rubi said:Well, I believe that experimenters can provide us with a bunch of numbers, but I don't really commit to anything beyond that. Apparently, something is really odd about nature, since the idea that we can assign numbers to all properties of its parts in a consistent way must be given up, and I have no idea what that implies for the interpretation of the measurement results. This is of course an interesting philosophical question, but physicists must accept it as a fact, just like they must accept the constancy of the speed of light.
I don't have a cut. It would be consistent with QM if the present me believes to have measured a bunch of numbers and the future me concludes that the present me was in a superposition of having measured one set of numbers and another set of numbers. That can happen if the observables that correspond to the knowledge of the present me and the future me don't commute. Hopefully decoherence comes to the rescue and ensures that the present me and the future me don't disagree so much.atyy said:So you still have a cut - why do you think this is different from the Heisenberg cut you reject?
rubi said:I don't have a cut. It would be consistent with QM if the present me believes to have measured a bunch of numbers and the future me concludes that the present me was in a superposition of having measured one set of numbers and another set of numbers. That can happen if the observables that correspond to the knowledge of the present me and the future me don't commute. Hopefully decoherence comes to the rescue and ensures that the present me and the future me don't disagree so much.
[emoji15] Ouch. Wouldn't it require a cut between the multiple "present you(s)" to arrive at the single later you?rubi said:I don't have a cut. It would be consistent with QM if the present me believes to have measured a bunch of numbers and the future me concludes that the present me was in a superposition of having measured one set of numbers and another set of numbers. That can happen if the observables that correspond to the knowledge of the present me and the future me don't commute. Hopefully decoherence comes to the rescue and ensures that the present me and the future me don't disagree so much.
Let's assume I can be described by quantum mechanics as well, just as any other kind of matter in the universe. Let's work in the Heisenberg picture. There is a time-independent quantum state ##\Psi##. Let's assume for simplicity that my knowledge at time ##t## of the measurement results is encoded by a single observable ##X(t)## for every ##t##. It might be that ##\Psi## is an eigenstate of ##X(10)##: ##X(10)\Psi = x\Psi##. The information of the future me (##t=10##) about the measurement results is encoded in the real number ##x##. However, it might be that ##[X(0),X(10)]\neq 0##, so they don't share a common basis of (generalized) eigenvectors and thus the vector ##\Psi##, expanded in the eigenbasis of ##X(0)## might be given by a superposition ##\Psi=\sum a_i \phi_i##. Of course, if the ##X(t)## commute, this isn't an issue.atyy said:Why doesn't the present you believe yourself to be in a superposition?
rubi said:Let's assume I can be described by quantum mechanics as well, just as any other kind of matter in the universe. Let's work in the Heisenberg picture. There is a time-independent quantum state ##\Psi##. Let's assume for simplicity that my knowledge at time ##t## of the measurement results is encoded by a single observable ##X(t)## for every ##t##. It might be that ##\Psi## is an eigenstate of ##X(10)##: ##X(10)\Psi = x\Psi##. The information of the future me (##t=10##) about the measurement results is encoded in the real number ##x##. However, it might be that ##[X(0),X(10)]\neq 0##, so they don't share a common basis of (generalized) eigenvectors and thus the vector ##\Psi##, expanded in the eigenbasis of ##X(0)## might be given by a superposition ##\Psi=\sum a_i \phi_i##. Of course, if the ##X(t)## commute, this isn't an issue.
I don't need a cut. I have a quantum state ##\Psi## and lots of observables that account for any question that I could ask. If some of these observables don't commute, then they can't have definite values at the same "time". Of course, it's very uncommon to include actual physicists into the description of the quantum system.Feeble Wonk said:[emoji15] Ouch. Wouldn't it require a cut between the multiple "present you(s)" to arrive at the single later you?
It doesn't explain anything. It just describes it. As I said earlier, I have no idea how to interpret the fact that nature prohibits us to describe it using a bunch of numbers that can be known simultaneously. I'm just saying that it is internally consistent, although it may seem pretty weird sometimes. QM has made many weird predictions in the past and all of them have been shown to be consistent with experiments.atyy said:Isn't that the reply for why your future self believes the present self to be in a superposition?
How does it explain why the present self believes the present self not to be in a superposition?
rubi said:It doesn't explain anything. It just describes it. As I said earlier, I have no idea how to interpret the fact that nature prohibits us to describe it using a bunch of numbers that can be known simultaneously. I'm just saying that it is internally consistent, although it may seem pretty weird sometimes. QM has made many weird predictions in the past and all of them have been shown to be consistent with experiments.
