(a) The Copenhagen Interpretation is incoherent, and for that reason it’s obviously wrong. I wish everyone would just agree never to talk about it again.
(b) It’s a delicate philosophical question whether and how far a formal mathematical theory produces a “picture for the person inside”.
(c) MWI can mean several different things. If, temporarily, we take it to mean “QM without collapses or hidden variables + whatever subjective consequences follow from that” then you have somewhere between a lot of work and an impossible task to deduce the Born probabilities.
(d) I’m not a Bohmian. I think ultimately we will attain a satisfactory understanding of how the Born probabilities are, after all, ‘deducible’ from the rest of QM. Some promising directions include Zurek’s work on decoherence and einselection, Hanson’s notion of “Mangled Worlds”, and cousin_it’s ideas about how to ‘reduce’ the notion of probability to other things.
(a) By the copenhagen interpretation, do you mean what I meant, i.e. the status-quo interpretation used in most of physics? Would you please explain how it’s obviously incoherent?
(b, c, and some discouragement for d) The delicacy is more a property of philosophers than the universe. If people are built out of ordinary matter, then in thought experiments (e.g. Schrodinger’s cat, but with people) we can swap them for any other system with the right number of possible states (one state per possible outcome). Since we don’t ever subjectively experience being in a superposition, it’s fairly obvious that you have to get rid of the resulting superposition if you ask what a person subjectively experiences. To do that you want to do a thing called tracing out the environment (Sorry, no good page on this, but it’s this operation) that in short changes entanglement to probabilistic correlation. 3 guesses what the probabilities are (though this really just moves the information about Born probabilities are from an explicit rule to the rules of density matricies, so it’s not really “deducible”).
If the wavefunction collapses upon measurement, and no adequate definition of the term “measurement” has been given, then the theory as it stands is incoherent. (I realize that a Copenhagenist thinks that they can get around this by simply denying that the wavefunction exists, but the price of that move is that they don’t have any coherent picture of reality underneath the mathematics.)
Since we don’t ever subjectively experience being in a superposition
OK, but let’s note in passing that the MWI believer needs show this a priori, whether from the mathematics of QM or by deconstructing the concept of “experiencing a superposition” or both. I don’t think that should be particularly difficult, though.
To do that you want to do a thing called tracing out the environment
I know what that means.
The trouble is at some point you need to explain why our measurement records show sequences of random outcomes distributed according to the Born rules. Now it may be the case that branches where measurement records show significant deviation from the Born rules have ‘low amplitude’, but then you need to explain why we don’t experience ourselves in “low amplitude branches”. More precisely, you need to explain why we seem to experience ourselves in branches at rates proportional to the norm squared of the amplitudes of the branches (whatever this talk of ‘experiencing ourselves’ is supposed to mean, and whatever a ‘branch’ is supposed to be). Why should that be true? Why shouldn’t the subjective probabilities simply be a matter of ‘counting up’ branches irrespective of their weighting? After all, the wavefunction still contains all of the information even about ‘lightly weighted’ branches.
The MWI believer thinks that, by talking about reduced density matrices obtained by ‘tracing out’ the environment, you’ve thereby made good progress towards showing where the Born probabilities come from. But the MWI skeptic thinks that the ‘last little bit’ that you still have to do (i.e. explaining why we experience ourselves in heavily weighted branches more than lightly weighted ones) is and always was the entire problem.
no adequate definition of the term “measurement” has been given
Not even the quantum-information-ey definition of “transfer of information from the measuree to the measurer?”
I realize that a Copenhagenist thinks that they can get around this by simply denying that the wavefunction exists
What I’m taking from this is that you don’t know many copenhagenists familiar with Bell’s theorem.
The trouble is at some point you need to explain why our measurement records show sequences of random outcomes distributed according to the Born rules.
Well I suppose I could tell the MWI (or any sort of) skeptic about what density matricies and mixed states are (other readers: to wikipedia!), and how when you see a mixed state it is by definition probabilistic.
But the MWI skeptic thinks that the ‘last little bit’ that you still have to do (i.e. explaining why we experience ourselves in heavily weighted branches more than lightly weighted ones) is and always was the entire problem.
Well, even after the next question of “why do density matrices work that way?”, you can always ask “why?” one more time. But eventually we, having finite information, will always end with something like “because it works.” So how can we judge explanations? Well, one “why” deeper is good enough for me.
