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

[David Byrden]

How would you describe the polarization of a photon emitted by an electron dropping to a lower orbital? I would say it has no polarization until measured on some basis.

Just guessing, but would that one be in a "mixed state" ?

David

 

[David Byrden]

Can you explain this in more detail?

Well, I'm not expert in how such apparatus need to be configured, but as a general approach:
The machine measures some quantum observable (?) that has 2 orthogonal values.
The machine sets a filter to one of two positions, depending on the measured value.
The positions are 90 degrees apart.
A pulse of photons is fired through the filter.
The photons that transit it are then in one of two orthogonal polarities, depending on what value was measured.

If we need to use a single photon rather than a pulse of photons, we would create the photon with a known polarisation, and use a series of filters to rotate its polarity gradually. Setting the filters at small angles apart, we can make the probability of absorption arbitrarily small by adding more filters.

David

 

[DrChinese]

...we would create the photon with a known polarisation, and use a series of filters to rotate its polarity gradually. Setting the filters at small angles apart, we can make the probability of absorption arbitrarily small by adding more filters.

Using the technique you describe, you cannot make the probability of absorption arbitrarily small by adding more filters. Obviously, arbitrarily small would include 0 probability. However, you can rotate the polarization state using a wave plate.

 

[Nugatory]

Once again I must apologise for not making myself clear.
My intent was:
1. a quantum measurement with 2 outcomes, is made inside the box, by the machine
2. the machine kills the cat, or not, according to the result
3. the machine configures its filters according to the same result, and begins to send out photons

That's fine, but I'm not clear on where you are going here (certainly not any sort of "steering" or "nudging" from outside the box).

Once the measurement in step #1 has been performed, we have a box with either a dead cat in it or a live cat, and filters configured in such a way that the box emits photons in one state if the cat is alive and in an orthogonal state if the cat is dead. There's no superposition or entanglement here, we just have an unusually complex apparatus (the cat is an inhumane alternative to a recording device attached to a photon detector, the emitted photon tells us what the measurement result was just as surely as if it were being reflected from the cat through a window in the box to our eyes) for measuring the polarization of the photon in the box.

If the photon measured in step #1 was entangled with a photon outside the box before the measurement, then a measurement of that photon will of course tell us the dead/live state of the cat (as will any photons sent later, as step #3). But our measurement of that photon has no effect on what's going on inside the box (otherwise the no-signalling theorem would be violated). All we have is two possibilities: 1) The cat is now dead and our external measurement says the cat is dead; 2) The cat is now alive and our external measurement says the cat is alive.

 

[David Byrden]

Once the measurement in step #1 has been performed, we have a box with either a dead cat in it or a live cat

Are you asserting that the Schrödinger's Cat experiment does not produce a cat in a superposition of "alive" and "dead" ? Because my box, in case I wasn't clear, is the same kind of box, with the added mechanisms that I described.

Davd

 

[Nugatory]

Are you asserting that the Schrödinger's Cat experiment does not produce a cat in a superposition of "alive" and "dead"?

Yes, and that's the same assertion I made in post #16 and the last paragraph of #4 above.

However (as I also suggested in #4) this issue is something of a red herring if you want to examine the effects of entanglement as your thread title and initial post suggest. If you can't nudge one particle towards a particular state, you can't nudge $10^{25}$ particles either.

 

[PeroK]

Are you asserting that the Schrödinger's Cat experiment does not produce a cat in a superposition of "alive" and "dead" ? Because my box, in case I wasn't clear, is the same kind of box, with the added mechanisms that I described.

Davd

Suppose that instead of opening the box, you measure how much oxygen is in the box. If the cat died immediately, then there will be a lot of oxygen left in the box; and, if it lived, then there will a lot less oxygen in the box. And, if it existed in a superposition of half-alive and half-dead, then it would have, presumably, consumed half the oxygen of a living cat.

When you measure the oxygen, you get either a lot of oxygen (consistent with the cat being alive all the time) or not much oxygen (consistent with the cat being dead all the time). You won't get a level of oxygen consistent with a superposed half-dead-half-alive cat.

 

[David Byrden]

If you can't nudge one particle towards a particular state, you can't nudge $10^{25}$ particles either.

But for different reasons, no?

With one particle, you can't generate the stream of emitted photons unless you have multiple interactions with the one particle, which, as you pointed out, achieves nothing.

But with 10^25" particles you can construct a machine as I described, to remember the "seed" measurement result and repeatedly polarise photons to represent it.
You have also said, if I understand you, that this version won't work because the lab's contents will decohere into a mixed state rather than a superposition, simply because they are so complex. Yes?

Therefore; different reasons.