It doesn't need to believe that. The formalism says that the present me will use one of of the eigenvalues of ##X(0)## correpsonding to the eigenvectors ##\phi_i## as the information about the measurement results and if I were to repeat this experiment many times, this choice will be distributed according to the probabilities ##|a_i|^2##.atyy said:No, I don't mean "explain" in that sense. I would like to know where in the formalism it says that the present self believes itself not to be in a superposition.
rubi said:It doesn't need to believe that. The formalism says that the present me will use one of of the eigenvalues of ##X(0)## correpsonding to the eigenvectors ##\phi_i## as the information about the measurement results and if I were to repeat this experiment many times, this choice will be distributed according to the probabilities ##|a_i|^2##.
The observables ##X(t)## encode my knowledge of the measurement results. The measurement results themselves are contained in an observable ##A## corresponding the the apparatus. At every point in time, I believe to have obtained a measurement result. Quantum theory doesn't predict, which one. It's just that this knowledge isn't consistent over time unless the observables commute (which is hopefully ensured by decoherence).atyy said:But you never actually get a measurement result, do you? At least not from the viewpoint of future you?
bhobba said:That's impossible - utterly impossible. A cat can never - never be alive and dead. Cats are decohered to have definite position. The position of the constituent parts of a cat are different for alive and dead cats.
I'm clearly missing something critical here. My understanding was that the "warm and noisy" environment of the brain essentially guarantees decoherence and associated state reduction.rubi said:In principle, the matter that consitutes the physicist should be governed by the same laws as the rest of the universe and the knowledge of the physicist should somehow be encoded in the motion of the particles in his brain, so in principle it should be possible to eliminate the cut completely.
Thanks. But the question is, what do we mean by an "isolated system"? Standard approaches cannot explain what gives rise to non-unitary collapse. Under TI, unitary dynamics takes place in the absence of responses from absorbing systems. As soon as you have absorber response, you get the non-unitary von Neumann measurement transition.A. Neumaier said:Unitary dynamics for small quantum systems is extremely well disproved - people in quantum optics always have to work with dissipative, nonunitary dynamics to describe their small systems quantitatively. Thus it is an experimental fact that small quantum systems cannot be described by unitary evolution.
The reason is that they are almost never isolated enough to justify the unitary approximation. The state reduction or collapse accounts for that.
On the other hand, if one makes a quantum system big enough that its interaction with the neglected environment can be ignored (which is often the case in macroscopic situations) or can be described by classical external interaction terms then unitary dynamics is valid to a very good approximation.
Thus state reduction (= collapse) is not in contradiction with the unitary dynamics of an isolated system.
Did you see my discussion of Wallace's 'auxiliary condition' as ostensibly part of the 'bare' (Unitary-only) theory? http://arxiv.org/abs/1603.04845bhobba said:That I am not sure of.
Regarding Zurek it boils down to the typical modelling thing - there are hidden assumptions in Zurek for sure - but if they are 'benign' or not is the debate. An example is the decision theoretic approach of Wallace. I have read his book and its pretty tight if you accept using decision theory is a valid approach. For some (me include) its rather obvious - for others - it makes no sense. Personally I find Zurek just another interpretation - and not my favoured one.
Thanks
Bill
naima said:The sum of |dead><dead| and|alive><alive| is diagonal . Why are you talking about dead AND alive?
rkastner said:Did you see my discussion of Wallace's 'auxiliary condition' as ostensibly part of the 'bare' (Unitary-only) theory? http://arxiv.org/abs/1603.04845
Well, you can add them and if you properly normalize them, it corresponds to a statistical mixture of dead and alive.naima said:If we consider that we have |dead><dead| and|alive><alive| can we get an inner composition law thar generalises the superposition law?
Yes, the brain is a pretty classical object and there should be a lot of decoherence. That's why the phenomenon I described should be very unlikely. State reduction is only apparent, but that doesn't cause problems, since the relative frequencies predicted by state reduction and apparent state reduction are the same and only those are observable.Feeble Wonk said:I'm clearly missing something critical here. My understanding was that the "warm and noisy" environment of the brain essentially guarantees decoherence and associated state reduction.
It doesn't differ. It's the same phenomenon as in the Schrödinger cat experiment, but now applied to physicists at different times. In both situations, decoherence is supposed to account for the observed classicality.Regardless of your interpretational preference, I'm still confused by the idea that the "post-observation" physicist could retrospectively view his brain as being in superposition (with respect to the observation outcome) at the time of observation.
