Interpretation of Schrodinger's Cat

[Pleonasm]

[Moderator's note: Discussion spun off from another thread.]

You are assuming this ridiculous fallacy without any physical justification or evidence. There is no such thing.

I guess you don't get the thought experiment then... Schrödinger devised it precisely because it's the inevitable consequences of the standard model of QM, though not with regards to cats specifically due to decoherence (which wasn't known when Schrödinger wrote his paper).

 

[Mentz114]

I guess you don't get the thought experiment then... Schrödinger devised it precisely because it's inevitable the consequences of the standard model of QM, though not with regards to cats specifically due to decoherence (which wasn't known when Schrödinger wrote his paper).

Nothing can be dead and alive at the same time. That was Schrödinger's point. Blindly assuming that every mathematical fact is a physical fact leads to absurdity.

 

[Pleonasm]

Nothing can be dead and alive at the same time. That was Schrödinger's point. Blindly assuming that a mathematical fact is a physical fact leads to absurdity.

Subatomic particles are physical facts of nature, not mathematical. The state of being dead and alive at the same time is rendered impossible by decoherens which (again) was not known when Schrödinger tried to be clever.

 

[PeterDonis]

The state of being dead and alive at the same time is rendered impossible by decoherens

No, it isn't. Decoherence is what ensures that the "dead" and "alive" branches of the wave function do not interfere with each other. But decoherence cannot take a wave function that is a superposition of "dead" and "alive" branches and change it into a wave function that only has one of the two branches.

 

[Pleonasm]

No, it isn't. Decoherence is what ensures that the "dead" and "alive" branches of the wave function do not interfere with each other. But decoherence cannot take a wave function that is a superposition of "dead" and "alive" branches and change it into a wave function that only has one of the two branches.

I'll rephrase it then; the cat can't be in a superposition since it is part of classical mechanics. The probabilistic nature of observation however is not physical, which was Schrodingers point. Probabilistic is a mathematical concept, not a physical one. An object cannot be in a state of "probability X". Probability is a measure of what we know about the object, not the object itself.

 

[PeterDonis]

the cat can't be in a superposition since it is part of classical mechanics

That was more or less the conclusion that (AFAIK) Schrödinger was trying to get to with his thought experiment: that since a superposition of dead and alive obviously makes no sense, quantum mechanics cannot be applied to the cat, at least not the way the thought experiment applies it.

However, "classical mechanics" is not the same as "decoherence", so your claim that decoherence is what keeps the cat from being in a superposition is still not correct.

 

[Pleonasm]

That was more or less the conclusion that (AFAIK) Schrödinger was trying to get to with his thought experiment: that since a superposition of dead and alive obviously makes no sense, quantum mechanics cannot be applied to the cat, at least not the way the thought experiment applies it.

However, "classical mechanics" is not the same as "decoherence", so your claim that decoherence is what keeps the cat from being in a superposition is still not correct.

I accept your correction. Like I wrote, however, Schrodingers objection was not just about the bizarre state of the cat. It was two-fold.

1. That cat could not possibly be in such a state (experience alone tells us this).

2. The probabilities of quantum mechanics are not imposed on the objects themselves. This should be an obvious point to anyone, but reading people who think chance is an element of (subatomic) nature due to QM math, it isn't.

 

[PeterDonis]

The probabilities of quantum mechanics are not imposed on the objects themselves.

This is interpretation dependent. Not all interpretations view probabilities this way.

 

[Pleonasm]

This is interpretation dependent. Not all interpretations view probabilities this way.

I'm saying this is Schrodingers view of Quantum Mechanics. I would like to know which interpretation view probabilities as imposed on the objects themselves.

 

[PeterDonis]

I would like to know which interpretation view probabilities as imposed on the objects themselves.

Any interpretation that views the wave function as physically real. For example, MWI.

 

[Pleonasm]

Any interpretation that views the wave function as physically real. For example, MWI.

MWI posits that everything happens. I don't see how that's compatible with what I wrote.

 

[PeterDonis]

MWI posits that everything happens. I don't see how that's compatible with what I wrote.

There is certainly an open issue with MWI as to how probabilities arise (or, to put it another way, how the Born rule arises). But it is clear that MWI does not view probabilities as reflecting our knowledge about systems, as opposed to some property of the systems themselves.

