I Can I steer myself into one of the Many Worlds like this?

[PeterDonis]

A superposition? Not a mixed state?

A superposition according to the many worlds interpretation. According to the MWI, the whole system is always in a pure state, but "the whole system" includes all the measuring devices and everything that interacts with them, including you. The pure state of the whole system is an entangled superposition in which each term is the product of matching states for each subsystem--the quantum particle, the measuring device, the filter, etc.

An "improper mixed state" is what we use to describe a portion of a system when we cannot know about the state of the rest of it (or even whether "the rest of it" exists, as we'll see in a moment). If you observe one particular measurement result from all this process--meaning, in your scenario, you see a stream of photons with one particular polarization coming from the box--then you "are" in one particular term of the superposition I described above, and since you have no way of knowing whether or not the other term (in this case there would be only two since the quantum measurement is only done once and has two possible outcomes) is there or not--there's no measurement you can make to tell--then you describe the system as being in an improper mixed state. That is what @Nugatory was describing.

The difference between the many worlds interpretation of QM and "single world" interpretations is that the MWI says the other term in the superposition is really there, even though you have no way of telling it is by making any measurements. Single world interpretations say that since you only observe one outcome, there is only one outcome; the other term isn't there.

it was my understanding that if you have a photon in a superposition of two pure states of polarisation, it has - for all intents and purposes - a single polarisation which is their normalised vector sum.

The term "superposition" is ambiguous. You are using it here to describe an isolated photon, not entangled with anything else, whose polarization is a pure state that happens not to be one of the two basis vectors you have chosen for your representation. In this sense, all but two of the possible polarization states of a single isolated photon will be superpositions (since there will be only two basis vectors). So whether or not a state is a "superposition" in this sense depends on what basis you choose: for any pure polarization state of a single isolated photon, you can always choose a basis such that that state is one of the basis vectors.

But as I used the term "superposition" above, I was using it to describe a state of a total system that has multiple subsystems, all of which are entangled with each other. "Entangled" means that there is no way to write the state as a single product of pure states for each of the subsystems; the state can only be expressed as a superposition of multiple such product states. Whether or not a state is entangled in this sense is independent of your choice of basis. But a single isolated photon is not such a system; the minimal possible such system would be two photons (or two qubits more generally) which are entangled.

It's unfortunate that the term "superposition" gets overloaded in this way, but it does and you just have to be aware of that and use the context to determine which meaning is intended.

 

[PeterDonis]

I do realize that this won't happen unless the two copies of the photon are indistinguishable in every other way.

You switched systems here--before you were talking about a single photon in a superposition of basis polarization states. Now you're talking about two photons. The Hilbert space for two photons, considering only polarization, has four basis states, not two, and the term "superposition" can have a different meaning when describing a state of such a system, as I explained in my previous post just now.

 

[PeterDonis]

Oh, no, I'm sure that is not the case.

You shouldn't be. Particularly as someone who has already said they're new to QM, and who still has not given a single textbook that you are trying to learn it from, instead giving a Wikipedia article on a particular speculative interpretation.

Some aspects of QM are open to interpretation, but I think it's certain that the only real boundary in the Schrodinger experiment, is the box.

You are wrong. The only real boundary in the experiment is between the single quantum event that gets measured, and everything else that happens after that measurement occurs. The presence of the box is irrelevant; even if the box itself is a perfectly isolating box, so that nobody outside can interact at all with anything inside until the box is opened, the box contains a huge number of degrees of freedom--something like $10^{25}$ inside the cat, plus those inside whatever other macroscopic objects are required to make the quantum measurement and activate its consequences, like releasing the poison that kills the cat. The net effect of all those macroscopic objects is to amplify the binary result of the quantum measurement into the effect on the fate of the cat; and very, very, very early in that process, the whole thing will decohere so that the cat is really alive or dead. Whether or not you think both "alternatives" exist after this happens depends on which interpretation (many worlds vs. single world) of QM you adopt; but experimentally the consequences are the same: a single outcome is observed, and that outcome is fixed by decoherence very, very, very early in the whole process, long before the degrees of freedom inside the cat are even involved, let alone those inside anyone who opens the box.

 

[PeterDonis]

the significance of the Schrodinger box is that it blocks the flow of information.

It's true that an idealized Schrodinger box blocks the flow of information from inside to outside, so to anyone on the outside before the box is opened, they will not know what has happened inside the box and so cannot predict what they will see when it is opened, other than the obvious 50-50 chance of seeing a live cat or a dead cat. But that is completely irrelevant to whether or not the cat is alive or dead before the box is opened; see my previous post just now.

 

[PeterDonis]

It's an interesting paper, it describes an apparatus that really obliges you to think in terms of Relative State; but it contains an error and its conclusion is wrong, in my opinion. Also, what they call "single world" is "many worlds" as far as I can see. They have their box contents in superposition, just like I have.

This discussion belongs in a separate thread (and your argument for your claim about the paper's conclusion being wrong would probably have to be reviewed by the moderators first).

 

[David Byrden]

PeterDonis;

Thank you very much for that explanation of mixed states. I'll do some reading over the holiday and get back here in the new year.