How does this differ from opening the box and seeing whether the cat is dead or alive, then closing the box and claiming that it's state is still unknown?
rubi said:Well, you can add them and if you properly normalize them, it corresponds to a statistical mixture of dead and alive.
rubi said:The observables ##X(t)## encode my knowledge of the measurement results. The measurement results themselves are contained in an observable ##A## corresponding the the apparatus. At every point in time, I believe to have obtained a measurement result. Quantum theory doesn't predict, which one. It's just that this knowledge isn't consistent over time unless the observables commute (which is hopefully ensured by decoherence).
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By the way, I'm not convinced that the domain of applicability of QM extends to such scenarios, but one can pretend it does and see what follows from it. In principle, the matter that consitutes the physicist should be governed by the same laws as the rest of the universe and the knowledge of the physicist should somehow be encoded in the motion of the particles in his brain, so in principle it should be possible to eliminate the cut completely. Of course, this is nowhere near practical. In quantum gravity, such considerations are forced upon us, because we are dealing with a fully constrained Hamiltonian system and all physics is supposed to arise from looking at correlations.
I understand that he proposes additional ways to add density matrices and it might be useful in some situations, but I don't see how it is relevant to the interpretation of QM. A density matrix contains the information about all probability distributions of the observables, but in order to obtain these distributions, it doesn't matter where this density matrix came from.naima said:Bhobba did not read the manko paper. Did you?
Manko gives a recipe to get all the ways to "add" the density matrices. the first is to add rhe density matrices. another corresponds to add the vectors. And between them you have other inner composition laws with various fringe visibility.
He uses a trick to manage the phases.
The week end is coming. Take the time to read it!
arxiv.org/pdf/quant-ph/0207033
Well, I put all matter on the quantum side, so there is nothing left on the "other side of the cut". The "knowledge of the measurement results" is just my way to avoid having to explain how information is encoded in the brain. As a toy model, we could certainly assume that the information about a spin measurement is encoded in the spin of a certain electron within some neuron. Light rays are reflected from the pointer of the measurement apparatus and hit the eye of the physicist. The matter of the eyes interacts with the brain matter and the brain might eventually store the information in the spin of some electron. This is almost certainly not how it works, but I'm not a neuroscientist and modeling the realistic way of how information is stored within the brain just makes the model more complex, but not conceptually different. The point is that if all matter in the universe is described on the quantum side, then nothing remains on the classical side, so there is no Heisenberg cut.atyy said:I don't think you have gotten rid of the cut, since you still refer to your "knowledge of the measurement results". So you need the concept of something which can have knowledge, by which you presumably don't include a single electron.
rubi said:I understand that he proposes additional ways to add density matrices and it might be useful in some situations, but I don't see how it is relevant to the interpretation of QM. A density matrix contains the information about all probability distributions of the observables, but in order to obtain these distributions, it doesn't matter where this density matrix came from.
rubi said:Well, I put all matter on the quantum side, so there is nothing left on the "other side of the cut". The "knowledge of the measurement results" is just my way to avoid having to explain how information is encoded in the brain. As a toy model, we could certainly assume that the information about a spin measurement is encoded in the spin of a certain electron within some neuron. Light rays are reflected from the pointer of the measurement apparatus and hit the eye of the physicist. The matter of the eyes interacts with the brain matter and the brain might eventually store the information in the spin of some electron. This is almost certainly not how it works, but I'm not a neuroscientist and modeling the realistic way of how information is stored within the brain just makes the model more complex, but not conceptually different. The point is that if all matter in the universe is described on the quantum side, then nothing remains on the classical side, so there is no Heisenberg cut.
All the things like POVM's, open quantum systems, and so on, aren't really a generalization of standard QM. They have an equivalent description in standard QM with a larger Hilbert space. So in order to discuss foundational issues, we can just discuss standard QM and then later take partial traces and so on if we want to restrict to subsystems. If we can clarify the interpretational issues in standard QM, we automatically clarify them for open quantum systems as well.naima said:I know that we can go on to decompose everything in term of vectors, to add them, to square them, to multiply each case by a probability, to add them again. It works very well. But...
