Is the Many-Worlds Interpretation truly deterministic?

[DennisN]

I wonder if it is like the path integral formulation of QM in that the multiple worlds which are close re-inforce each other and those that are radically divergent cancel out leaving the observer to observe the most likely universes forming the experience.

You may find this PF thread about a paper from 2014 interesting: Many Interacting Worlds.

 

[vanhees71]

I'm puzzled then as Mermin doesn't seem so clear on it.

http://scitation.aip.org/content/aip/magazine/physicstoday/article/57/5/10.1063/1.1768652

I'm not sure whether Feynman ever verbatim wrote about "shut up and calculate", but if you read the introductory chapter on QM, where he discusses carefully the double-slit experiment with particles and its physical meaning, you can summarize his view on "interpretation" by this phrase, and I think that's the right attitude. As with any other mathematical model about the world there is a mathematical formalism (in QM there's a Hilbert space with operators acting on vectors in this space representing states (statistical operator) and observables) and a minimal interpretation of it to apply it to observations about nature (probabilities, expectation values, S-matrix elements in QFT and so on), and that's it. From a physics point of view you don't need anything more, let alone some hokus pokus like many worlds or Bohm-de Broglie trajectories and the like all of which are not observable by declaration and thus not part of physics.

According to QT there is no answer to the question, why in an experiment on a specific system described by quantum theory the outcome is the observed one. There are only probabilities for that outcome given the preparation (state) of the system. You can test this prediction by repeating the observation very often on independently and equally prepared systems, and so far the predictions of QT were always found to be very accurate, and that's why QT is taken as the best and most comprehensive theory we have to describe nature.

That doesn't mean that QT is the last word about how to model nature mathematically. Maybe one day one finds a discrepancy with the predictions of QT, and one has to build a better theory. That's how science works, and not some philosophical speculations that cannot be anwered by careful observation and quantitative measurements.

As the example of Bell's work show, it can still happen, that a purely philosophical speculation like the idea about "reality" set up in a quite vague sense by Einstein, Podolsky, and Rosen in their no famous paper (although Einstein himself didn't like this paper too much, and he has written a much better one as a single author later: A. Einstein, Quantenmechanik und Wirklichkeit (Quantum Mechanics and Reality), Dialectica 2, 320 (1948)) can be sharpened to a scientific question that can be answered by observation and measurement and thus becomes part of the exact sciences: Bell thought about local deterministic hidden-variable theories and derived an inequality for certain correlation functions that are violated by the predictions of (minimally interpreted!) quantum theory, and as many experiments show in the meantime, this inequality is violated with an amazing statistical significance and (at the same significance!) quantum theory has been confirmed.

As I said above, this doesn't mean that QT is the final answer, but a worldview a la EPR, i.e., that nature may be after all describable by a deterministic local hidden-variable theory is ruled out. There may be nonlocal ones, but so far nobody has been able to formulate a convincing one that is as successful as QT.

 

[stevendaryl]

No ... the problem that drives the invention of mwi is how the universe chooses between the eigenvalues of an operator. This ignores the fact that operators, eigenvalues and their associated probabilities are mathematical abstractions. In the real world there is dissipation, non-unitary evolution, absence of superposition and other noise that let's the outcome be decided by the current state of the universe - at the time and place of the measurement.

That seems false to me. Do you have a reference that makes that claim?

[added later]
I think there is general agreement that decoherence is responsible for destroying interference patterns, and making it impossible for a subsystem to be in a superposition of states. But I don't think there is any consensus that environmental effects select one possibility for the result of a measurement over another.

 

[stevendaryl]

The same comment I made previously applies here: these things are only relevant for the MWI if quantum superpositions play a meaningful role. Do they? I don't see how they do for die rolls. Cups of water spontaneously freezing, possibly, but I'm doubtful.

I don't understand your remarks. What, exactly, are you doubtful about? Are you still talking about the issue of whether very weird outcomes actually happen in MWI?

 

[stevendaryl]

According to QT there is no answer to the question, why in an experiment on a specific system described by quantum theory the outcome is the observed one. There are only probabilities for that outcome given the preparation (state) of the system. You can test this prediction by repeating the observation very often on independently and equally prepared systems, and so far the predictions of QT were always found to be very accurate, and that's why QT is taken as the best and most comprehensive theory we have to describe nature.

