Schrödinger's cat measurement

[oknow]

TL;DR Summary

How measurements inpact one or more wave function collapses in the Schrödinger's cat thought experiment

In the Schrödinger's cat thought experiment in its standard configuration, before the experimenter opens the box that contains the cat, has any relevant QM measurement been made by any objects involved in this instance of this experiment?

My speculation/understanding: Yes, the cat knows (is continuously measuring) whether it is dead or alive (i.e. whether a radioactive decay happened) which, from the cat's point of view, is an exceptionally relevant QM measurement. This measurement happens before the experimenter opens the box and peers inside. This is an ideal box, so not even information escapes it, and no entanglement is involved. Consequently, QM-wise nothing changes for those outside the box: for the experimenter it appears like no measurement had been made. Before the experimenter opens the box and sees the cat, from that experimenter's point of view a standard Copenhagen superposition of states exists.

I gather some deem it a scientific error to say the cat measures its state before the experimenter does, even if to the experimenter it appears like no measurement had been made.

Is it that some consider there to be one "master" experiment wave function that collapses for all from the cat knowing whether it is dead or alive? If you see things that way, for a moment please pretend the cat and the experimenter have separate relevant wave functions that can collapse separately from each other. I would like to learn what negative consequences can follow from such an interpretation. What experiment data contradict this understanding?

 

[phinds]

Well, suppose you consider that the "wave function has not collapsed" until the experimenter opens the box. Fine. Now, how about the guy outside of the closed door of the lab? As far as he is concerned, the wave function STILL has not collapsed. You see how taking this point of view eventually requires the entire universe to determine whether or not the "wave function has collapsed"?

 

[Nugatory]

In the Schrödinger's cat thought experiment in its standard configuration, before the experimenter opens the box that contains the cat, has any relevant QM measurement been made by any objects involved in this instance of this experiment?

The short answer is "Yes".
However, the long answer may be more interesting:
The cyanide vial and the clockwork that operates it (not to mention the cat itself) are sufficiently complex that decoherence quickly eliminates any possible superposition. Thus there is never any weird quantum mechanical half-dead/half-alive superposed cat; we have either a dead cat in the box or a live cat in the box. This is a completely classical situation, no different than a tossed coin which will be heads-up or heads-down whether we look or not.

You may be the victim of a common misunderstanding. When Schrodinger proposed his thought experiment, he was not suggesting (and no one else was either) that the cat might be in a superposition of dead and alive until we opened the box. He was pointing out a problem in the then-current understanding of quantum mechanics: nothing in the theory explained why the cat wouldn't be in such a superposition, even though that's clearly not how cats and other macroscopic objects behave. However, that was a century ago; since then we have learned about decoherence and how the normal evolution of a quantum system quickly turns these macroscopic superpositions into classical outcomes, whether we look at the result or not.

In one of your other threads I recommended Lindley's book "Where does the weirdness go?". It's a must-read if you're planning on following this line of thought.

 

[Nugatory]

If you see things that way, for a moment please pretend the cat and the experimenter have separate relevant wave functions that can collapse separately from each other.

That is just not how the math - and do remember that the truth is in the math not the words we wrap around it! - works.

When we speak of the wave function of the box/cat/poison/atom without considering the experimenter and everything else outside the box we are using an approximation that says that the interactions between the box and everything else are weak enough to ignore. This approximation allows us to calculate as if there were two separate wave functions without losing significant accuracy, but in fact there is only one wave function for the entire quantum system including box and experimenter. And of course if the experimenter is going to interact with the box in any way (which kind of has to happen if they're doing experiments with it) we cannot use this approximation so cannot think of in terms of two separate wave functions, let alone separate collapses.

This might be a bit clearer if you look through some of our threads on how entanglement between the measuring device and the thing beng measured works in the MWI . But do recognize that this entire problem comes about because you have chosen to treat the experiementer as a quantum system (you did this when you mentioned their wave function). More often we treat all the macroscopic parts of the system (experimenter, cat, poison vial, box, ...) as classical objects and let decoherence explain why our classical cat is dead or not whether we open the box or not.

 

[StevieTNZ]

Do remember decoherence is a FAPP solution to why the cat is either dead or alive. In principle, a superposition exists.

 

[oknow]

"However, that was a century ago; since then we have learned about decoherence and how the normal evolution of a quantum system quickly turns these macroscopic superpositions into classical outcomes, whether we look at the result or not."

