post #19 just now.

 

[Demystifier]

Which, to me, means that the thought experiment is a reductio ad absurdum of that assumption.

Well, that's a legitimate opinion, but as far as I can see nobody holds that opinion in the recent published literature on the extended Wigner friend experiment.

Essentially you are saying that certain kinds of experiments are possible for small systems but impossible for big systems. And not just impossible in practice, but in principle. I find such a principle rather odd. That's like saying that some physical law is valid for any number of particles less or equal to 3420, but suddenly for 3421 particles or more the law becomes invalid.

 

[gentzen]

Essentially you are saying that certain kinds of experiments are possible for small systems but impossible for big systems. And not just impossible in practice, but in principle. I find such a principle rather odd. That's like saying that some physical law is valid for any number of particles less or equal to 3420, but suddenly for 3421 particles or more the law becomes invalid.

Initially, it looked like certain kinds of experiments would be possible for small systems. But then came [...], which caused my reaction

This starts to get ridiculous: Even if you could "exactly" prescribe $H(t)$, it would still remain completely open (and unclear) what you could to do to reverse the wave function.

At this point, I suggest that you either find a really convincing argument, or else concede the point to PeterDonis (for the moment).

So it currently looks like those experiments are not even possible for small systems, at least not "exactly". So the real situation is rather that assuming those experiments to be possible is a good and harmless idealisation for small systems. But this doesn't tell me much about whether those experiment are possible for big systems, or whether assuming them to be possible is harmless.

That's like saying that some physical law is valid for any number of particles less or equal to 3420, but suddenly for 3421 particles or more the law becomes invalid.

This argument doesn't convince me in the current context. I guess it won't convince PeterDonis either.
However, I do admit that in general, this is an important question:

• A sufficiently small probability is not really different from 0, but any explicit threshold can and will be attacked as ridiculous. Sometimes the lifetime of the universe or the lifetime of a human can be used to defend certain bounds. But many opponents will still remain unconvinced.
• Temperature 0K cannot be reached, but again any explicit threshold woud be open for ridicule. The temperature of the microwave background (2.725 Kelvin) provides some base reference for which temperatures are small. The boiling point of liquid helium (4.2 Kelvin) provides a similar base reference. (The lowest temperature that matter has been cooled to is 38 picoKelvin. This temperature was achieved by a group of researchers from the QUANTUS Team (DEU) in Bremen, Germany, in August 2018. The results were published in Physical Review Letters 30 August 2021.)

 

[Demystifier]

So it currently looks like those experiments are not even possible for small systems, at least not "exactly". ...
Temperature 0K cannot be reached, but again any explicit threshold woud be open for ridicule.

I think you are missing the point of thought experiments. Their main point is to better understand the theory, not to learn something from actual experiments. For that purpose, it's sufficient that the experiment can be done in theory, that is, in principle. In the case of Wigner friend experiments, their point is to better understand what quantum theory tells us about objectivity of events (or about locality, or some other deep fundamental principle). If quantum theory were true, not merely as an effective theory but as a fundamental theory, then what this would tell us about objectivity of events?

 

[PeterDonis]

Essentially you are saying that certain kinds of experiments are possible for small systems but impossible for big systems. And not just impossible in practice, but in principle.

Yes, that's implied by my saying that the Wigner's friend thought experiment is a reductio ad absurdum of the claim that such things are possible in principle for macroscopic systems.

I find such a principle rather odd.

There's no way of dealing with the implications of QM that isn't odd. The question is simply what you think is more odd (or unpalatable). I find it less unpalatable to believe that there are aspects of physics we don't understand yet, that come into play when you try to do a Wigner's friend type experiment on something like a human and prevent such experiments from doing what QM, taken literally, implies, than to take QM as applying literally, in all respects, in such a case. Your mileage may vary.

 

[gentzen]

I think you are missing the point of thought experiments. Their main point is to better understand the theory, not to learn something from actual experiments. For that purpose, it's sufficient that the experiment can be done in theory, that is, in principle.

I am still waiting for a convincing argument that the experiment can be done in principle. My "This starts to get ridiculous" reaction was triggered when it turned out that it "remains completely open (and unclear)" whether in principle, it can be done.

Additionally, even if those thought experiments only try to stimulate discussion, those discussions won't have a chance to increase our understanding, if we just accept every argument, no matter how unconvincing. So I had to argue against your: "That's like saying that some physical law is valid for any number of particles less or equal to 3420, but suddenly for 3421 particles or more the law becomes invalid."