3 guesses what the probabilities are
Sorry, I don’t know what you’re talking about.
Tsk, fine, 0 guesses then: the probabilities you get from tracing out the environment are the Born probabilities. But as I said this doesn’t count as deducing them, they’re hidden in the properties of density matrices, which were in turn determined using the Born probabilities.
Not even the quantum-information-ey definition of “transfer of information from the measuree to the measurer?”
That sounds fine, but there’s no objective way of defining what a “measurer” is. So essentially what you have is a ‘solipsistic’ theory, that predicts “the measurer’s” future measurements but refuses to give any determinate picture of the “objective reality” of which the measurer herself is just a part.
I have to concede that many thinkers are prepared to live with this, and scale down their ambitions about the scientific enterprise accordingly, but it seems unsatisfactory to me. Surely there is such a thing as “objective reality”, and I think science should try to tell us what it’s like.
What I’m taking from this is that you don’t know many copenhagenists familiar with Bell’s theorem.
Well, even after the next question of “why do density matrices work that way?”, you can always ask “why?” one more time. But eventually we, having finite information, will always end with something like “because it works.” So how can we judge explanations? Well, one “why” deeper is good enough for me.
Perhaps. My post in the discussion section, and my subsequent comments, try (and fail!) to explain as clearly as I can what troubles me about MWI.
It’s true that an MWI non-collapsing wavefunction has ‘enough information’ to pin down the Born probabilities, and it’s also true that you can’t get the empirical predictions exactly right unless you simulate the entire wavefunction. But it still seems to me that in some weird sense the wavefunction contains ‘too much’ information, in the same way that simulating a classically indeterministic universe by modelling all of its branches gives you ‘too much information’.
But it still seems to me that in some weird sense the wavefunction contains ‘too much’ information, in the same way that simulating a classically indeterministic universe by modelling all of its branches gives you ‘too much information’.
I know what you mean, but as I’m sure you know it’s not mere perversity that has led many to accept “modeling all the branches” of the QM universe. In the case of a classically indeterministic universe, you can model just one indeterministic branch, but in the case of the QM universe you can’t do that, or you can’t do it anywhere near as satisfactorily. The “weirdness” of QM is precisely that aspect of it which (in the eyes of many) forces us to accept the reality of all the branches.
Is there a formal expression of the theory of measurement (in a universally agreed upon language) where [the fact that one doesn’t need to ‘add something’ to obtain a many worlds theory, whereas one does need to ‘add something’ to obtain a single world theory] can be demonstrated?
Based on your previous replies to me, it’s evident that you both believe in, and have a fairly sophisticated understanding of, the idea that you can extract the empirical predictions of quantum mechanics from unitary evolution alone (with no hidden variables) and without ‘adding anything’ (like Many Minds or whatever).
Since one obviously does need to ‘add something’ (e.g. rules about collapse, or Bohmian trajectories) in order to obtain a ‘single universe’ theory, it sounds as though you’ve answered your own question. Or at least, it’s not clear to me what kind of answer you were expecting other than that. (I don’t understand how it helps or why it’s necessary to use a ‘formal expression of the theory of measurement’, or even what such a thing would mean.)
Every interpretation is “adding something.” Just because interpreters choose to bundle their extra mechanisms in vague English language “interpretations” rather than mathematical models does not mean they aren’t extra mechanisms. Copenhagen adds an incoherent and subjective entity called “the observer.” MWI adds a preposterous amount of mechanism involving an infinite and ever-exponentially-expanding number of completely unobservable clone universes. Copenhagen grossly violates objectivity and MWI grossly violates Occam’s Razor. Also, MWI needs a way to determine when a “world” splits, or to shove the issue under the rug, every bit as much as collapse theories need to figure out or ignore when collapse occurs. If as many “interpreters” like to claim QM itself is just the wavefunction, then collapse and world-splits are both extra mechanisms.