Thank you for the informative replies. Let me see if I understand. "Whether we look at the results or not"... so, are you saying that even if no one opens this experiment's ideal box to check on the cat, the state of the quantum event inside the box propagates to those outside it?

 

[Nugatory]

so, are you saying that even if no one opens this experiment's ideal box to check on the cat, the state of the quantum event inside the box propagates to those outside it?

I have no idea what you mean by “quantum event” or “propagates to those outside” but I’m pretty sure that that’s not what I’m saying.

I am saying that the cat in the box is either classically dead or classically alive (similar to how a tossed coin is either heads-up or heads-down) and it will be that way whether anyone looks inside the box or not. I am also saying that any claim that Schrödinger’s thought experiment suggests otherwise is based on misunderstanding or misrepresentation.

 

[oknow]

Apologies, Nugatory, I was not clear about that. What I meant by the "quantum event" is the experiment's radioactive decay. Now, I think I see what you were saying. The cat's alive or dead whether the box is opened or not. Yes, that makes sense to me.

Now, before the box is opened, do those outside the box have a way of definitively knowing whether the cat is alive or dead? If not, does current QM say a superposition of states exists?

 

[Nugatory]

Now, before the box is opened, do those outside the box have a way of definitively knowing whether the cat is alive or dead?

No.

If not, does current QM say a superposition of states exists?

The cat is not in a coherent superposition of dead and alive.

 

[PeroK]

Now, before the box is opened, do those outside the box have a way of definitively knowing whether the cat is alive or dead? If not, does current QM say a superposition of states exists?

The cat is in a superposition of a huge number of states (probably so big you can't write it down). And, each of these states has a probability amplitude.

1) There are a huge numbers of these states that correspond to something that would be recognizable as a live cat - and, more precisely, consistent with a cat that has remained alive throughout the experiment. For example, the expected amount of oxygen has been consumed by the cat.

2) There are also a huge number of these states that correspond to something that would be recognizable as a dead cat - and, more precisely, a cat that has been dead since some appropriate time. For example, the cat would have the expected rigor mortis and/or level of decomposition.

3) There are a huge number of states that are between these two sets and would (to a varying degree) not be recognizable as live or dead cat, but something in between.

Decoherence helps model the probability amplitudes for each of these sets of states. The states in 1) and 2) have probability amplitudes that tend to be reinforced and end up collectively as representing a probability of 1/2. The states in 3) have probability amplitudes that randomly cancel each other out and end up collectively representing a probability of 0.

What we have is a superposition, but it amounts to something that is practically the same as a classical system that is in one of two unknown states. And, for a system as complex as a cat with trillions of QM interactions per second, the process of decoherence is practically instantaneous.

This process of some sets of states reinforcing each other and others cancelling each other randomly occurs across QM. For example, it's a very similar argument that explains light refracting or reflecting. See, for example:

https://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter

 

[Lord Jestocost]

However, that was a century ago; since then we have learned about decoherence and how the normal evolution of a quantum system quickly turns these macroscopic superpositions into classical outcomes, whether we look at the result or not.

Decoherence cannot effect that a macroscopic superposition turns into classical mixed state - the math is unambiguous. As Daniel Greenberger puts it - and that is - so to speak - "the state of the art":

"Decoherence merely scrambles up the phases so that it would be impossible, from a practical point of view, to unscramble them. But it does not solve the basic problem that a pure state does not evolve by the Schrödinger equation into a mixed one."

 

[Lord Jestocost]

Summary:: How measurements inpact one or more wave function collapses in the Schrödinger's cat thought experiment

My speculation/understanding: Yes, the cat knows (is continuously measuring) whether it is dead or alive (i.e. whether a radioactive decay happened) which, from the cat's point of view, is an exceptionally relevant QM measurement.

The crucial point is that the formalism of quantum mechanics doesn’t change one whit between the microscopic and macroscopic levels. Carl Friedrich von Weizsäcker in “The Structure of Physics” (original title: Der Aufbau der Physik):

“Schrödinger accomplished a heightening of the paradoxical impression by considering a living being as an example. The poor cat is treated here simply as a measurement instrument to illustrate the irreversibility of the measurement process by means of the striking, and to us humans, moving contrast between the states of life and death. We have argued above (Sect. 9.2e) that in quantum theory there is no inherent reason why it could not be applied to living beings. But we do not need this assumption for the discussion of Schrödinger’s example. It suffices to remark that obviously there cannot be a clear description of a quantum theoretical thought experiment if on the one hand one uses living organisms as its integrating parts but on the other hand one does not take seriously the application of quantum theory, i.e., here simply the concept of probability, to the organisms.”

