Quantum Physics Interpretation
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Quantum Physics Interpretation
Which quantum physics interpretation do you favor the most?
I love the informationbased one. (Does it has a name?)
FYI, here's "the most embarrassing graph in modern physics"
(P.S. I know this is NOT news, just want to know your interpretation.)
I love the informationbased one. (Does it has a name?)
FYI, here's "the most embarrassing graph in modern physics"
(P.S. I know this is NOT news, just want to know your interpretation.)
George Carlin wrote:Think of how stupid a average person is, and realize half of them are stupider than that.
Re: Quantum Physics Interpretation
I like Everett's, preferred it ever since 3rd year QM.
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Re: Quantum Physics Interpretation
GeoffreyY wrote:Which quantum physics interpretation do you favor the most?
I love the informationbased one. (Does it has a name?)
FYI, here's "the most embarrassing graph in modern physics"
(P.S. I know this is NOT news, just want to know your interpretation.)
Is the fact that it adds up to more than 100% a deliberate QP joke? Probably being thick here...
How can I think my way out of the problem when the problem is the way I think?
Re: Quantum Physics Interpretation
tomandlu wrote:GeoffreyY wrote:Which quantum physics interpretation do you favor the most?
I love the informationbased one. (Does it has a name?)
FYI, here's "the most embarrassing graph in modern physics"
(P.S. I know this is NOT news, just want to know your interpretation.)
Is the fact that it adds up to more than 100% a deliberate QP joke? Probably being thick here...
I suppose they people to give multiple answers.
George Carlin wrote:Think of how stupid a average person is, and realize half of them are stupider than that.
Re: Quantum Physics Interpretation
See my sig.
(I went with manyworld.)
(I went with manyworld.)
 doogly
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Re: Quantum Physics Interpretation
Consistent histories. It's essentially Copenhagen for grown ups though.
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Re: Quantum Physics Interpretation
doogly wrote:Consistent histories. It's essentially Copenhagen for grown ups though.
I agree with this sentiment, and voted the same way. I'll admit I'm sympathetic towards many worlds, though.
Re: Quantum Physics Interpretation
schrodingasdawg wrote:doogly wrote:Consistent histories. It's essentially Copenhagen for grown ups though.
I agree with this sentiment, and voted the same way. I'll admit I'm sympathetic towards many worlds, though.
Is there a good site that covers the interpretations and their various pros/cons?
How can I think my way out of the problem when the problem is the way I think?
Re: Quantum Physics Interpretation
Where's the "shut up and calculate" interpretation?... oh, right, Everett...
Our universe is most certainly unique... it's the only one that string theory doesn't describe.

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Re: Quantum Physics Interpretation
tomandlu wrote:Is there a good site that covers the interpretations and their various pros/cons?
I'm not aware of any. I think such a site would be a great idea though, if it could be done impartially.
Re: Quantum Physics Interpretation
Tchebu wrote:Where's the "shut up and calculate" interpretation?... oh, right, Everett...
Everett is the exact opposite of 'shut up and calculate', it gives you no prescription to make calculations!
I voted for the statistical interpretation, but I could just has easily have gone with consistent histories. My intuition is strongly that eventually an information theoretical interpretation will happen, but no one yet has managed it.
Re: Quantum Physics Interpretation
What *is* an interpretation of QM?
I'm a mathematician, rather than a physicist, so that may bias my thinking, but I was of the opinion that QM (and physics, generally) was basically just maths  you put some numbers in, do the relevant calculations, and you get some numbers out that tell you what's supposed to happen next. None of these interpretation differ on what those calculations are or what they predict (I assume), so what does it mean to believe one particular interpretation over another?
I'm a mathematician, rather than a physicist, so that may bias my thinking, but I was of the opinion that QM (and physics, generally) was basically just maths  you put some numbers in, do the relevant calculations, and you get some numbers out that tell you what's supposed to happen next. None of these interpretation differ on what those calculations are or what they predict (I assume), so what does it mean to believe one particular interpretation over another?
