In general that's true, but in my view of Bohmian mechanics those two types of incompleteness are closely related. See the paper linked in my signature.DarMM said:I think this mixes up the incompleteness of the Standard Model (mass and coupling parameters) with the incompleteness of Quantum Theory in general (measurement problem, meaning of contextuality).
microsansfil said:is it not possible to verify the completeness of any mathematical axiomatization of quantum mechanics?
The measurement problem is a problem in QM that interpretations try to solve, but it is a real issue as much as the masses and couplings. It might be the case that the explanation of couplings and masses is related to the measurement problem or it might not, from where we stand now they are two separate problems.ftr said:SM is part of QM, measurement problem is an "interpretation" issue but mass and coupling is real/clear issue. I think understanding will come when the later is addressed first.
Some examples of complete theories are: https://en.wikipedia.org/wiki/Complete_theorybhobba said:It is not possible to verify the axiomatic completeness of any system as strong as arithmetic.
Demystifier said:I use it colloquially.
What is the mathematical description of the collapse process?jambaugh said:Yes the wave function collapses
If the quantum state is epistemic then throwing away one branch doesn't correspond to a physical process which needs a more detailed mathematical description, it's simply (generalized) Bayesian updating.Avodyne said:I don't see why it matters whether one views the quantum state as epistemic or ontological.
Well, for quantum field theory you may need the thermal interpretation, where observers can be part of the system and collapse happens as an approximate effect due to the ignored environment.Avodyne said:Lüders rule, as I understand it (see below), seems to require an observer outside the system being measured. This is not the case in QFT, where observers and everything else are comprised of excitations of the quantum fields.
http://philsci-archive.pitt.edu/4111/1/Lueders_rule_BuschLahti.pdf
How does this affect an epistemic view? Even if you include the observer themselves within the quantum description there is no need for the quantum state to be a physical/ontic object and thus no need for a dynamical or mathematically detailed description of where the other branches "go".Avodyne said:Lüders rule, as I understand it (see below), seems to require an observer outside the system being measured. This is not the case in QFT, where observers and everything else are comprised of excitations of the quantum fields.
http://philsci-archive.pitt.edu/4111/1/Lueders_rule_BuschLahti.pdf
Because you still need rules to decide when to modify the state by chopping off branches. If you do it under the wrong circumstances, you will destroy observable quantum coherence effects.DarMM said:How does this affect an epistemic view?
You remove the branches related only to unobtained outcomes for the systems you actually observe. This is not in contradiction with a superobserver retaining a superposed description of your entire lab. See for example Richard Healey's "The quantum revolution in philosophy" Chapter 11 for a good summary of this.Avodyne said:Because you still need rules to decide when to modify the state by chopping off branches. If you do it under the wrong circumstances, you will destroy observable quantum coherence effects.
That paper concerns psi-epistemic views where there is an underlying ontic space obeying the ontological framework axioms, just like the PBR theorem. It says nothing about epistemic theories in general such as for example acausal views. It's not really an issue for any of the epistemic views actually being worked on. Especially ones where there is no underlying ontic hidden variable space.Avodyne said:Psi-epistemic interpretations have all sorts of other problems as well:
https://arxiv.org/abs/1303.2834
Alice and Bob prepare an electron so that it is a superposition of spin-up and spin-down. [\quote]
fine so far.Yes and so you should then taking into account that she made this measurement and recorded her result in a classical copiable memory by describing Alice + electron via a density operator:Alice measures the spin. According to orthodox quantum mechanics, she either gets spin-up with such-and-such probability, or she gets spin-down with such-and-such probability.
[tex] \rho =\rho_A\otimes \left( \begin{array}{cc} 0.5&0\\0&0.5\end{array}\right)[/tex]
If Bob does this he is making a grave mistake. Alice is not at zero entropy and so cannot be described sharply. He, if he wishes to describe Alice plus electron before the physical and dynamic act of measurement Alice will make occurs would presumably use a density operator to include the entropy dump Alice necessarily must utilize to amplify the electron's spin component into a macroscopic record.But Bob, considering the composite system of Alice + electron, will predict that that composite system will evolve into a superposition of "the electron is spin-up and Alice measured spin-up" and "the electron is spin-down and Alice measured spin-down".
From Bob's point of view, if he has correctly represented the measurement process of Alice, if he correctly represents the dynamic that makes her recording of the electron spin possible, he will end up with a density operator of the form I mentioned above. In short Alice as an observer necessarily must interact with the system entropically and decoher it. At this point Bob is not describing this Alice but any such Alice electron pair given the same or equivalent initial conditions. Then Bob classically measures the record of Alice and collapses the classical probability distribution down to a single classical sharp state just the same way that the LOTTO commission does each time they bounce their ping pong balls and collapse the value distribution over the tickets to sharp "win" or "lose" states.From Bob's point of view, Alice doesn't get a definite result, but somehow turns herself into a superposition of both results.
