Can QM interpretations be reconciled?

[Dirk Pons]

Subsequently a related question arose: whether the stochastic behaviour of particles is the fundamental reality.

There is no reason to believe this is the case. While it is true that some QM theorists believe that reality is fundamentally stochastic or even mathematical, this is their personal belief not a fact of science. Serious attempts have been made via the Bell type inequalities to settle this matter, but all they have proved is that if you start with the premise that particles are 0-D points then you conclude that such particles cannot have internal structure. Which is self-evident, and does not really move things forward.

This is important, because if there is a new physics, it seems it will not be an extension of quantum mechanics (http://dx.doi.org/10.1038/ncomms1416). It will have to be something else, and it is reasonable to expect that there might be structure at the sub-particle level. But how to develop a theory for this? String/M theory might do it, but is nowhere near that task just yet. Another option are the non-local hidden-variable (NLHV) theories. No proof has ever excluded all NLHV theories. This is not contentious. However neither have the NLHV theorists been very successful in offering new theories for inspection. So the hidden sector has not been productive either.

There is also the need for any new theory to be at least as good as QM in quantitative power. This is a big challenge, as QM is impressively accurate in its specialist areas. It predicts numbers that are well-supported by empirical evidence.

 

[Dirk Pons]

So where does that leave us regarding the central question of whether there will ever be a better theory than QM.

If a better new theory does exist, then it may have these attributes: (1) reconceptualise structures at the sub-particle level, (2) offer a formalism (presumably mathematical but not necessarily) that subsumes and goes beyond the quantitative machinery of QM, and (3) (preferably) be grounded in realism.

At that stage fundamental physics would become more intuitive and these types of questions could have meaningful answers. New theories of physics already exist, but right now there is no alternative theory that addresses all of 1, 2, 3 above. Our own team can do (1) and (3) using NLHV theory, which gives satisfying albeit conjectural explanations of many phenomena that otherwise are only explained by QM. But (2) is not yet solved. There appears to be no ‘slight change’ in mathematics that would give a new physics. Instead it seems it will require a new mathematics, and much theoretical work. It has taken thousands of PhD theses and lifetimes of research to get quantum theory to its current level of excellence.

So for the moment, quantum mechanics gives the best quantitative formalism of quantum effects. Other theories are arguably better at qualitative explanations that make sense in terms of a realist interpretation, but are still in the protophysics stage.

 

[kvantti]

No one interpretation explains everything, and none give answers that are satisfactory from the perspective of physical realism (not the same as local realism).

As far as I know the many-worlds interpretation offers a physical mechanism for every phenomena of quantum theory while preserving locality and realism. If you interpret the path integral formulation of QM as being literally "sum over all possible histories"-description of nature this becomes fairly obvious.

 

[vanhees71]

Subsequently a related question arose: whether the stochastic behaviour of particles is the fundamental reality.

There is no reason to believe this is the case. While it is true that some QM theorists believe that reality is fundamentally stochastic or even mathematical, this is their personal belief not a fact of science. Serious attempts have been made via the Bell type inequalities to settle this matter, but all they have proved is that if you start with the premise that particles are 0-D points then you conclude that such particles cannot have internal structure. Which is self-evident, and does not really move things forward.

To the contrary, there's no reason to believe that this is NOT the case. I'm not aware of a single observation contradicting quantum theory. If so that would be sensational and demand for a new revolution in physics comparable to that of the discovery if quantum theory itself!

 

[Dirk Pons]

many-worlds interpretation offers a physical mechanism for every phenomena of quantum theory while preserving locality and realism

Well, that is only partly correct. Many worlds does offer a partial explanatory mechanism, but one can hardly call it 'physical' if it can never be tested. It is beyond ('meta') the physical relationships that apply to this universe.

 

[Dirk Pons]

I'm not aware of a single observation contradicting quantum theory.

Hmmm... That's a different point and not what I was saying. It is true that QM proposes a mechanics based on stochastic behaviour of point particle, and it is also true that the resulting mechanics provides excellent quantitative representation of empirical results. But that does not mean that physics stops there. QM is premised on particles being stochastic points, but does not actually prove that. As I pointed out above, QM has never managed to exclude all NLHV solutions. QM just happens to be a good fit. That is circumstantial evidence that QM could be the correct theory at the particle level: i.e. that QM is a sufficiently accurate theory at the level at which particles can be considered 0-D points with intrinsic stochastic properties. But nothing in QM has ever excluded the possibility that QM might be merely a stochastic approximation to some deeper mechanics involving structures at the sub-particle level. That might be an uncomfortable thought to quantum purists ... but that is the nature of scientific progress and we have to keep an open mind to the possibilities.

Your point is also debatable at another level, since there are many empirical phenomena that contract quantum theory QM. Gravity for one.

 

[kvantti]

Well, that is only partly correct. Many worlds does offer a partial explanatory mechanism, but one can hardly call it 'physical' if it can never be tested. It is beyond ('meta') the physical relationships that apply to this universe.

Actually the many-worlds universe (or multiverse) is directly predicted by quantum theory if we let the universe evolve as a superposition of entangled quantum states which continuously decohere to parallel non-interfering states during "measurement" (which is just entangling the state of the environment with the decohered state of the measured system within the state function of the universe).

In other words the many-worlds universe follows directly from QM itself if we assume that the state function never collapses but during experiment the measurement device only gets entangled with one possible (decohered) state of the measured system and that objectively all the possible states exist (and all the possible results of the experiment exist with the probability of finding yourself in a world with certain result is given by the Born rule in accordance with the statistical branching within the state function of the universe).

