What has changed since the Copenhagen interpretation?

[DarMM]

Then you are consistent with Frauchiger-Renner. QM taking the subjective collapse view, unlike General Relativity or Kolmolgorov probability theory, is not consistent with inter-agent logic.

You cannot consider other agents and their outcomes, even in principal.

Take the Wigner's friend case where the friend agreed to measure a spin. It seems odd to say that Wigner cannot even consider "If my friend got spin up", but if you think so then Frauchiger-Renner has nothing new to say for you. It's simply that some thought there was a version of Copenhagen where you can at least consider the outcomes of other agents in general.

 

[atyy]

Then you are consistent with Frauchiger-Renner. QM taking the subjective collapse view, unlike General Relativity or Kolmolgorov probability theory, is not consistent with inter-agent logic.

You cannot consider other agents and their outcomes, even in principal.

Take the Wigner's friend case where the friend agreed to measure a spin. It seems odd to say that Wigner cannot even consider "If my friend got spin up", but if you think so then Frauchiger-Renner has nothing new to say for you. It's simply that some thought there was a version of Copenhagen where you can at least consider the outcomes of other agents in general.

OK, I haven't studied FR closely enough yet, but at least at the qualitative level we seem to agree.

One can consider "other" agents, but they must all be on the same classical side of the classical-quantum cut, maybe for example the demonstration that collapse and unitary evolution from all different special relativistic frames of reference produce consistent results (even though the states in different frames are not related by unitary transformation)

Are there really Copenhagen versions in which an agent can be on both sides of the quantum-classical cut? I mean, it would be like saying that the cat is both "dead and alive" and "dead or alive", which seems ridiculous. Maybe QBists try to do that, since I think FR say QBism is inconsistent?

 

[DarMM]

Before I respond to that post I just want to ask, when you say an agent on both sides of the cut, in the Wigner's friend case, the friend is on the classical side of the cut for himself, but on the quantum side for Wigner.

So he is on both sides of the cut, but it's a different side for different agents. I assume you are asking about being on both sides for one agent.

 

[atyy]

Before I respond to that post I just want to ask, when you say an agent on both sides of the cut, in the Wigner's friend case, the friend is on the classical side of the cut for himself, but on the quantum side for Wigner.

So he is on both sides of the cut, but it's a different side for different agents. I assume you are asking about being on both sides for one agent.

Yes, I believe the usual version of Copenhagen is one in which Wigner only grants "agent" or "reality" status to things on the same side of Wigner's classical-quantum cut.

 

[atyy]

So let's say in the Wigner's friend scenario, Wigner should be using a mixed state, not the pure state:
$$\frac{1}{\sqrt{2}}\left(|\uparrow, A_{\uparrow}\rangle + |\downarrow, A_{\downarrow}\rangle\right)$$
with $A_{\uparrow}, A_{\downarrow}$ device states?

Let's try a different answer from the one I gave in post #54, where I said Wigner uses a pure state.

I think another possibility is that Wigner accepts that his friend has done a measurement. In this case, Wigner and his friend are on the same classical side of the classical-quantum cut, and A represents the friend's ancilla. If the friend performs a measurement, but does not tell Wigner the result, and if Wigner accepts his friend's measurement as a measurement, then Wigner should use a mixed state.

 

[stevendaryl]

I think Haag's and Peres's statements are pretty fundamental parts of QM. If Frauchiger and Renner break it, I'm not sure what they are talking about can be called QM.

Anyway, would you agree with Demystifier that collapse in BM is objective (post #17)?

It's a little ambiguous. One meaning of "wave function collapse" is that after a measurement, the wave function changes discontinuously to the collapsed wave function. That does not happen in BM. Another meaning is that upon collapse, one or more possible outcome is selected. In BM, all outcomes are predetermined, so in a sense, everything is pre-collapsed. I'm not exactly sure what @Demystifier would say about it, but it seems to me that BM is not consistent with the usual idea of wave function collapse.

The "pilot wave" wave function always evolves according to Schrödinger's equation. But that's the wave function for the entire universe, in the sense of Many-Worlds. If you instead focus on an effective wave function for just part of the universe, a single system, then the effective wave function might have something like collapse.

 

[stevendaryl]

Let's try a different answer from the one I gave in post #54, where I said Wigner uses a pure state.

