QM Interpretations: Most Popular & Why?

[curiousphoton]

The following are the interpretations of QM:

Bohmian · CCC · Consistent histories · Copenhagen · Ensemble · Hidden variable theory · Many-worlds · Pondicherry · Quantum logic · Relational · Transactional

Which is the most accepted by the theoretical physics community? Obviously all have some supporters but I'm interested in finding out which is the most popular and why?

Thanks.

 

[DrChinese]

There have actually been surveys done on this here. And I have seen some informal surverys as well. In many ways the most popular answer may be "Don't know, not sure if I should care". Not saying that is my opinion or that most specialists hold that view, but I would say it reflects the viewpoint of a lot of working physicists.

 

[Bob_for_short]

Ensemble, of course. It is not so opposite to the others though.

Why ensemble? Because one point does not give you all information about the quantum state. One point is a too poor experiment. You cannot even tell/prove where it comes from.

As in the macroscopic case, in the microscopic case you also deal with compound systems. And any compound system needs many exchanges to reveal its true face. More pixels, better image.

 

[RUTA]

I find the majority of physicists don't care about interpretations, subscribing to Mermin's "shut up and calculate." Physics Today 57, #5, 10-11 (2004).

 

[Bob_for_short]

I find the majority of physicists don't care about interpretations, subscribing to Mermin's "shut up and calculate." Physics Today 57, #5, 10-11 (2004).

They keep exactly to the ensemble interpretation: everybody calculates probabilities in our, single Universe according to the wave (quantum) mechanics.

 

[hamster143]

They keep exactly to the ensemble interpretation: everybody calculates probabilities in our, single Universe according to the wave (quantum mechanics).

That's like saying that all agnostics are Buddhists, because Buddhism allows the possibility of all other gods.

Among physicists who do express preference for an interpretation, many-worlds interpretation is very popular.

 

[Demystifier]

The following are the interpretations of QM:

Bohmian · CCC · Consistent histories · Copenhagen · Ensemble · Hidden variable theory · Many-worlds · Pondicherry · Quantum logic · Relational · Transactional

I never heard about CCC and Pondicherry. What are those? Some links?

 

[Bob_for_short]

Among physicists who do express preference for an interpretation, many-worlds interpretation is very popular.

How about the experimentalists? Are they content with one-point data in a double-slit experiment or do they care about measurement statistics in this world?

 

[vanesch]

How about the experimentalists?

I also prefer Many Worlds - and I am (or used to be) an instrumentalist/experimentalist. But I don't consider MW necessarily as "true", I only consider it as a very helpful mental picture to get some intuition for quantum-mechanical experiments. It avoids the difficult question of "what is a measurement" and "when does the wave function collapse" - and when you do so, all apparent paradoxes of EPR experiments and of retarded quantum erasers and so on disappear.

 

[Bob_for_short]

I also prefer Many Worlds - and I am (or used to be) an instrumentalist/experimentalist. But I don't consider MW necessarily as "true", I only consider it as a very helpful mental picture to get some intuition for quantum-mechanical experiments. It avoids the difficult question of "what is a measurement" and "when does the wave function collapse" - and when you do so, all apparent paradoxes of EPR experiments and of retarded quantum erasers and so on disappear.

Sorry to hear that.

 

[vanesch]

Sorry to hear that.

 

[curiousphoton]

Among physicists who do express preference for an interpretation, many-worlds interpretation is very popular.

So far many-worlds is my favorite. Is the fact that you have 12 interpretations of QM (and you may basically choose a favorite because one is not technically more correct than another) a major downfall to the theory?

I never heard about CCC and Pondicherry. What are those? Some links?

Wikipedia

 

[Count Iblis]

My opinion is that either MWI is true or QM itself is not exactly valid.

 

[f95toli]

How about the experimentalists? Are they content with one-point data in a double-slit experiment or do they care about measurement statistics in this world?