Perhaps it is getting off-topic to raise this objection to what you're saying, but my issue with the standard formulation of quantum theory is not about the irreducible probabilities---it's about the fact that probabilities are described as probabilities for measurement results. If a measurement is a process describable by ordinary physics (and thus, by QM), then it should be possible to reformulate the Born rule so that it doesn't mention measurements at all.

Suppose (for instance) that a measurement of an observable O on a microscopic system can be described as an interaction between the microscopic system and a macroscopic measuring device D such that different values of O lead to different macroscopically distinguishable states of D. Such an interaction would probably involve irreversibility. So a candidate for a replacement of the Born rule that doesn't single out measurement as special might be something along the lines of:

"When a microscopic system interacts with a macroscopic system to cause an irreversible change in the latter, then ..."

But that doesn't sound very fundamental, either. What happens to a macroscopic system should be derivable from what happens to microscopic systems, using the usual techniques of statistical mechanics for dealing with huge numbers of particles.

So ultimately, it seems to me that there should be a formulation of QM that doesn't mention anything about macroscopic concepts such as measurements or expectation values or irreversibility. Those statements should, in my opinion, be derivable from statements about what goes on at a microscopic level. And pure QM doesn't have such a description.

 

[vanhees71]

But it is precisely what quantum statistics does for you! It describes the behavior of classical, macroscopic systems in terms of the "relevant" macroscopic observables and explains, why these quantities behave in almost all case as described by classical physics. Classicality is the result of a sufficiently coarse-grained description. There is no other way to observe nature in its microscopic details than to use "amplification" and "measurement devices" that are macroscopic to make these observables comprehensible finally to our senses.

 

[stevendaryl]

But it is precisely what quantum statistics does for you! It describes the behavior of classical, macroscopic systems in terms of the "relevant" macroscopic observables and explains, why these quantities behave in almost all case as described by classical physics.

I don't think so. If macroscopic phenomena such as measurements are described in terms of microscopic phenomena, then the axioms of quantum mechanics should be expressible solely in terms of the microscopic phenomena. So there would be no need for an axiom saying "A measurement results in an eigenvalue with a probability given by..."

 

[A. Neumaier]

If a measurement is a process describable by ordinary physics (and thus, by QM), then it should be possible to reformulate the Born rule so that it doesn't mention measurements at all.

So ultimately, it seems to me that there should be a formulation of QM that doesn't mention anything about macroscopic concepts such as measurements or expectation values or irreversibility. Those statements should, in my opinion, be derivable from statements about what goes on at a microscopic level. And pure QM doesn't have such a description.

Such an improved formulation was given here.

My thermal interpretation is fundamental in the sense you require. It is meaningful without mentioning measurement at all, and implies the Born rule in the cases where the latter is appropriate. It is fully compatible with statistical mechanics (the theory of macroscopic implications of quantum mechanics, including irreversibility), from which it was in fact abstracted. And statistical mechanics is also the discipline in terms of which real measurement processes with real detectors can be analyzed. Indeed, to design good detectors one uses statistical mechanics and not the Born rules!

The thermal interpretation doesn't contain anything essentially new - it just places the emphasis in a way that makes the obvious more obvious instead of (as traditional interpretations do) placing counterintuitive axioms such as Born's rule (which are valid only in special contexts) into the center of attention.

 

[stevendaryl]

Such an improved formulation was given here.

No offense, but I don't agree that your reformulation solves the problem. Basically, you're saying that if we have a large system of many, many particles, then macroscopic variables (such as field averages) can have well-defined values. But that seems to me to be a matter of choosing a setting where the peculiarities of quantum mechanics are swamped out. It's not an explanation. You can still have quantum mechanics of a small number of particles; for example, in the EPR experiment. QM makes definite predictions about observations for such systems, and those predictions don't require any kind of thermal limit.

 

[A. Neumaier]

No offense, but I don't agree that your reformulation solves the problem. Basically, you're saying that if we have a large system of many, many particles, then macroscopic variables (such as field averages) can have well-defined values. But that seems to me to be a matter of choosing a setting where the peculiarities of quantum mechanics are swamped out. It's not an explanation. You can still have quantum mechanics of a small number of particles; for example, in the EPR experiment. QM makes definite predictions about observations for such systems, and those predictions don't require any kind of thermal limit.

Note: Expectation values are just values with an objective meaning in each state, whether macroscopic or microscopic. Expectations of a macroscopic observable are measurable by a single macroscopic measurement. Unlike measurements, expectations are part of the standard theory (shut-up-and-calculate). If you see the need to ban expectation values from a fundamental description you would also need to ban observables, and the theory would become impossible to formulate.