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Re: Quantum Physics Interpretation
My uninformed understanding is that "interpretation" covers the nonobservable parts. Whether you believe the wavefunction is really "out there", if you believe collapse is real or an artifact of your splitting consciousness, etc. Philosophy, in a sense.
Re: Quantum Physics Interpretation
eternauta3k wrote:My uninformed understanding is that "interpretation" covers the nonobservable parts. Whether you believe the wavefunction is really "out there", if you believe collapse is real or an artifact of your splitting consciousness, etc. Philosophy, in a sense.
As an outsider, this is always my worry with QP. Given the waveparticle duality, it seems suspicious that every time physicists look for evidence to validate a particular theory, they keep finding the behaviour or particle they're looking for. It sometimes looks as though the universe is playing tricks on us, and rather clever ones at that.
How can I think my way out of the problem when the problem is the way I think?
 doogly
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Re: Quantum Physics Interpretation
When you say, "given wave particle duality," do you have any idea what you're talking about?
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Keep waggling your butt brows Brothers.
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Re: Quantum Physics Interpretation
What *is* an interpretation of QM?
I'm a mathematician, rather than a physicist, so that may bias my thinking, but I was of the opinion that QM (and physics, generally) was basically just maths  you put some numbers in, do the relevant calculations, and you get some numbers out that tell you what's supposed to happen next. None of these interpretation differ on what those calculations are or what they predict (I assume), so what does it mean to believe one particular interpretation over another?
An interpretation is a different set of axioms that leads to the same (or very similar) mathematical structure. Sometimes its even a very different formal structure. In Von Neumann axiomatic quantum mechanics, an explicit postulate exists to tell us how to turn the mathematical structure (the wavefunction) in to actual predictions. Generally interpretations modify that axiom.
Re: Quantum Physics Interpretation
tomandlu wrote:Is there a good site that covers the interpretations and their various pros/cons?
The Wikipedia page on Interpretations of quantum mechanics gives brief descriptions of the main interpretations, with links to more indepth pages.

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Re: Quantum Physics Interpretation
Consistence Histories and Modal are nice, in that there's no "special" thing going on with respect to "collapsing a wave".
But until there's a unified consistent model covering everything from the (oddly named) "quantum" world to astrophysical distances and properties I'll just assume we're missing something and just say I've no preferred model.
As for what an "interpretation" is, I've never seen it nearly as useless as some think of it. It's a structure that should hopefully inform thought and real experiments. I mean, if multiple worlds is real then maybe there's some way to prove it, and so thinking along those lines can hopefully produce a workable experiment to show one way or another. After all, just because we've equations that produce good results doesn't mean we're "right". That's what a professor told Max Planck upon him entering as a physics major. Or rather as Feynman said (I think it was Feynman? Maybe not, please correct me) [In physics] "you can never prove that anything is right, only that it is not wrong."
But until there's a unified consistent model covering everything from the (oddly named) "quantum" world to astrophysical distances and properties I'll just assume we're missing something and just say I've no preferred model.
As for what an "interpretation" is, I've never seen it nearly as useless as some think of it. It's a structure that should hopefully inform thought and real experiments. I mean, if multiple worlds is real then maybe there's some way to prove it, and so thinking along those lines can hopefully produce a workable experiment to show one way or another. After all, just because we've equations that produce good results doesn't mean we're "right". That's what a professor told Max Planck upon him entering as a physics major. Or rather as Feynman said (I think it was Feynman? Maybe not, please correct me) [In physics] "you can never prove that anything is right, only that it is not wrong."
Re: Quantum Physics Interpretation
I do find it interesting that Copenhagen was the most popular amongst the interviewed groups; I've never been a big fan of waveform collapse (especially the requirement of interacting with a 'classical' object, whatever that is), especially when coupled with the quantum eraser (I can uncollapse it?).
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Re: Quantum Physics Interpretation
PM 2Ring wrote:tomandlu wrote:Is there a good site that covers the interpretations and their various pros/cons?
The Wikipedia page on Interpretations of quantum mechanics gives brief descriptions of the main interpretations, with links to more indepth pages.