I think another possibility is that Wigner accepts that his friend has done a measurement. In this case, Wigner and his friend are on the same classical side of the classical-quantum cut, and A represents the friend's ancilla. If the friend performs a measurement, but does not tell Wigner the result, and if Wigner accepts his friend's measurement as a measurement, then Wigner should use a mixed state.

That's the practical approach to resolving paradoxes in QM: Assume that there is no such thing as a pure state consisting of a superposition of macroscopically different states. There can only be mixed states.

However, I find that assumption to be a "soft contradiction". QM does not in any way limit the size or complexity of the systems that can be described by it.

 

[Auto-Didact]

It's a little ambiguous. One meaning of "wave function collapse" is that after a measurement, the wave function changes discontinuously to the collapsed wave function. That does not happen in BM. Another meaning is that upon collapse, one or more possible outcome is selected.

One or more? Surely only one; given that it is only one then those two meanings are equivalent.

In other words, the (wave function) collapse is a discontinuous collapse resulting in a random selection of one of the possible outcomes.

This discontinuity in the time evolution of $\psi$ is the key clue that $\psi$ needs to be modeled by some non-continuous equation; the linear PDE is a simplification which preserves unitarity.

 

[stevendaryl]

That's the practical approach to resolving paradoxes in QM: Assume that there is no such thing as a pure state consisting of a superposition of macroscopically different states. There can only be mixed states.

However, I find that assumption to be a "soft contradiction". QM does not in any way limit the size or complexity of the systems that can be described by it.

Let me state, more precisely, what I think the contradiction is. But first, let me formulate an alternative to the Born rule: Instead of saying "A measurement of a system always produces an eigenvalue of the operator that is measured, with a probability given by blah blah blah", you say: "At any given time, the probability that the universe is in some particular macroscopic configuration is given by blah blah blah". This is a specific case of the Born rule, in which the system is the entire universe, and the observable is the universe's macroscopic configuration. You don't need the general Born rule because by definition, a measurement of a microscopic quantity means setting up a measurement so that the microscopic quantity is amplified to produce a macroscopic effect. So if you know the probabilities for macroscopic configurations, then that tells you the probabilities for various measurement results (since they are macroscopically different).

This form of the Born rule can be mathematically described this way: If we let $\Pi_j$ be the projection of the state of the universe onto the macroscopic state number $j$ (you can't have continuum many macroscopically distinguishable configurations, so it's enough to consider a countable collection of projection operators), and you let $|\psi(0)\rangle$ be the initial state, at time $t=0$, then the probability of being in state $j$ at a later time $t > 0$ is given by:

$P(j) = \langle \psi| e^{iHt/\hbar} \Pi_j e^{-iHt/\hbar} |\psi\rangle$

Then the issue of collapse can be stated this way: What if, we ask what the probability is of being in state $j$ at time $t_1$ and then later being in state $k$ at time $t_2$? Here are two possible answers:

1. $P_{collapse}(j,k) = \langle \psi| e^{iH t_1/\hbar} \Pi_j e^{iH(t_2 - t_1)/\hbar} \Pi_k e^{-iH(t_2 - t_1)/\hbar} \Pi_j e^{-iHt_1/\hbar} |\psi\rangle$
2. $P_{no-collapse}(j,k) = \langle \psi| e^{iH t_2/\hbar} \Pi_k e^{-iH t_2/hbar} |\psi\rangle$

If the state $|\psi\rangle$ is itself a pure macroscopic state ($\Pi_i |\psi\rangle = |\psi\rangle$ for some macroscopic configuration $i$), then there will be negligible difference between these two numbers. That's because the macroscopic configuration $k$ includes the record of having previously gotten some particular result for some past measurement. So for each $k$, the probability $P_{collapse}(j,k)$ will be approximately zero for all except one value of $j$. For that value of $j$, there will be a negligible difference between $P_{collapse}$ and $P_{no-collapse}$.

So under the assumption that the world currently is in a macroscopically pure state, the collapse assumption is harmless. Assume it or not, it makes no difference.

Eventually, though, the state of the universe will drift away from being macroscopically pure, and the distinction between $P_{collapse}$ and $P_{no-collapse}$ will grow larger and larger.