Remember that not everyone who is doing "QM experiments" are working in optics. The double slit is a nice "toy" but it is far from the only system where you can see "weird" quantum effects.
There are plenty of people (me included) who work on system where there is only a single "quantum object" and not an ensemble, this includes just about everyone working with single qubits (solid state systems, ion traps etc).

Personally I am in the "shut up and calculate" camp, and so is just about everyone else I work with.

 

[Bob_for_short]

...There are plenty of people (me included) who work on system where there is only a single "quantum object" and not an ensemble, this includes just about everyone working with single qubits (solid state systems, ion traps etc).
Personally I am in the "shut up and calculate" camp, and so is just about everyone else I work with.

The more you will work with your "single quantum object", the more data you will analyse, the better you will understand what an "ensemble" means. It is an ensemble of data about your single system, it goes without saying, and that's why it is sufficient to shut up and calculate.

 

[Demystifier]

My opinion is that either MWI is true or QM itself is not exactly valid.

My opinion is that MWI is correct but not complete.
(MWI by itself in its minimal form cannot explain the origin of the Born rule.)

 

[f95toli]

The more you will work with your "single quantum object", the more data you will analyse, the better you will understand what an "ensemble" means. It is an ensemble of data about your single system, it goes without saying, and that's why it is sufficient to shut up and calculate.

True, but that is hardly a unique property of quantum systems. Most experiments involves taking averages of some sort at one point or another even if it just means increasing the integration time of your multimeter; but that has more to do with achieving a better signal-to-noise ratio than of any fundamental property of the system you are measuring.
There are certainly examples where one can -at least in principle- see the "quantumness" of a systems using a single shot readout. An obvious example being to first manipulate a single using MW pulses and then reading out its state using a measurement pulse. Now, the final result of such a procedure is obviously single-valued (since the qubit will end up in one of two states) but what comes before that (the manipulation) is very much a series of "quantum operations".
Any interpretation (or -in my case- lack of interpretation) should surely take into account not only what we see after the measurement pulse but also what is happening when we are manipulating the qubit; because even though we are not measuring we are certainly doing SOMETHING to the qubit with our pulses.

 

[Demystifier]

Wikipedia

CCC = consciosness causes collapse

Pondicherry interpretation: as I understand it, seems to be a variant of the instrumentalist interpretation - QM is nothing but a tool for calculating probabilities.

Am I correct?

 

[Dmitry67]

So far many-worlds is my favorite. Is the fact that you have 12 interpretations of QM (and you may basically choose a favorite because one is not technically more correct than another) a major downfall to the theory?

There is a problem with Born rule. THere were claims that it hadbeen succesfully derived from 'pure' QM formalism, and another claims, that the derivation was circluar.

But MWI is deterministic, so it is not clear what the 'probability' means in that context. So yes, there is some mystery, but I don't see it as a weakness, instead, it is a hint that we are missing something interesting about the reality.

Then, the 'appearence' of the classical world is based on the Quantum Decoherence. QD has some difficulties:

The choice of basic of decoherence is arbitrary. So you should define the basic based on some definition of the 'macroscopic system'. When 'macroscopic system' and basis are defined, you can define the 'branch'. But systems have different states, and in some branches we even don't exist! So the choice of a basic is branch-dependent.

But these difficulties are rather technical: we don't know how the brain works, but it is not a fatal probalem for physics. So we can not correctly and completely define a 'state' and 'basis' or complicated system, but it is not fatal.

And it is much better that that 'collapse' nonsense from CI - CI is absurd, it just can't be true.

 

[Bob_for_short]

...But MWI is deterministic, so it is not clear what the 'probability' means in that context. So yes, there is some mystery, but I don't see it as a weakness, instead, it is a hint that we are missing something interesting about the reality.

The missing part is simple: we have to recognize that even in a microscopic world we need many points of measurement to get some information. Information is not reduced to one point. On the contrary, the more points, the more accurate information about a system. Just like a photograph. The trick is that we think of microscopic world as of elementary, reducable-to-one-point world. It is this idea that fails.

The classical world also "appears" as the inclusive picture (sum of many different QM events). Again, a photograph is a right example.