Another way to understand many-worlds is to regard all the possible histories of a quantum system as equally real if the precise information about the history of the system does not physically exist, ie. a specific history has not affected the evolution of rest of the universe. The results of the delayed choice quantum eraser experiment strongly suggest that this indeed is the case, even if the physical information about the history of the system is erased after the final position of the particle is detected.

https://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser

 

[vanhees71]

Hmmm... That's a different point and not what I was saying. It is true that QM proposes a mechanics based on stochastic behaviour of point particle, and it is also true that the resulting mechanics provides excellent quantitative representation of empirical results. But that does not mean that physics stops there. QM is premised on particles being stochastic points, but does not actually prove that. As I pointed out above, QM has never managed to exclude all NLHV solutions. QM just happens to be a good fit. That is circumstantial evidence that QM could be the correct theory at the particle level: i.e. that QM is a sufficiently accurate theory at the level at which particles can be considered 0-D points with intrinsic stochastic properties. But nothing in QM has ever excluded the possibility that QM might be merely a stochastic approximation to some deeper mechanics involving structures at the sub-particle level. That might be an uncomfortable thought to quantum purists ... but that is the nature of scientific progress and we have to keep an open mind to the possibilities.

Your point is also debatable at another level, since there are many empirical phenomena that contract quantum theory QM. Gravity for one.

Why should QM exclude "all NLHV solutions"? I'm not aware of any such scheme working in the same realm of validity as QT.

 

[stevendaryl]

In other words the many-worlds universe follows directly from QM itself if we assume that the state function never collapses but during experiment the measurement device only gets entangled with one possible (decohered) state of the measured system and that objectively all the possible states exist (and all the possible results of the experiment exist with the probability of finding yourself in a world with certain result is given by the Born rule in accordance with the statistical branching within the state function of the universe).

Well, sort of. If you just take standard QM and throw away the collapse rule, you get a universal wavefunction evolving merrily, without any special role for measurements. But without that special role for measurements, which says that a measurement produces an eigenvalue with a probability given by the Born rule, then it's hard to relate the mathematics of QM to what we actually observe. You can rephrase the Born rule, as you suggest, to the probability of finding yourself in a possible world, but what is the "yourself" in that phrase, and how do we divide up the wave function into possible worlds? Those notions don't appear in pure quantum mechanics.

 

[Jilang]

Another way to understand many-worlds is to regard all the possible histories of a quantum system as equally real if the precise information about the history of the system does not physically exist, ie. a specific history has not affected the evolution of rest of the universe. The results of the delayed choice quantum eraser experiment strongly suggest that this indeed is the case, even if the physical information about the history of the system is erased after the final position of the particle is detected.

https://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser

I like this explanation as it intuitively dovetails with the path integral formulation. The worlds converging rather than diverging so to speak.

 

[Dirk Pons]

Why should QM exclude "all NLHV solutions"?

QM does't, but it sometimes tries to. QM is incompatible with NLHV solutions, because QM requires its particle to be a 0-D point with intrinsic parameters, whereas hidden variable solutions propose internal structure at the sub-particle level. There have been many deliberate attempts via the inequality methods and loop-hole free entanglement tests to disprove the viability of hidden variable solutions on theoretical and empirical grounds respectively. These results favour QM, and rule out local hidden variable solutions. However no proof or experiment has ruled out all non-local hidden variable solutions.

I'm not aware of any such scheme working in the same realm of validity as QT

True, there are no NLHV solutions that are as quantitatively robust as QM. That does not mean that no partial solutions exist.

 

[kvantti]

But without that special role for measurements, which says that a measurement produces an eigenvalue with a probability given by the Born rule, then it's hard to relate the mathematics of QM to what we actually observe. You can rephrase the Born rule, as you suggest, to the probability of finding yourself in a possible world, but what is the "yourself" in that phrase, and how do we divide up the wave function into possible worlds? Those notions don't appear in pure quantum mechanics.

In the MWI "measurement" is just the entanglement of the environment/measuring device with the decohered states of the state function and all the possible decohered entangled states continue their own evolution within the (state function of the) universe. "Yourself" also continues to evolve with all the possible worlds, so it is just a random luck of "who" of those "YOU" are (if that makes any sense, you can also think that when the worlds decohere/split that you are cloned with the worlds and the square of the probability amplitude tells you the statistical proportion of the the worlds within the state function, ie. if the probability of measuring a certain eigenvalue is eg. 0.15 then in 15% of the decohered worlds that is the outcome of the measurement).

bcrowell gave a nice link explaining the basics of it on the first page of this thread:
http://www.preposterousuniverse.com...hanics-is-given-by-the-wave-function-squared/

Any other questions should be answered by the Everett FAQ.

I like this explanation as it intuitively dovetails with the path integral formulation. The worlds converging rather than diverging so to speak.

Indeed, the path integral formulation explicitly shows how the "parallel worlds" interfere with each other at the quantum level and that the worlds can also converge rather than just diverge as long as the quantum state of the system in question remains coherent.

QM is incompatible with NLHV solutions, because QM requires its particle to be a 0-D point with intrinsic parameters, whereas hidden variable solutions propose internal structure at the sub-particle level.

de Broglie-Bohm theory is a NLHV solution which is compatible with QM and the particles are regarded as 0-D with the pilot wave guiding them in accordance with the Schrödinger equation.

Anyway in quantum field theory, even tho the basic mathematics deals with point particles, it is hardly correct to say that eg. an electron is a "point particle": rather, the closer you zoom into the electron the more of a "fuzzy cloud" of energy it looks like. You start your calculations with a point particle but after you take into account all the possible probability amplitudes going on with the electron you end up with a mess of virtual photons, virtual electron-positron pairs and all the interactions between them, so the electron is "really" a mess of interacting quantum fields - a quantized oscillation of the fields, so to speak.

 

[Dale]

It seems like everyone has had a chance to say their piece, so we will close it here.