 

[gentzen]

As Daniel Greenberger puts it - and that is - so to speak - "the state of the art":

"Decoherence merely scrambles up the phases so that it would be impossible, from a practical point of view, to unscramble them. But it does not solve the basic problem that a pure state does not evolve by the Schrödinger equation into a mixed one."

What it means to scramble up the phases can depend on the perspective, I guess. I was thrilled when I read Decoherence is Dephasement, Not Disjointness:

If you’re wondering why you haven’t heard of this form of macroscopic interference, well, I haven’t either. I’m not basing this on any article or folklore of professional physicists, but my own attempt to reason with the underlying physical laws. Tell me if someone published this before, I haven’t checked.

Model 1: Isolated equilibrium system

The simplest model system is an equilibrium gas perfectly isolated from its environment.

(I wish he would fix one small mistake and publish it as a short paper.) My guesss is that the perspective that phases are merely scrambled even for a (nearly) perfectly isolated model system is not "the state of the art".

At least it was illuminating to me "that often all you need is that interference gets suppressed, no need to invoke disjointness". But my interpretation is rather that decoherence can also be caused by dephasement, not that disjointness would never be relevant. I honestly believe that there are scenarios where disjointness is the most appropriate picture.

 

[EPR]

What it means to scramble up the phases can depend on the perspective, I guess. I was thrilled when I read Decoherence is Dephasement, Not Disjointness:

(I wish he would fix one small mistake and publish it as a short paper.) My guesss is that the perspective that phases are merely scrambled even for a (nearly) perfectly isolated model system is not "the state of the art".

At least it was illuminating to me "that often all you need is that interference gets suppressed, no need to invoke disjointness". But my interpretation is rather that decoherence can also be caused by dephasement, not that disjointness would never be relevant. I honestly believe that there are scenarios where disjointness is the most appropriate picture.

Phases of what? Of probability?

Wavefunctions live in Hilbert space.

 

[Nugatory]

Decoherence cannot effect that a macroscopic superposition turns into classical mixed state - the math is unambiguous. As Daniel Greenberger puts it - and that is - so to speak - "the state of the art":

"Decoherence merely scrambles up the phases so that it would be impossible, from a practical point of view, to unscramble them. But it does not solve the basic problem that a pure state does not evolve by the Schrödinger equation into a mixed one."

Do remember decoherence is a FAPP solution to why the cat is either dead or alive. In principle, a superposition exists.

Yes, all we have is a FAPP explanation for the absence of non-classical coherent macroscopic superpositions of dead/alive or other macrostates; the foundational issues are still there (and probably out scope for this thread).

I haven't seen any satisfactory way of explaining, in a no-math thread, what decoherence does without glossing over these foundational issues. In this thread that may be a tolerable oversimplification, but I'd be delighted to see a level-appropriate explanation that fudges less.

 

[gentzen]

Yes, all we have is a FAPP explanation for the absence of non-classical coherent macroscopic superpositions of dead/alive or other macrostates

Does the absence of coherent macroscopic superposition really help? Even incoherent macroscopic superposition doesn't (seem to) imply the cat being either dead or alive.

 

[PeroK]

I think we should take a step back at this point. This is a "B" level thread posted by someone who wants to better understand the Schrodinger's cat experiment.

Some recent posts appear to do nothing to help achieve that aim. In fact, I'm not sure what some of the recent posts are trying to say. And, certainly, it's not B level material that is being posted.

 

[gentzen]

I think we should take a step back at this point. This is a "B" level thread posted by someone who wants to better understand the Schrodinger's cat experiment.

Some recent posts appear to do nothing to help achieve that aim. In fact, I'm not sure what some of the recent posts are trying to say. And, certainly, it's not B level material that is being posted.

Sorry, you are right. I now deleted my answer to EPR. I couldn't delete the initial post, because EPR had replied to it. It is OK for me if a moderator deletes both my initial post and EPR's reply.

On the other hand, I still believe that my reply to Nugatory is appropriate. Explanations why coherent superposition is suppressed are not enough to explain why the cat is either dead or alive.