 

[Dmitry67]

It might make sense, but it not the MWI... on the other side, QD is not a part of MWI either... I mean, it is not absolutely required... so may be you're right...
But I've heard about the Informational Interpretation, looks like it is close to what you are explaining.

 

[DrChinese]

Is the fact that you have 12 interpretations of QM (and you may basically choose a favorite because one is not technically more correct than another) a major downfall to the theory?

Not at all. And that is why it is not such a big deal to many working in the field. To many, the subject of interpretations is more of a minor curiosity than anything else.

But it does mean that there is the "possibility" that additional refinements to theory may be possible. Since any refinement would almost certainly be an extension to current theory - which is now 80+ years old - it is exciting to consider. So there is a lot of research going into discovering theoretical differences between one interpretation or another. For example: Bohmian type interpretations require some assumptions which may make them explicitly testable. Just yesterday, I started a thread about a newly proposed test to distinguish their viability.

But even the discovery of one particular interpretation being correct would not invalidate existing physical theory.

 

[Demystifier]

But MWI is deterministic, so it is not clear what the 'probability' means in that context. So yes, there is some mystery, but I don't see it as a weakness, instead, it is a hint that we are missing something interesting about the reality.

I agree. What I disagree with you, is what that reality might be.

 

[vanesch]

The missing part is simple: we have to recognize that even in a microscopic world we need many points of measurement to get some information. Information is not reduced to one point. On the contrary, the more points, the more accurate information about a system. Just like a photograph. The trick is that we think of microscopic world as of elementary, reducable-to-one-point world. It is this idea that fails.

The classical world also "appears" as the inclusive picture (sum of many different QM events). Again, a photograph is a right example.

The problem with the "ensemble" view of quantum mechanics is that there's nothing to understand, so you cannot devellop a "feeling" for what "goes on" (even if it doesn't go on that way, at least you can imagine it). Of course the ensemble view is a "correct" view of quantum theory: you scribble weird symbols on paper, apply formal calculation rules and in the end you crunch out probability distributions.

That's nice for the guy for whom one has made a measurement instrument, and one tells him that the instrument measures "this". But it is a pain for the one that makes an instrument: how are you supposed to make it ? If you set up an experiment, you need some kind of intuition of "what goes on", and so you need a kind of mental picture. Why do we say that a beam splitter splits a beam ? It is easier to picture it that your photon wave packet comes in, gets split into two packets by the beam splitter, that these two packets do this and do that, then recombine, and click here or there. But if you do that, you are actually thinking in MWI terms: you've considered that after the beam splitter, your photon is *simultaneously* in one branch and in another. For a single photon, this might still be feasible as a "classical light pulse", but if you apply the same reasoning to EPR pairs and so on, you can really make a parallel between "things happening in parallel" and the actual calculation. If you now make one extra step, and say that upon measurement, the measurement apparatus ALSO gets into two simultaneous states, then you are completely in MWI.

When do you apply the Born rule ? When it comes to you ! You tell yourself that you are also simultaneously observing different results, but "you" are one of those you's, and your "you" ensemble distribution is then given by the Born rule. It sounds crazy, it is maybe crazy, but it gives you quite some intuition on "how to picture things". I've never met any other interpretation that gives you such a close link between the formal calculation and the "lab situation".

 

[Fredrik]

Pondicherry interpretation: as I understand it, seems to be a variant of the instrumentalist interpretation - QM is nothing but a tool for calculating probabilities.

Mohrhoff has certainly been pushing that view too (e.g. in an article called "Quantum theory needs no interpretation", if I remember the title correctly), but I think his "Pondicherry" interpretation is a lot more weird than that. I skimmed the Pondicherry article a few years ago and I don't remember much of it, but it contains some stuff about the nature of space and time. For example, he thinks that a photon that goes through a double slit doesn't consider the two slits as being at different locations in space.

If you search for Ulrich Mohrhoff at arxiv.org, you'll find a large number of articles that all seem to be saying roughly the same thing. I read some of the others too (a few years ago) and I thought they were interesting and inspirational, but not very useful.

