RogueAIJune 03, 2020 at 00:299225 views46 comments
What if you shrunk people down to the size of an electron and used them in the famous "double slit experiment"? Would you get the same results? What would the experiences of the people be?
Reply to RogueAI If people "shrink down to electrons", then they behave exactly like electrons, because now they are electrons.
As for what the experience of those electrons is, which I think is what you really want to get at, it's nothing particularly special. The electron doesn't experience any kind of self-interaction, as in the electron's charge, spin, mass, momentum, all of its properties remain unchanged by the interference of its wavefunction with itself. It only experiences something when it interacts with the screen it hits, and it only hits the screen at once place... per world. Exactly the distribution of places it hits across the possible worlds is what changes from its wavefunction's self-interaction, but it had a range of possible places it could have hit anyway before that.
As for what it's like to have your wavefunction collapse upon interacting with something else, that's basically the whole story of the Many-Worlds Interpretation: when the scientists watch the double-split experiment, they only see each photon hit in one place per world, but upon firing each photon, and its "wavefunction collapsing" to that one location from their point of view, they get entangled with the electron's wavefunction distribution, and a different version of them sees each possible outcome of the experiment in a different possible world. But none of them are any the wiser of their other selves.
And since everything is quantum, this is happening everywhere all the time, including to you right now, so you're intimately familiar with what it's like already. It's pretty ordinary.
If people "shrink down to electrons", then they behave exactly like electrons
You misquoted me. If X is shrunk to the size of Y, X does not turn into Y. In the thought experiment, people shrunk down to the size of electrons would not "behave exactly like electrons". They would behave like people.
What would that tiny person experience as they go through one at a time if the MWI of QM is correct? If the Copenhagen Interpretation is correct?
Particle behavior will manifest as the electron-size person would know which slit he went through. What happens if s/he closes his/her eyes or if s/he was blind is a different story.
It only experiences something when it interacts with the screen it hits, and it only hits the screen at once place... per world. Exactly the distribution of places it hits across the possible worlds is what changes from its wavefunction's self-interaction, but it had a range of possible places it could have hit anyway before that.
But it's a little person right, so it has eyes :-), what does it experience before the wavefunction collapses/splits, all possible positions at once... and then they all but one disappear when it hits the screen?
ChatteringMonkeyJune 03, 2020 at 11:11#4199150 likes
It only experiences something when it interacts with the screen it hits, and it only hits the screen at once place... per world. Exactly the distribution of places it hits across the possible worlds is what changes from its wavefunction's self-interaction, but it had a range of possible places it could have hit anyway before that.
— Pfhorrest
But it's a little person right, so it has eyes :-), what does it experience before the wavefunction collapses/splits, all possible positions at once... and then they all but one disappear when it hits the screen?
Or would it, because it has eyes instantly collapse/split because it gets entangled with itself and as such never see all positions at once?
The OP question is not as stupid as it sounds. I would reformulate it as "What does it feel like to be in a quantum superposition state?" There is some discussion of this and related questions in the literature on the foundations of quantum mechanics.
The OP question is not as stupid as it sounds. I would reformulate it as "What does it feel like to be in a quantum superposition state?" There is some discussion of this and related questions in the literature on the foundations of quantum mechanics.
Presumably, that depends mainly on your interpretation of the equations, i.e. on metaphysical speculation. If it's many worlds, maybe you are an infinite number of persons at once.
what does it experience before the wavefunction collapses/splits, all possible positions at once... and then they all but one disappear when it hits the screen?
Living cats don't smell poison.
ChatteringMonkeyJune 03, 2020 at 13:13#4199370 likes
Normal sized Schrodinger's cat is in superposition; why would mini-electron sized cats be different?
If a normal living cat is in superposition why doesn't it smell poison then? Doesn't superposition entail that it's neither exclusively living nor dead?
If a normal living cat is in superposition why doesn't it smell poison then?