John Gribbin has a book on the subject, aptly titled Schroedinger's Kittens, which would be a nice supplement to browsing the web for the sufficiently curious. He's a very good writer and studied Physics at the graduate level.
Re: Quantum Physics Interpretation
But until there's a unified consistent model covering everything from the (oddly named) "quantum" world to astrophysical distances and properties I'll just assume we're missing something and just say I've no preferred model.
Why does it have to be unified? Lets say Weinberg is right, and GR IS asymptotically safe. That means our existing standard model+GR works great without changing anything why should whether or not gravity is asymptotically safe affect our ability to interpret quantum mechanics?
John Gribbin has a book on the subject, aptly titled Schroedinger's Kittens, which would be a nice supplement to browsing the web for the sufficiently curious. He's a very good writer and studied Physics at the graduate level.
I've only skimmed Gribbin's book, but as I recall its entirely about the positives of many worlds, and never discusses all the problems inherent in the interpretation.
I do find it interesting that Copenhagen was the most popular amongst the interviewed groups; I've never been a big fan of waveform collapse (especially the requirement of interacting with a 'classical' object, whatever that is), especially when coupled with the quantum eraser (I can uncollapse it?).
Partly its a bias toward what is taught. Several friends of mine report teaching a course from Bob Griffith's consistent histories book, which lead to whole departments full of students who think its obviously correct.
I'm surprised by people who find many world's plausible. I think its because they've never tried to do calculations with it. Take the Von Neumann axioms, get rid of the measurement axiom, and actually try to calculate something. You will not get very far.
Re: Quantum Physics Interpretation
doogly wrote:When you say, "given wave particle duality," do you have any idea what you're talking about?
I think so. The physical properties of photons change according to how you examine them (with the added fun that a single photon can produce observable wavelike interference, even though that shouldn't be possible without multiple particles). If 'stuff' changes its behaviour and properties according to how you study it, then how reliable are our observations?
Do we 'understand' this basic contradiction? My understanding is 'no', and if that's the case, can we reliably say we understand the implications? My instinct (and that's all it is) is to wonder if there's some fundamental aspect of QP, both weird and simple, that has not yet been understood (by a sortof QP Darwin, as it were). I'm not suggesting that QP is wrong or invalid, and it's hardly shocking to suggest that the theory is incomplete  but perhaps that incompleteness is not in the details but at a more primary level? Can we be certain that we're not a bunch of blind men trying to decide what an elephant is? We're getting the details right, but missing the overall picture.
How can I think my way out of the problem when the problem is the way I think?
Re: Quantum Physics Interpretation
PM 2Ring wrote:tomandlu wrote:Is there a good site that covers the interpretations and their various pros/cons?
The Wikipedia page on Interpretations of quantum mechanics gives brief descriptions of the main interpretations, with links to more indepth pages.
Ah  that's helpful. Many thanks. I had the odd notion last night of producing a Top Trumps/Magiclike carddeck for the different interpretations  "I'm playing von Neumann", "curses, you've collapsed the wavefunction, thus invalidating my Stochastic interpretation card".
How can I think my way out of the problem when the problem is the way I think?
Re: Quantum Physics Interpretation
SU3SU2U1 wrote:I'm surprised by people who find many world's plausible. I think its because they've never tried to do calculations with it. Take the Von Neumann axioms, get rid of the measurement axiom, and actually try to calculate something. You will not get very far.
The calculations we do don't depend on the interpretation we choose... it's still just linear operators acting on a Hilbert space.
What I meant when I said it's the "shut up and calculate" approach is that it literally follows the math of operators on a hilbert space evolving according to a hamiltonian, without any magic like wavefunction collapse.
Maybe I'm misunderstanding some claim that manyworlds makes?
In either case I don't think ease of calculations affects the plausibility of any theory at all. GR equations are obnoxiously hard to solve, but that doesn't make the description of gravity it provides any less compelling.
Our universe is most certainly unique... it's the only one that string theory doesn't describe.