 

[Fredrik]

The following are the interpretations of QM:

Bohmian · CCC · Consistent histories · Copenhagen · Ensemble · Hidden variable theory · Many-worlds · Pondicherry · Quantum logic · Relational · Transactional

An "interpretation of QM" is an attempt to interpret the mathematics of QM as statements about what's "actually happening" in physical processes that can't be described classically. Therefore, I don't consider the "ensemble interpretation" an interpretation. It's just the rejection of the idea that QM is telling us something about what's "actually happening".

I also don't consider "quantum logic" an interpretation. It's just an attempt to state the theory in a different way. Instead of having axioms that define a mathematical structure on the set of states of physical systems, we use axioms that define a mathematical structure on the set of experimentally verifiable statements.

I consider "consciousness causes collapse" complete crackpot nonsense.

A lot of people consider the Copenhagen interpretation to be the statement that measuring devices are classical and that wave function collapse is exact. I don't think anyone actually believes that. In particular I don't think Bohr and Heisenberg thought that. If we remove the craziness by instead saying that a measurement is a physical interaction that entangles the eigenstates of the system with macroscopically distinguishable states of a system (the measuring device) that's approximately classical, then the Copenhagen interpretation is indistinguishable from the ensemble interpretation, and also completely consistent with decoherence and quantum logic.

Decoherence is a phenomenon that can be studied in the framework of the ensemble interpretation, so I don't know why anyone would consider that an interpretation. The study of decoherence has improved our understanding of measurements. It has given us a definition of what a measurement is (see the preceding paragraph), but it doesn't tell us much about what's "actually happening".

I haven't had time to study Bohm yet, but I'm under the impression that it at least consists of a set of well-defined statements that can be used to predict the probabilities of possible results of experiments. That makes it a theory. Consistent histories might fall into that category too, but I don't fully understand it. All the others seem to be nothing more than loosely stated ideas about what sort of things are happening. None of them seems to be defined by a list of well-defined statements, or give us a consistent set of answers to the question "What's actually happening?" in every conceivable scenario. So I can't consider them to be anything more than failed attempts to interpret QM.

 

[Dmitry67]

BTW, the list in not complete: there is also "Objective Collapse" theory: it is not an interpretation (even Wiki puts it in a list of interpretations) because it is experimentally verifiable.

I remember Penrose liked the idea of "Gravitation caused collapse" but I think it is less and less popular.

Frederik, I hope MWI does not fall for you in the category of "nothing more than loosely stated ideas about what sort of things are happening"?

 

[hamster143]

It seems to me that ensemble is basically a lipstick-on-a-pig version of hidden variables, which were falsified more than 40 years ago. If there's only a single unique universe, and every system exists in no more than one state at a time, then our inability to see things as such (which gives rise to the appearance of wavefunction) is due to our ignorance of "hidden variables", describing the system on some deeper level. But local hidden variables were killed by Bell in 1964, and nonlocal hidden variables are too much of a stretch.

 

[Count Iblis]

It seems to me that ensemble is basically a lipstick-on-a-pig version of hidden variables, which were falsified more than 40 years ago. If there's only a single unique universe, and every system exists in no more than one state at a time, then our inability to see things as such (which gives rise to the appearance of wavefunction) is due to our ignorance of "hidden variables", describing the system on some deeper level. But local hidden variables were killed by Bell in 1964, and nonlocal hidden variables are too much of a stretch.

Not everyone agrees that local hidden variables are ruled out:

http://arxiv.org/abs/0908.3408

http://arxiv.org/abs/0707.4568

http://arxiv.org/abs/quant-ph/0701097

 

[Fredrik]

Frederik, I hope MWI does not fall for you in the category of "nothing more than loosely stated ideas about what sort of things are happening"?

It does, but I admit that it's possible that I have just failed to understand it.

