Schrodinger's Cat and the thermal interpretation

[Demystifier]

[Moderator's note: spin-off from a previous thread since this discussion is a separate topic.]

If you are able to prepare a particular spin state (a superposition, say), it means that at the time of preparation, the state of the universe is such that the reduced density matrix of the spin is in this state. (See post #22 for full details.)

In this sense, the Schrodinger's famous thought experiment prepares the cat in a superposition of dead and alive. I still don't see how TI can possibly prevent it.

 

[A. Neumaier]

In this sense, the Schrodinger's famous thought experiment prepares the cat in a superposition of dead and alive.

No; only the atom is prepared in a superposition of undecayed and decayed. Schrödinger arrives at your conclusion only by assuming that the subsystem consisting of a decaying atom and the cat is isolated, which is never the case.

Only the whole universe is isolated. The subsystem is open, interacting with the bottom of the box and with the air in it. Increasing the size of the subsystem does not help. This openness is sufficient to make the system dissipative; the quantum H-theorem (whose statistical mechanics derivation you conceded to be acceptable as proof) provides a proof of this. Thus the arguments of Section 5 of my Part III apply and produce a definite final state for the atom (undecayed or decayed) and the cat (alive or dead).

The validity of the quantum H-theorem also shows that increasing entropy does not prove that the system must end up in experimentally relevant times in an equilibrium state, thus making Valentini's and your conclusion of Bohmian mechanics soon being in quantum equilibrium as unwarranted.

 

[stevendaryl]

No; only the atom is prepared in a superposition of undecayed and decayed. Schrödinger arrives at your conclusion only by assuming that the subsystem consisting of a decaying atom and the cat is isolated, which is never the case.

Only the whole universe is isolated.

Right, but I don't think that really changes anything, does it? Instead of a cat that is in a superposition of alive and dead, you have the whole universe in a superposition of a universe with a dead cat and a universe with a live cat.

 

[stevendaryl]

Right, but I don't think that really changes anything, does it? Instead of a cat that is in a superposition of alive and dead, you have the whole universe in a superposition of a universe with a dead cat and a universe with a live cat.

In terms of density matrices, the evolution would produce something like this:

$\rho = p_1 \rho_{alive} + p_2 \rho_{dead} + \rho_{cross}$

where $\rho_{cross}$ represents the cross terms like $|dead\rangle\langle alive|$ and $|alive\rangle\langle dead|$ ("alive" and "dead" referring to states of the whole universe, not just the cat).

If you ignore the cross-terms, this can be interpreted as the cat having a probability of $p_1$ of being alive and a probability of $p_2$ of being dead. With the cross-terms, it's a little hard to say.

Regular quantum evolution is not going to change the probabilities $p_1$ and $p_2$. So I don't think that the universe will ever evolve into a state where the cat is definitely dead.

 

[A. Neumaier]

Right, but I don't think that really changes anything, does it? Instead of a cat that is in a superposition of alive and dead, you have the whole universe in a superposition of a universe with a dead cat and a universe with a live cat.

Superposition makes no sense for density operators.

We have a universe with an evolving density operator, and at the preparation time we have a binary subsystem whose reduced density operator is prepared as $\psi^S=\psi_S\psi_S^*$ with a superposition $\psi_S\in C^2$, and another subsystem describing a binary live/dead variable for a cat in local equilibrium, whose reduced density operator $\psi^C$ is prepared as $\psi_C\psi_C^*$ with $\psi_C={1\choose 0}$, where $A=\pmatrix{1 & 0\cr 0 & 0}$ is the degree of aliveness. The question is what happens to the reduced density matrix $\psi^C$ under the unitary evolution applied to the density operator of the universe. The claim is that only two states are stable under small perturbations.

 

[A. Neumaier]

In terms of density matrices, the evolution would produce something like this:

$\rho = p_1 \rho_{alive} + p_2 \rho_{dead} + \rho_{cross}$

where $\rho_{cross}$ represents the cross terms like $|dead\rangle\langle alive|$ and $|alive\rangle\langle dead|$ ("alive" and "dead" referring to states of the whole universe, not just the cat).

