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I've been wondering why nobody seems to talk about the gravitational effects of a macroscopic quantum system. In the cat in a box with poison experiment, we consider the cat to be in a dead or alive state superposition, till measured, as a possible scenario, given that the box is a perfect seal of information. However I'm doubting the validity of such a superposition. First, the cat and everything inside must be cooled to absolute zero in-order to prevent information leakage through blackbody radiation. But even if that is achieved, how can we neglect the gravitational waves generated by the walking cat inside? Once it drops dead, the center of gravity of the box changes and this change might be measured from outside. So the cat never really was in a superposition, as information was always leaking out from the start. The same can be said about molecules which maybe in superposition of position but are unknowable simply because gravity is weakened at that scale.

Another possibility is that the cat was asleep so it never really changed positions when it died leaving the COG as it is. We can consider the gravitational time dilation effects for the box system. The top parts of the box would experience less time than the bottom parts of the box and this might be sufficient to decohere the cat-box system.

How would then one achieve such a superposition since gravity will always play a role, in other words, what kind of a box would shield from gravity? The same can be said about mass-less particles (light for example) always interacting with the electromagnetic field. Are particles really in superposition because of weak gravity?

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  • $\begingroup$ This is an idealized experiment: gravity does not enter into this. $\endgroup$ – ZeroTheHero Jan 14 at 14:48
  • $\begingroup$ @ZeroTheHero I'm afraid I disagree. $\endgroup$ – Weezy Jan 14 at 14:50
  • $\begingroup$ @Weezy Don't be afraid. Just think about it! $\endgroup$ – Deschele Schilder Jan 14 at 15:00
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    $\begingroup$ Re, "the cat and everything inside must be cooled to absolute zero..." I think that you are taking it too literally. It's a thought experiment. It's OK to assume perfect conditions (e.g., the "box" is a perfect barrier to information) when you're describing a thought experiment. $\endgroup$ – Solomon Slow Jan 14 at 15:23
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    $\begingroup$ If you start considering seriously the quantum state of a cat, the presence or absence of gravity is going to be the least of your problems. For one thing, the cat will never be in a superposition of two simplistic alive and dead states only. As others have said, this is simply a though experiment, actually very simple and to the point, but unfortunately gone completely wild in the collective psyche. $\endgroup$ – Stéphane Rollandin Jan 14 at 16:06
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This is yet more of why I favor a subjective and information-based understanding of quantum theory.

First off, I should point out that what you have come up with is really more of taking the experiment a bit too literally or strictly, when what it really is is a conceptual issue with quantum theory that, while as you've pointed out runs into some troubles it being able to actualize this specific literal version of, doesn't go away if we migrate it to more realistic scenarios.

But in the toy scenario, yes, we assume the box to be absolutely ideal. Nothing goes out - no radiation, not even gravitational, until opening the box. Yes, this requires a Universe with somewhat different physics, but which still uses the heart of quantum theory, namely the mathematical structure of Hilbert spaces, quantum vectors, Schrodinger and "wave function collapse" rules, which is what its point is "really" about - the conceptual issue it gets at resides in those and thus we can, with a bit of effort, formulate scenarios that do gel with our Universe's actual physics.

And this is the thing: In the contrived setup (and any suitable analogue), there is no empirical difference, in terms of the observed end result, between a situation in which the cat is "objectively" "in a superposition" between commencement of the experiment all the way up to opening the box ("environmental interaction causes collapse"), the superposition extending even past opening it up to the point of cognition in the human's consciousness ("consciousness causes collapse" aka. "quantum mysticism"), the superposition gets cut off sometime between box closure and opening spontaneously ("objective collapse"-like ideas), or any of a number of other scenarios, as long as the final probabilities generated by the Schrodinger equation at the time of observation by the human in the situation, starting from the initial conditions, for what sie will observe, are upheld in that final observation. ANY of these, thus, could be the "true, objective" scenario.

And it is this inability to distinguish which is why I believe quantum theory is best understood subjectively - if it is so, then we can fold all of these under its umbrella without contradiction, since it's not actually talking about which one is true, and they become new, additional, empirically equivalent theories that coexist with and extend, not contradict, it.