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Re: Quantum Physics Interpretation
It seems to me that without collapse you're dragging along an alternate universe. With collapse, after I prepare a beam of polarized atoms, I have a bunch of polarized atoms. Without collapse, my whole lab/city/light cone is in a quantum superposition of states (but I only really care about one).Tchebu wrote:What I meant when I said it's the "shut up and calculate" approach is that it literally follows the math of operators on a hilbert space evolving according to a hamiltonian, without any magic like wavefunction collapse.
Again, uninformed opinion.
Re: Quantum Physics Interpretation
The calculations we do don't depend on the interpretation we choose...
Of course they do! Compare working with Hamilton's least action principle and Newtonian mechanics.
it's still just linear operators acting on a Hilbert space.
Wavefunctions and linear operators on a Hilbert space don't give you any predictions! To make predictions, you need an additional postulate, something like "when I make a measurement, I always get an eigenvalue with probability proportional to the amplitude of the wavefunction squared." Everett said "explicitly referencing measurement is causing all kinds of headaches. Maybe, we don't need that postulate, get rid of it and we can figure out some new way to make predictions," but no one has actually figured out HOW.
Re: Quantum Physics Interpretation
After measurement, my measuring device is described by a density matrix, which is diagonal in the basis corresponding to the possible measurement outcomes. So essentially the state is a classical probabilistic ensemble. This is exactly the statement that "I always get an [outcome corresponding to an] eigenvalue with probability proportional to the amplitude of the wavefunction squared"...
Fair point on the Newton's laws vs Least Action Principle though.
Fair point on the Newton's laws vs Least Action Principle though.
Our universe is most certainly unique... it's the only one that string theory doesn't describe.
 doogly
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Re: Quantum Physics Interpretation
This sounds like magic at best and shenanigans at worst. There is a preferred basis (one strike) in which a quantum mechanical probabilities have become classical probability ensembles (two), which takes place after measurement (which I thought MWI people hated having a special role for? third.)
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Re: Quantum Physics Interpretation
To add to what Doogly said, you also are begging the question. Without additional postulates, how did you construct the density matrix in the first place?
In particular, you use the Born probability axiom to construct the fact that expectation of an observable is trace(density matrix*observable operator). So yes, assuming a construction built on Born probabilities you can show that you recover the Born probabilities.
In particular, you use the Born probability axiom to construct the fact that expectation of an observable is trace(density matrix*observable operator). So yes, assuming a construction built on Born probabilities you can show that you recover the Born probabilities.
Re: Quantum Physics Interpretation
By measurement, I mean a process described by the usual unitary time evolution of the measured system coupled to the measurement apparatus which evolves a state
(aa>+bb>+...)something>
into the entangled state
aa>A>+bb>B>+...
the density matrix is then simply the density matrix which describes the resulting state of the measurement apparatus alone. This density matrix, by definition, is
<i(aa>A>+bb>B>+...)(...+b*<B<b+a*<A<a)i>
summed over i, which runs over a,b,... so this is just
diag{a^2, b^2, ...}
which corresponds to a statistical ensemble of states, each of which corresponds to having measured a specific eigenstate of the measured system. And the weights of the resulting outcomes in this ensemble happen to be the mod squares of the coefficients in the original measured state. This happens as a result of pure unitary time evolution and not magic.
(aa>+bb>+...)something>
into the entangled state
aa>A>+bb>B>+...
the density matrix is then simply the density matrix which describes the resulting state of the measurement apparatus alone. This density matrix, by definition, is
<i(aa>A>+bb>B>+...)(...+b*<B<b+a*<A<a)i>
summed over i, which runs over a,b,... so this is just
diag{a^2, b^2, ...}
which corresponds to a statistical ensemble of states, each of which corresponds to having measured a specific eigenstate of the measured system. And the weights of the resulting outcomes in this ensemble happen to be the mod squares of the coefficients in the original measured state. This happens as a result of pure unitary time evolution and not magic.
Our universe is most certainly unique... it's the only one that string theory doesn't describe.
Re: Quantum Physics Interpretation
This isn't strictly true, in general there will always be offdiagonal elements of varying (small) sizes.