No, a brain is just matter like everything else. And information isn't a primitive concept at all. These concepts don't have a special status. If there is no brain, then all the processes still happen. There is just nobody who think about them. For instance, there might be a Hamiltonian that describes the whole universe and it just doesn't make matter accumulate into things like brains. A brain is just a certain constellation of matter, just like a chair or a molecule, although a quite complex one. (Note that this has nothing to do with consciousness or so. I just describe all the matter in the universe within the same quantum theory, including the matter that makes up physicists. If this matter is governed by the laws of quantum mechanics as well, then this should certainly be possible.)atyy said:But you still need "brain" or "information" as something special. If there is no brain in the universe, then does the theory predict that anything happens?
rubi said:No, a brain is just matter like everything else. And information isn't a primitive concept at all. These concepts don't have a special status. If there is no brain, then all the processes still happen. There is just nobody who think about them. For instance, there might be a Hamiltonian that describes the whole universe and it just doesn't make matter accumulate into things like brains. A brain is just a certain constellation of matter, just like a chair or a molecule, although a quite complex one. (Note that this has nothing to do with consciousness or so. I just describe all the matter in the universe within the same quantum theory, including the matter that makes up physicists. If this matter is governed by the laws of quantum mechanics as well, then this should certainly be possible.)
You don't only have a wave function ##\Psi##, you also have observables ##\hat X\phi^{\hat X}_a = \lambda^{\hat X}_a\phi^{\hat X}_a## for all possible physical questions and you have the Born rule ##P(X\in A)=\int_A |\left<\phi^{\hat X}_a,\Psi\right>|^2\mathrm d a##. The wave function ##\Psi## contains all the data you need in order to obtain the answer to any (probabilistic) question you might ask. If you have a question to the system, you just choose the appropriate observable ##\hat X## and then the Born rule allows you to compute the probability for something happening. In order for something to happen, there need not be a human who observes it. I'm not using the MWI interpretation, there is only one world in my interpretation. I'm just saying that the state ##\Psi## allows me to calculate probabilities for all possible physical events. Of course only one of these events will ever happen, but if we accept that nature is intrinsically random, then we can't do better than to have a theory that calculates only probabilities and there is no underlying mechanism that selects one of them.atyy said:But how does this work? Let's say we have only a wave function of the universe, with deterministic unitary time evolution. What happens? Either nothing is happening since we only have a wave function, or we have many worlds since the wave function is a superposition and all branches happen.
I don't deny that Gleason's theorem is a great theorem, but it has nothing to do with decoherence. Decoherence is the mechanism that ensures that the probability distributions of QM don't show oscillatory behaviour, so we don't usually get interference patterns, unless we face a situation, where decoherence doesn't play a role. Decoherence is just standard QM of very large, unisolated systems.naima said:Gleason an Gleason/Busch theorems were a major step forward in QM.
They are talking about "events" that sum to Id. They have a scalar product and a norm (the trace norm).
Decoherence is not about vectors in the Hilbert space. Decoherence is about events.
rubi said:You don't only have a wave function ##\Psi##, you also have observables ##\hat X\phi^{\hat X}_a = \lambda^{\hat X}_a\phi^{\hat X}_a## for all possible physical questions and you have the Born rule ##P(X\in A)=\int_A |\left<\phi^{\hat X}_a,\Psi\right>|^2\mathrm d a##. The wave function ##\Psi## contains all the data you need in order to obtain the answer to any (probabilistic) question you might ask.
That's right, but it's not a problem of QM. The violation of Bell's inequality shows that it is in principle impossible to improve this situation (unless you want to exploit loopholes). It's not QM that hinders us to ask that question, but nature itself. So in some sense, QM is a theory that already achieves everything that a physical theory can possibly achieve. (Of course it's not the only theory that can achieve everything, but it's one of them.) QM just accepts it as a fact that nature forces these questions to be meaningless.stevendaryl said:That's not really true. There are probabilistic questions that don't have answers: "What is the probability that this electron has spin-up in the x-direction and the y-direction?" There are specific questions that you're allowed to ask in QM, and it answers all of those, but that's sort of tautological: It answers the questions that it can answer.
rubi said:You don't only have a wave function ##\Psi##, you also have observables ##\hat X\phi^{\hat X}_a = \lambda^{\hat X}_a\phi^{\hat X}_a## for all possible physical questions and you have the Born rule ##P(X\in A)=\int_A |\left<\phi^{\hat X}_a,\Psi\right>|^2\mathrm d a##. The wave function ##\Psi## contains all the data you need in order to obtain the answer to any (probabilistic) question you might ask. If you have a question to the system, you just choose the appropriate observable ##\hat X## and then the Born rule allows you to compute the probability for something happening. In order for something to happen, there need not be a human who observes it. I'm not using the MWI interpretation, there is only one world in my interpretation. I'm just saying that the state ##\Psi## allows me to calculate probabilities for all possible physical events. Of course only one of these events will ever happen, but if we accept that nature is intrinsically random, then we can't do better than to have a theory that calculates only probabilities and there is no underlying mechanism that selects one of them.