If you ignore the cross-terms, this can be interpreted as the cat having a probability of $p_1$ of being alive and a probability of $p_2$ of being dead. With the cross-terms, it's a little hard to say.

Regular quantum evolution is not going to change the probabilities $p_1$ and $p_2$. So I don't think that the universe will ever evolve into a state where the cat is definitely dead.

It is more complicated; only the q-expectation of $A$ of the cat needs to evolve such that a binary decision can be made. I'll provide some analysis in a separate thread, but not today; I need time to work out a reasonably intuitive form and to type the details.

 

[Demystifier]

It is more complicated; only the q-expectation of A of the cat needs to evolve such that a binary decision can be made. I'll provide some analysis in a separate thread, but not today; I need time to work out a reasonably intuitive form and to type the details.

I'm looking forward to see that. This might clarify some important things about TI.

 

[A. Neumaier]

It is more complicated; only the q-expectation of $A$ of the cat needs to evolve such that a binary decision can be made. I'll provide some analysis in a separate thread, but not today; I need time to work out a reasonably intuitive form and to type the details.

I'm looking forward to see that. This might clarify some important things about TI.

See Section 3 of my new paper here!

 

[A. Neumaier]

In terms of density matrices, the evolution would produce something like this: $\rho = p_1 \rho_{alive} + p_2 \rho_{dead} + \rho_{cross}$
where $\rho_{cross}$ represents the cross terms like $|dead\rangle\langle alive|$ and $|alive\rangle\langle dead|$ ("alive" and "dead" referring to states of the whole universe, not just the cat).

A detailed discussion of how Born's rule follows from the evolution of the state of the universe is given in the analysis in Section 3 of my Part IV. (Please discuss details in that thread.) The point is that one only needs to consider a binary pointer variable for the property ''atom decayed'' (or not), and that this decision is definitely made in a macroscopically noticeable way within a finite (macroscopically short) time, using the standard approximations used everywhere in statistical mechanics. Thus the cat is definitely dead or alive except during a short moment where the decay happens and nothing definite can be said.

 

[Demystifier]

The point is that one only needs to consider a binary pointer variable for the property ''atom decayed'' (or not), ... Thus the cat is definitely dead or alive except during a short moment where the decay happens and nothing definite can be said.

1. If the variable is binary, then it has only two possible values. Then how can there be a short moment where it does not have any of those two values? Did you actually mean that it has a continuum of values, but only two stable values?

2. What determines the time during which nothing definite can be said? Is it essentially the same as the decoherence time?

 

[A. Neumaier]

1. If the variable is binary, then it has only two possible values. Then how can there be a short moment where it does not have any of those two values? Did you actually mean that it has a continuum of values, but only two stable values?

Any actual binary display needs time for switching between 0 and 1, and cannot be meaningfully read during the switching time. Read Section 3 of Part IV for the details; everything is specified there.

2. What determines the time during which nothing definite can be said? Is it essentially the same as the decoherence time?

My argument is asymptotic and gives no information about the time needed. It surely depends on the response mechanism of the binary display and cannot be discussed in abstracto.

For a complicated binary decision, such as whether a cat is alive or dead, it might take minutes to make a solid decision. But if one doesn't use poison and a cat to register the decay then the decoherence time might be enough.

 

[charters]

For a complicated binary decision, such as whether a cat is alive or dead, it might take minutes to make a solid decision. But if one doesn't use poison and a cat to register the decay then the decoherence time might be enough.

Thus the cat is definitely dead or alive except during a short moment where the decay happens and nothing definite can be said.

But this is inconsistent with what you've said or agreed to elsewhere regarding the existence of deterministic hidden variables in the TI. In any deterministic HV interpretation, the real ontic state is always associated with *either* a cat that lives or a cat that dies, at all times. I think this is @Demystifier's point And here the Born rule is simply the result of respecting an equilibrium condition when assigning HVs. So you are creating unnecessary work for yourself that is obviated by concessions you make elsewhere.