Also, as mentioned above, using a density matrix construct is question begging, as its build on the Born probabilities.
Also, as mentioned above, using a density matrix construct is question begging, as its build on the Born probabilities.
Re: Quantum Physics Interpretation
Yeah, of course, but those offdiagonal terms simply indicate the imperfection of the measurement and can be made arbitrarily small depending on the specifics of the coupling between the systems. It's essentially the same as perfect voltmeters being impossible because they always have finite resistance.
I'm not sure what you mean by the density matrix being built on Born probabilities? I'm not saying "we know we have to get these probabilities so my density matrix is going to be that", rather I'm saying that such a matrix can be achieved through unitary time evolution through an appropriate coupling of the studied system to some suitable measurement apparatus. From there the only probabilities are those given by the density matrix but they can be shown to be equal to the Born probabilities.
Unless you mean that the interpretation of the matrix entries as being probabilities of any sort at all rely on interpreting inner products as being probabilities of outcomes?
I'm not sure what you mean by the density matrix being built on Born probabilities? I'm not saying "we know we have to get these probabilities so my density matrix is going to be that", rather I'm saying that such a matrix can be achieved through unitary time evolution through an appropriate coupling of the studied system to some suitable measurement apparatus. From there the only probabilities are those given by the density matrix but they can be shown to be equal to the Born probabilities.
Unless you mean that the interpretation of the matrix entries as being probabilities of any sort at all rely on interpreting inner products as being probabilities of outcomes?
Our universe is most certainly unique... it's the only one that string theory doesn't describe.

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Re: Quantum Physics Interpretation
Tchebu wrote:Unless you mean that the interpretation of the matrix entries as being probabilities of any sort at all rely on interpreting inner products as being probabilities of outcomes?
Well, think about it this way. Normally, when you do quantum mechanics, you have a bunch of operators that represent observables instead of numbers. But we measure numbers, not operators, so we need a rule for translating the operators into expected values. The state, together with the Born rule and projection postulate—which really just define what the state actually means—give us this rule.
In many worlds, you say that this very state is the underlying reality, but that the measurement postulates which gave it meaning in the first place don't hold—at least not at a fundamental level. In some way or other, the density matrix describes an underlying reality, and in some cases becomes approximately diagonal in a particular basis. But then, since the measurement postulates are not assumed, why should its entries be interpreted as probabilities for anything? It's just "the underlying, unitarily evolving reality," with no connection between this underlying reality and the world we experience postulated. Somehow, the advocates of the many worlds theory have to demonstrate that the density matrix can be interpreted as probabilities, and how it is that this interpretation comes about by dynamics alone.
I know there are folks working on this. David Wallace and some others claim to get the Born rule through decision theory, but I think this is beside the point. If you're going to derive a rule in physics, the decisions made by rational agents seems like a red herring.
Re: Quantum Physics Interpretation
Fair enough, I understand the objection now and it's a fair one. I would point out thought that when we "measure numbers", we're really making statements like "I saw the light on my device turn green, which is a configuration that results from being coupled to eigenstate with eigenvalue +1/2".
Now what if we assume that density matrices represent statistical ensembles. This assumption turns out to be equivalent to the Born rule, but at least now we get actual statistical probabilities in an ensemble of states along with a dynamical description of how a pure state evolves into such an ensemble, which to me is somewhat more satisfying than just saying "the wavefunction collapses randomly into one of these eigenstates".
In other words I'll concede that MWI doesn't reduce the number of assumptions required, but I still stand by its plausibility and definitely don't think it complicates the calculations any more than digging deep into the details of how a voltmeter functions does.
Now what if we assume that density matrices represent statistical ensembles. This assumption turns out to be equivalent to the Born rule, but at least now we get actual statistical probabilities in an ensemble of states along with a dynamical description of how a pure state evolves into such an ensemble, which to me is somewhat more satisfying than just saying "the wavefunction collapses randomly into one of these eigenstates".
In other words I'll concede that MWI doesn't reduce the number of assumptions required, but I still stand by its plausibility and definitely don't think it complicates the calculations any more than digging deep into the details of how a voltmeter functions does.
