Can QM interpretations be reconciled?

[vanhees71]

I don't think it's that simple that dBB is the same as the Copenhagen interpretation. Specifically for position measurements, you can show that, under the assumption that the initial position of a particle is randomly chosen according to the $|\psi|^2$ distribution at one time, the probability of finding the particle at a particular location at a future time is again $|\psi|^2$ (evolved forward in time according to the Schrodinger equation).

That's what usual QT says without assuming Bohmian trajectories on top of the usual QT formalism. So what's gained by dBB compared to the standard "shutup and calculate" interpretation?

But, beyond that, there are questions about the equivalence (or at least, I have questions--the answers might be well-known to someone else):

1. If you do two measurements in sequence, what wave function $\psi$ do you use after the first measurement? The original, or the "collapsed" one? If you use the original one, then for the second measurement, your assumption about the relationship between $\psi$ and the probability of the particle being in some position is no longer true---you know exactly where it as after the first measurement.
2. What about other sorts of measurements that are not about position---for example, energy measurements or spin measurements, or momentum measurements? It's been claimed that in practice, all we ever measure is position, and that we infer other dynamic quantities from this. We estimate velocities (and thus momenta) by positions at two different times. We compute spin by noting which way a particle is deflected by a magnetic field. Etc. So it might be the case that dBB is for all practical purposes equivalent to Copenhagen, but it's not as trivial a conclusion as it first appears.

ad 1) I don't know. It depends on what happened to the system during the measurement, i.e., on the specific apparatus you used to measure the observable.

ad 2) Do you have a specific example? I guess you refer to single particles. Then such an example was how to measure momentum of a particle. For simplicity let's assume we know which particle we have, i.e., its mass and electric charge. Then you can e.g., use a bubble chamber (it's just the most simple example that comes to my mind; nowadays one uses all kinds of electronics, but that doesn't matter for the principle argument) in a magnetic field. The particle leaves a track in the bubble chamber (why it does so was derived by Mott from quantum mechanics as early as 1929); then you can measure the curvature of the track, and with the given mass, charge, and the magnetic field strength you know which momentum the particle had when entering the bubble chamber. Of course, in a way you measured position and inferred from this the momentum of the particle. All this doesn't need any additions to standard "shutup-and-calculate" QT.

 

[mikeyork]

Many of the difficulties in finding consensus around QM have their origin in the relationship between underlying reality and the observer's space-time context. Unravelling that relationship will, I suspect, resolve many of the paradoxes that challenge our common sense (such as the contradiction between non-locality and special relativity).

 

[microsansfil]

We are not capable of interpreting QM if we think classically, that's for sure!

Sure; Neither with ontological interpretation
Patrick

 

[rkastner]

Many of the difficulties in finding consensus around QM have their origin in the relationship between underlying reality and the observer's space-time context. Unravelling that relationship will, I suspect, resolve many of the paradoxes that challenge our common sense (such as the contradiction between non-locality and special relativity).

I offer an account of that relationship that reconciles QM with relativity by acknowledging that QM processes are not spacetime processes (relativistic light-speed limitation applying only to spacetime processes). But that doesn't mean QM processes are not 'real'. The point is that we may need to examine the usual uncritical assumption that 'real' = 'existing in spacetime'. Spacetime may be just the 'tip of the iceberg'. (I discuss this in my new book for the layperson, Understanding Our Unsen Reality--chapter 1 available for free on amazon)

 

[rkastner]

Sure; Neither with ontological interpretation
Patrick

We can certainly provide an ontology for QM. It's just not a classical one. I've offered one. See my post above.