rubi said:That's right, but it's not a problem of QM. The violation of Bell's inequality shows that it is in principle impossible to improve this situation (unless you want to exploit loopholes). It's not QM that hinders us to ask that question, but nature itself. So in some sense, QM is a theory that already achieves everything that a physical theory can possibly achieve. (Of course it's not the only theory that can achieve everything, but it's one of them.) QM just accepts it as a fact that nature forces these questions to be meaningless.
stevendaryl said:It's not at all clear to me how much of the QM formalism is about the way nature is. The Born rule that says that "if you measure observable O you'll an eigenvalue with such-and-such a probability" is not really about nature. In nature, we don't have observables. Not directly, anyway. You set up an experiment and the result of the experiment is this or that macroscopically distinguishable state of a detector. So what you're observing is not (directly) any property at all of the system under investigation (an electron, for example). You're observing a property of a macroscopic object, the position of a pointer, or the location of a dark spot on a photographic film, etc. So, to me, the whole mathematical apparatus of Hermitian operators and their expectation values seems removed from what's really going on in nature. I'm not exactly sure what I would like in a quantum theory, but I think that there should be a way to formulate it that doesn't mention measurements or observables or a macroscopic/microscopic distinction. Those should be derived concepts, not primitives.
Well, if you like it better, I could have written "questions that the universe might have to decide upon". It's not necessary for some being to ask the questions in order to have the universe decide upon them. But if you are a being, made of matter, governed by the laws of QM, then the evolution of the universe (containing yourself) might make you become aware of the answer that the universe has assigned to these questions. The word "observable" is also not to be taken literally. It's just a name for the mathematical objects that refer to parts of the universe, whether they are observed or not.atyy said:But if you have the observables too, and you use words like "questions you might ask", then the "you" is still postulated as something that you need to know that is not defined by the wave function alone.
That's one way to phrase the Born rule, but you can also phrase it in a way that doesn't use the word measurement: "With such-and-such a probability, the eigenvalue ##\lambda## will be physically realized by nature."stevendaryl said:It's not at all clear to me how much of the QM formalism is about the way nature is. The Born rule that says that "if you measure observable O you'll an eigenvalue with such-and-such a probability" is not really about nature.
Observables refer to some parts of the universe. Of course, not all of these parts are accessible to humans, so humans can usually only learn about observables corresponding to macroscopic objects. But in the physical theory, observables are just how the correspondence between the theory and the real world is made, independent of whether humans can access them. The word "observable" is probably not very good.In nature, we don't have observables. Not directly, anyway. You set up an experiment and the result of the experiment is this or that macroscopically distinguishable state of a detector. So what you're observing is not (directly) any property at all of the system under investigation (an electron, for example). You're observing a property of a macroscopic object, the position of a pointer, or the location of a dark spot on a photographic film, etc.
Well, I think one can formulate the theory without mentioning words like measurement. We just have to choose our words more carefully. We just usually don't do this, because we are used to the physics slang. When I use these words, I don't really have their literal meaning in mind.So, to me, the whole mathematical apparatus of Hermitian operators and their expectation values seems removed from what's really going on in nature. I'm not exactly sure what I would like in a quantum theory, but I think that there should be a way to formulate it that doesn't mention measurements or observables or a macroscopic/microscopic distinction. Those should be derived concepts, not primitives.
Well, in BM, at least position is a primitive observable, although it can't be accessed directly. In many worlds, observables are avoided by just specifying a basis directly, which essentially corresponds to specifying a preferred set of observables. There always needs to be some correspondence between the physical theory and some parts of the universe, otherwise the theory can't make predictions about those parts. I use the word "observable" for this correspondence.stevendaryl said:Both Many-Worlds and Bohmian interpretations DO formulate QM without observables being primitives. I'm not completely satisfied with either of those, but they are more along the lines of what I would want, I think.
rubi said:That's one way to phrase the Born rule, but you can also phrase it in a way that doesn't use the word measurement: "With such-and-such a probability, the eigenvalue ##\lambda## will be physically realized by nature."