But, looking at your post #53, it seems I failed to make my interpretation of QM even close to clear, because you're not contradicting me there.

The way I see QM (which is apparently a naive version of Relative QM), it's correct to say that decoherence will drive the box' contents into one of two states almost immediately; but I don't accept that then "the cat is really alive or dead".

In the words of President Clinton, "It depends on what the meaning of the word 'is' is."

I suppose that what "is" depends on where you are standing.

I suppose that two branches of the MWI exist inside the box; that they are confined to the box because information cannot escape it; and that those outside the box can't say what the cat "is" until the wave function inside the box interacts with the wave function outside, at which time the "split" between two MWI branches will grow to encompass the observers and perhaps eventually the universe. (I'm curious about whether it ever peters out.)

I imagine that the "worlds" of MWI are areas that differ in that they hold different information about a quantum state. I don't believe that every quantum event spawns entire universes; I believe that information about it propagates through the universal wave function, splitting that into multiple local branches, one for each outcome. This explains entanglement neatly, as far as I can see.

A consequence of this interpretation is that the branches of reality can be made to merge again, if the information that defines them is erased. This is how I explain the Young's Slit fringes and the quantum eraser.

So, when I imagine Schrodinger looking at his box, I don't believe that "the cat is alive" is a true statement for him. Nor "the cat is dead". I believe that, because his wave function doesn't contain even the most imperceptible trace of information about the quantum measurement that happened inside the box, that for him it is undecided. He is in a world where the quantum measurement remains unmade. And the cat exists twice, each of it in a world where the measurement was made.

And because I regard both of those cat-worlds as equally real, I sought to influence the otherwise random choice that Schrodinger would make by opening the box and entangling the outside world with its contents. I wanted to merge, not the entire box contents, but only the photons emitted by the machine in the box. To recombine the photons from the two MWI branches inside the box seems possible to me. It is, as far as I can see, what happens in the screen of Young's experiment.

David

 

[PeterDonis]

it seems I failed to make my interpretation of QM even close to clear

If you are making a claim that depends on a particular interpretation of QM, then there's no way to test it experimentally, so it really comes down to personal preference. You are welcome to your personal preference on QM interpretation, but there's no point in arguing about it since there's no way of telling who is right.

However, the claim you are making in this thread does not look like a claim that depends on which interpretation of QM you adopt. It looks like a straightforward claim about being able to affect experimentally measured probabilities in a certain way by doing certain things. No such claim can depend on which interpretation of QM you adopt, so you should not be relying on a particular intepretation of QM to justify it. You should look at the math of QM and the experimental predictions that it makes, and that's it. Others in the thread are basing their responses to you on that, not on their preferred interpretations of QM.

 

[PeterDonis]

I'm curious about whether it ever peters out.

According to the MWI, no, it doesn't. The state of the entire universe has multiple branches that never go away.

A consequence of this interpretation is that the branches of reality can be made to merge again, if the information that defines them is erased.

This is not how the MWI works. Under the MWI, "branching" only occurs when decoherence occurs, and if you can quantum erase the information, decoherence cannot have occurred; quantum erasure only works if quantum coherence is maintained. (Note that this latter claim is not interpretation dependent; all of the quantum erasure experiments have as a key requirement that the systems have to stay isolated so quantum coherence is maintained.)

So consider the question that you appear to be implicitly asking, namely: suppose we run the "box" experiment with the cat inside. Could we then "quantum erase" what happened and restore everything to the initial condition without opening the box? (Say, by pressing a big "erase" button on the box.) And the answer is no, you can't, because there is no way to maintain quantum coherence among $10^{25}$ or more degrees of freedom.

 

[David Byrden]

Could we then "quantum erase" what happened and restore everything to the initial condition without opening the box?

Thank you again, that's helpful.

But I'm not sure that this particular sentence is quite right.
My thought experiment didn't seek to return anything to "initial condition" and neither does a quantum erasure experiment, as far as I can see.

I think that the erasure experiments demonstrate what I was saying above; that information about a quantum event spreads via the Wave Function, and that if this information gets into you (or, to be more accurate, permeates the environment you're sitting in) then, for you, "relative to you", the event happened.
And if you don't get such information, it didn't happen - for you.
The extent ot the information defines an MWI "world".
The erasure experiment, to my way of thinking, gives you the choice of letting the information leak out of the apparatus or keeping it confined therein.

So, the erasure experiment creates a "world" branch and either let's it grow or terminates it. Whereas my thought experiment had two "world" branches, both of which would grow without limit once the box was opened, and I sought to select the one that I would find myself in. Nothing in that is a return to initial conditions.

David

 

[Nugatory]

It just seems obvious to me, after Wigner's Friend etc., that we can't have the same state for everyone.

You may be misunderstanding Wigner's Friend in the same way that you misunderstood Schrödinger's cat.

Remember that Wigner proposed his thought experiment in 1961 or thereabouts, so a decade or more before decoherence was understood. Thus he was arguing in the same context and along the same lines as Schrodinger with his cat thirty years earlier: long-lived macroscopic superpositions of complex systems lead to absurd/impossible results; the current (1960-vintage) understanding of quantum mechanics says that unitary evolution leads to such superpositions; therefore something is wrong with that understanding.