Spekken's toy model gives an epistemic set of states that have interference at the observer + system level, while having a definite outcome at the system level. Superpostion of the total system isn't incompatible with definite outcomes for subsystems. If it was epistemic views would be finished.stevendaryl said:I don't think you can consistently treat the latter as epistemological
jambaugh said:Yes and so you should then taking into account that she made this measurement and recorded her result in a classical copiable memory by describing Alice + electron via a density operator:
Right, but to give a valid pure state description of a measuring device requires you break the device by measuring it so exactly its entropy becomes zero. This precludes it being a measuring device. That's the fallacy of Wigner's friend arguments.stevendaryl said:No, you shouldn't. That's introducing an ad hoc element to quantum mechanics. Through unitary evolution a pure state never turns into a mixed state. It becomes a mixed state through a modeling decision on OUR part. We can trace over unobservable degrees of freedom and produce a mixed state, but as I said, that's something WE do. It's not a physical effect.
jambaugh said:Right, but to give a valid pure state description of a measuring device requires you break the device by measuring it so exactly its entropy becomes zero. This precludes it being a measuring device. That's the fallacy of Wigner's friend arguments.
From Bob's perspective the system evolves unitarily and by virtue of the measurment having occurred the description will necessarily involve entanglement between measuring device and system measured.
You're thinking in terms of classical states. You disagree with getting a mixed state after the fact. I point out that your problem is starting with as sharp state and claiming part of the system is able to make a measurement.stevendaryl said:I consider that completely bogus. You don't have to know the initial state precisely in order to do reasoning about it. You do conditional reasoning: If it is in state x, then it will evolve into state y.
jambaugh said:You're thinking in terms of classical states.[/QUOTES]
That's not true. Schrodinger's equation tells us how to evolve a quantum state from one time to another.
I point out that your problem is starting with as sharp state and claiming part of the system is able to make a measurement.
Why don't you restate what you're claiming without mentioning the word "measurement"? A measurement is nothing more than interaction that causes a macroscopic variable (such as whether there is a spot on a photographic plate at a particular location) to become correlated with a microscopic variable, such as the z-component of the electron's spin. You can (presumably) derive from physics the fact that if a spin-up electron passes through the magnetic field then it will be deflected in one direction and will produce a spot over here. If a spin-down electron passes through the magnetic field then it will be deflected in the opposite direction and will produce a spot over there.
But the linearity of quantum mechanics implies that a superposition of spin-up and spin-down will result in a superposition of the dot being here and the dot being there. (Okay, since the macroscopic device interacts with the rest of the universe, the prediction would be that the whole universe ends up in a superposition of states. Thus Many-Worlds, fantasy or not, is a consequence of quantum mechanics. It really is. Unless you want to add hidden variables that say that only one of the possibilities is "real").
Ok. Let me try it without that, basically a deferred measurement scenario let "Alice" be a simple enough system to be sharply described in a pragmatic sense. To say "Alice measured the electron" Alice and the electron become maximally entangled. Bob's proper description of the Alice-electron composite necessarily represents this and so Bob cannot describe it in terms of Alice's state and the electron's state. To speak of Alice alone he must trace over the electron's density operator (while the composite is still sharp) yielding a mixed state of Alice with 50-50 percent probabilities of having a "up" vs a "down" record of the electron state. Likewise to describe the electron alone Bob must trace over Alice's density matrix yielding again a mixed state of the electron in that 50-50 classical superposition of outcomes. And we're back to playing Lotto.
As I said earlier, this business of tracing over degrees of freedom is something WE do. It isn't a physical interaction. It's a modeling decision. We model the situation in which you have a system entangled with the rest of the universe as if there was a collapse to one of a number of macroscopically distinguishable states, and the mixed state represents the lack of information about exactly which state it is. But that's really bogus. The mixed state resulted from our decision to draw the boundary of the system we are interested in. There can't be physical consequences of a modeling choice.
I like what you've written because tracing out 'Me' has physical justification. But it cannot be a physical process because the entanglement is not broken. So it seems the tracing is to remove information that is inaccesible and not because of a change of any state.jambaugh said:[..]
I cannot access the photon any more since I am now outside its future light cone. I must discard any hope of recovering its part of our entangled information and trace it out. I alone now have a "mixed state".
( It grates on me to use this "my state" language because it is the very source of confusion by pretending one is making ontic descriptions using QM. But it is the language of the intended audience.)
DarMM said:Spekken's toy model gives an epistemic set of states that have interference at the observer + system level, while having a definite outcome at the system level. Superpostion of the total system isn't incompatible with definite outcomes for subsystems. If it was epistemic views would be finished.
To explain briefly in Spekkens toy model superposition arises from the structure of the space of probability distributions under the presence of an epistemic limit. When considered over "system + environment" that limit has a different form than over just "system", so we have a superposition for the former, but a definite outcome for the latter.
Actual epistemic views are more complicated than this, but it gives a good example of how superpositions are compatible with definite subsystem outcomes.
Certainly, as I mentioned above there are two classes of epistemic views ##\psi##-statistical and ##\psi##-doxastic. Spekkens toy model is more in the tradition of the former kind.atyy said:Spekkens's toy model assumes quantum mechanics is incomplete, ie. that there are hidden variables. Spekkens's work is motivated by the measurement problem, and aims to build on things like Bohmian Mechanics, and ask whether any other types of completions of quantum mechanics are possible. So I don't think Spekkens's use of "epistemic" is the same as @jambaugh's, since @jambaugh doesn't seem to be a fan of ontic states.
Okay let's look at Spekkens toy model. We have a system with an electron, a measuring device and then the lab environment. We'll model each with a qubit.stevendaryl said:So if you want to insist that Alice's measurement of the electron's spin (along the z-axis, say) always produces the result of Alice having measured spin-up or the result of Alice having measured spin-down, then that means that we have to be able to interpret a superposition of macroscopically different states as being either in one state or the other.