"Normal sized living cat" is not in superposition; "normal sized cat" is (or more realistically, the contents of the box). The box is in a superposition between two states; A and B. State A has a living cat that smells no poison. State B has a dead cat in it. In MWI terms, once "Schrodinger" opens the box, he just gets entangled with this system. Then you have State A, Schrodinger sees a living cat, and State B, Schrodinger sees a dead cat. Then, the Schrodinger who saw a living cat "smells no poison" (sees no broken vials).
In other words, what it is like to be in superposition is the same thing as what it's like to not be in superposition. You're just a classical-ish thing that is a portion of the wavefunction, not interacting meaningfully with other portions of the wavefunction in superposition, even if that other thing is "a you" that evolved differently. (In MWI terms your "classical" portion would be a world).
ChatteringMonkeyJune 03, 2020 at 14:16#4199480 likes
"Normal sized living cat" is not in superposition; "normal sized cat" is (or more realistically, the contents of the box). The box is in a superposition between two states; A and B. State A has a living cat that smells no poison. State B has a dead cat in it.
So then what does the cat in superposition experience, is still the question.
So the branches are allready there before they 'branch'?
Not quite. The cat branched when it "observed" (smelled) a system in superposition (between poison in the air and no poison in the air, resulting from broken vial and no broken vial, due to detection/no detection). That observation entangles the cat with this system, but that makes two "worlds". To the one Schrodinger, those two worlds are in superposition, until he opens the box; then his wavefunction entangles with this result, branching him into two Schrodingers.
ChatteringMonkeyJune 03, 2020 at 14:37#4199580 likes
Not quite. The cat branched when it "observed" (smelled) a system in superposition (between poison in the air and no poison in the air, resulting from broken vial and no broken vial, due to detection/no detection). That observation entangles the cat with this system, but that makes two "worlds". To the one Schrodinger, those two worlds are in superposition, until he opens the box; then his wavefunction entangles with this result, branching him into two Schrodingers.
Alright, I'm not sure i'm getting it entirely yet. Does this mean that when something branches it doesn't create an 'entire world'? Say when the cat branches the wavefunction, there are two cats but still only one schrödinger until he observes it and 'joins' the two branches. Or does the cat observing it create a entire second world, and then two schrödingers observing it create another third and fourth entire world? I guess from your wording, it's the former?
Edit: Or I guess that there is yet another possibility that they each branch entirely seperately, and that branching does not create an entire world in each instance?
Does this mean that when something branches it doesn't create an 'entire world'?
Correct. The worlds aren't fundamental; they're emergent. Also the name MWI is a bit of a misnomer; MWI doesn't posit multiple worlds... it posits that wavefunction collapse isn't "real". That leaves only the evolving wavefunction. In fact, the title of Everett's seminal work is "The Theory of the Universal Wavefunction".
Worlds are, rather, simply portions of the universal wavefunction that don't meaningfully interact with other portions. The wavefunction never collapses; instead, when an "observer" measures a system in superposition, the observer simply entangles with it, creating a new wavefunction state where the observer too is in superposition, which in essence becomes multiple portions of the wavefunction that don't interact with each other meaningfully, aka "worlds".
But in SC, the "original" split is the decay versus non-decay of the radioactive material, which is in superposition. Then the detector observes this, thus entangling with it, making a detected decay versus undetected non-decay, resulting in a broken versus non-broken vial of poison (as the vial "observes" the detector), and so on. MWI is simply the idea that we keep going this way when Schrodinger opens the box, rather than apply a brand new rule ("real" wavefunction collapse) to him. So think of this as not an absolute split, but rather, a "propagating" split; observing a split splits you.
ChatteringMonkeyJune 03, 2020 at 15:28#4199640 likes
Reply to InPitzotl Thanks, my mistake was indeed in thinking 'classical' worlds were created. This was really helpful, much appreciated.