I want to say one thing; the only reason I considered this as a possibility is that Renner and Frauchiger published a 2016 paper, alleging an incompatibility in QM, and in it they postulated "labs" very much like mine. They contained people in superpositions, and the paper assumed that they could be measured in arbitrary bases.

David

 

[David Byrden]

Suppose that instead of opening the box, you measure how much oxygen is in the box.

I believe it is agreed by all physicists, using all QM interpretations, that the Schrödinger catbox won't work unless it achieves perfect isolation. No information must come out from inside the box, or at the very least, no information that could allow you to infer the state of the contents. That includes photons, phonons, particles, and anything else you can think of.

One question that I've never seen asked or answered, is this; will Schrödinger's box work if information can get into it from outside?

David

 

[PeroK]

I believe it is agreed by all physicists, using all QM interpretations, that the Schrödinger catbox won't work unless it achieves perfect isolation. No information must come out from inside the box, or at the very least, no information that could allow you to infer the state of the contents. That includes photons, phonons, particles, and anything else you can think of.

One question that I've never seen asked or answered, is this; will Schrödinger's box work if information can get into it from outside?

David

No information comes out of the box. Not for a while in any case. Instead of opening the box to see whether the cat is alive or dead, you measure the oxygen - which doesn't simply tell you whether the cat is alive or dead, but also tells you whether it's been alive or dead from the start.

 

[PeterDonis]

The machine measures some quantum observable (?) that has 2 orthogonal values.
The machine sets a filter to one of two positions, depending on the measured value.
The positions are 90 degrees apart.
A pulse of photons is fired through the filter.
The photons that transit it are then in one of two orthogonal polarities, depending on what value was measured.

Ok, so this is just producing a stream of photons in a known polarization state, and which known polarization state it is depends on the result of a binary quantum measurement. To me, using the term "cloning" to describe this process is a misnomer, because you are not making multiple copies of an unknown quantum state. You are preparing multiple systems in a known quantum state, which of course does not violate the no cloning theorem.

In "Schrödinger's cat" language, which of the two polarization states the stream of photons is in corresponds to whether the cat is alive or dead. And in "many worlds" language, the machine itself would be in a superposition of two different states, entangled with the quantum observable it measures, and so the filter would also be in a superposition of two different positions, entangled with the machine, and the stream of photons would also be in a superposition of different polarizations, entangled with the filter. And the question of why we would only observe one of the two alternatives (value #1 measured for quantum observable - filter in position #1 - stream of photons in polarization state #1, or value #2 measured for quantum observable - filter in position #2 - stream of photons in polarization state #2) is the same as the question of why we only observe cats to be alive or dead.

 

[David Byrden]

Well, thank you all for an educational refutation.
But could you please explain something else to me?

Suppose we had a Schrödinger Box (totally isolating, allows zero information to escape) and a maltreated cat inside it, as originally proposed. And the quantum event does or does not release the poison, in the usual way.

How would this differ from an ordinary box?

I mean, obviously Schrödinger won't hear the cat, but will there be consequences that can only be explained by quantum mechanics?

David

 

[David Byrden]

...the stream of photons would also be in a superposition of different polarizations, entangled with the filter.

A superposition? Not a mixed state? I am confoosed. Nugatory told us that this experiment will fail because the box contents will decohere into a mixed state.

You see, 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.

I do realize that this won't happen unless the two copies of the photon are indistinguishable in every other way. For example, the "live cat" must not cause the photon emitter to emit photons a nanosecond later than if there was a "dead cat". So, in the idealised Byrden Box, the machine is designed with this in mind.

So, if the photons then emerge in a superposition state, as you say, and they are otherwise indistinguishable, as I say, then why can we detect them only in the polarisation states #1 and #2, rather than the summed polarisation?

David

 

[David Byrden]

No information comes out of the box...you measure the oxygen

Ahhhhh, but a measurement of the oxygen is information.

David

 

[PeroK]

Ahhhhh, but a measurement of the oxygen is information.

David

Well, so is looking in the box to see whether the cat is alive or dead. My point was that the normal cat experiment cons the reader, to some extent, into thinking that a single measurement of aliveness or deadness is the whole story for a cat. But, unlike the spin on an electron, or the polarisation of a photon, it is not the whole story. You can tell in several ways, for example, how long the cat has been dead. Oxygen in the box, its state of rigor mortis etc.

The whole point of the thought experiment is that QM does not change these properties of a cat - and there is no such thing as a half-alive-half-dead cat existing in limbo for some period. The question is not whether such cats exist, but why do they not exist.

Your experiment, if I understand it, is to try to influence the evolution of a macroscopic system - that is isolated from you - by a clever choice of polarisation angles. This presupposes that the system inside the box evolves not according to the classical laws of biology but, because you've set up a "quantum experiment", starts to behave like a simple quantum system instead. With the complex biology of a cat reduced to the same status as the spin on an electron. That is not the case. QM may indeed shed some light on biology, but it doesn't immediately give us a way to subvert biological processes in a cat and replace them with simple quantum properties like those of an electron.