 

[vanhees71]

Subatomic particles are physical facts of nature, not mathematical. The state of being dead and alive at the same time is rendered impossible by decoherens which (again) was not known when Schrödinger tried to be clever.

I cannot agree more. It's also a wrong statement of the many bad popular-science books on quantum mechanics to claim that if a system is in a proper superposition of eigenvectors of an operator that represents an observable this system "takes the corresponding eigenvalues at the same time".

To the contrary: In this case the observable's value is objectively indetermined, i.e., it doesn't take a specific value but the state tells us (and only tells us) the probabilities to obtain any possible value (an eigenvalue of the operator representing that observable) when it is accurately measured.

 

[Lord Jestocost]

The state of being dead and alive at the same time is rendered impossible by decoherens which (again) was not known when Schrödinger tried to be clever.

Anthony Leggett in “ELEGANCE AND ENIGMA The Quantum Interviews” (Editor: Maximilian Schlosshauer):

"Now, following Schrödinger, let us consider a thought experiment in which the quantum-mechanical description of the final state, as obtained by appropriate solution of the time-dependent Schrödinger equation, contains simultaneously nonzero probability amplitudes for two or more states of the universe that are, by some reasonable criterion, macroscopically distinct (in Schrödinger’s example, this would be “cat alive” and “cat dead”). Of course, just about everyone, including me, would accept that because of, inter alia, the effects of decoherence, it is likely to be impossible, at least for the foreseeable future, to experimentally demonstrate the interference of such states. (On the other hand, as the late John Bell was fond of pointing out, the “foreseeable future” is not a very well-defined concept. In fact, as late as 1999, not a few people were confidently arguing that because of the inevitable effects of decoherence, the projected experiments to demonstrate interference at the level of flux qubits would never work. In this case, the “foreseeable” future lasted approximately one year. As Bell used to emphasize, the answers to fundamental interpretive questions should not depend on the accident of what is or is not currently technologically feasible.) But the crucial point is that the formalism of quantum mechanics itself has changed not one whit between the microscopic and macroscopic levels. Are we then entitled to embrace, at the macrolevel, an interpretation that was forbidden at the microlevel, simply because the evidence against it is no longer available?

I would argue very strongly that we are not, and would therefore draw the conclusion:
also at the macrolevel, when the quantum-mechanical description assigns simultaneously nonzero amplitudes to two or more macroscopically distinct possibilities, then it is not the case that each system of the relevant ensemble realizes either one possibility or the other."

[Emphasis by LJ]

 

[Pleonasm]

But it is clear that MWI does not view probabilities as reflecting our knowledge about systems, as opposed to some property of the systems themselves.

That is not clear to me. It could be that the wave function under MWI assumption is partly real (branches), partly representation of knowledge restriction (which world to end up with based on probability calculus) or something to that effect.

 

[PeterDonis]

t could be that the wave function under MWI assumption is partly real (branches), partly representation of knowledge restriction (which world to end up with based on probability calculus) or something to that effect.

No, it could not be any of these possibilities. The MWI explicitly says that the wave function is real, and that it is the only thing that is real.

 

[Pleonasm]

No, it could not be any of these possibilities. The MWI explicitly says that the wave function is real, and that it is the only thing that is real.

MWI also explictly states that every possible branch happens, which means that something cannot be in a state of 50% probability physically.

 

[PeterDonis]

MWI also explictly states that every possible branch happens, which means that something cannot be in a state of 50% probability physically.

Sure it can, if you define "a state of 50% probability" as meaning there are two branches that have equal weight.

 

[StevieTNZ]

The post by LJ answers your query. Decoherence does not cause one outcome to actualise - only for all practical purposes, but not in principle.

 

[Pleonasm]

Sure it can, if you define "a state of 50% probability" as meaning there are two branches that have equal weight.

Equal weight in relation to what? The words you are using and the terminology makes no sense in a MW assumption.

 

[Grinkle]

if you define "a state of 50% probability" as meaning there are two branches that have equal weight.

I consider MWI as saying that the number of extant universes doubles here with half of them including one of the 50% branches and half including the 50% other branch. The probability of me being one of the me's that sees a live cat is equal to the probability of me being one of the me's that sees a dead cat (50/50 for any unique version of me).