Alternatively, in part IV section 3 you are saying the q-expectations/beables are just the reduced density matrices. This is actually pretty similar to Wallace and Timpson's Spacetime State Realism (https://arxiv.org/abs/0907.5294). But as they show, density operators as beables will not unitarily evolve to a single macroscopic world.

Put another way, you must commit once and for all as to whether the universal density operator represents a proper or improper mixture. Right now you seem to move between these two views. If the global mixture is proper, then the TI is an HV interpretation, and the q-expectations as density operators are not in fact the complete set of beables. The HVs are also beables. If the global mixture is improper, the density operators are the only beables, but it is many worlds under unitary time evolution.

 

[A. Neumaier]

But this is inconsistent with what you've said or agreed to elsewhere regarding the existence of deterministic hidden variables in the TI.

No.

you must commit once and for all as to whether the universal density operator represents a proper or improper mixture. [...] it is many worlds under unitary time evolution.

Time evolution is unitary, and all density matrices represent improper mixtures; the notion of a proper mixture (and hence the distinction) makes no sense in the TI. But the meaning is very different from that in the MWI.

In MWI, only state decompositions in terms of a preferred basis have an interpretable meaning, with many terms implying many worlds.

In the TI, such decompositions are completely irrelevant. Instead, certain linear functionals of them (the q-expectations) have meaning, and these are unique at every time, so that there is only one world.

Wallace and Timpson's Spacetime State Realism (https://arxiv.org/abs/0907.5294). But as they show, density operators as beables will not unitarily evolve to a single macroscopic world.

Which theorem there do you refer to? There is no interpretation-independent concept of a world, and arguments about worlds don't mean anything in the TI.

In any deterministic HV interpretation, the real ontic state is always associated with *either* a cat that lives or a cat that dies, at all times.

Why? Positing hidden variables does not imply any claim about what these mean, except that they exist independent of any observation or measurement.

The existence of the TI is a counterexample to your assertion. Its beables are ontic, hence are hidden variables in the conventional sense, and they evolve deterministically.

Its goal is to explain the real world, in which binary decisions cannot be made during a change of their value, and not a theoretical caricature where they are claimed to have binary values even when reality shows otherwise.

the Born rule is simply the result of respecting an equilibrium condition

The TI dispenses with such an equilibrium condition - this is one of its strength. Its probabilities are of the same nature as the probability of being in the left or right part of a Lorenz attractor. The probabilities are determined by the deterministic dynamics itself together with a limited temporal resolution, and not by any assumed equilibrium condition!

 

[charters]

Time evolution is unitary, and all density matrices represent improper mixtures

Ok I'd like to focus on the first part of 3.4 in paper IV, up to eq (14). Tell me at which step you claim I go wrong.

1) A detector is completely described by q-expectation value beables for any relevant observable, which is given by the partial trace/reduced density matrix of the detector subsystem within the universal density matrix.

2) Like a standard EV in textbook QM, a q-expectation value that commutes with the Hamiltonian will be constant under unitary time evolution.

3) In section 3.4, you say to "consider an environmental operator $X^E$ that leads to a pointer variable $X_t$ which moves in a macroscopic time t > 0 a macroscopic distance to the left (in microscoic units, large negative) when p = 0 and to the right (large positive) when p = 1."

4) The q-expectation value of the detector pointer, prior to the measurement, is such that it is "pointing up" or 0.5, if we identify the left tilt with 0, and right tilt with 1.

5) The q-expectation value of the beam being measured can be prepared to also be 0.5 where the relevant observable commutes with the Hamiltonian. A concrete example of step 4 and 5 is just an n=1 beam prepared as $\sqrt 1/2 \left| up+down \right>$ that will undergo a spin measurement by a properly calibrated device.

6) By point 2, after the unitary interaction between beam and detector, the relevant q-expectation values for both beam and detector must still be 0.5.