 

[rkastner]

That's what usual QT says without assuming Bohmian trajectories on top of the usual QT formalism. So what's gained by dBB compared to the standard "shutup and calculate" interpretation?
ad 1) I don't know. It depends on what happened to the system during the measurement, i.e., on the specific apparatus you used to measure the observable.

ad 2) Do you have a specific example? I guess you refer to single particles. Then such an example was how to measure momentum of a particle. For simplicity let's assume we know which particle we have, i.e., its mass and electric charge. Then you can e.g., use a bubble chamber (it's just the most simple example that comes to my mind; nowadays one uses all kinds of electronics, but that doesn't matter for the principle argument) in a magnetic field. The particle leaves a track in the bubble chamber (why it does so was derived by Mott from quantum mechanics as early as 1929); then you can measure the curvature of the track, and with the given mass, charge, and the magnetic field strength you know which momentum the particle had when entering the bubble chamber. Of course, in a way you measured position and inferred from this the momentum of the particle. All this doesn't need any additions to standard "shutup-and-calculate" QT.

deB/B may be falsified; see http://arxiv.org/pdf/1410.2014v1.pdf
However there is a nice physical account of entanglement experiments via TI. See Chapter 5 of my CUP book.

 

[vanhees71]

Very interesting, but it's not a real surprise since dBB is known to have notorious trouble with relativistic QFT. Photons are good candidates for falsifying it, because there's not even a position operator for photons.

 

[microsansfil]

We can certainly provide an ontology for QM.

Of course. It is your faith.

Patrick

 

[C Davidson]

In short: Interpretations are a philosophical or metaphysical issue of pretty little relevance to physics. The physical part is pretty convincingly solved with the just achieved loophole-free Bell experiments. All unanimously lead to the conclusion that local realism is ruled out and quantum theory is correct. The physical part of the quantum theoretical interpretation, i.e., the minimal interpretation is unique and thus the various ideas of metaphysics behind the formalism are very interesting but irrelevant for physics as a science. It's of course of high relevance for philosophy.

Except if you go with Einstein, who said the biggest loophole in QM is that quantum theory is incomplete. The Universe is real and local and no Bell theorem test to date disproves that. Look up T-duality and understand 1/R space first. String theory has a way out. For the "shut up and calculate" crowd, what if the math produces the right answer, but you have the wrong model?

 

[DrChinese]

For the "shut up and calculate" crowd, what if the math produces the right answer, but you have the wrong model?

I can't see how that would bother them. In that view, there is no model other than the math itself.

 

[vanhees71]

If the math produces the right answer, it's the right model. QT can be formulated adequately only in mathematical form. There's no other intuition than the math!

 

[zonde]

deB/B may be falsified; see http://arxiv.org/pdf/1410.2014v1.pdf

This paper is faulty. It attributes to deBB open contradictions with relativity. In derivation length contraction is ignored. But this is not accurate. You still have to use Lorentz transformations when you calculate something in moving frame or alternatively you can derive specific laws for bodies at motion in preferred frame.

 

[atyy]

Very interesting, but it's not a real surprise since dBB is known to have notorious trouble with relativistic QFT. Photons are good candidates for falsifying it, because there's not even a position operator for photons.

But in fact standard QED is not relativistic, because of the Landau pole.

 

[vanhees71]

Well, at the energy-momentum scale defined by the Landau pole I'd not trust any of our contemporary QFTs. I don't see what this has to do with dBB or QED being "not relativistic". It's simply undefined at energy-momentum scales, where it is inapplicable. All QFTs are effective theories, no matter whether they are Dyson renormalizable or not.

 

[atyy]

Well, at the energy-momentum scale defined by the Landau pole I'd not trust any of our contemporary QFTs. I don't see what this has to do with dBB or QED being "not relativistic". It's simply undefined at energy-momentum scales, where it is inapplicable. All QFTs are effective theories, no matter whether they are Dyson renormalizable or not.

For example, is QED consistent with lattice QED at small but finite lattice spacing?

 

[vanhees71]

I'm not aware of anything problematic concerning lattice QED.

 

[haushofer]

Yes, one can. As Einstein said (talking about theoretical physicists), look at their deeds rather than listening to their words. This means, you should look at how the theory is applied to describe the outcome of real-world experiments. Then you know what's the physical core of a theory. Everything else is metaphysics and philosophy. I don't deny that these are important from a cultural point of view and should be addressed, but it's not of much relevance for physics itself.