Presumably, that depends mainly on your interpretation of the equations, i.e. on metaphysical speculation. If it's many worlds, maybe you are an infinite number of persons at once.
Not infinite, the number of superposition states in a finite system would be finite. And assuming that we are in a superposition state at any time (or at all times, as per Everett), then there had better be a coherent account of how it is that we feel as if we were always in a pure state, i.e. all the classical observables always seem to have definite values. A number of such accounts, more or less detailed, have been proposed using somewhat different assumptions regarding conscious observers and with different interpretations of QM.
Note that one does not necessarily need to have a fully worked out theory of consciousness to answer these questions, nor is there necessarily a need for any mysticism. Some explanations posit nothing more than a system with memory, like a photographic plate for instance, one that can keep a record of measured eigenvalues.
Schrodinger's Cat was not originally meant to be taken seriously. It was an illustration of the problems with emerging quantum mechanics at the time.
A lot of this confusion about things not happening until we 'observe' them has to do with a conflation between detection and observation, as if they were the same thing. But they are not.
Observation is when a scientist looks at the results of an experiment. That has nothing to do with how the experiments takes place or what the results are.
Detection is when a particle in the quantum universe/spacetime collides with an object (experimental apparatus) in physical spacetime. This is what determines the result of the experiment. Observation has nothing to do with it. After all, a scientist could wait months before observing the results of an experiment. Does that mean there are no results until he observes those results? I don't think so.
A lot of pseudo books have been sold on this 'changing reality by observing it' notion...
Observation is when a scientist looks at the results of an experiment. That has nothing to do with how the experiments takes place or what the results are.
You will find actually that Schrodinger himself leaned towards Schopenhauer and Vedanta, both of which he wrote about in his later career.
In 1958, Schrödinger, inspired by Schopenhauer from youth, published his lectures Mind and Matter. Here he argued that there is a difference between measuring instruments and human observation: a thermometer’s registration cannot be considered an act of observation, as it contains no meaning in itself. Thus, consciousness is needed to make physical reality meaningful. As Schrödinger concluded, "Some of you, I am sure, will call this mysticism. So with all due acknowledgement to the fact that physical theory is at all times relative, in that it depends on certain basic assumptions, we may, or so I believe, assert that physical theory in its present stage strongly suggests the indestructibility of Mind by Time."
What if you shrunk people down to the size of an electron and used them in the famous "double slit experiment"? Would you get the same results? What would the experiences of the people be?
Each person would see that they pass through either the left slit or the right slit. As long as you couldn't obtain which-way information from the people or apparatus (e.g., their memory was erased after passing through the slit), then you would observe interference, otherwise not.
I just wanted to make an additional comment on the matter of the double slit experiment. It's said that the experimental electron comes off as if self-aware, capable of making observations and decisions based on these observations. If memory serves, some scientists have even gone to the extent of claiming the experimental electron comes to know if an observation has been made/not and makes a decision how to behave. Eerily close to what we mean by "person" - an agency that gathers information about the world and makes decisions based on that information. Basically, electrons behave like conscious people, albeit in a very limited way.
What if you shrunk people down to the size of an electron and used them in the famous "double slit experiment"? Would you get the same results? What would the experiences of the people be?
Either wavey or particley, depending on if you checked on their progress through the slits.
cartesiangothicJune 15, 2020 at 14:39#4240860 likes
I think what is meant by this question has been misunderstood.
Do you mean having two slits and a stream of people in single file who must pass through one slit?
In this case we might potentially have different results, given that people can think, and can choose which slit to pass through, whereas electrons cannot.
There was a paper recently that was quite interesting, I'll see if I can dig it out (no joy so far). In QM, we're used to thinking of something like an electron being in a superposition of states in a lab setup like the double-slit experiment that is in a well-defined state (i.e. the position of the slits and screen being well-defined, because they're macroscopic). The paper basically asked, as applied to this context, what does the slit-and-screen setup "look like" from the electron's "point of view"? Iirc this gist is that there should be some transformation you can make that takes you from superposed-electron/defined-lab to frame with a well defined electron state, e.g. a well-defined electron position. What does the lab setup look like in this frame?