A cat is not a simple quantum object that is amenable to the Schroedinger experiment and its derivaties. Instead, the real question is why not? And that took the decoherence into mixed states to explain and was not a trivial question.

 

[David Byrden]

...there is no such thing as a half-alive-half-dead cat existing in limbo...

...Your experiment, if I understand it,...presupposes that the system inside the box evolves not according to the classical laws of biology but, because you've set up a "quantum experiment", starts to behave like a simple quantum system instead. With the complex biology of a cat reduced to the same status as the spin on an electron.

Oh, no, that's not my assumption at all. I'm not assuming that the cat will behave like a quantum particle just because it's in the box. I'm not trying to interfere with the biological processes of the cat !

It's my understanding that the perfectly isolating box (which we cannot really build) allows its contents to divide their timelime, their history, into multiple parallel branches or "worlds". With an ordinary cardboard box, information about such branches would leak out somehow in the universal Wave Function, and we the observer would become entangled and end up in one branch of the history. The point of the special box is to keep such information out of our environment. Relative to us, the contents of the box (in my understanding) can be in multiple states.

So, I'm assuming that the cat will follow the ordinary laws of biology, living or dying appropriately. But there will be multiple branches of the reality inside the box, therefore multiple cats.

To open the box is, as far as I understand, equivalent to making a measurement of a quantum system. The measuring device, observer and environment become entangled with the state of the thing measured, and divide themselves into multiple copies, for each of the multiple possible outcomes. In other words, before opening the box we have Schrödinger and two cats; but after he opens it, we have two Schrodingers and two cats, and they could theoretically be inside a much larger box, with another observer outside, relative to which they are in a superposition or mixed state.

And when Schrödinger opens the box, to "quantum measure" the environment within it, the choice of which branch he will find himself in is determined by the Born rule in the usual way.

The statistics of that choice are what I wanted to interfere with.

David

 

[kith]

The relevant boundary is not between Schrödinger and the box but between the cat and the environment inside the box. Even if the cat somehow reached a superposition of a dead state and an alive state, its interaction with the environment inside the box would lead to decoherence on an extremely small time scale.

This happens regardless of the question whether there's an additional interaction with the outside of the box.

 

[David Byrden]

The relevant boundary is not between Schrödinger and the box but between the cat and the environment inside the box.

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

Some aspects of QM are open to interpretation, but I think it's certain that the only real boundary in the Schrödinger experiment, is the box. The cat and its environment are linked by billions of atomic and other interactions. I visualise the entire interior of the box as being in a superposition.

In my view, information spreads via the universal Wave Function. An object's state, relative to you, is nothing more than the information you've obtained about it. So the significance of the Schrödinger box is that it blocks the flow of information.

David

 

[PeroK]

So, I'm assuming that the cat will follow the ordinary laws of biology, living or dying appropriately. But there will be multiple branches of the reality inside the box, therefore multiple cats.

There is only ever one cat and it's only ever in one state. But, that state can be a superposition of states (in fact, it must be a superposition) and it can be a mixed state.

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

Some aspects of QM are open to interpretation, but I think it's certain that the only real boundary in the Schrödinger experiment, is the box. The cat and its environment are linked by billions of atomic and other interactions. I visualise the entire interior of the box as being in a superposition.

In my view, information spreads via the universal Wave Function. An object's state, relative to you, is nothing more than the information you've obtained about it. So the significance of the Schrödinger box is that it blocks the flow of information.

David

My guess is that these are ideas from RQM that you referenced. In standard QM, there is no sense of the state of a system being relative to an observer. My other guess is that whereas the observer outside the box does not know whether the cat is alive or dead, the cat itself knows whether it's alive or dead, and that is the basis of the argument that QM is inconsistent with a single world, as in the paper you referenced.

The point is, however, that if you want to be understood you need to make it clear when you are working to an unusual interpretation of QM; especially one that claims that other interpretations may be inconsistent.

 

[David Byrden]

My guess is that these are ideas from RQM that you referenced. In standard QM, there is no sense of the state of a system being relative to an observer.

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

...the argument that QM is inconsistent with a single world, as in the paper you referenced.

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.

if you want to be understood you need to make it clear when you are working to an unusual interpretation of QM; especially one that claims that other interpretations may be inconsistent.

I apologise.

David

 

[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 Schrödinger 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 Schrödinger box is that it blocks the flow of information.

It's true that an idealized Schrödinger 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 Schrödinger 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 Schrödinger 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 Schrödinger 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 Schrödinger's in two important ways:
1) Wigner greatly sharpened the argument. Schrödinger 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".