Our universe is most certainly unique... it's the only one that string theory doesn't describe.
Re: Quantum Physics Interpretation
Now what if we assume that density matrices represent statistical ensembles. This assumption turns out to be equivalent to the Born rule
It turns out that its very hard to make the assumption you want without using EXACTLY the Born rule, in the form used in the ensemble/statistical interpretation of quantum. So you basically are championing a decoherence based approach to a Ballentine type ensemble interpretation.
This is perfectly reasonable, but not many worlds many worlds/Everett is a SPECIFIC thing, the idea being that we can just ax the measurement postulate.
There are many interpretations between Copenhagen and Everett.
In other words I'll concede that MWI doesn't reduce the number of assumptions required, but I still stand by its plausibility
This is incoherent, because the definition of many worlds is the set of Von Neumann axioms  measurement. If you aren't talking about that specific set of axioms, you aren't discussing many worlds anymore. So your sentence is basically "Many worlds doesn't work, but its plausible."
Re: Quantum Physics Interpretation
Fair enough, I didn't realize the term was that specific. Thanks for the chance to flesh out my thoughts better.
Our universe is most certainly unique... it's the only one that string theory doesn't describe.
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Re: Quantum Physics Interpretation
SU3SU2U1 wrote:Now what if we assume that density matrices represent statistical ensembles. This assumption turns out to be equivalent to the Born rule
It turns out that its very hard to make the assumption you want without using EXACTLY the Born rule, in the form used in the ensemble/statistical interpretation of quantum. So you basically are championing a decoherence based approach to a Ballentine type ensemble interpretation.
This is perfectly reasonable, but not many worlds many worlds/Everett is a SPECIFIC thing, the idea being that we can just ax the measurement postulate.
There are many interpretations between Copenhagen and Everett.
Hm, I've never heard MWI being defined so narrowly. I mean, MWI people do *hope* to kill the measurement axiom and recover the Born probabilities "naturally", rather than them being more or less an assumed constant, but I haven't heard them describe theories where the Born probabilities are assumed as something other than MWI. MWI is just the family of theories where (macroscopic) reality is multivalued (for some reasonable definitions of the term).
I assume this is just a case of some people constructing a bigger tent out of the term, and is probably part of why you and a couple of other posters on this board are so hostile to "MWI"  you've constrained it to a very narrow definition, which doesn't yet have the theoretical underpinning it strives for, and then assume that everyone else mentioning the term means the same thing.
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Re: Quantum Physics Interpretation
Hm, I've never heard MWI being defined so narrowly.
This is probably a technical literature vs. popular description issue. Every paper ever written on the Everett interpretation is referring to the Von Neumann axioms with the measurement axiom removed. Some paper add more postulates to try to assume in a new version of the Born probabilities, such interpretations usually go by 'manyminds', although there may be other variants I am unaware of. Also, the additional work needed to recover Born leads to postulates that most find ludicrous (infinite sets of potential minds that section off as the "worlds" branch).
Also, a second issue is that I think that perhaps quantum mechanics is being taught fairly poorly. All calculations and no theory I recently taught a class of seniors who had already been through three semesters of quantum and (as a class working together!) they couldn't come up with the quantum axioms! Also, with single particle problems they repeatedly confuse space (half of space/time) with the Hilbert space. Ironically, the students who seem to have a clue are all CS majors. The quantum information course must be doing a great job perhaps the nature of the subject forces you to think more about how the theory works.
I'm starting to wonder if maybe I should spend a day or two on Bohmian mechanics when I teach intro quantum, so students understand what an interpretation looks like.
I haven't heard them describe theories where the Born probabilities are assumed as something other than MWI. MWI is just the family of theories where (macroscopic) reality is multivalued (for some reasonable definitions of the term).
Its very hard to assume the Born probabilities and still end up with "mutlivalued reality" as a necessary implication. Lets use the above conversation as an example
Tchebu's idea of using decoherence had him suggesting a postulate along the lines of "a diagonal density matrix corresponds to a classical probability ensemble." This does something important: we can no longer describe single systems, only ensembles of systems (otherwise you couldn't define the classical probability ensemble). So now, the natural probability interpretation involves what fraction of an ensemble ends up in state A and what fraction ends up in state B.