It would look pretty crazy. The positions of everything in the lab would be put into the converse superposition. So the electron would find that no slit had yet reached us, a slit had already passed us but the screen had not, and the screen had already hit us, all with associated probabilities prior to the lab's wavefunction collapse. The position of the screen that it hit would be smudged out in a banded way, which takes some working through, but is due to the fact that any point on the screen (i.e. relative to one corner) is a) already in a superposition and b) can only be hit with the moderating probability of both slits already having passed behind the electron. All of this will have happened, be happening, and be yet to happen because our well-defined electron position has made a nonsense of momentum. Then something unknown happens and the lab collapses to a single well-defined position with one point on the screen at the origin
Ah, here's the preprint: https://arxiv.org/pdf/1712.07207.pdf
Lots of maths, but check out Fig. 3. Unless you like maths, in which case I'm a douche because I basically just said: "You don't need to read it if it's too hard, just look at the pretty pictures". Damned either way, I guess :rofl:
Unfortunately the paper doesn't directly address the double-slit experiment. It seems to me that even if the apparatus is in superposition in the electron's reference frame, the electron still needs to go through one of the slits which is then effectively an interaction with the apparatus. However the which-way information is not available to the observer (since there are no detectors on the slits), so the process remains unitary in the observer's reference frame.
This is similar to the Wigner's friend thought experiment, where Wigner's friend makes a definite measurement while the process remains unitary from Wigner's perspective.
It seems to me that even if the apparatus is in superposition in the electron's reference frame, the electron still needs to go through one of the slits which is then effectively an interaction with the apparatus.
But the electron doesn't 'go' in its rest frame, by lieu of a) it's its rest frame and b) its momentum is undefined. (That said, the paper isn't bothered about rest frames as much as un-superposed frames.) At any time, either slits already have a nonzero probability of being behind the electron.
But the electron doesn't 'go' in its rest frame, by lieu of a) it's its rest frame and b) its momentum is undefined. (That said, the paper isn't bothered about rest frames as much as un-superposed frames.) At any time, either slits already have a nonzero probability of being behind the electron.
OK, but the puzzle is to account for what happens when the two apparatus slits go past the electron in the electron's rest frame.
If the apparatus remains in superposition when the slits go past the electron, then the apparatus should similarly remain in superposition when the back screen hits the electron. That is, no definite measurement event would ever occur in the electron's reference frame.
If a definite measurement event does occur at the back screen in the electron's reference frame then a definite measurement event should also have occurred at the slit. It seems to be a similar kind of physical interaction and so should be treated similarly.
As I see it, the electron does go through a specific slit in the electron's reference frame. That is consistent with the relational approach that the paper uses (see quote below), which is that whether a definite measurement occurs or not depends on the frame of reference.
We find that a quantum state and its features — such as superposition and entanglement — are only defined relative to the chosen reference frame, in the spirit of the relational description of physics [16–19, 23, 24]. For example, a quantum system which is in a well-localised state of an observable for a certain observer may, for another observer, be in a superposition of two or more states or even entangled with the first observer.
OK, but the puzzle is to account for what happens when the two apparatus slits go past the electron in the electron's rest frame.
This isn't really in the picture, though. The probability of being beyond the slits grows. That is the closest you can get to "the two apparatus slits go past the electron". You can say, e.g., the probability of the slits being behind the electron is now > 50% for thr first time. That's doable.
That is, no definite measurement event would ever occur in the electron's reference frame.
There's no reason why, if a superposed electron can spontaneously and probabilistically collapse, a superposed laboratory cannot. In fact, I'd suggest the opposite: in the electron's rest frame, the collapse is almost immediate. It seems longer to us due to time dilation.
If a definite measurement event does occur at the back screen in the electron's reference frame then a definite measurement event should also have occurred at the slit.
