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Famously, Schrödinger's cat is found to be both dead and alive within a closed system - at the mercy of quantum mechanics. But why is the cat "both dead and alive"? For the Copenhagen interpretation, according to Heisenberg "the wave-function represents a probability, but not an objective reality itself in space and time."

The conceptual construct of "dead" or "alive" is a 100% non probabilistic state (at least as conceived by an individual within his frame of reference). This 100% certainty can be seen as an 'objective reality' for the individual with that information.

If I knew that someone (that I was not observing) was driving a car and had a 50% chance of death, they would not be objectively "both alive and dead" to me, rather given the probabilities they would be "neither alive nor dead". Any positive truth statement cannot be backed up by (non-existent) observational evidence, so no positive truth statement, beyond some assumed estimate of the probabilities, is valid.

Does it make more sense to say that when a quantum system is not observable (is closed), whether a wave function or a cat, non-probabilistic conceptual statements with regards to what is inside the system will be incomplete?

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    Schrodinger was criticizing the Copenhagen interpretation, and I think he may have been somewhat uncharitable. – Era Jul 8 '16 at 15:13
  • Cross posted: physics.stackexchange.com/questions/266981/… – user19730 Jul 8 '16 at 17:25
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    There is a distinction between "there is an equal chance that it is currently alive as that it is currently dead" and "it is currently in a state that is equally alive as dead". – David Schwartz Jul 8 '16 at 17:27
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    You should read Luboš Motl's eye-opening answer to Schrödinger's cat; why was it necessary?. – user19730 Jul 8 '16 at 17:36
  • @DavidSchwartz, In the quantum mechanical description of the system, the cat is "equally alive as dead." Schrödinger's point was that it would be absurd to accept the quantum mechanical description of any system as large and as complex as a living cat as the true reality. – Solomon Slow Jul 8 '16 at 21:21
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It is weirder than that: The wave function actually represents the square root of a probability, to the degree that makes any sense. (The simplest mathematical contrivance modeling this is that a particle's mass is re^it where t is time. So it 'rotates' in complex space, and its energy and mass are split into real and imaginary components.) When you multiply two of them together, only then do you get a real number, a probability.

The reason to consider the cat both alive and dead is the timing of the event of death. If the cat decides it is alive it will have been alive all along. And if it is dead it will also have been dead the whole time. Time passes for the cat as though the event were decided when the (as yet unresolved) cause, caused it.

If you think of it as a probability, there is too much temptation to imagine the event would happen when the probability was resolved. But it happened already, whichever way it came out. It misses one of the distinctive characteristics of the paradox. So the framing explicitly rules out that way of thinking of it for effect.

  • Time does pass for the cat, from its frame of reference, but what does the cat's time mean for an external 'observer' of the closed system.. Surely all the information we get is a superposition? Also, doesn't saying "both alive and dead" stands against the relativity of simultaneity? – Ilya Grushevskiy Jul 8 '16 at 15:18
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    Yes, and avoiding the awkward framing seems to eliminate that conflict. But that conflict is unresolved, and that is an important part of the paradox itself. Either you have a basic incompatibility with relativity, or (in your proposed framing) causation actually flows backward, or time branches. Quantum field theory is starting to look at it the way you do, but early on, the idea of time that is not a single unified 4D manifold offended people more. Schroedinger is, after all many years before Evertt's Many Worlds interpretation. – jobermark Jul 8 '16 at 15:28
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    Also, the status of the cat, as seen from a frame of reference within the closed system, is evident at each point of time.. the cat finds out if it is alive or dead at each instant of its observation. However, our observation of the cat's life or death - from our external frame of reference - is only possible once we look into the closed system.. doesn't this mean that the resolution of the probability (for us as the observer) occurs at a different time to the cat's resolution (when it observes)? – Ilya Grushevskiy Jul 8 '16 at 15:29
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    Well, no. It is resolved already for all the particles in the box with the cat, so it is resolved. We are not the only things in the universe. You have to have a theory that deals with the cat, the air in the box with the cat, the box, the rest of the world, and us. Mentalism just won't do. – jobermark Jul 8 '16 at 15:31
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    As it is, we have two resolutions for the 'problem', Many Worlds and the sharing of properties between particles. Both can be explained both ways. The cat is alive in one timestream, dead in another, or the cat and we are entangled at the point we affect it, and our entangled effect is resolved when we test the interaction. Both of these made no sense to Schroedinger. – jobermark Jul 8 '16 at 15:39
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Schrodingers little gedanken-experminent is a drama dramatising the conceptual, ontological & epistemological problems that occur in the physics of the small; when its scaled up from that small world to our own human world, these situations, like you say don't apply - though there are subtleties.