QM makes indeed lots of predictions about expectations of observations for microscopic systems, and those predictions don't require any kind of thermal limit. These expectations are correctly described by the thermal interpretation, even for microscopic systems. That the motivation of the interpretation comes from statistical mechanics doesn't mean that the interpretation itself is limited to macroscopic systems.

 

[vanhees71]

I don't think so. If macroscopic phenomena such as measurements are described in terms of microscopic phenomena, then the axioms of quantum mechanics should be expressible solely in terms of the microscopic phenomena. So there would be no need for an axiom saying "A measurement results in an eigenvalue with a probability given by..."

I don't understand what you want. The natural sciences are about observations/measurements of nature. It's not about fairy tales concerning some "underlying truth", or however you want to name it. Quantum statistics is by the way nothing else than the application of the quantum-theoretical formalism to macroscopic objects, i.e., it delivers in a scientific sense what you want, namely the understanding of macroscopic behavior from the underlying fundamental/microscopic dynamics.

 

[stevendaryl]

I don't understand what you want.

A formulation of quantum mechanics in terms of microscopic properties, such that the macroscopic rule--"When you measure an observable, you get an eigenvalue of the corresponding operator with a probability given by ..."--is derivable, rather than postulated. I thought that's what I said.

 

[vanhees71]

The question is derivable from what, and if you find such a formulation, what's the advantage compared to the "traditional" formulation which starts from what's really measured in the lab?

 

[stevendaryl]

The question is derivable from what, and if you find such a formulation, what's the advantage compared to the "traditional" formulation which starts from what's really measured in the lab?

What does "advantage" mean, here? Science was created to understand phenomena--light, planetary motion, properties of gases and liquids, the behavior of substances when they interact---that exist independent of any lab. Labs are invented to help get more information about the world, but the world and its phenomena don't depend on labs for their existence. Nuclear processes in stars work the same way even when there are no nuclear physicists around.

I can certainly understand the point of view that the only thing that is important for scientists is to explain the observations of scientists, but I think that's a sterile, solipsistic view of science. Nobody becomes a scientist with that interpretation of science in mind---that the point of science is to explain what happens in science labs. They become scientists because they are curious about what goes on outside the lab.

 

[A. Neumaier]

Nuclear processes in stars work the same way even when there are no nuclear physicists around.

But nothing ever is measured then.

"When you measure an observable, you get an eigenvalue of the corresponding operator with a probability given by ..."--is derivable, rather than postulated.

See the derivation in Section 10.5 (p.239) of my online book (version v2).

 

[nikkkom]

The same comment I made previously applies here: these things are only relevant for the MWI if quantum superpositions play a meaningful role. Do they? I don't see how they do for die rolls. Cups of water spontaneously freezing, possibly, but I'm doubtful.

MWI says that there is no collapse, ever. When you open the box, cat doesn't become dead or alive. Instead, you are now entangled with the cat's state, and both states of "I see dead cat and feel depressed" and "I see live cat and feel happy" exist in superposition.

IOW, MWI says that every possibility which (like cat state) arises from quantum superposition, is realized. And presumably, fair dice rolls depend on past history of the dice cubes and the person throwing it, and there is more than enough variability in their past that every result of dice roll result is possible, and therefore, according to MWI, every of those possibilities is realized in some branches.

 

[Mentz114]

That seems false to me. Do you have a reference that makes that claim?

I think there is general agreement that decoherence is responsible for destroying interference patterns, and making it impossible for a subsystem to be in a superposition of states. But I don't think there is any consensus that environmental effects select one possibility for the result of a measurement over another.

What else can it be ? Are you proposing that something that something outside the universe universe is affecting this ?

I've heard of thinking outside the box but come on ! That is not physics.

 

[stevendaryl]

What else can it be ? Are you proposing that something that something outside the universe universe is affecting this ?

I'm not proposing anything. QM does not specify how one alternative is chosen out of a set of possibilities. You seem to be claiming that it does, and I think that's false.

 

[stevendaryl]

I'm not proposing anything. QM does not specify how one alternative is chosen out of a set of possibilities. You seem to be claiming that it does, and I think that's false.

I should say that it's not part of standard mechanics. To quote Bill Hobba from this thread:
https://www.physicsforums.com/threads/decoherence-and-standard-formalism.890882/#post-5604515

there are 3 parts to the measurement problem.