 

[MaxwellsDemon]

I'm fascinated by the sheer number of Many Worlds Interpretation supporters here. Do you know if this interpretation is gaining in popularity? Most of the "classic" textbooks on quantum mechanics tend toward the Copenhagen Interpretation. I was under the impression that was the default orthodox way of thinking about quantum phenomena. Although I guess most of the physicists I've known tend toward the "shut up and calculate" view when really pressed with quantum conceptual questions. Most quantum physicists seem to me to be modern day Pythagoreans...all that matters is mathematical consistency and mathematical "beauty"...conceptual beauty and simplicity seem to take a back seat. Perhaps that's the only viable option with so few physical concepts to latch on to. Without physical intuition to serve as a guide, it might be best to adhere to strict linguistic formalism. Still, better to know only a little bit and understand it, than to know a lot but understand little. When faced with many different interpretations that don't make any unique testable predictions, perhaps we should apply the philosophical criteria of Occam's Razor and ask, "Which is the simplest?" Which interpretation is most pleasing philosophically? If you had to start from scratch to understand quantum phenomena, what would you say are the most basic physical concepts? Personally I think the uncertainty principle would be a good starting point...even though its usually derived from what I consider to be more complicated postulates.

 

[Dmitry67]

It does, but I admit that it's possible that I have just failed to understand it.

Fredrik, you're right: usually when you start reading about MWI you hit the wordy stuff. I can explain why:

The axiomatic system of MWI is very simple: there is only unitary evolution of the waves and nothing else Period. In that sense it is NULL interpretation and very close to 'shut up and calculate'

But then you have to explain how we observe the classical world, and we start explaining the decoherence, branching etc. This is very useful to understand how it works, but many people get an impression that the wordy stuff about the branches is a part of axiomatics of MWI. it is not.

P.S.
I know Demistifier (?) distinguish 2 versions of MWI: "strong" and "weak"

 

[Dmitry67]

Which interpretation is most pleasing philosophically?

I can explain why I like MWI:

1. (the most important) MWI allows having very simple initial conditions at the Big Bang (God did not have a choice when created a Universe - or had a very little choice).
2. It is the only interpretation consistent with Mathematical Universe Hypotesis (Max Tegmark)
3. It is deterministic. God does not play dice
4. It is minimalistic - no new axioms

 

[Gerenuk]

I hope I understood the MWI correctly. Provided so:

Does it make sense to assume that there are many worlds, when we are not going to see them anyway? It reminds me of
http://en.wikipedia.org/wiki/Russell's_teapot
What do we gain from assuming things that cannot be detected anyway?

Maybe a more general question is:
What is the criterion for how good an interpretation is?
Is the interpretation maybe the key to find a better formulation of QM?

Btw, is quantum mechanics considered to be absolutely correct? There are calculations that show an amazing agreement with experiment. Is that a special case? Maybe many-particle effects and entanglement are actually exactly as predicted by QM?

 

[Dmitry67]

We don’t need to 'assume' that they exist: their existence is an unavoidable result of unitary evolution. On the contrary, to deny their existence you need to provide some mechanism. For example, in Copenhagen that elimination mechanism is called ‘collapse’. In Bohmian (please correct me if I am wrong) it is called 'empty waves' of something. So the burden of prrof is on those who claim that only one branch exists.

 

[ConradDJ]

Just to put in a word for Rovelli's Relational QM... which probably has no large following among physicists. But I think it's the most straightforward interpretation of quantum experiments, in particular the "quantum eraser" experiments.

The idea is that the "collapse" is a real physical event, but not an "objective" (observer-independent) event. The superposition "collapses" exactly to the extent that information about a system S is communicated to any other system O. However the collapse is "relative to O". For another system P, the combined S-O system remains in an entangled superposition until information about its state gets communicated to P.

I don't think this has much significance for physics, yet, but I think it should. It shifts the picture from --

A) systems exist in a paradoxical superposition of states, and then at some point are transformed... not exactly into a single determinate state, but a state which is more determinate with respect to some parameters and less determinate with respect to others; to --

B) at bottom the world consists not of things-in-themselves but of "the information systems have about other systems." The world is not a structure of things, but of communcations.​

However, this interpretation is useful only if you want to head into almost unexplored conceptual territory -- i.e. considering how "communication of information" actually happens, in physics... how the world actually works, as a communications system.