 

[PeterDonis]

it "remains completely open (and unclear)" whether in principle, it can be done.

Part of the issue here might be that whether it is possible even in principle depends on which interpretation of QM you're using. In a straightforward "collapse is a physical process" interpretation, for example, a physical collapse takes place when the friend makes his measurement, and there's nothing Wigner can do to undo that no matter what kind of quantum operation he tries.

 

[Demystifier]

I am still waiting for a convincing argument that the experiment can be done in principle.

For that we would first need to agree on the general principles. For a start, do you accept the following principles?
1. Any physical system (however large) is, in principle, a quantum system described by quantum mechanics.
2. Any observable (that is, self-adjoint operator on the Hilbert space of a quantum system) can, in principle, be measured by a projective measurement.
3. Any state in the Hilbert space of a quantum system can, in principle, be prepared.

 

[gentzen]

For that we would first need to agree on the general principles. For a start, do you accept the following principles?
1. Any physical system (however large) is, in principle, a quantum system described by quantum mechanics.

Yes, for your purposes. There is no relevant distinction between macroscopic and microscopic system.
(When a physical system has the size of the universe, or nearly that size, then some stuff that people would commonly assume one can do or say might no longer be true.)

2. Any observable (that is, self-adjoint operator on the Hilbert space of a quantum system) can, in principle, be measured by a projective measurement.

No. For example, if that observable would be a sum between something on Andromeda and something on earth, then there must be a justification why that specific observable can be measured, even in principle. And the same applies if Andromeda is replaced by the moon. Maybe there are good arguments why such observables are measurable, in principle, at least when we are just talking about the earth and the moon. Maybe not. But I need an argument here.

3. Any state in the Hilbert space of a quantum system can, in principle, be prepared.

Oh well, I start to see your point. From a practical point of view, this is of course not true. On the other hand, there are no "in principle" obstacles against preparation of some state which is a coherent sum of something on the earth and something on the moon.
But then again, how are states actually prepared? On the one hand, there is this "wait long enough until it is in the thermal state". Cool it down sufficiently, and you know it that state is the ground state.
On the other hand, there is the measure and filter suitable approach. And the approach to apply suitable unitary transformations to known (nearly) pure states.

Maybe this last one is the best suited for my "but I need an argument here" reply: It is fine for me that you can prepare some pure states, in principle. What needs an argument for me is that you can construct a suitable unitary transformation, which transforms a suitable one of those to the desired given pure state, that you want to prepare.

 

[PeterDonis]

Any physical system (however large) is, in principle, a quantum system described by quantum mechanics.

That is one of the principles that the Wigner's friend thought experiment might be a reductio ad absurdum of. (Actually it could be a reductio ad absurdum of any of the three, but questioning your second and third principles IMO ultimately means questioning the first.)

 

[Demystifier]

What needs an argument for me is that you can construct a suitable unitary transformation, which transforms a suitable one of those to the desired given pure state, that you want to prepare.

Perhaps that's not really needed. Let me try to convince you in a few steps.

1. The reversion (undoing) of the measurement is not really essential, as explained in [1] Sec.II.E. The reversion is introduced in some (but not all) versions of the thought experiment to avoid measurements on a complicated system (involving both a simple particle and a friend who measures it), but operationally a version with reversion is equivalent to a version without the reversion. If you are not convinced, please look at the mentioned reference for details.

2. The thought experiment in [2] (the "local friendliness" paper) does not involve a reversion.

3. The work [2] also demonstrates that this experiment is possible in principle by actually performing a simpler version of the experiment in which the friend is replaced by a photon.

4. The review [1] argues that the work [2] is the most convincing one among all the existing extended Wigner friend papers. The conclusion of [2] is not that absoluteness of observed events is necessarily wrong. Instead, its conclusion is that (at least) one of the following three assumptions is wrong:
(i) no superdeterminism
(ii) locality
(iii) absoluteness of observed events
This leaves options for various interpretations. For example, those who prefer to view the Bell theorem as a proof of non-locality, should prefer to view [2] in the same manner, as yet another proof of non-locality.

[1] arXiv:2308.16220
[2] Nature Physics volume 16, pages1199–1205 (2020); arXiv:1907.05607

If that doesn't convince you, then, I'm afraid, I cannot provide anything more convincing than that.