7) A q-expectation value of 0.5 after measurement means the detector pointer did not even measure the beam, the pointer did not move. Alternatively, if the detector does move, and there is still only one world, its q-expectation is changing non-unitarily, ie it is not constant under time evolution even though the observable commutes with the Hamiltonian. In a sense MWI can be read as the explanation of how pointers can move while allowing the q-expectations to not change - because the left tilt in one world is offset by the right tilt in the other.

I think maybe you intend to say that somehow uncontrolled degrees of freedom in the environment solve this problem - that the deterministic outcomes are imprinted in these other degrees of freedom which are not considered above. But then, since the detector-environment split is arbitrary, this is really a way of saying the assumption of well calibrated detectors is flawed - in fact, when the pointer looks like it is "straight up" whether it is going to favor the left or right is already imprinted in the q-expectation of the nearby air, so the calibration is secretly false.

But if so, then to return to my original point, you never, not even briefly, have to worry about the state of Schrodinger's cat being alive *and* dead. To the extent it ever looks this way, its an artifact of the choice to ignore the degrees of freedom that already predict the outcome. It is not presenting the ontological issue that people are usually worried about when saying a cat is "alive AND dead".

However, I separately worry this environmental degrees of freedom story is afoul of Von Neumann's HV theorem (see https://arxiv.org/abs/1006.0499) as the environment seems to be simultaneously, deterministically encoding outcomes of measurements on all possible bases. I don't think VN's theorem allows you to just use other quantum subsystems as HVs, I think it requires an additional layer of beables like in Bohmian mech.

 

[A. Neumaier]

Ok I'd like to focus on the first part of 3.4 in paper IV, up to eq (14). Tell me at which step you claim I go wrong. [...]

5) The q-expectation value of the beam being measured can be prepared to also be 0.5 where the relevant observable commutes with the Hamiltonian. A concrete example of step 4 and 5 is just an n=1 beam prepared as $\sqrt 1/2 \left| up+down \right>$ that will undergo a spin measurement by a properly calibrated device.

In step 5 you add the unwarranted assumption that relevant quantities commute with the Hamiltonian. But such quantities cannot measure anything, as you correctly argue. Thus pointer variables don't commute with the Hamiltonian.

 

[charters]

Thus pointer variables don't commute with the Hamiltonian.

Then measurement records won't even be stable in time/under decoherence. Zurek even defines the pointer variables by the fact they commute with the Hamiltonian: https://arxiv.org/abs/quant-ph/9805065

But such quantities cannot measure anything, as you correctly argue.

It works fine in the Everettian/decoherence story.

 

[A. Neumaier]

Then measurement records won't even be stable in time/under decoherence. Zurek even defines the pointer variables by the fact they commute with the Hamiltonian: https://arxiv.org/abs/quant-ph/9805065

My definition is different from Zureks: my pointer variables are not operators but special q-expectations that have the property defined before (14). This is possible only if $X^E$ does not commute with the Hamiltonian.

Note that I didn't model the amplification process that goes into a real measurement ending up with a true pointer on a scale, but only the initial step where something microscopic (e.g., an electron in a photodetector) is moved by a macroscopic distance (where it would trigger an amplifying cascade). On this level, a temporary microscopic position would be the pointer. The sign of the motion decides already the final amplified binary result - the amplification only makes it macroscopically visible and irreversible. This sign is dynamically stable in the situation analyzed.

- that the deterministic outcomes are imprinted in these other degrees of freedom which are not considered above. But then, since the detector-environment split is arbitrary,

Note that there is no arbitrary detector-environment split, only the (obviously necessary) distinction of the variable that produces the binary decision! My argument in Section 3 encodes the effects of all degrees of freedom of the universe. It involves no approximation at all, apart from the replacement of finite times in Subsection 3.4 by an infinite time limit, as usual in arguments about microscopic scattering processes, and the final discussion at the end of Subsection 3.4.

 

[charters]

Ok, I'll try one more approach, the prior wasn't effective.