But that doesn't mean the "subjective" theory is devoid of physical content, either. Clearly, the "objective" state of the universe - including embedded agents - has to be constrained in how it operates to such a way as to produce the statistics regarding our observation, otherwise the theory would not work. Force terms, etc. in the Hamiltonian definitely have physical meaning, for example. Moreover, Bell theorem-like results show that, unless we want to sacrifice basic principles like causality or kinematic relativity, this "objective" state cannot be classical. Hence, it would be better to say that quantum theory constrains what the "objective" state could be, but it does not logically determine it (per the simple notion of logical consequence: Y is a logical consequence of X if and only if there is no conceivable scenario where X holds and Y fails), and any attempts to try and "reason" something like that out of it will always fail to be conclusive.

The most mature subjective understanding, as far as I can tell, of quantum theory is this:

  1. There are no “isolated systems” in the classical sense in quantum theory. Instead, the minimal unit of analysis in quantum theory is a system-agent pair. The “system” is a source of information, the “agent” is an information retainer, and the basic unit of account of events are transfers of information from system to agent.
  2. The state of the “system” is not directly described. Instead, only the state of the agent’s information store is described. This is what the quantum vector $|\psi\rangle$ represents.
  3. $|\psi\rangle$ maps to information via quantum operators, which represent questions to be asked. These give probability distributions which then correspond to a certain number of bits, per Claude Shannon.
  4. The fundamental operation - information transfer - is represented by a step change in $|\psi\rangle$, often called "collapse". This should not be assigned a physical time span: instead, it is a logical time unit in the agent: the agent’s information evolves one transfer at a time, discretely, not continuously. Asking how long it takes is to reify |psi> as once again not being first and foremost subjective/informational. Of course, since these operations are ultimately physical in nature, but you should think about, say, a computer program, and how it looks from the “logical” point of view of the computer processor, not the physical implementation thereof.
  5. The Schrodinger equation is not an evolution law, but rather an inference rule that enables one to infer from information gathered at a physical time point, what information one may get by requesting it from the system at a later physical time point. Indeed, this means collapse is more fundamental to the architecture of the theory than the Schrodinger equation, which is a bit opposite of much of the "orthodox" thinking on the subject.
  6. The “objective” physical content of the theory is that assuming relativistic causality, the Universe has limited and non-classical information *content* in that the answers to all questions that can be asked about a system at any given point must “objectively” fail to exist to an extent that is neither necessarily total nor necessarily zero: rather, if, say, the classical answer would take $b$ bits, then in reality, there exists a possibly fractional number of bits, $b_\mathrm{real}$, such that $0 \le b_\mathrm{real} \le b$.
  7. When you make a “full-determination measurement”, that singles out a unique quantum vector, such as measuring (asking question for) all three of $(n, l, m)$ in a hydrogen atom, then at that point, the full physical “objective” information is exactly that much, for all questions, including the electron position, which then must be, per principle 6, reduced in information content, to the order of spatial resolution of $10^{-10}\ \mathrm{m}$.
  8. But immediately following that, as time begins to march forward, that may no longer be the case. The theory is silent beyond that the “objective” information must be at least as informative as the Schrodinger equation moving forward from that point on, so that its predictions are useful, and cannot exceed the bounds of Heisenberg’s principle without violating relativistic casuality.

In other words, the real trick with quantum theory is that it is a subjective theory of an “objectively fuzzy” Universe, and it does not give us the objective state at all times, but also at none. It is incomplete, if we are asking for an “objective” story, but not entirely so, and it is complete enough to dispel classical mechanics.

So, in short, what can we say "truly" about Schrodinger's cat? Simple:

  1. At the time the box closes, the cat is alive.
  2. At the time we see it, after opening the box, it is alive or it is dead, depending on which one is actually seen.
  3. At any time in between, whatever the objective state of the cat is, we can infer that it is something which defines, per the Schrodinger probabilities, that the observation will come out with those probabilities.

In particular, given the sketch just made, because we can have the cat definitively alive or dead at any given time, $b_\mathrm{real}$ could be anything, and with any content, in between.

Underwhelming? Perhaps, but that is all we're left with without going beyond the theory. As long as we have not had any empirical evidence which cannot be made to work in a quantum-theoretic framework, we are left with that. In other scenarios, we may be able to say more, but again, not everything.