 

[PeterDonis]

Equal weight in relation to what?

"Weight" in the MWI just means the coefficients of the branches in the wave function. If there are two branches and the coefficients are equal (more generally, if they are complex numbers with equal squared moduli), we have equal weight.

 

[PeterDonis]

I consider MWI as saying that the number of extant universes doubles here with half of them including one of the 50% branches and half including the 50% other branch.

But there is only one wave function; the wave function doesn't get duplicated. And in the MWI, the "universe" is the wave function, so it does not seem right to interpret multiple branches of the wave function as "multiple universes".

The probability of me being one of the me's that sees a live cat is equal to the probability of me being one of the me's that sees a dead cat (50/50 for any unique version of me).

This is how the MWI uses the term "probability", yes. But it raises a problem that nobody, AFAIK, has ever been able to solve: "the probability of me being one of the me's that sees a live cat" doesn't make sense, because both of the branches after the measurement are "you". "You" before the measurement does not become one or the other branch after the measurement, with some chance of each; "you" before the measurement becomes both branches after the measurement. This is the issue I referred to before as the problem of explaining where the Born rule comes from in the MWI.

 

[Grinkle]

his is the issue I referred to before as the problem of explaining where the Born rule comes from in the MWI.

@PeterDonis Can you post a link the parent thread?

 

[PeterDonis]

Can you post a link the parent thread?

I was referring to post #12 in this thread.

 

[Pleonasm]

. But it raises a problem that nobody, AFAIK, has ever been able to solve: "the probability of me being one of the me's that sees a live cat" doesn't make sense, because both of the branches after the measurement are "you". "You" before the measurement does not become one or the other branch after the measurement, with some chance of each; "you" before the measurement becomes both branches after the measurement. This is the issue I referred to before as the problem of explaining where the Born rule comes from in the MWI.

That appears to be a conceptual objection, rather than a scientific one. Not going to refute a theory that way.

Anyway, we don't need to go down this path. The equations work. The wave function evolves deterministically regardless of which interpretation one takes. Determinism and probabilities is not an oxymoron. The probabilities most likely (no pun intended) represent our knowledge of the system. As long as it obeys the laws of physics, I can sleep well at night.

 

[PeterDonis]

That appears to be a conceptual objection, rather than a scientific one

Agreed; it's an objection against a particular interpretation, but there's no way to test it by experiment.

The wave function evolves deterministically regardless of which interpretation one takes

Except when a measurement occurs and you either have a collapse (if you are using a collapse interpretation) or you have to treat the wave function as if there had been a collapse (if you are using a no collapse interpretation like the MWI). The MWI claims that the "whole" wave function, including the branches that you did not actually observe as the result of the measurement (which is what deterministic evolution of the wave function would give you), is still "there", but nobody actually uses that "whole" wave function to make predictions about future experiments. They use the reduced wave function that describes just the result that was actually observed.

 

[Pleonasm]

Agreed; it's an objection against a particular interpretation, but there's no way to test it by experiment.
Except when a measurement occurs and you either have a collapse (if you are using a collapse interpretation) or you have to treat the wave function as if there had been a collapse (if you are using a no collapse interpretation like the MWI). The MWI claims that the "whole" wave function, including the branches that you did not actually observe as the result of the measurement (which is what deterministic evolution of the wave function would give you), is still "there", but nobody actually uses that "whole" wave function to make predictions about future experiments. They use the reduced wave function that describes just the result that was actually observed.

Wrong. We have determinism regardless:

"Quantum physics is completely deterministic, as far as the time-evolution of the solution of the equation of state is concerned. In the early days of QM, some people were disturbed because the solution itself is in terms of probability amplitudes, but it remains true that those amplitudes evolve deterministically."

/Rory Coker

 

[PeterDonis]

Wrong. We have determinism regardless

Link, please? Unsourced quotations out of context are useless.

 

[PeterDonis]

Quantum physics is completely deterministic, as far as the time-evolution of the solution of the equation of state is concerned. In the early days of QM, some people were disturbed because the solution itself is in terms of probability amplitudes, but it remains true that those amplitudes evolve deterministically.

As long as no measurement takes place, yes. Not once a measurement takes place. Ask anyone who actually does QM for a living.