You claim the TI is unitary and has deterministic outcomes of measurements. You also claim macroscopic cats/measuring devices evolve from a state of ontic uncertainty during the measurement, into a fixed state of the measurement basis, specifically:

Thus the cat is definitely dead or alive except during a short moment where the decay happens and nothing definite can be said

But unitary transformations cannot take a state of ontic uncertainty (a superposition or improper mixture) on some basis into a state of certainty on that basis, or vice versa. T'Hooft (who I generally disagree with on foundations, but on this he is certainly right) has actually just put out a paper calling this a "conservation of ontology" principle: https://arxiv.org/abs/1904.12364

So, either the TI is not deterministic, or the uncertainty associated with the cat/detector is just an epistemic uncertainty, due to ignoring the external/environmental subsystems or (more reasonably) HVs whose state deterministically predicts the outcome. In a deterministic interpretation, you don't need to, shouldn't want to, and can't talk about "dead AND alive" states, even ephemerally.

 

[A. Neumaier]

You claim the TI is unitary and has deterministic outcomes of measurements.

yes.

You also claim macroscopic cats/measuring devices evolve from a state of ontic uncertainty during the measurement, into a fixed state of the measurement basis

No.
A basis never figures in my argument. I only claim that there is a stable sign of expectations, enough to get a decision based on the TI beables. Also, there is no uncertainty at all in my arguments, except in the details about the probabiliy with which a given sign is obtained - which depends on the state of the universe at preparation time and on the precise dynamics.

In a deterministic interpretation, you don't need to, shouldn't want to, and can't talk about "dead AND alive" states, even ephemerally.

I never talked about that. I only talk about the microscopic anlogue of an apparently dying cat - during the time where the sign cannot yet be read off with certainty.

 

[charters]

Ok, I don't think we're going to make progress. I just don't agree it is possible in principle to have unitary, determinsitic, single world quantum mechanics in which the subsystems are exhaustively described by improper mixtures, ie states that display ontic uncertainty. One needs additional hidden variables to underwrite this single world determinism at all times, effectively rendering the mixtures proper. I see all this as following from the definitions of these terms, and as such the point is too general to be sensitive to any idiosyncracies of the TI or any particular interpretation. But I guess I'm not able to convey the argument effectively.

 

[PeterDonis]

states that display ontic uncertainty

As I understand it, there is no ontic uncertainty in the TI. The ontic state is the q-expectation, and q-expectations are not uncertain. The uncertainty is epistemic--we can't make infinitely precise measurements of the q-expectations.

 

[charters]

As I understand it, there is no ontic uncertainty in the TI. The ontic state is the q-expectation, and q-expectations are not uncertain. The uncertainty is epistemic--we can't make infinitely precise measurements of the q-expectations.

But the q-expectations are described by reduced density matrices/partial traces (see 3.3 in paper IV; axiom A5 in paper I). The uncertainty of these mathematical objects is ontic by definition (this fact is the core of the measurement problem). Equivalently, the uncertainty of improper mixtures is ontic, whereas proper mixtures encode epistemic uncertainty. And, at least in #71 above, Arnold says:

all density matrices represent improper mixtures; the notion of a proper mixture (and hence the distinction) makes no sense in the TI

 

[PeterDonis]

The uncertainty of these mathematical objects is ontic by definition

Not if you don't define it that way. I don't see how you can declare by fiat that a particular mathematical object can only have one ontic meaning. Mathematical objects don't have any ontic meaning at all apart from definitions we choose.

 

[charters]

It's a requirement of the uncertainty principle/noncommuting observables that some of the uncertainty in quantum theory (without hidden variables) is ontic. The (state vector or) density matrix can be in an eigenstate when basis A is diagonal, but not when we diagonalize for conjugate observable B. To say the uncertainty is epistemic is to say the system is *really* in an eigenstate of two conjugate bases at once, and we are just ignorant of which they are. But due to interference effects and the mathematical framework, we know the uncertainty of quantum systems has no such simple ignorance interpretation.

I stress the truth of this is interpretation independent. In fact, interpretations exist only because we aren't sure how to handle ontic uncertainty and the Born rule at the same time.