rubi said:Well, if you like it better, I could have written "questions that the universe might have to decide upon". It's not necessary for some being to ask the questions in order to have the universe decide upon them. But if you are a being, made of matter, governed by the laws of QM, then the evolution of the universe (containing yourself) might make you become aware of the answer that the universe has assigned to these questions. The word "observable" is also not to be taken literally. It's just a name for the mathematical objects that refer to parts of the universe, whether they are observed or not.
stevendaryl said:I don't think it makes any sense to phrase it that way. Suppose I put an electron into a state state that is spin-up in the z-direction. We can compute a probability of \frac{1}{2} associated with the statement "The electron has spin-up in the x-direction". How long do I have to wait for that statement to be "physically realized by nature"? It's never going to be physically realized. If I don't act on the electron, it'll continue to be spin-up in the z-direction forever.
atyy said:But if you do that, then you the universe will simultaneously decide upon a particle's position and momentum, since the wave function allows you to calculate the distribution of both observables.
rubi said:The following answer applies to both of you:
This is where the consistency requirement comes in. The universe doesn't decide on all these facts individually, but it chooses one history among a set of consistent histories. So if the universe has decided for a history that has a definite spin-z value at ##t=t_1##, then it didn't decide for a history, in which spin-x had a value at ##t=t_1##. If the universe has decided for a history that had a well-defined position at ##t=t_1##, then it didn't decide for a history with a well-defined momentum at ##t=t_1##.
If you're interested, there is a very nice book called "Consistent Quantum Theory" by Robert Griffiths.stevendaryl said:Okay, I do not know enough about consistent histories to make an intelligent argument
That depends on the time. The electron has spin-z up at ##t=t_1##. Then there are several histories in which the electron has spin-x up at later time ##t=t_2##, but during the time evolution, the probabilities might have changed. If the time evolution doesn't touch the electron anymore, then you are right.I put an electron into a state of being spin-up in the z-direction. So I have a probability of \frac{1}{2} of it being spin-up in the x-direction. The meaning of that is that for all histories in which the electron has a spin in the x-direction (which might be none), half of them have spin-up and half have spin-down.
rubi said:The following answer applies to both of you:
This is where the consistency requirement comes in. The universe doesn't decide on all these facts individually, but it chooses one history among a set of consistent histories. So if the universe has decided for a history that has a definite spin-z value at ##t=t_1##, then it didn't decide for a history, in which spin-x had a value at ##t=t_1##. If the universe has decided for a history that had a well-defined position at ##t=t_1##, then it didn't decide for a history with a well-defined momentum at ##t=t_1##.
rubi said:If you're interested, there is a very nice book called "Consistent Quantum Theory" by Robert Griffiths.
I'm not sure if I understand what you mean by "weaker sense of reality" here. Could you expand on that?atyy said:I certainly recognize a weaker sense of reality as a reasonable approach to solving the measurement problem.
Feeble Wonk said:I'm not sure if I understand what you mean by "weaker sense of reality" here. Could you expand on that?
atyy said:consistent histories does not admit a single fine grained reality
So, if I'm understanding this properly, this theory would suggest that Nature is fundamentally deterministic, but not fully predictable even in principle. Correct?atyy said:However, the coarse grained set is not obtainable by coarse graining the fine grained set. A way to escape this is to allow probabilities that are negative or greater than one: http://arxiv.org/abs/1106.0767 (I'm not advocating this solution, but this paper has a good explanation of the problem).
Feeble Wonk said:So, if I'm understanding this properly, this theory would suggest that Nature is fundamentally deterministic, but not fully predictable even in principle. Correct?
No, Wallace doesn't bypass the problem. He just helps himself to already disjoint Hilbert space descriptions as ostensibly part of the 'bare theory'. This fails to account for the emergence of classical distinguishability--i.e, 'system' as distinct from its 'environment'. And it wrongly describes contingent information (the empirical situation at hand) as part of the pure theory.bhobba said:'However, classicality is implicitly contained in 2 and 3 through the partitioning of the universal degrees of freedom into separable, localized substructures interacting via Hamiltonians that do not re-entangle them, so (given U-O) one has to put in classicality to get classicality out'
That's the factorisation issue. Its a legit issue but as I have said many times far too much is made of it IMHO. We do the same thing in classical mechanics for example but no one jumps up an down about that.
That said I have read Wallaces book and he uses an approach based on histories that seems to bypass it.
Thanks
Bill