You can find his presentation here. It moves beyond Schrodinger's in two important ways:
1) Wigner greatly sharpened the argument. Schrodinger showed an implausible result (the dead and alive cat) that neither he nor his contemporaries could take seriously; but Wigner's Friend leads to an outright contradiction.
2) Wigner could clearly articulate and draw on the consciousness-causes-collapse argument; it had not been fully developed in Schrödinger's time.
Nonetheless, it's the same basic problem and the resolution is the same: decoherence eliminates these macroscopic superpositions (and provides a convincing alternative to consciousness-causes-collapse). We place the von Neumann cut at the point of decoherence, the post-decoherence state is a mixed state not a superposition, classical outcomes ensue, and... yes, we can and do "have the same state for everyone".

 

[StevieTNZ]

I apologise if this is an error, but I have not read the thread in detail.

Are you basically asking, can I choose the outcome of a measurement (e.g. photon polarized horizontal versus vertical, 1/2 probability for each polarization)? The standard answer is no, but there are papers and books from persons who entertain that idea.

 

[PeterDonis]

My thought experiment didn't seek to return anything to "initial condition" and neither does a quantum erasure experiment, as far as I can see.

That is exactly what "quantum erasure" does--it reverses whatever unitary interaction took place during the experiment. The term "measurement" should not be used for that interaction precisely because it is reversible. Measurements are not reversible: once a result has occurred, it has occurred and can't be undone.

I think that the erasure experiments demonstrate what I was saying above

You are wrong. They don't.

The erasure experiment, to my way of thinking, gives you the choice of letting the information leak out of the apparatus or keeping it confined therein.

Your way of thinking is wrong. That's not what a quantum erasure experiment does. Any "leakage"--interaction with the outside world--destroys the experiment; it has to be kept isolated.

In MWI terms, quantum erasure experiments never split worlds.

You really, really, really need to tell us what sources you are learning QM from. You seem to be misunderstanding things all over the place, which indicates to me that you are not using good sources. If all of your sources are Wikipedia articles or papers on advanced topics that depend on you already understanding the basics (like the Frauchiger Renner paper you linked to earlier), that's not surprising.

 

[David Byrden]

Are you basically asking, can I choose the outcome of a measurement (e.g. photon polarized horizontal versus vertical, 1/2 probability for each polarization)?

I'm entering a busy time now, so I can't get into discussions until the New Year. But, I'll summarise what I was thinking;

- An isolated system is in a superposition of two known orthogonal states.
- Both copies of it create and send photons
- The photons' timing etc. is so precisely controlled that they are not affected by the decoherence between the two copies of the system
- The photons therefore interfere, and we receive a photon whose state is a proxy for the qubit that split the isolated system in the first place
- So, if the received qubit has a polarity aH + bV, where H and V are the polarities of the photons created in the two superposed copies of the isolated system, then the entire isolated system is in a |state1> + b |state2>

- It collapses to one of our new basis vectors, with very high probability (if it collapses to the other one, the game is over and we lose)
- My assumption was that the isolated state, relative to us, now has the corresponding state. We have adjusted a and b.
- Repeat the process. The isolated state keeps sending us photons. We keep rotating the measurement basis very slightly with each measurement.
- Eventually we can adjust a and b to a desired outcome, with very high probability.

I'm interpreting QM in the "relative" way. I believe the state of the isolated system is not objective, but is relative to the information that we hold about it. And, although we have a lot of information about the contents (which we put in there), we originally have zero information about the qubit that split the contents into two states. For us, that decision literally has not happened.

Therefore, by manipulating that information, I am manipulating our knowledge of the system's state, not the system itself. I'm not trying to revive a dead cat; I believe that a live cat and a dead cat are both in there, equally real, in two distinct "worlds", and I am trying to manoevre myself around to align with one of those two "worlds".

David

 

[PeterDonis]

- An isolated system is in a superposition of two known orthogonal states.
- Both copies of it

You're not making sense. Is there one isolated system? Or are there two, prepared the same way?

- The photons' timing etc. is so precisely controlled that they are not affected by the decoherence between the two copies of the system

How can there be decoherence if the two copies are isolated? They aren't interacting if they're isolated, so there's nothing to decohere.

- The photons therefore interfere, and we receive a photon whose state is a proxy for the qubit that split the isolated system in the first place

What qubit? And what does "split the isolated system" mean? How can an isolated system "split"? It's isolated; that means it isn't interacting with anything.

I'm interpreting QM in the "relative" way.

As I've already said, I don't think your claims have anything to do with a particular interpretation of QM. You are making claims that have direct experimental consequences, which means they should be analyzable using just the basic math of QM, without any interpretation.

At this point I don't see any value in keeping this thread open, since you have repeatedly refused to say what source you are learning from QM from, you have repeatedly shown serious misunderstandings of QM and have not responded to corrections, and you are evidently trying to construct and analyze a scenario that is way too advanced for a person who by their own admission is new to QM.

Thread closed.