That the world in fact does this is beyond dispute -- that it communicates information about itself through physical interaction. The strength of Relational QM is that it allows every interaction to be a "measurement"... instead of assuming that some "cause a collapse" and others don't. But it's not very clear what this implies, for physics.

Even so, for me it's more interesting to think about what we know actually happens in the world, than to explore notions like the splitting of the universe into infinitely many universes.

 

[Bob_for_short]

We don’t need to 'assume' that they exist: their existence is an unavoidable result of unitary evolution. On the contrary, to deny their existence you need to provide some mechanism. For example, in Copenhagen that elimination mechanism is called ‘collapse’... So the burden of proof is on those who claim that only one branch exists.

Let us consider a lotto. Its results are probabilistic. All different results form the ensemble of events describe this lotto as a system. Each particular result is an element of the ensemble rather than a collapsed probability.
In QM each particular result (point) is considered as a collapsed wave-function. Why? The wave function does not describe a specific event but ensemble of them. Make many elementary measurements: one-by-one in a sole installation or one in many different but similar installations, whatever, and you will determine the system properties. The system properties are not reduced to one point. There is no a WF collapse in an elementary measurement.

 

[Fredrik]

The axiomatic system of MWI is very simple: there is only unitary evolution of the waves and nothing else Period. In that sense it is NULL interpretation and very close to 'shut up and calculate'

Is the usual probability rule of QM included in the axioms or not? If it is, then what exactly distinguishes the MWI from the ensemble interpretation? If it isn't, then the theory is crippled and can't make any predictions at all. It's not even a theory anymore.

...many people get an impression that the wordy stuff about the branches is a part of axiomatics of MWI. it is not.

That's precisely why I've been suggesting that the MWI is a failed attempt to interpret QM, and that it's only giving us a rough idea about what sort of things are actually happening. An interpretation should at least be able to make a claim (that may or may not be correct) about what exactly is happening.

I really haven't been able to figure out what MWI proponents think is really happening, or what they consider a mathematical representation of a "world". I know that they think it makes sense to consider the Hilbert space of possible states of the entire universe. Penrose calls it the "omnium" rather than the "universe", since it's the physical system that contains all the worlds. I'll call it that from now on.

I think the Born rule is essentially equivalent to the assumption that a Hilbert space of states of a physical system can be expressed as a tensor product of component systems. We can decompose the omnium into subsystems in many different ways. When we decompose it into only two subsystems, we can call one of them "the system" and the other "the environment". The state of the omnium can be expressed as

\sum_{\alpha, \beta}c_{\alpha\beta}|S_\alpha\rangle\otimes|E_\beta\rangle

where the S states are eigenstates of some observable and the E states are basis vectors for the Hilbert space of the environment. Decoherence theory tells us that any interaction between the system and the environment will transform the state (by unitary time evolution) into the form

\sum_\alpha c_\alpha|S_\alpha\rangle\otimes|P_\alpha\rangle

where the P states are "pointer states" of the environment. Now each term of this expression can be interpreted as representing the state of a different "world". But note that each of these terms is a vector in the Hilbert space of the omnium. So the Hilbert space of a "world" is the same as the Hilbert space of the omnium, and that means they're actually the same physical system. Every world is the same physical system as every other world. So why do we call them "worlds"?

Apparently we do because the systems that include at least one human observer always perceive themselves as a term in the second mathematical expression above, rather than as the sum of the terms. Note however that nothing in the MWI explains why, or even states explicitly that they do. Even decoherence can't really explain it. I'm sure decoherence can tell us that the eigenstates of some observable of my brain must be correlated with pointer states of my environment, but it can't tell us why every experience I have is represented by an eigenstate of that observable. So maybe we do need to talk about consciousness?! It seems that we need to prove that all conscious experiences are represented by eigenstates of some observable. What observable would that be? Is there a consciousness observable? Do we need a better theory of consciousness to answer that? It seems to me that as long as these issues haven't been worked out, the MWI is just a set of loosely stated ideas rather than an actual interpretation.