This is not an argument from quantum theory, I gather, more a philosophical argument as to how quantum mechanics ought to be. The double slit experiment suggests that electron collapse at the slit only occurs if we attempt to observe it at the slit, e.g. if we put something in the way of the slit that causes earlier collapse, such as an electron detector.
The double slit experiment suggests that electron collapse at the slit only occurs if we attempt to observe it at the slit, e.g. if we put something in the way of the slit that causes earlier collapse, such as an electron detector.
Right, the electron detector provides which-way information that collapses the electron superposition in the lab observer's reference frame.
But that doesn't imply anything about what happens in the electron's reference frame when there is no detector. On a relational view, since an interaction occurs at the slit, collapse occurs in both the electron and apparatus reference frames. But collapse doesn't occur for the lab observer since which-way information is not available in the lab-observer's reference frame. So collapse is reference frame-dependent. This is analogous to a Wigner's Friend experiment where a definite measurement event occurs in the friend's reference frame but remains in superposition in Wigner's reference frame.
On a relational view, since an interaction occurs at the slit, collapse occurs in both the electron and apparatus reference frames.
No, the electron is in a fixed state in its frame, that's the point of the paper I linked to. The transformation takes us from a frame in which the lab is in a well-defined position and the electron in superposition to one in which the lab is in superposition and the electron has a well-defined position. It is the lab that undergoes collapse.
However, no reason not to consider an intermediate frame in which both are in superposition. But the wording of the OP, an electron-sized person's point of view, suggested specifically the frame in which the electron's position is defined.
This is analogous to a Wigner's Friend experiment where a definite measurement event occurs in the friend's reference frame but remains in superposition in Wigner's reference frame.
In the Wigner's friend experiment, collapse is observer-dependent even with a given frame, e.g. the lab frame, and there's some evidence that this is correct (it is experimentally verifiable). However there's a nice symmetry here, you're right, insofar as both Wigner and his friend are well-defined wrt themselves and superposed wrt each other. It might not be a coincidence that the experimental verification of Wigner and the paper on frame transformation roughly coincided... perhaps QM is coming of age. :)
Comments (46)
...then anything follows.
Is imagination dead here?
As for what the experience of those electrons is, which I think is what you really want to get at, it's nothing particularly special. The electron doesn't experience any kind of self-interaction, as in the electron's charge, spin, mass, momentum, all of its properties remain unchanged by the interference of its wavefunction with itself. It only experiences something when it interacts with the screen it hits, and it only hits the screen at once place... per world. Exactly the distribution of places it hits across the possible worlds is what changes from its wavefunction's self-interaction, but it had a range of possible places it could have hit anyway before that.
As for what it's like to have your wavefunction collapse upon interacting with something else, that's basically the whole story of the Many-Worlds Interpretation: when the scientists watch the double-split experiment, they only see each photon hit in one place per world, but upon firing each photon, and its "wavefunction collapsing" to that one location from their point of view, they get entangled with the electron's wavefunction distribution, and a different version of them sees each possible outcome of the experiment in a different possible world. But none of them are any the wiser of their other selves.
And since everything is quantum, this is happening everywhere all the time, including to you right now, so you're intimately familiar with what it's like already. It's pretty ordinary.
You misquoted me. If X is shrunk to the size of Y, X does not turn into Y. In the thought experiment, people shrunk down to the size of electrons would not "behave exactly like electrons". They would behave like people.
What would that tiny person experience as they go through one at a time if the MWI of QM is correct? If the Copenhagen Interpretation is correct?
Probably; “Bucky balls” give an interference pattern, and they are monstrous compared to elementary particles.
Quoting RogueAI
If they’re still people, why wouldn’t they have people experiences?
But there aren't many Einsteins on the forum.
But it's a little person right, so it has eyes :-), what does it experience before the wavefunction collapses/splits, all possible positions at once... and then they all but one disappear when it hits the screen?