So Schrodingers cat - as a cat and not as a stand in for some very small particle - and as you say, is either dead or alive - and not both.

Its in the physics of the small that these paradoxes arise, as already famously pointed out by Zeno & Nagarjuna, but not usually thought in this way.

One suggestion, going back to Kochen in the 70s and probably earlier, and also advocated more recently by Smolin and Rovelli is that this means ontology is relativised; they think of measurement or observation as interaction.

NB

I can't help pointing out here that in buddhist atomism, atoms are considered to be atoms of perception; of course when we think of perception we think of the human mind, that is cognitively - so this looks strange, if not bizarre; but it maybe the case, that this isn't quite what these thinkers were thinking of; after all, look at what Rovelli et al just did, to move from observation by a human observer to measurement or interaction by a particle; but this would require a closer look at these texts, to see quite what it is they mean by perception in this context.

  • Do you have a ref or resource for Buddhist atomism? – Alexander S King Jul 8 '16 at 21:44
  • @AlexanderSKing: there's wikipedia - which is where I first found out about it; but I'm afraid its pretty basic; I'm still looking for something better... – Mozibur Ullah Jul 9 '16 at 2:28
  • It's not correct that quantum mechanics only reigns in “the physics of the small” – it describes large-scale objects just as well. Only, you normally can't distinguish the predictions of quantum- and classical mechanics on the scales of “out human world”. The reason is not so much the length scale as the high temperature: thermal motion smears out the coherence patterns of wave functions, so in statistics the thing that remains consistent is the expectation value which, according to the Ehrenfest theorem, agrees between classical and quantum mechanics. – leftaroundabout Jul 9 '16 at 10:52
  • @leftaroundabout: its an interesting physical question how bulk properties emerge from the small, for example the stability of matter from Paulis exclusion principle; but I'm not sure this is the best place to discuss it; I merely said that it 'doesn't apply', I mean who would use/apply QM to explain the motion of the earth around the sun and by analogy, I was saying that the ontological/epistemological puzzles don't scale. – Mozibur Ullah Jul 10 '16 at 2:56
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The conceptual construct of "dead" or "alive" is a 100% non probabilistic state (at least as conceived by an individual within his frame of reference). This 100% certainty can be seen as an 'objective reality' for the individual with that information.

This is where QM gets strange, and departs from how classical physics behaves. There is no "individual with the information," so there is no "objective reality." Such would require an "observer" which would have an effect such as collapsing the waveform a. la. Copenhagen interpretation.

What you describe is known as a "local hidden variable" in the quantum mechanics community. By that theory, the cat is either alive or dead, and it knows it, but nobody else knows it. It's hidden from everyone, and its local, meaning it's only known to the cat itself. Unfortunately for those of us who want quantum mechanics to be intuitive, such local hidden variables do not actually describe the behaviors of the quantum mechanical world. We kind of wish they do, but they simply do not fit the data.

Bell's Inequalities would be the de facto location I would go to disprove such a local hidden variable theory. His theory involves the case of entangled particles, such as having two entangled radioactive isotopes, or perhaps two entangled cats. He proved that if there are local hidden variables (in other words, if the cat actually is "alive" or "dead," just nobody knows it but the cat), certain inequalities must hold true. Experimental evidence proves that those inequalities do not hold true. Thus the behavior of the world at a quantum level simply cannot be described using local hidden variables.

The only valid solution to Schrodinger's cat is to treat the cat using quantum mechanics, rather than classical mechanics. In such a treatment, the cat may be a superposition of alive and dead, and that's okay by QM's standards. Any simpler treatment, where the cat is alive or dead but not any strange mix of the two, simply does not match empirical testing of how the world works at the quantum level. Schrodinger's cat may be an extreme example, designed to prove a point, but its QM theory is sound and there are direct corollaries to Schrodinger's cat which can be demonstrated and do show that the cat is not alive nor dead.