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Schrodinger's cat is a vivisectional example of a detector.

Detectors of quantum effects give classical values, because we live in the classical framework, even though the underlying framework is quantum mechanical. The many particle problem is treated with the density matrix formalism in quantum mechanics, and when dimensions are large enough, the density matrix loses the off diagonal elements and one is in the classical frame and classical physics objects. A cat is a classical physics object and cannot be considered a large quantum mechanical superposition ( the way a superconducting wire is).

The quantum mechanics is in the probability of decay, all the rest is the method of detecting if a decay has happened or not.

Instead of using a Geiger counter, which if in a box and no information comes out, will either have a count when opened or not, the vivisectionist will use a poison capsule and if a count comes, will poison the cat. As far as detecting the actual quantum mechanical effect, the decay of a particle, the two experimental setups are equal, but the geiger counter is more humane.

edit for clarification :

The cat in the Schrodinger box is a detector. A single probabilistic quantum mechanical decay of the nucleus will trigger the poison that will kill the cat. What is unknown is when the nucleus will decay , that is given by a quantum mechanical probability distribution, i.e. the wavefunction of the particle decaying complex conjugate square, as far as quantum theory goes. Thus the specific nucleus is in a state where it may or may not decay, with a given probability. If nobody detects it, its state will not be known. If the cat in the box detector detects it , it means there was a decay, i.e. a measurement in the probability distribution of the nucleus decay.

I've been wondering why nobody seems to talk about the gravitational effects of a macroscopic quantum system.

Thus the gravitational effect to the quantum state of the problem means gravitational effects on individual nuclei wave functions, that give the probability of decay, not effects on the mass the cat. The coupling constant of gravity, if we accept an effective quantizations of gravity, is so small with respect to the other three forces, that it is impossible to measure at the single atom level.

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    $\begingroup$ This doesn't seem to address the question, since the question is specifically about gravity. $\endgroup$ – user4552 Jan 14 at 19:52
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Thanks to a moderatore I've changed my answer. I think it's more addressed now.

Are particles really in superposition because of weak gravity?

There is much to be found here.
Maybe here you can find the answer to your question.

My own answer. You write:

Once it drops dead, the center of gravity of the box changes and this change might be measured from outside.

I have strong doubt this can be measured in practice. In fantasy, or theoretically, it can be done of course. So let's assume it can be measured.

The cat is never without motion, when alive. But who says the cat is alive? If it's dead then gravity will not cause it to be alive again. When it's alive then gravity "measurement" (if the cat is in a superposition) will cause the cat to be either alive or dead.

The question then boils down to: was the cat already dead or alive before the measurement. Obviously not, because it's in a superposition between dead and alive. So, gravity doesn't cause the superposition but gravity causes the collapse.

When the outcome of the measurement is a living cat, the cat happily (though I would say sadly) ever after, emitting gravitational waves (though staying alive at nearly absolute zero seems not very likely). When the cat's dead, it's...uh...dead. In the freezing cold of nearly absolute zero Kelvin.

Man, how you came up with this question? Have you seen this in a nightmare?

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    $\begingroup$ Let me note first that for a macroscopic object the chance to exist in a superimposed state (dead or alive) is very near zero if not zero. This doesn't make sense. Quantum mechanics doesn't restrict what states can be superpositions. You can't have such a restriction without defining a preferred basis, and quantum mechanics doesn't have a preferred basis. This answer also doesn't address the question, which is specifically about gravity. $\endgroup$ – user4552 Jan 14 at 19:51
  • $\begingroup$ @BenCrowell Is it better like this? $\endgroup$ – Deschele Schilder Jan 15 at 7:42
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The experiment describes an ensemble of cats. This solves the paradox. Some cats in the ensemble are dead, other alive. As we are dealing with a partially or fully incoherent state, a density matrix or sum of these is needed. The state cannot be considered to be a superposition, which suggests coherence. To bring in gravity does not make much sense. If you insist on talking the cat literally, an occasional meow has near infinitely more effect.

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  • $\begingroup$ Making sense is not very popular these days. $\endgroup$ – my2cts Jan 15 at 8:58

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