1. The problem of non observance of interference
2. How the preferred basis emerges.This is why, for example, classical objects nearly always have a definite position
3. How an improper mixed state becomes a proper one.

The first 2 is explained by decoherence, the third some interpretations simply assume, while others explain.

The meaning of "how an improper mixed state becomes a proper one" is the issue of how one possibility is selected out of a set of possibilities. It is not explained by decoherence or environmental effects. Or at least, there is no consensus that it is.

 

[vanhees71]

This argument goes in circles. There is the state of a quantum system, described by a statistical operator. The state is called pure if the statistical operator is a projection operator otherwise it's called a mixed state. It is impossible to distinguish between what you call proper vs. improper mixed state. We have clarified this several times now.

 

[Mentz114]

The meaning of "how an improper mixed state becomes a proper one" is the issue of how one possibility is selected out of a set of possibilities. It is not explained by decoherence or environmental effects. Or at least, there is no consensus that it is.

This is getting off-topic. We've had this discussion before and we disagree deeply on this issue.

 

[stevendaryl]

This argument goes in circles. There is the state of a quantum system, described by a statistical operator. The state is called pure if the statistical operator is a projection operator otherwise it's called a mixed state. It is impossible to distinguish between what you call proper vs. improper mixed state. We have clarified this several times now.

I don't agree with your "clarification", but if you're happy with it, fine. Not everybody is.

 

[stevendaryl]

This is getting off-topic. We've had this discussion before and we disagree deeply on this issue.

I was responding to your claim "In the real world there is dissipation, non-unitary evolution, absence of superposition and other noise that let's the outcome be decided by the current state of the universe".

The outcome being determined by the current state of the universe is the part that I'm claiming is false.

 

[Mentz114]

I was responding to your claim "In the real world there is dissipation, non-unitary evolution, absence of superposition and other noise that let's the outcome be decided by the current state of the universe".

The outcome being determined by the current state of the universe is the part that I'm claiming is false.

Fair enough. That is my central thesis. What else could possibly decide ?

 

[stevendaryl]

Fair enough. That is my central thesis. What else could possibly decide ?

I'm not saying that I know the answer, I'm saying that the answer does not come from standard QM by taking into account the environment.

 

[Mentz114]

I'm not saying that I know the answer, I'm saying that the answer does not come from standard QM by taking into account the environment.

That's a reasonable view. Any ire I have is directed at MWI.

However, I think classical statistical mechanics and standard QM together offers an explanation. I would heartily recommend a close reading of chapter 2, especially section 2.6 of "The Quantum Theory of Motion" by Peter Holland. I get a clear mental structure from this, and no mystery.

I'm sure this is also done in the 'Thermal interpretation' but Hollands discussion is easier ( for me anyway).

[edited the title of the book]

 

[stevendaryl]

I'm not saying that I know the answer, I'm saying that the answer does not come from standard QM by taking into account the environment.

I don't want to spend more time on this, except to say that it would seem to me that the assumption that facts about the rest of the universe determine the outcome of measurements would contradict Bell's inequality. Maybe there is a loophole, but there certainly is no consensus that there is such a loophole.

 

[Jilang]

I don't want to spend more time on this, except to say that it would seem to me that the assumption that facts about the rest of the universe determine the outcome of measurements would contradict Bell's inequality. Maybe there is a loophole, but there certainly is no consensus that there is such a loophole.

I am reminded to remind you that quite recently you showed how the Bells inequality is violated for probabilities but not the probability amplitudes. In QT Amplitudes add, probabilities don't. Hidden variables only become a problem when one considers the probabilities rather than the amplitudes. Now, what would that suggest? (I have no suggestions)

 

[stevendaryl]

I am reminded to remind you that quite recently you showed how the Bells inequality is violated for probabilities but not the probability amplitudes. In QT Amplitudes add, probabilities don't. Hidden variables only become a problem when one considers the probabilities rather than the amplitudes. Now, what would that suggest? (I have no suggestions)

Yes, that is an interesting observation, but I don't know what to make of it.

 

[Mentz114]

I don't want to spend more time on this, except to say that it would seem to me that the assumption that facts about the rest of the universe determine the outcome of measurements would contradict Bell's inequality. Maybe there is a loophole, but there certainly is no consensus that there is such a loophole.

(my emphasis)
Do you mean through non-locality ?
What makes photon detectors click is correlations between probability amplitudes that happen right at the detector. These correlations could have been present after preparation - or is that just another NLHV theory ?

[Stephen, do you have a ref to the post where you did the work referred to by jilanq?]