A 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.

 

[A. Neumaier]

The uncertainty in QM must be ontic because we observe interference between the different possibilities the state of a single subsystem ranges over

What interference are you talking about?

In the TI, beables are q-expectations, not wave functions. The reduced density matrix is only a tool to compute these. In case of a 2-state system, one can instead use the Bloch vector to encode the q-expectations, ranging over a unit ball. Interference does not apply to this representation.

We observe approximations to the ontic values. The same observed highly peaked bimodal distribution of observations in a large sample of trials can be interpreted either as the observation of a tiny random true binary value $\pm\hbar/2$ of the system measured, with small bell-shaped measurement error - this is the TI interpretation of the observations regarded as measuring the detector beable. Or it can be interpreted as the observation of a single true value of the order of $O(\hbar)$ with a bimodal measurement error - this is the TI interpretation of the observations regarded as measuring the system beable.

Only the convention used - for which beable the measurement is and what is regarded as its true value - can decide between the two possibilities, and say anything about the relation between the measurement of the detector beable and what it means for the system beable.

The possibilities in an epistemic probability distribution cannot exhibit interference, as only one of them actually exists.

A single observation gives a value approximating the corresponding beable of the detector, which approximates the corresponding beable of the measured system, with an unknown error (if one does not assume to know beables).

This is independent of any epistemic analysis. The latter is about what an observer knowing only approximate observations is rationally entitled to imagine about success rates of future predictions.

 

[charters]

Having thought over this some more, I want to share where I've landed:

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.

So then it isn't the case that

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

Rather, like in Bohmian mech, the cat's fate is already, definitively decided at ALL times, before, during, and after the interaction/measurement. This informationnis encoded in these cross-universe correlations. In any interpretation of this variety, we do not conventionally say the cat is "alive AND dead." This is all I was trying to point out back in #70. I think what you really mean here is that there is a finite window during which the evolution of the *local* q-expectations from alive-to-alive and alive-to-dead will look the same, so as a local matter, the fact briefly seems ontologically undecided. This is what you are calling "alive AND dead" or "not definitely one or the other." That's a valid detail to highlight, but this is not the type of uncertainty that is at issue in Schrodingers cat as it is generally understood, and it isn't going to be productive to try to redefine a deeply embedded idea/term like this.

I also think some of our confusion has been related a lack of clarity/terminology agreement over the following idea: the TI universe is described by q-expectations, which are (using the definitions familiar to me) states of non-zero ontic uncertainty. But since we can't know all the exact q-expectations, the true state is embedded inside a proper mixture, but one whose elements are themselves improper mixtures rather than exact, classical states. In this way the TI beables are unlike in Bohm of T Hooft's interpretation, and require a "lighter touch," so to speak.

As a concrete example, consider an electron that we know has been prepared in the ground state of either Box A or Box B. The TI sees the electron as a fundamentally extended object, as a fieldlike object filling one box or the other, with a variable ontological density in different subregions of a single box. This can be seen as an ontically uncertain, improper mixture of classical positions within a single box. But, given the preparation constraint, there is *also* a proper mixture (epistemic ignorance) in respect of whether it is A or B that is filled at all.

For Bohm, however, the electron is instead a single classical point, so there is a proper mixture in respect of whether the electron is in A or B, but even when it is known box A is occupied, there is *another* proper mixture in respect of whether it is in subregion A1, A2, etc. The TI does away with the need for this secondary inquiry by treating this uncertainty as ontic rather than epistemic. Equivalently, the TI does not think it is a reasonable question to ask where in an atomic orbital the electron is. The electron is the entire orbital.

Now let us suppose Box A and Box B are connected. Here, the TI electron would unitarily disperse between the two boxes, becoming even more ontologically extended.