 

[stevendaryl]

One or more? Surely only one; given that it is only one then those two meanings are equivalent.

Well, in an experiment such as measuring the spin in the x-direction of an electron that has been prepared to be spin-up in the z-direction, there is, a priori, more than one possible outcome, spin-up or spin-down. In BM, which is deterministic, only one of them is actually possible, and we only consider them both possible because we have incomplete knowledge of the current state.

In other words, the (wave function) collapse is a discontinuous collapse resulting in a random selection of one of the possible outcomes.

In that sense, BM has no collapse. Nothing discontinuous ever happens. Except in the classical sense of changing a probability distribution based on acquiring more information.

 

[Auto-Didact]

Well, in an experiment such as measuring the spin in the x-direction of an electron that has been prepared to be spin-up in the z-direction, there is, a priori, more than one possible outcome, spin-up or spin-down. In BM, which is deterministic, only one of them is actually possible, and we only consider them both possible because we have incomplete knowledge of the current state.

Of course there is more than one outcome possible, no one is arguing that. The point is that there is only one outcome out of all possibilities selected in a measurement.

 

[atyy]

That's the practical approach to resolving paradoxes in QM: Assume that there is no such thing as a pure state consisting of a superposition of macroscopically different states. There can only be mixed states.

However, I find that assumption to be a "soft contradiction". QM does not in any way limit the size or complexity of the systems that can be described by it.

I was thinking a bit differently. If Wigner accepts that a measurement has been performed, then the wave function collapses. If Wigner knows the measurement outcome, then his state is the pure state obtained after collapse. However, if he does not know the outcome, then he uses a state that he considers a proper mixture (the collapsed states for the different outcomes weighted by the Born rule probabilities).

 

[stevendaryl]

I was thinking a bit differently. If Wigner accepts that a measurement has been performed, then the wave function collapses. If Wigner knows the measurement outcome, then his state is the pure state obtained after collapse. However, if he does not know the outcome, then he uses a state that he considers a proper mixture (the collapsed states for the different outcomes weighted by the Born rule probabilities).

That's what I would call a "soft contradiction". Wigner thinking of his friend as a collection of atoms that obey Schrödinger's equation tells him one thing. Thinking of his friend as an observer capable of performing measurements tells him something else.

 

[atyy]

That's what I would call a "soft contradiction". Wigner thinking of his friend as a collection of atoms that obey Schrödinger's equation tells him one thing. Thinking of his friend as an observer capable of performing measurements tells him something else.

Isn't that's just the measurement problem?

 

[stevendaryl]

Isn't that's just the measurement problem?

I suppose so.

 

[DarMM]

Maybe QBists try to do that, since I think FR say QBism is inconsistent?

FR more says that if you want to have subjective collapse, you have to move to a position like yours or QBism, i.e. Wigner must not even consider his friend's events.

QBism is like your view and is explicitly compatible with FR.

As Matthew Pusey says in his summary it strengthens positions like yours and QBism.

Are there really Copenhagen versions in which an agent can be on both sides of the quantum-classical cut? I mean, it would be like saying that the cat is both "dead and alive" and "dead or alive", which seems ridiculous.

This is essentially what I was saying to @Demystifier , yes it seems ridiculous, but is has never been proven to actually be contradictory until now. That's really all FR is in a way.

As @Demystifier said the only surprising thing is that you need such an extreme scenario to demonstrate the contradiction.

I don't have the freedom for a long post right now but when I do I'll go into why some people thought it might be possible to consider an agent on both sides of the cut.

 

[ftr]

Why does the particle have to be in superposition in the first place.

 

[PeterDonis]

In BM, which is deterministic, only one of them is actually possible, and we only consider them both possible because we have incomplete knowledge of the current state.

But after the measurement, our knowledge of the current state has changed, because we know which outcome occurred. And we reflect that changed state of knowledge in the new wave function we use to predict further measurement results. So it seems like BM is perfectly consistent with an epistemic view of wave function collapse.

 

[DarMM]

Why does the particle have to be in superposition in the first place.

Which particle?

 

[ftr]

Say particle in a box for example, or electron in hydrogen atom ... etc

 

[atyy]

This is essentially what I was saying to @Demystifier , yes it seems ridiculous, but is has never been proven to actually be contradictory until now. That's really all FR is in a way.