Sometimes a subsystem is not in *any* local eigenstate, so it has this ontic uncertainty on every basis, rather than merely having ontic uncertainty on most bases. An example is one of the qubits when the state is a Bell state. In this case, we say the qubit's state is an improper mixture, rather than a pure state.

One can choose different definitions for terms, but doing so would not change the reality of the situation, which is that quantum mechanics requires additional (hidden) variables to admit a purely epistemic uncertainty interpretation similar to classical mechanics.

Also, just think about the idea of an expectation value being a beable (this btw is also how MWI works). If the uncertainty that necessitated the use of an EV was merely epistemic, just a matter of our ignorance about the state, it would make no sense to ever suggest the EV was a beable. The beable would obviously just be the underlying ontic state. Classical mechanics works exactly like this, where the beables are represented by a point in phase space, which is embedded in a probability distribution over the same phase space, to represent our lack of exact knowledge of the point. In this case, we would call a random sampling of possible underlying points a proper mixture.

 

[lukesfn]

My understanding is only very rudimentary, but I come up with similar issues as expressed in this thread with trying to figure TI.

A basis never figures in my argument. I only claim that there is a stable sign of expectations, enough to get a decision based on the TI beables. Also, there is no uncertainty at all in my arguments, except in the details about the probabiliy with which a given sign is obtained - which depends on the state of the universe at preparation time and on the precise dynamics.

This kind of point sounds like something starting conditions could be considered as implicit hidden variables.

You could look at TI from the point of view of it being a generalization of Bohmian Mechanics, or other non-local hidden variable interpretations, but without all the explicit details that would bring any additional hidden variables or poincare invariance, or super determinism into the light.

 

[PeterDonis]

It's a requirement of the uncertainty principle/noncommuting observables that some of the uncertainty in quantum theory (without hidden variables) is ontic

I think this statement, like your previous one about density matrices, is interpretation dependent. As I understand the TI, the inability to simultaneously make exact measurements of non-commuting observables is due to the dynamics; it's not due to any ontic uncertainty in the state. Unless that counts as "some of the uncertainty is ontic", then "some of the uncertainty is ontic" would seem to me to be interpretation dependent.

Sometimes a subsystem is not in *any* local eigenstate

The TI doesn't say eigenstates are ontic, so this is irrelevant to the TI. The TI says q-expectations are ontic.

An example is one of the qubits when the state is a Bell state. In this case, we say the qubit's state is an improper mixture, rather than a pure state.

But each qubit still has q-expectations, and those aren't uncertain.

If the uncertainty that necessitated the use of an EV was merely epistemic, just a matter of our ignorance about the state, it would make no sense to ever suggest the EV was a beable.

You've got the TI backwards. If the q-expectation is a beable, then what doesn't make sense is to talk about "the uncertainty that necessitated the use of an EV". The EV is the ontic state; any talk about other objects like state vectors or density matrices is what would be necessitated by uncertainty, i.e., our inability to make infinitely precise measurements of the q-expectation, the ontic state.

 

[charters]

You are missing my point. I have no objection to this ontology in principle - like I said, the basic notion of ontic q-expectation beables is already pretty similar to some forms of MWI. The issue is: if the q-expectation is exhaustive of the beable/ontic state, fine, but then the beables do not deterministically predict measurement outcomes.

Or, I suppose you will have to explain to me the following: how can one simultaneously say the complete description of a balanced qubit is EV = 0.5 and also that this statement alone contains enough information to predict whether an upcoming measurement of the qubit will reveal 0, rather than 1? How can you simultaneously say the description of a detector pointer is exhausted by saying it has an EV of "pointing up" and that this alone is enough information to predict whether the pointer will, once a beam is incident, lean left, rather than right?