Finally, keep the boxes connected and replace the electron with a baseball. In this case, while there is always some small uncertainty/ontic extendedness in the center of mass of the baseball, even after infinite time, in the TI, the baseball never evolves to be extended over macroscopically distinct positions. Rather, nonlocal variables/correlations will steer the baseball's center of mass q-expectation so that it is non-dispersive on macro scales, so there is no need to worry about many worlds branching.

In sum, the TI uses "mild" hidden variables to the degree necessary to prevent many worlds, but without over-classicalizing the micro-ontology.

So, to tie this together, I now think the root of the confusion/dispute has been that when you say there is a window of time when the cat is alive AND dead, I hear something tantamount to "the baseball is ontologically extended over box A and B when connected, just like the electron." Once you open the door to this degree of ontic uncertainty, you have gone too far and will have many worlds. But I don't think this is what you meant to claim after all in the 2nd quote up above.

 

[PeterDonis]

the TI universe is described by q-expectations, which are (using the definitions familiar to me) states of non-zero ontic uncertainty

It doesn't matter how familiar that definition is to you; it's not the definition used in the TI, and in fact in the TI it's obviously false--in the TI the q-expectations are the beables so by definition they have zero ontic uncertainty. So you can't just help yourself to this definition when talking about the TI; it makes everything you say about the TI logically inconsistent.

 

[PeterDonis]

The TI sees the electron as a fundamentally extended object, as a fieldlike object filling one box or the other, with a variable ontological density in different subregions of a single box.

Yes.

This can be seen as an ontically uncertain, improper mixture of classical positions within a single box.

Not according to the TI, it can't. According to the TI, the "fieldlike object filling one box or the other" is the ontic state. All this talk of "classical positions" is simply irrelevant.

The TI does away with the need for this secondary inquiry by treating this uncertainty as ontic rather than epistemic.

No, it does away with the need for the secondary inquiry by not even using the concept of classical position at all.

 

[PeterDonis]

when you say there is a window of time when the cat is alive AND dead, I hear something tantamount to "the baseball is ontologically extended over box A and B when connected, just like the electron.

Suppose the baseball is in the connecting tunnel between A and B. Is it in A or B? There is no well-defined answer. Even if you draw an arbitrary line down the middle of the tunnel and say that there is the boundary between A and B, there will be some period of time when part of the baseball is on one side of the line and part is on the other side, and during that period of time, the question "is the baseball in A or B?" has no well-defined answer.

The "alive to dead" transition for the cat is something like the connecting tunnel in the above; while it is happening, there is no well-defined answer to the question "is the cat alive or dead?". You can try to draw arbitrary boundaries, but they're arbitrary, just as in the tunnel above, and there is no reason to think that the entire cat must always be on one side or the other of any boundary you draw.

Btw, I don't think the above has much to do with the TI in particular; it's just a general feature of macroscopic systems when you try to draw exact, hard-edged categories for them. Thinking that the categories we find it useful to draw for our human understanding must always be embedded somehow in the physics of the objects themselves is a simple map-territory confusion, like thinking that the Earth's prime meridian must somehow be physically set apart, at the level of individual molecules, from the rest of the Earth.

 

[charters]

It doesn't matter how familiar that definition is to you; it's not the definition used in the TI, and in fact in the TI it's obviously false--in the TI the q-expectations are the beables so by definition they have zero ontic uncertainty. So you can't just help yourself to this definition when talking about the TI; it makes everything you say about the TI logically inconsistent.

It matters that we understand each other's terms to have an effective conversation.

According to the TI, the "fieldlike object filling one box or the other" is the ontic state. All this talk of "classical positions" is simply irrelevant.

Yes. I am simply trying to explain that when I use the term "ontic uncertainty" I am talking about precisely this type of entity, which is extended over a range of classical states, and is not definitely in any single classical state.
If you don't like this word choice, that is your prerogative, but at least we can realize we're arguing labels rather than substance. So I am trying to clarify, so at least you understand my meaning, and we don't get hung up on something that is ultimately a non-issue between us.