But QM is not just the wavefunction. QM is also the Born probabilities. The wavefunction predicts nothing if we do not square it to find the probabilities of the events we actually observe. Of all the interpretations, objective collapse adds the least to quantum mechanics as it is actually practiced. Everybody who uses QM for practical purposes uses the Born probabilities or the direct consequences thereof (e.g. spectra). Thus—despite the many who shudder at the nondeterminism of the universe and thus come up with interpretations like Copenhagen and MWI to try to turn inherent nondeterminism into mere subjective ignorance—the nondeterministic quantum event whereby a superposition of eigenvectors reduces to a single eigenvector (and the various other isomorphic ways this can be mathematically represented) is every bit as central to QM as the nominally deterministic wavefunction. The Born probabilities are not in any way “extra mechanism” they are central to QM. Even more central than the wavefunction, because all that we observe directly are the Born random events. The wavefunction we never observe directly, but only infer it as defining the probability distribution of the nondeterministic events we do observe.
Thus any interpretation of QM as it is actually practiced must take the Born probabilities as being at least as objective and physical as the wavefunction. If the Born probabilities are objective, we have objective collapse, and neither Copenhagen nor MWI are true.
Wikipedia has a bare-bones description of objective collapse:
Further experimental evidence: if the Born probabilities do not represent an objective and physical randomness that is inherent to the universe, then the EPR/Bell/Aspect/et,. al. work tells us that FTL signaling (and more importantly a variety of related paradoxes, FTL signaling not itself being paradoxical in QM) is possible. QM is not special relativity. Special relativity can’t explain the small scale or even certain macroscale effects like diffraction that QM explains. Special relativity is just an emergent large-scale special case of QM (specifically of QFT), it is QM that is fundamental. QM itself, in the EPR/et. al. line of work, tells is that it is the objective and physical randomness inherent in the universe, not causal locality, that stands in the way of FTL signaling and its associated paradoxes.
MWI adds a preposterous amount of mechanism involving an infinite and ever-exponentially-expanding number of completely unobservable clone universes.
There’s no mechanism to it other than the mechanism that every interpretation of QM already has for describing the evolution of non-macroscopic quantum systems. MWI just says that large systems and small systems aren’t separate magisteria with different laws.
Also, MWI needs a way to determine when a “world” splits, or to shove the issue under the rug, every bit as much as collapse theories need to figure out or ignore when collapse occurs.
“Worlds” and “branching” are epiphenomenal concepts; they’re simplifications of what MWI actually talks about (see Decoherence is Pointless).
It doesn’t matter whether branching occurs at a point of or at during some blob of time, probabilistic or otherwise, it’s a central part of MWI and you need an equation to describe when it happens. And that equation should agree with the Born probabilities up to our observational limits. Likewise for collapse in theories that invoke collapse. Otherwise it’s just hand-waving not science.
What is or is not a “branch” is unimportant. If you have read the link you’ll know that a “branch” is not a point mass but a blob spread out in configuration space. All MWI needs is “the probability density of finding oneself in point x in the wavefunction is the amplitude squared at that point”. It’s standard probability theory then to integrate over a “branch” to find your probability of being in that branch. But the only reason to care about “branches” is because the world looks precisely identical to an observer at every point in that branch.
(a) The Copenhagen Interpretation is incoherent, and for that reason it’s obviously wrong. I wish everyone would just agree never to talk about it again.
(b) It’s a delicate philosophical question whether and how far a formal mathematical theory produces a “picture for the person inside”.
(c) MWI can mean several different things. If, temporarily, we take it to mean “QM without collapses or hidden variables + whatever subjective consequences follow from that” then you have somewhere between a lot of work and an impossible task to deduce the Born probabilities.
(d) I’m not a Bohmian. I think ultimately we will attain a satisfactory understanding of how the Born probabilities are, after all, ‘deducible’ from the rest of QM. Some promising directions include Zurek’s work on decoherence and einselection, Hanson’s notion of “Mangled Worlds”, and cousin_it’s ideas about how to ‘reduce’ the notion of probability to other things.
(a) By the copenhagen interpretation, do you mean what I meant, i.e. the status-quo interpretation used in most of physics? Would you please explain how it’s obviously incoherent?
(b, c, and some discouragement for d) The delicacy is more a property of philosophers than the universe. If people are built out of ordinary matter, then in thought experiments (e.g. Schrodinger’s cat, but with people) we can swap them for any other system with the right number of possible states (one state per possible outcome). Since we don’t ever subjectively experience being in a superposition, it’s fairly obvious that you have to get rid of the resulting superposition if you ask what a person subjectively experiences. To do that you want to do a thing called tracing out the environment (Sorry, no good page on this, but it’s this operation) that in short changes entanglement to probabilistic correlation. 3 guesses what the probabilities are (though this really just moves the information about Born probabilities are from an explicit rule to the rules of density matricies, so it’s not really “deducible”).