More simply, EVs by definition do not contain information about which outcome will obtain in any given single event (determinism requires this). If you know any poker lingo, my EV with pocket aces pre-flop is promising, but that doesn't determine whether I am actually destined to win or lose on that specific hand - among other things, the card order in the rest of the deck controls that

So, in the TI, either this information encoding specific outcomes is A) in an additional HV, B) the time evolution is nonunitary/nondeterministic so that outcomes are unpredictable, or C) the need for the choice itself is obviated by a many-worlds "everything happens" claim.

 

[PeterDonis]

The issue is: if the q-expectation is exhaustive of the beable/ontic state, fine, but then the beables do not deterministically predict measurement outcomes.

The beables of the measured system by itself don't, no. But the beables of the measured system plus the measuring device do. See below.

how can one simultaneously say the complete description of a balanced qubit is EV = 0.5 and also that this statement alone contains enough information to predict whether an upcoming measurement of the qubit will reveal 0, rather than 1?

You can't, and that's not what the TI says. The TI says that, to be able to predict whether the upcoming measurement of a single qubit will reveal 0 or 1, you need to know, not just the beable of the qubit (which is just its q-expectation, which by hypothesis is 0.5), but all of the relevant beables of the measuring device and the detector. As I understand it, the TI says that random fluctuations inside the detector, which in practice we can't measure or control, are what cause the result to be 0 or 1 (more precisely, for a dot to be observed in either the "0" or the "1" spot on the detector). @A. Neumaier has compared this to the dynamics of an object in a double well potential that starts at the peak in between the wells.

in the TI, either this information encoding specific outcomes is A) in an additional HV

Yes, it's A), but the "HV" is just more beables--the beables of the measuring device and the detector, as above.

 

[PeterDonis]

The beables of the measured system by itself don't, no. But the beables of the measured system plus the measuring device do.

The discussion in this thread is relevant:

https://www.physicsforums.com/threa...-interpretation-explain-stern-gerlach.969296/

 

[charters]

Yes, it's A), but the "HV" is just more beables--the beables of the measuring device and the detector, as above.

Well, this is the same thing I said back in #72, but it didn't get picked up as the thread continued. It's not really a HV story, but a false detector calibration story. I am not sure it is actually valid for outcomes to be imprinted on accessible degrees of freedom (ie degrees of freedom that would appear in a fine grained, condensed matter QFT description of the device) due to 1) Von Neumann's theorem, see the paper linked in #72, and 2) the causality issues with outcomes being encoded in non-hidden variables, well known in the Bohmian context, but not restricted to it.

 

[A. Neumaier]

improper mixtures, ie states that display ontic uncertainty

The uncertainty of these mathematical objects is ontic by definition

By whose definition, in which interpretation? (As ''ontic'' is not a mathematical notion of the quantum formalism, your statement must be based on some interpretation to be meaningful!)

It's a requirement of the uncertainty principle/noncommuting observables that some of the uncertainty in quantum theory (without hidden variables) is ontic.

The uncertainty principle is just an inequality between certain functions of q-expectations. The TI interprets these differently than traditional interpretations. They are just measures providing a lower bound on how accurately one can know the ontic values of a subsystem through measurments on a detector system.
It limits the possible amount of epistemic information one can gather about the ontic state.

Note that states of subsystems are never eigenstates but always reduced density matrices (encoding the values of the subsystem's q-expectations). Eigenstates never matter, except as mathematical tools in the asymptotic stability analysis of model systems.

if the q-expectation is exhaustive of the beable/ontic state, fine, but then the beables do not deterministically predict measurement outcomes.

You fail to provide a proof of this statement. The predicted (and approximately realized) measurement outcomes are (by definition) functions of q-expectations of the detector, hence are deterministically predicted by the state of the universe, though not by the state of (measured object plus pointer variable).

The beables of the measured system by itself don't, no. But the beables of the measured system plus the measuring device do.

yes, but strictly speaking only when taking the remainder of the universe as the detector.

the "HV" is just more beables--the beables of the measuring device and the detector, as above.

the "HV" are just more beables -- all beables of the universe. With fewer, no determinism.