Or would it, because it has eyes instantly collapse/split because it gets entangled with itself and as such never see all positions at once?
Presumably, that depends mainly on your interpretation of the equations, i.e. on metaphysical speculation. If it's many worlds, maybe you are an infinite number of persons at once.
all over the place, I imagine.
'What did you do to the cat, Erwin? It looks half-dead' ~ Ms Schrodinger.
Living cats don't smell poison.
Maybe hypothetical mini-electron sized cats do?
Normal sized Schrodinger's cat is in superposition; why would mini-electron sized cats be different?
If a normal living cat is in superposition why doesn't it smell poison then? Doesn't superposition entail that it's neither exclusively living nor dead?
"Normal sized living cat" is not in superposition; "normal sized cat" is (or more realistically, the contents of the box). The box is in a superposition between two states; A and B. State A has a living cat that smells no poison. State B has a dead cat in it. In MWI terms, once "Schrodinger" opens the box, he just gets entangled with this system. Then you have State A, Schrodinger sees a living cat, and State B, Schrodinger sees a dead cat. Then, the Schrodinger who saw a living cat "smells no poison" (sees no broken vials).
In other words, what it is like to be in superposition is the same thing as what it's like to not be in superposition. You're just a classical-ish thing that is a portion of the wavefunction, not interacting meaningfully with other portions of the wavefunction in superposition, even if that other thing is "a you" that evolved differently. (In MWI terms your "classical" portion would be a world).
So then what does the cat in superposition experience, is still the question.
Which one? Dead cats tell no tales, but the living cat smells no poison. (Make sure to see all edits above).
So the branches are allready there before they 'branch'? Makes sense... for conservation of energy and the like.
Not quite. The cat branched when it "observed" (smelled) a system in superposition (between poison in the air and no poison in the air, resulting from broken vial and no broken vial, due to detection/no detection). That observation entangles the cat with this system, but that makes two "worlds". To the one Schrodinger, those two worlds are in superposition, until he opens the box; then his wavefunction entangles with this result, branching him into two Schrodingers.
Alright, I'm not sure i'm getting it entirely yet. Does this mean that when something branches it doesn't create an 'entire world'? Say when the cat branches the wavefunction, there are two cats but still only one schrödinger until he observes it and 'joins' the two branches. Or does the cat observing it create a entire second world, and then two schrödingers observing it create another third and fourth entire world? I guess from your wording, it's the former?
Edit: Or I guess that there is yet another possibility that they each branch entirely seperately, and that branching does not create an entire world in each instance?
Correct. The worlds aren't fundamental; they're emergent. Also the name MWI is a bit of a misnomer; MWI doesn't posit multiple worlds... it posits that wavefunction collapse isn't "real". That leaves only the evolving wavefunction. In fact, the title of Everett's seminal work is "The Theory of the Universal Wavefunction".
Worlds are, rather, simply portions of the universal wavefunction that don't meaningfully interact with other portions. The wavefunction never collapses; instead, when an "observer" measures a system in superposition, the observer simply entangles with it, creating a new wavefunction state where the observer too is in superposition, which in essence becomes multiple portions of the wavefunction that don't interact with each other meaningfully, aka "worlds".
But in SC, the "original" split is the decay versus non-decay of the radioactive material, which is in superposition. Then the detector observes this, thus entangling with it, making a detected decay versus undetected non-decay, resulting in a broken versus non-broken vial of poison (as the vial "observes" the detector), and so on. MWI is simply the idea that we keep going this way when Schrodinger opens the box, rather than apply a brand new rule ("real" wavefunction collapse) to him. So think of this as not an absolute split, but rather, a "propagating" split; observing a split splits you.
Quoting RogueAI
Quoting ChatteringMonkey
This.
:100: :clap: I was hoping someone would give a more complete explanation of MWI while I was gone.