The fact that the decomposition into "the system" and "the environment" is arbitrary seems to mean that two different subsystems of the universe can't agree on what the worlds are. Each subsystem would describe what it considers "the world" from its own point of view. We're entering the territory of the "relational interpretation" here. I think that the MWI also needs to be supplemented by a set of statements similar to a "relational interpretation" before we can consider it an actual interpretation.

 

[Fredrik]

We don’t need to 'assume' that they exist: their existence is an unavoidable result of unitary evolution. On the contrary, to deny their existence you need to provide some mechanism.

Only if you have assumed that QM really describes the world, but this assumption is naive and unjustified. A set of statements only needs to be falsifiable to qualify as a theory, and for that it's sufficient that it tells us the probabilities of possible results of experiments. It doesn't have to include a model of the real world. MWI proponents believe that Hilbert space together with the Schrödinger equation is a mathematical structure that's approximately "isomorphic" to the real world. We "ensembleists" believe that this isn't true. It's only if we assume that your unjustified belief is correct that what you're saying in the quote is true.

QM doesn't look like a description of anything to me. It looks like a toy model that mathematicians would come up with if we ask them to think of the simplest possible theory that predicts non-trivial probabilities (i.e. not always 0 or 1) of possible results of experiments.

 

[Count Iblis]

It seems that we need to prove that all conscious experiences are represented by eigenstates of some observable. What observable would that be? Is there a consciousness observable?

I think that's true. Formally it is easier to replace a biological human by an artificial intelligence and then consider the classical bits of the computer. Whatever consciousness really is, the operators that descibe it will be diagonal in the basis spanned by the classical bit states.

 

[Hurkyl]

Let me make a statement about qubits, which is hopefully nontrivial enough to serve as an analogy that says something interesting.


The algebra of "observables" of a qubit is generated by the three "spin about the * axis" operators. IIRC, the set of all states for this algebra can be arranged into a geometric object: the Bloch sphere and its interior.


Now, suppose for some reason I do not have access to all observables -- let's say I only have access for the spin about the x-axis observable. The state space for this algebra is just the interval [-1,1]. The endpoints are the only pure states.

My algebra doesn't have enough observables to tell apart the points on/in the Bloch sphere: on any of my observables, (x,y,z) and (x,y',z') have the same expectation.

Algebraically restricting the operator algebra just to what I have available has the geometric effect of projecting the Bloch sphere onto the x axis.

On the pure states on the Bloch sphere, if you grind through the process of mapping it to the Bloch sphere, projecting down to [-1,1], then rewriting it as a statistical mixture of the pure states, the result is that the ket

a |x^-> + b |x⁺>​

is converted into the statistical mixture

x^- with proportion |a|²
x⁺ with proportion |b|²​

So while the "true" state space of our qubit is the Bloch sphere, the fact I only have access to a limited algebra of observables means that I only see a restricted view of the quantum state. The Born rule pops out of the partial trace. There is no arbitrary choices, artificial decomposition, or anything like that involved.




Local quantum field theory incorporates this. Two different kinds of locality are involved here.

The first kind of locality is that we may want to restrict our attention merely to a particular region of space-time, rather than the entire universe -- and so we get a restriction of the full state space, much as in my example of the qubit.

The second kind of locality says that if the region V is causally determined by the region U (e.g. the past light-code of every point in V has a cross-section lying entirely in U), then the quantum state local to V is completely determined by the state local to U -- time evolution is local.

In particular, this means that if the quantum state local to U is a statistical mixture of some pure states, then time-evolving to V is required to preserve this mixture!

 

[Fredrik]

I think that's true. Formally it is easier to replace a biological human by an artificial intelligence and then consider the classical bits of the computer. Whatever consciousness really is, the operators that descibe it will be diagonal in the basis spanned by the classical bit states.