If the wavefunction collapses upon measurement, and no adequate definition of the term “measurement” has been given, then the theory as it stands is incoherent. (I realize that a Copenhagenist thinks that they can get around this by simply denying that the wavefunction exists, but the price of that move is that they don’t have any coherent picture of reality underneath the mathematics.)
OK, but let’s note in passing that the MWI believer needs show this a priori, whether from the mathematics of QM or by deconstructing the concept of “experiencing a superposition” or both. I don’t think that should be particularly difficult, though.
I know what that means.
The trouble is at some point you need to explain why our measurement records show sequences of random outcomes distributed according to the Born rules. Now it may be the case that branches where measurement records show significant deviation from the Born rules have ‘low amplitude’, but then you need to explain why we don’t experience ourselves in “low amplitude branches”. More precisely, you need to explain why we seem to experience ourselves in branches at rates proportional to the norm squared of the amplitudes of the branches (whatever this talk of ‘experiencing ourselves’ is supposed to mean, and whatever a ‘branch’ is supposed to be). Why should that be true? Why shouldn’t the subjective probabilities simply be a matter of ‘counting up’ branches irrespective of their weighting? After all, the wavefunction still contains all of the information even about ‘lightly weighted’ branches.
The MWI believer thinks that, by talking about reduced density matrices obtained by ‘tracing out’ the environment, you’ve thereby made good progress towards showing where the Born probabilities come from. But the MWI skeptic thinks that the ‘last little bit’ that you still have to do (i.e. explaining why we experience ourselves in heavily weighted branches more than lightly weighted ones) is and always was the entire problem.
Sorry, I don’t know what you’re talking about.
Not even the quantum-information-ey definition of “transfer of information from the measuree to the measurer?”
What I’m taking from this is that you don’t know many copenhagenists familiar with Bell’s theorem.
Well I suppose I could tell the MWI (or any sort of) skeptic about what density matricies and mixed states are (other readers: to wikipedia!), and how when you see a mixed state it is by definition probabilistic.
Well, even after the next question of “why do density matrices work that way?”, you can always ask “why?” one more time. But eventually we, having finite information, will always end with something like “because it works.” So how can we judge explanations? Well, one “why” deeper is good enough for me.
Tsk, fine, 0 guesses then: the probabilities you get from tracing out the environment are the Born probabilities. But as I said this doesn’t count as deducing them, they’re hidden in the properties of density matrices, which were in turn determined using the Born probabilities.
That sounds fine, but there’s no objective way of defining what a “measurer” is. So essentially what you have is a ‘solipsistic’ theory, that predicts “the measurer’s” future measurements but refuses to give any determinate picture of the “objective reality” of which the measurer herself is just a part.
I have to concede that many thinkers are prepared to live with this, and scale down their ambitions about the scientific enterprise accordingly, but it seems unsatisfactory to me. Surely there is such a thing as “objective reality”, and I think science should try to tell us what it’s like.
That may very well be true, but how does pointing out that the Copenhagen Interpretation denies the objective existence of the wavefunction entail it?
Perhaps. My post in the discussion section, and my subsequent comments, try (and fail!) to explain as clearly as I can what troubles me about MWI.
It’s true that an MWI non-collapsing wavefunction has ‘enough information’ to pin down the Born probabilities, and it’s also true that you can’t get the empirical predictions exactly right unless you simulate the entire wavefunction. But it still seems to me that in some weird sense the wavefunction contains ‘too much’ information, in the same way that simulating a classically indeterministic universe by modelling all of its branches gives you ‘too much information’.
I know what you mean, but as I’m sure you know it’s not mere perversity that has led many to accept “modeling all the branches” of the QM universe. In the case of a classically indeterministic universe, you can model just one indeterministic branch, but in the case of the QM universe you can’t do that, or you can’t do it anywhere near as satisfactorily. The “weirdness” of QM is precisely that aspect of it which (in the eyes of many) forces us to accept the reality of all the branches.