Not infinite, the number of superposition states in a finite system would be finite. And assuming that we are in a superposition state at any time (or at all times, as per Everett), then there had better be a coherent account of how it is that we feel as if we were always in a pure state, i.e. all the classical observables always seem to have definite values. A number of such accounts, more or less detailed, have been proposed using somewhat different assumptions regarding conscious observers and with different interpretations of QM.
Note that one does not necessarily need to have a fully worked out theory of consciousness to answer these questions, nor is there necessarily a need for any mysticism. Some explanations posit nothing more than a system with memory, like a photographic plate for instance, one that can keep a record of measured eigenvalues.
Schrodinger's Cat was not originally meant to be taken seriously. It was an illustration of the problems with emerging quantum mechanics at the time.
A lot of this confusion about things not happening until we 'observe' them has to do with a conflation between detection and observation, as if they were the same thing. But they are not.
Observation is when a scientist looks at the results of an experiment. That has nothing to do with how the experiments takes place or what the results are.
Detection is when a particle in the quantum universe/spacetime collides with an object (experimental apparatus) in physical spacetime. This is what determines the result of the experiment. Observation has nothing to do with it. After all, a scientist could wait months before observing the results of an experiment. Does that mean there are no results until he observes those results? I don't think so.
A lot of pseudo books have been sold on this 'changing reality by observing it' notion...
You will find actually that Schrodinger himself leaned towards Schopenhauer and Vedanta, both of which he wrote about in his later career.
Quantum Mysticism: Gone but not Forgotten
Well, that goes without saying. How can meaning exist outside a mind? I think he is talking about something slightly different here.
Each person would see that they pass through either the left slit or the right slit. As long as you couldn't obtain which-way information from the people or apparatus (e.g., their memory was erased after passing through the slit), then you would observe interference, otherwise not.
It's similar to the Wigner's friend thought experiment.
Either wavey or particley, depending on if you checked on their progress through the slits.
Do you mean having two slits and a stream of people in single file who must pass through one slit?
In this case we might potentially have different results, given that people can think, and can choose which slit to pass through, whereas electrons cannot.
There was a paper recently that was quite interesting, I'll see if I can dig it out (no joy so far). In QM, we're used to thinking of something like an electron being in a superposition of states in a lab setup like the double-slit experiment that is in a well-defined state (i.e. the position of the slits and screen being well-defined, because they're macroscopic). The paper basically asked, as applied to this context, what does the slit-and-screen setup "look like" from the electron's "point of view"? Iirc this gist is that there should be some transformation you can make that takes you from superposed-electron/defined-lab to frame with a well defined electron state, e.g. a well-defined electron position. What does the lab setup look like in this frame?
It would look pretty crazy. The positions of everything in the lab would be put into the converse superposition. So the electron would find that no slit had yet reached us, a slit had already passed us but the screen had not, and the screen had already hit us, all with associated probabilities prior to the lab's wavefunction collapse. The position of the screen that it hit would be smudged out in a banded way, which takes some working through, but is due to the fact that any point on the screen (i.e. relative to one corner) is a) already in a superposition and b) can only be hit with the moderating probability of both slits already having passed behind the electron. All of this will have happened, be happening, and be yet to happen because our well-defined electron position has made a nonsense of momentum. Then something unknown happens and the lab collapses to a single well-defined position with one point on the screen at the origin
Or: blur, blur, blur, hit by a screen.
Ah, here's the preprint: https://arxiv.org/pdf/1712.07207.pdf
Lots of maths, but check out Fig. 3. Unless you like maths, in which case I'm a douche because I basically just said: "You don't need to read it if it's too hard, just look at the pretty pictures". Damned either way, I guess :rofl:
Nice find. Also here's a brief media summary of that paper, aptly titled How does a quantum particle see the world?
Unfortunately the paper doesn't directly address the double-slit experiment. It seems to me that even if the apparatus is in superposition in the electron's reference frame, the electron still needs to go through one of the slits which is then effectively an interaction with the apparatus. However the which-way information is not available to the observer (since there are no detectors on the slits), so the process remains unitary in the observer's reference frame.