As @Demystifier said the only surprising thing is that you need such an extreme scenario to demonstrate the contradiction.

If FR is a technical result about the extent to which the classical-quantum cut can be shifted, could it be understood as an extreme variant of Hay and Peres's "Quantum and classical descriptions of a measuring apparatus" https://arxiv.org/abs/quant-ph/9712044 ?

 

[stevendaryl]

But after the measurement, our knowledge of the current state has changed, because we know which outcome occurred. And we reflect that changed state of knowledge in the new wave function we use to predict further measurement results. So it seems like BM is perfectly consistent with an epistemic view of wave function collapse.

My comment was in reference to @atyy saying:

Anyway, would you agree with Demystifier that collapse in BM is objective (post #17)?

I would think that objective means that it's not epistemic.

 

[Demystifier]

I'm not exactly sure what @Demystifier would say about it, but it seems to me that BM is not consistent with the usual idea of wave function collapse.

Let me put it in a slightly metaphorical form. In BM, there is no collapse from the bird's view, but there is from the frog's view.

 

[Demystifier]

If FR is a technical result about the extent to which the classical-quantum cut can be shifted, could it be understood as an extreme variant of Hay and Peres's "Quantum and classical descriptions of a measuring apparatus" https://arxiv.org/abs/quant-ph/9712044 ?

Yes, it seems related.

 

[Demystifier]

So it seems like BM is perfectly consistent with an epistemic view of wave function collapse.

In BM there are two different notions of the wave function: (i) the wave function of the full system and (ii) the wave function of the subsystem. The collapse of (i) is epistemic, but the collapse of (ii) is ontic.

Let me explain a bit. Suppose that the full system consists of two particles, with positions $x_1$ and $x_2$. The full wave function is $\Psi(x_1,x_2,t)$. In BM there are also particle trajectories $X_1(t)$ and $X_2(t)$. Then the wave function of the subsystem 1 is
$$\psi_1(x_1,t)=\Psi(x_1,X_2(t),t)$$
The wave function $\psi_1(x_1,t)$ is ontic, it does not always satisfy the Schrödinger equation, and in a measurement setup it may collapse. This collapse of $\psi_1(x_1,t)$ is ontic.

Not also that standard QM does not have an analog of $\psi_1(x_1,t)$. To describe a subsystem, the standard QM must use a density matrix (a partial trace of the full density matrix), rather than a wave function.

 

[A. Neumaier]

In BM there are two different notions of the wave function: (i) the wave function of the full system and (ii) the wave function of the subsystem. The collapse of (i) is epistemic, but the collapse of (ii) is ontic.

What if there are three nested systems? Doesn't the full system have to be the whole universe? Otherwise the nature of the wave function changes depending on what one regards as the full system.

 

[Demystifier]

What if there are three nested systems?

Than only the biggest one is counted as the full system, while the other two are subsystems. One of those two is in fact a sub-subsystem, but it doesn't change much.

Doesn't the full system have to be the whole universe?

Strictly speaking, yes. But if a smaller system is not much entangled with the rest of the Universe, then one can use an approximation by treating this system as a "full" system.

Otherwise the nature of the wave function changes depending on what one regards as the full system.

Fortunately this is no the case, because there is a well defined criterion for a definition of full system - a system with zero (or small, for practical purposes) entanglement entropy.

 

[A. Neumaier]

if a smaller system is not much entangled with the rest of the Universe

But any observable system is significantly entangled with the rest of the universe. Otherwise we (being part of the rest of the universe) cannot observe it.

 

[Demystifier]

But any observable system is significantly entangled with the rest of the universe. Otherwise we (being part of the rest of the universe) cannot observe it.

If that was true, then we could never use pure states in quantum theory, except when we describe the whole Universe. Obviously, it is not true. Sure, when Prof. Zeilinger performs measurement of an electron, then the electron is entangled with the measuring apparatus and with Prof. Zeilinger. In this case, the full system consists of electron, measuring apparatus and Prof. Zeilinger. But it still does not need to include the whole Universe. The entanglement between Prof. Zeilinger and his dog, for instance, can be neglected for the purpose of studying the electron in the Zeilinger's laboratory.

 

[martinbn]

Can BM treat the whole universe at least in principle, or any infinite number of particles?