The "alive to dead" transition for the cat is something like the connecting tunnel in the above; while it is happening, there is no well-defined answer to the question "is the cat alive or dead?". You can try to draw arbitrary boundaries, but they're arbitrary, just as in the tunnel above, and there is no reason to think that the entire cat must always be on one side or the other of any boundary you draw.

Btw, I don't think the above has much to do with the TI in particular;

Agreed fully. But this is not what the notion of "in Box A AND in Box B" means in standard discussions of the measurement problem. It is not limited to a case of a system straddling an arbitrary boundary, but also, say, a case where the baseball is only in the opposite far corners of Box A and B, never in the intervening space, yet not definitely in either corner. Unlike MWI, the TI doesn't allow macro objects to exist simultaneously in multiple macroscopically distinct states like this, it only allows the type of straddling you describe.

I am basically just saying that as a reader, I got confused when a very familiar idea like Schrodinger' cat was used to make a different point from what it normally is about. You can blame me for not immediately understanding this subtle shift from my preexisting experience if you want. But I think if you hope to effectively communicate a new interpretation of QM, you should plan on taking your audience as you find them.

 

[PeterDonis]

I am talking about precisely this type of entity, which is extended over a range of classical states

But in the TI, it doesn't. That's the point. The very definition "extended over a range of classical states" implies a particular class of interpretations, to which the TI does not belong.

Unlike MWI, the TI doesn't allow macro objects to exist simultaneously in multiple macroscopically distinct states

Agreed. You could set up a situation where, for example, a baseball was sent to the far corner of one box or the other using a gate controlled by a quantum event like a radioactive decay (the gate flips to divert to box B instead of A only if the decay occurs during the experimental time period), and the MWI and the TI would place a different ontic interpretation on the resulting mathematical description of the state.

as a reader, I got confused when a very familiar idea like Schrodinger' cat was used to make a different point from what it normally is about

That's understandable. But I don't think it helps to clear up such confusion if assumptions are made that depend on a particular interpretation or set of interpretations, even if the assumptions are only (ostensibly) made for the purpose of choosing terminology. As I think I've said before about the MWI in other PF threads, it's very important in discussing interpretations to be extremely clear and precise about what each interpretation actually says, even if (or perhaps especially if) you are going to end up disagreeing with the interpretation.

 

[charters]

That's understandable. But I don't think it helps to clear up such confusion if assumptions are made that depend on a particular interpretation or set of interpretations, even if the assumptions are only (ostensibly) made for the purpose of choosing terminology.

But I think the sociological context is important. I think the meanings I assume are quite standard across pretty much every other interpretation. I've read a good deal on this topic and never have I felt before that I had to re-tailor the meaning of "alive OR dead" versus "alive AND dead" for any particular interpretation. The TI does not have macroscopic "AND" states under the standard meaning, and life will be easier if proponents stick to this.

But just one reader's perspective in the end, so grain of salt, I guess.

 

[A. Neumaier]

like in Bohmian mech, the cat's fate is already, definitively decided at ALL times, before, during, and after the interaction/measurement.

Yes, but the fate isn't strictly 2-valued 'dead' or 'alive' but there is an intermediate grey zone where the criteria to decide aliveness cannot be reliably checked, so that during this time one can neither say that the cat is dead nor that it is alive. It is this grey zone that is present in all binary measurements.

we do not conventionally say the cat is "alive AND dead."

the root of the confusion/dispute has been that when you say there is a window of time when the cat is alive AND dead

Where did I say this? If I said this at all it must have been a slip of the pen.

Your argument sounds like we were discussing the first goal in a football match and you were claiming that as long as the score is still 0:0, both sides have achieved a goal...

I think what you really mean here is that there is a finite window during which the evolution of the *local* q-expectations from alive-to-alive and alive-to-dead will look the same, so as a local matter, the fact briefly seems ontologically undecided.

No; ontologically everything is determined at all the time. But the pointer upon which deadness or aliveness is evaluated has a continuum of values, and only its (reliably readable) asymptotic sign decides upon the epistemic (in physical terms not precisely specified) notion of being dead or alive.