I find exploration of the world of QM is best backed by a healthy list of example experiments which demonstrate the more curious non-intuitive facets of the mathematical predictions. There's a lot of QM that may of us (including myself) would be tempted to claim bull*#$(. However, for every one of those implausible claims, there's an experiment which demonstrates that it indeed occurs the way QM claims -- the bull*#@$ is right! My personal bane is the quantum eraser series. That series of experiments starts with the double slit experiment, and proceeds to get curiouser and curiouser as it progresses towards the delayed choice quantum eraser. Like it or not, the experiments have been done.

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Schrödinger's cat is not a very interesting thought experiment. It survives (the experiment, not the cat) because people don't understand quantum mechanics very well but do like fuzzy animals.

The classical probabilistic description of the situation is perfectly fine. In a quantum world, the classical description is wrong, but it gives the right answer. In a classical world, the quantum description is wrong, but it gives the right answer. The real world happens to be quantum, but we could never know that through Schrödinger's cat; we know it because of experiments like the Bell/EPR experiment that actually separate quantum from non-quantum worlds.

The usual defense is that it's just supposed to be a fun way to think about quantum mechanics versus classical mechanics. Along similar lines, a cat in a box is at rest in a geocentric world, but is in rapid motion in a heliocentric world. I guess there's no harm in saying that in a lecture to keep the students engaged. But to name it "benrg's cat", and call it an experiment, and repeat it verbatim for the next century, suggests a lack of understanding and imagination on the part of the people repeating it.

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The core difficulty here, in my opinion, is in the purely classical realm. Furthermore, it's not even a problem with the physics — it's a problem of logic, or specifically our language for it.

We often like to assign truth values to propositions, and tend to do so in a two-valued logic. However, this is not a requirement of classical propositional logic — if we are in the business of assigning truth values to propositions, we could use any Boolean algebra.

Our language for such things, however, is heavily tied to two-valued logic, so it's difficult to speak of it.

To see the problem, consider the simplest multi-valued Boolean algebra: the four-valued logic consisting of pairs (a,b) where a and b can each be either false or true.

Now consider the law of the excluded middle. In the form "P is true or P is false", it doesn't hold, because the truth of P could be (true, false). However, in the form "P ∨ ¬P is a tautology" it does hold, because that proposition is true (i.e. (true, true)) no matter which of the four truth values we assign to P.

This is the sort of thing that's happening with Schrödinger's cat; when we say it's both "dead and alive", that is meant from the "external" viewpoint; we are saying the truth of the proposition "it's alive" has true components and false components. However, from the "internal" viewpoint, the law of noncontradiction still holds e.g. alive ∧ ¬alive is purely false.


Putting physics back into the picture, the point is that quantum mechanics suggests, via decoherence, that that's how the universe really does work; the 'multi-valuedness' is an intrinsic part of the approximately classical picture that appears at macroscopic scales.

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There is no way to detect a particle in two locations at once, that's the whole idea. Saying that it is in two places at once is not an empirically meaningful statement. Neither is saying that the cat is alive and dead at the same time. Quantum mechanics definitely does not claim that the cat is alive and dead at the same time or that particles are in two places at once.

A better statement would be that the particle doesn't actually have any location until detection. Also that the cat has no properties at all until such properties are empirically determined. That was the problem with the EPR proposal, assuming "elements of reality" in-between interactions/measurements.

The conceptual construct of "dead" or "alive" is a 100% non probabilistic state (at least as conceived by an individual within his frame of reference). This 100% certainty can be seen as an 'objective reality' for the individual with that information..

This is not well put. Saying that a probabilistic statement is non-probabilistic because we are certain of the probabilities is really just a word game. Being certain that we don't know something is at best "subjective reality".

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In the "Many Worlds" hypothesis, where the wave function does not collapse, the cat is both dead and alive, but each is in a different universe.

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Agree with Hurkyl. A particle can exist in two states, or two locations, simultaneously. To read more, see the Wikipedia article on quantum superposition:

https://en.wikipedia.org/wiki/Quantum_superposition

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