This is similar to the Wigner's friend thought experiment, where Wigner's friend makes a definite measurement while the process remains unitary from Wigner's perspective.
Even better find! I was a lazy Googler; I'd read the paper before so new it existed. Thanks for making more of an effort.
Quoting Andrew M
But the electron doesn't 'go' in its rest frame, by lieu of a) it's its rest frame and b) its momentum is undefined. (That said, the paper isn't bothered about rest frames as much as un-superposed frames.) At any time, either slits already have a nonzero probability of being behind the electron.
OK, but the puzzle is to account for what happens when the two apparatus slits go past the electron in the electron's rest frame.
If the apparatus remains in superposition when the slits go past the electron, then the apparatus should similarly remain in superposition when the back screen hits the electron. That is, no definite measurement event would ever occur in the electron's reference frame.
If a definite measurement event does occur at the back screen in the electron's reference frame then a definite measurement event should also have occurred at the slit. It seems to be a similar kind of physical interaction and so should be treated similarly.
As I see it, the electron does go through a specific slit in the electron's reference frame. That is consistent with the relational approach that the paper uses (see quote below), which is that whether a definite measurement occurs or not depends on the frame of reference.
Quoting Quantum mechanics and the covariance of physical laws in quantum reference frames - Giacomini, Castro-Ruiz, Brukner
This isn't really in the picture, though. The probability of being beyond the slits grows. That is the closest you can get to "the two apparatus slits go past the electron". You can say, e.g., the probability of the slits being behind the electron is now > 50% for thr first time. That's doable.
Quoting Andrew M
There's no reason why, if a superposed electron can spontaneously and probabilistically collapse, a superposed laboratory cannot. In fact, I'd suggest the opposite: in the electron's rest frame, the collapse is almost immediate. It seems longer to us due to time dilation.
Quoting Andrew M
This is not an argument from quantum theory, I gather, more a philosophical argument as to how quantum mechanics ought to be. The double slit experiment suggests that electron collapse at the slit only occurs if we attempt to observe it at the slit, e.g. if we put something in the way of the slit that causes earlier collapse, such as an electron detector.
It's a relational interpretation (which the paper uses, see for example reference [23] in the earlier quote referring to Rovelli's RQM).
Quoting Kenosha Kid
Right, the electron detector provides which-way information that collapses the electron superposition in the lab observer's reference frame.
But that doesn't imply anything about what happens in the electron's reference frame when there is no detector. On a relational view, since an interaction occurs at the slit, collapse occurs in both the electron and apparatus reference frames. But collapse doesn't occur for the lab observer since which-way information is not available in the lab-observer's reference frame. So collapse is reference frame-dependent. This is analogous to a Wigner's Friend experiment where a definite measurement event occurs in the friend's reference frame but remains in superposition in Wigner's reference frame.
No, the electron is in a fixed state in its frame, that's the point of the paper I linked to. The transformation takes us from a frame in which the lab is in a well-defined position and the electron in superposition to one in which the lab is in superposition and the electron has a well-defined position. It is the lab that undergoes collapse.
However, no reason not to consider an intermediate frame in which both are in superposition. But the wording of the OP, an electron-sized person's point of view, suggested specifically the frame in which the electron's position is defined.
Quoting Andrew M
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Quoting Andrew M
In the Wigner's friend experiment, collapse is observer-dependent even with a given frame, e.g. the lab frame, and there's some evidence that this is correct (it is experimentally verifiable). However there's a nice symmetry here, you're right, insofar as both Wigner and his friend are well-defined wrt themselves and superposed wrt each other. It might not be a coincidence that the experimental verification of Wigner and the paper on frame transformation roughly coincided... perhaps QM is coming of age. :)
Sorry, yes, just got what you meant. We are more or less on the same page.
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