So you define physics as a science where phenomenology is more important than ontology? I'm fine with that, but I guess that choice is more or less physicist-dependent :P

Also, from the past we have seen that questions which seemed metaphysical then, turned out to be important to construct something which was called physics later. Think e.g. about the properties of spacetime. So I'm not convinved that one can make such a clear cut between "metaphysics" and "physics".

 

[vanhees71]

Well, in my opinion, the history of science shows that the phenomenological approach is the reason for the success of modern science. I'm not aware of any example, where "scholastic" thinking lead to a profound result in theoretical physics. Even a genius as Einstein has had no luck with the scholastic approach in his attempt to find a unified classical field theory of gravity and electromagnetism that substitutes quantum theory.

The properties of spacetime came into closer inspection by FitzGerald, Lorentz, Poincare and finally Einstein, entirely driven by the incompatibility of Maxwell theory with Galileo symmetry, and thus was very well based on empirical facts since Maxwell's electromagnetism was from the very beginning solidly based on the collected empirical knowledge about electromagnetic phenomena, particularly by the newest comprehensive investigations by Faraday.

In my opinion, the philsophy of science cannot provide much guidance to find new physical models or even theories, but it is of course important to analyze the physical models found by analysis of empirical findings and mathematical consistency in order to understand its wider cultural context.

From this point of view there's not much necessity in ontology, because the natural sciences are based on observations (or in terms of experiments which lead to quantitatively refined observations again) about really existing phenomena. Science doesn't tell you about something "deeper" than just the phenomena, and that's its "ontology" and nothing else.

 

[Jeff Rosenbury]

Isn't the idea that scientific explanations must be logically consistent a scholastic one? No experiment would be falsifiable without the ability to contradict.

 

[atyy]

I'm not aware of anything problematic concerning lattice QED.

At finite spacing lattice QED is non-relativistic, so it could mean that QED is consistent with a non-relativistic theory. Consequently, QED is not a good candidate to falsify dBB.

 

[A. Neumaier]

At finite spacing lattice QED is non-relativistic, so it could mean that QED is consistent with a non-relativistic theory.

There is nothing nonrelativistic about QED. It can be defined perturbatively from the start in a manifestly covariant form, using [URL='https://www.physicsforums.com/insights/causal-perturbation-theory/']causal perturbation theory[/URL]. Then there is no question of a cutoff or a lattice spacing.

 

[atyy]

There is nothing nonrelativistic about QED. It can be defined perturbatively from the start in a manifestly covariant form, using [URL='https://www.physicsforums.com/insights/causal-perturbation-theory/']causal perturbation theory[/URL]. Then there is no question of a cutoff or a lattice spacing.

No. Causal perturbation theory does not construct the theory.

 

[A. Neumaier]

No. Causal perturbation theory does not construct the theory.

Neither does lattice QED. Both construct approximations to QED.

Moreover, lattice QED is never used in practice. All high accuracy tests of QED are based on the covariant form and further approximations derived from it. Thus the physical QED is defined by the covariant definition, while lattice QED is a toy object only.

 

[Ralph Dratman]

But does there exist a model involving spacetime-stamps-labeling (information) when decoherence in the form of entanglement takes place?

Your idea sounds interesting, but I have no idea what you mean by spacetime-stamps-labeling. Explain, please.

 

[Dirk Pons]

The starting question related to whether the multiple interpretations of QM could be reconciled to each other or whether a 'completely different mathematical framework' would be required.

Suppose there would be found an entirely different interpretation covering all others, perhaps accompagnied by a slight change in math. Would such a thing be conceivable?

The different interpretations of QM all start from the same basic mathematical principles, and then offer different ways to make sense thereof, hence 'interpretations'. But the basic premises are the same: particles are zero-dimensional points with intrinsic properties that manifest stochastically over space.

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

 

[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.