The same issues appear already classically in the analogy of the football match, and indeed whenever one defines a decision based upon an alternative that requires a pointer to move to a particular position to read the result. While the pointer moves (and perhaps oscillates) no decision is possible although the pointer always has a definite position - but it need not have the one that counts as a reliable measurement.

All this has nothing to do with locality issues.

It matters that we understand each other's terms to have an effective conversation.

I defined precisely all terms I use in the description and explanation of the thermal interpretation. If you wish to use other terms, then please define precisely the meaning of your terms (or link to such a precise definition), in particular the term "ontic uncertainty" on which your arguments rest, so that we can have an effective conversation. (Needed only if the above does not yet settle the issue.)

 

[A. Neumaier]

Schrödinger' cat is defined by the following original statement:

Eine Katze wird in eine Stahlkammer gesperrt, zusammen mit folgender Höllenmaschine (die man gegen den direkten Zugriff der Katze sichern muß): in einem Geigerschen Zählrohr befindet sich eine winzige Menge radioaktiver Substanz, so wenig, daß I am Laufe einer Stunde vielleicht eines von den Atomen zerfällt, ebenso wahrscheinlich aber auch keines; geschieht es, so spricht das Zählrohr an und betätigt über ein Relais ein Hämmerchen, das ein Kölbchen mit Blausäure zertrümmert. Hat man dieses ganze System eine Stunde lang sich selbst überlassen, so wird man sich sagen, daß die Katze noch lebt, wenn inzwischen kein Atom zerfallen ist. Der erste Atomzerfall würde sie vergiftet haben.

(English translation: A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. )

as a reader, I got confused when a very familiar idea like Schrodinger' cat was used to make a different point from what it normally is about

No matter which points are normally made using this setting, it is completely legitimate to make the different point that it takes an uncertain amount of time for the poison to definitely have killed the cat, and that there is therefore a time interval where even a Laplacian quantum demon (adhering to a deterministic interpretation of quantum mechanics) cannot say objectively whether the cat is still alive or already dead. I cannot understand what is confusing about this observation.

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.

Note that what I discussed in Section 3 of Part IV was not Schrödinger' cat (which is a very poor measurement device for particle decay) but the observation of an arbitrary qubit state, which is a mathematically precisely formulated problem and its solution is also mathematically unassailable - apart from having not proved the precise probability distribution, which would need the discussion of a particular, mathematically well-defined model system for the measurement process.

This applies in particular to the observation of so-called Schrödinger cat states, but without all the complications of having to consider real cats (which in the TI cannot be modeled by pure states).

 

[charters]

the root of the confusion/dispute has been that when you say there is a window of time when the cat is alive AND dead

Where did I say this? If I said this at all it must have been a slip of the pen.

When you said:

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

I read "except" as meaning that the cat is alive AND dead during the "short moment."

No; ontologically everything is determined at all the time. But the pointer upon which deadness or aliveness is evaluated has a continuum of values, and only its (reliably readable) asymptotic sign decides upon the epistemic (in physical terms not precisely specified) notion of being dead or alive.

Right - I was trying to say that, after thinking some more, I realized this is what you meant and I was misunderstanding what you wrote. The "short moment" refers only to the fact that the pointer takes a finite time to shift and resolve a readable measurement. Its not an ontological claim (which would be problematic and bring you into MWI territory).

I think you'll be better off saying: Thus the cat is definitely dead or alive *at all times*, however during a short moment where the decay happens *this outcome cannot be known* by a local, finite observer/witness to the process. Schrodinger's cat, at least here in the 21st century, is broadly understood as a question of the ontological status of the cat. See, eg, page 35 here: https://arxiv.org/abs/quant-ph/0112148.

The upshot is I now don't have a concern that the TI is violating the basic constraints that I expect any viable interpretation to have to respect, whereas under my initial reading, I did.