Finally, let me return to your original question:
Based on your previous replies to me, it’s evident that you both believe in, and have a fairly sophisticated understanding of, the idea that you can extract the empirical predictions of quantum mechanics from unitary evolution alone (with no hidden variables) and without ‘adding anything’ (like Many Minds or whatever).
Since one obviously does need to ‘add something’ (e.g. rules about collapse, or Bohmian trajectories) in order to obtain a ‘single universe’ theory, it sounds as though you’ve answered your own question. Or at least, it’s not clear to me what kind of answer you were expecting other than that. (I don’t understand how it helps or why it’s necessary to use a ‘formal expression of the theory of measurement’, or even what such a thing would mean.)
Every interpretation is “adding something.” Just because interpreters choose to bundle their extra mechanisms in vague English language “interpretations” rather than mathematical models does not mean they aren’t extra mechanisms. Copenhagen adds an incoherent and subjective entity called “the observer.” MWI adds a preposterous amount of mechanism involving an infinite and ever-exponentially-expanding number of completely unobservable clone universes. Copenhagen grossly violates objectivity and MWI grossly violates Occam’s Razor. Also, MWI needs a way to determine when a “world” splits, or to shove the issue under the rug, every bit as much as collapse theories need to figure out or ignore when collapse occurs. If as many “interpreters” like to claim QM itself is just the wavefunction, then collapse and world-splits are both extra mechanisms.
But QM is not just the wavefunction. QM is also the Born probabilities. The wavefunction predicts nothing if we do not square it to find the probabilities of the events we actually observe. Of all the interpretations, objective collapse adds the least to quantum mechanics as it is actually practiced. Everybody who uses QM for practical purposes uses the Born probabilities or the direct consequences thereof (e.g. spectra). Thus—despite the many who shudder at the nondeterminism of the universe and thus come up with interpretations like Copenhagen and MWI to try to turn inherent nondeterminism into mere subjective ignorance—the nondeterministic quantum event whereby a superposition of eigenvectors reduces to a single eigenvector (and the various other isomorphic ways this can be mathematically represented) is every bit as central to QM as the nominally deterministic wavefunction. The Born probabilities are not in any way “extra mechanism” they are central to QM. Even more central than the wavefunction, because all that we observe directly are the Born random events. The wavefunction we never observe directly, but only infer it as defining the probability distribution of the nondeterministic events we do observe.
Thus any interpretation of QM as it is actually practiced must take the Born probabilities as being at least as objective and physical as the wavefunction. If the Born probabilities are objective, we have objective collapse, and neither Copenhagen nor MWI are true.
Wikipedia has a bare-bones description of objective collapse:
http://en.wikipedia.org/wiki/Objective_collapse_theory
Further experimental evidence: if the Born probabilities do not represent an objective and physical randomness that is inherent to the universe, then the EPR/Bell/Aspect/et,. al. work tells us that FTL signaling (and more importantly a variety of related paradoxes, FTL signaling not itself being paradoxical in QM) is possible. QM is not special relativity. Special relativity can’t explain the small scale or even certain macroscale effects like diffraction that QM explains. Special relativity is just an emergent large-scale special case of QM (specifically of QFT), it is QM that is fundamental. QM itself, in the EPR/et. al. line of work, tells is that it is the objective and physical randomness inherent in the universe, not causal locality, that stands in the way of FTL signaling and its associated paradoxes.
There’s no mechanism to it other than the mechanism that every interpretation of QM already has for describing the evolution of non-macroscopic quantum systems. MWI just says that large systems and small systems aren’t separate magisteria with different laws.
“Worlds” and “branching” are epiphenomenal concepts; they’re simplifications of what MWI actually talks about (see Decoherence is Pointless).
It doesn’t matter whether branching occurs at a point of or at during some blob of time, probabilistic or otherwise, it’s a central part of MWI and you need an equation to describe when it happens. And that equation should agree with the Born probabilities up to our observational limits. Likewise for collapse in theories that invoke collapse. Otherwise it’s just hand-waving not science.
What is or is not a “branch” is unimportant. If you have read the link you’ll know that a “branch” is not a point mass but a blob spread out in configuration space. All MWI needs is “the probability density of finding oneself in point x in the wavefunction is the amplitude squared at that point”. It’s standard probability theory then to integrate over a “branch” to find your probability of being in that branch. But the only reason to care about “branches” is because the world looks precisely identical to an observer at every point in that branch.