We COULD (well, maybe, its actually a bit tricky to stay consistent with quantum mechanics. Mike Weissman at UIUC has a nice attempt but it requires modifying the Schroedinger equation) just modify the concept of the classical probability ensemble to insist on multiple outcomes (roll a single die, get a 1,2,3,4,5 AND 6), but why would we?
I assume this is just a case of some people constructing a bigger tent out of the term, and is probably part of why you and a couple of other posters on this board are so hostile to "MWI"  you've constrained it to a very narrow definition, which doesn't yet have the theoretical underpinning it strives for
My hostility comes from the fact that these "big tent" definitions are almost always incoherent when you get down to the details. People who should know better (physicists by training!) haven't actually formalized their theory and just assume everything works out. They have some weird blindspot when it comes to quantum theories.
The serious Everett type proponents consistently grapple with the problem of their axioms (Deutsch, Wallace,etc) and readily admit in conversation that if the problem is unsolvable the theory is deadonarrival. A colleague of mine believes so strongly in many worlds that he has said that quantum mechanics PREDICTS space must be on a lattice (if space isn't continuous, you can recover Born probabilities in a finite number of measurements if you make some other weak assumptions). Thats great! I have no hostility towards people who have actually thought it through.
Re: Quantum Physics Interpretation
We COULD (well, maybe, its actually a bit tricky to stay consistent with quantum mechanics. Mike Weissman at UIUC has a nice attempt but it requires modifying the Schroedinger equation) just modify the concept of the classical probability ensemble to insist on multiple outcomes (roll a single die, get a 1,2,3,4,5 AND 6), but why would we?
I was thinking more along the lines of rolling a die and then saying that a neighborhood in phase space around the initial state of the die in our hand evolves towards six smaller by very distinct regions each corresponding to one of the possible outcomes. It doesn't seem completely nonsensical to say that the final state of the die after one throw is described by a probability distribution on phase space even if we only perform one throw. I guess I shouldn't have said "statistical ensemble" but rather "probability distribution".
What I then suggest is to replace the Born rule by the assumption (which I'm willing to recognize as necessarily being equivalent to the Born rule) that the correct quantum analogue to a classical probability distribution on the system's phase space is a diagonal density matrix on the system's Hilbert space. This statement makes sense for single measurements to the exact same extent that talking about probabilities for single dice rolls does. The only difference is that the density matrix of the measurement apparatus arises as a result of quantum entanglement with another system and not a highly chaotic classical evolution of a small region of phase space.
Now this is where people might get upset at applying probabilities to single outcomes and that's where we can toss in the idea of many worlds ACTUALLY branching out to let this probability distribution manifest itself as a statement about the statistics of an actual ensemble.
Our universe is most certainly unique... it's the only one that string theory doesn't describe.
Re: Quantum Physics Interpretation
I guess I shouldn't have said "statistical ensemble" but rather "probability distribution".
Its basically the same thing, if you take the frequentist definition of probability. Its still the case that probability distributions are features of multiple trials, not single trials. I recommend reading Ballentine's Intro Quantum book. Its very good pedagogically (he 'derives' the Schroedinger equation from the postulates + Galilean invariance), and its a solid exposition of the interpretation he champions.
Now, if you want to use a more Bayesian definition of probability (which seems somewhat natural to many, as 'wavefunction collapse' looks a lot like updating a probability distribution with new info) you run into all sorts of trouble, essentially because of the nohiddenvariable theorems.
Either way you are defining the wavefunction as a fundamentally statistical object this is very different from many worlds where the wavefunction IS the particle, and the 'probabilities' arise in some dynamic fashion. We have moved a bit beyond unitary evolution.
One important thing: the decoherence postulate DOES do one important thing for us it combines the correspondence principal and the measurement postulates into one statement. There are many reasons this is hugely important for defining quantum in a noncircular fashion.
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