 

[PeterDonis]

It's not really a HV story, but a false detector calibration story

This is interpretation dependent. On your interpretation, the "real" values being measured are the 0 or 1, the spin eigenstates, and they are being measured exactly. On the TI, the "real" value being measured is the q-expectation, 0.5, and it is being measured poorly. You can say you prefer the first story to the second, but that just means you prefer your interpretation to the TI. It doesn't mean the TI has "false detector calibration"; that's trying to interpret what the TI says in terms of your interpretation, which is just mixing different interpretations.

 

[charters]

This is interpretation dependent. On your interpretation, the "real" values being measured are the 0 or 1, the spin eigenstates, and they are being measured exactly. On the TI, the "real" value being measured is the q-expectation, 0.5, and it is being measured poorly. You can say you prefer the first story to the second, but that just means you prefer your interpretation to the TI. It doesn't mean the TI has "false detector calibration"; that's trying to interpret what the TI says in terms of your interpretation, which is just mixing different interpretations.

It doesn't matter whether the measurement is accurate. It simply matters that, as an empirical fact, the pointer slides left or right. We directly observe this. We agree determinism means there is information that objectively exists before the pointer starts moving, which predicts the pointer shift with certainty. If, as we also agree, this information is encoded in the detector itself (but see below, maybe we have this wrong), then it is fair to say the detector isn't really measuring the beam. It is just revealing its own pre-existing calibration/configuration. I see it as false calibration because a detector that informs on its own state, rather than the state of the target system, is not quite a detector at all. I think a detector has to extract information from an intentionally chosen target system outside itself. But I guess this is my preexisting bias of the meaning of the word.

the "HV" are just more beables -- all beables of the universe. With fewer, no determinism.

So to know with certainty which exit port of my open MZI will click, I have to know whether it is raining on a planet in the Andromeda galaxy?

 

[charters]

By whose definition, in which interpretation? (As ''ontic'' is not a mathematical notion of the quantum formalism, your statement must be based on some interpretation to be meaningful!)

The uncertainty in QM must be ontic because we observe interference between the different possibilities the state of a single subsystem ranges over (forgot to respond to this above). The possibilities in an epistemic probability distribution cannot exhibit interference, as only one of them actually exists.

 

[A. Neumaier]

I think a detector has to extract information from an intentionally chosen target system outside itself.

Indeed it does, in the analysis of Section 3 of Part IV. The information extracted is stochastic, the sign of the direction provides a realization of a binary random variable whose distribution gives precise information about the true state of the system measured. One cannot expect more to be revealed in a strongly chaotic deterministic dynamical system in which part of the state vector is used to predict another part.

That really something is measured (though inaccurately) can be seen that if one measures a a stationary beam of light, say, repeatedly, one can measure the whole distribution and thus gets the full system state. Indeed, this is what quantum tomography is about. It is like measuring the cosmic microwave background - single measurements are completely uninformative and seemingly consist of noise only but from sufficiently long sequences of observations one gets an accurate picture.

So to know with certainty which exit port of my open MZI will click, I have to know whether it is raining on a planet in the Andromeda galaxy?

In principle, yes, that's the inevitable consequence of nonlocal deterministic dynamics. You have the same in Bohmian mechanics. To predict with certainty the position of the Bohmian pointer variable at one point in the future you need to know now the positions of all particles in the universe, and the details of the wave function.

Of course, if you allow yourself some uncertainty in your knowledge (which is what everyone does) then you can probably ignore any rain in the Andromeda galaxy. But your assurance goes down from 100% to 99.9999999%. In practice, claimed exact knowledge (before observation) is far more uncertain. We ''know'' that switching on the light will lighten a room. But we know very well that this is not always the case - if an exception happens we explain it away by invoking previously hidden variables that took unexpected valus, like a broken fuse or a defective light bulb...

It is a matter of judgment and knoweldge of the sensitivity of a system - measurement situation to external influences that determines what one can safely neglect and what needs to be taken into account. The prevalence of decoherence, however, shows that preparing things in such a way that individual quantum predictions (e.g., quantum comouting results) are highly reliable is quite demanding a task.