That's a good point. I've heard it before, but I had forgotten about it. Even if we don't know the best possible definition of consciousness, it's safe to say that conscious experience involves changing memory states. I think that answers my concerns about consciousness. Suppose e.g. that we consider a physicist measuring S_z of a silver atom. In this case, all the "pointer states" of the environment (of the silver atom) have the physicist's memory in a state in which the stored information about the result of the experiment is well-defined (i.e. it's either "up" or "down", not a superposition of both), and that's why he can only experience the pointer states of the environment that he's a part of.

 

[Fra]

The following are the interpretations of QM:

Bohmian · CCC · Consistent histories · Copenhagen · Ensemble · Hidden variable theory · Many-worlds · Pondicherry · Quantum logic · Relational · Transactional

Which is the most accepted by the theoretical physics community? Obviously all have some supporters but I'm interested in finding out which is the most popular and why?

When this has been debated before it's clear that there is different ideas about "point" of an "interpretations".

(A) The I think most common point of an interpretation is as a way to come to a consensus with yourself, in the sense of finding a logically coherent view that incorporates what we know. A way to find a way to mentally handle factual weirdness.

As we know, there are many self-consistent views that corresponds to a finite set of knowledge. Ie. the interpretation is not unique.

(B) The other point is to consider what expectations a given choice of view, induces on the extension of the theory. Here I picture unification of forces and unification of GR and QM.

The latter points is the more interesting in my view, and the reason for my preferences. It seems to me that some of the interpretations doesn't not relaly have a clear ambition beyond the first (A) point. This is why these interpretation has not predictive value.

So I'm quite indifferent to the "interpretation-only" discussion. For me, the interpretations reflects my expectations for extendign the theory.

In this respect my "interpretation" of QM, is that it is a special limiting case (and thus an approximation) to a not yet found theory.

I would like to keep from QM the ambition of keeping it a "measurement theory". This is the distinguishing feature from classical realist physics. However, the physical realisation of measurements and possible state spaces are insufficiently understood. Somehow it's obvious that the QM structures like state space are observer dependent, but the evolution of the observer is not acknowledged. The only accounts for this is the decoherence style views where you picture an external observer, or the environment as an observer, where you can have both the observer andthe observed system as part of the system, and then apply the same QM. But this construct is fundamentally missing the point IMO. It just repeats the mistake. In particular does these imaginary observers vioalte the information capcity of arealy observer, and thus fails to explain the how to evaluation the action of a real observer because it unavoidably capture physical redundancies in evaluation the action.

This doens't fit in any of the major interpretation though. But it shares traits of rovellis' relational QM + smolins objection to reality of law + ariel catichas and ET Jaynes attempt to abstract the laws of physics as rules of inductive inference.

/Fredrik

 

[Fredrik]

Let me make a statement about qubits, which is hopefully nontrivial enough to serve as an analogy that says something interesting.

It's interesting, but I'm not sure it's relevant here. I was talking about decomposing a physical system into subsystems, and you chose a system that can't be decomposed. The Hilbert space of the larger system is supposed to be the tensor product of the Hilbert spaces of the subsystems. In your example the Hilbert space of the "large" system is 2-dimensional, so it can't be the tensor product of two Hilbert spaces.

On the pure states on the Bloch sphere, if you grind through the process of mapping it to the Bloch sphere, projecting down to [-1,1], then rewriting it as a statistical mixture of the pure states, the result is that the ket

a |x^-> + b |x⁺>​

is converted into the statistical mixture

x^- with proportion |a|²
x⁺ with proportion |b|²​

So while the "true" state space of our qubit is the Bloch sphere, the fact I only have access to a limited algebra of observables means that I only see a restricted view of the quantum state. The Born rule pops out of the partial trace. There is no arbitrary choices, artificial decomposition, or anything like that involved.

I don't quite follow you here. Can you post some details?

Local quantum field theory incorporates this. Two different kinds of locality are involved here.

The first kind of locality is that we may want to restrict our attention merely to a particular region of space-time, rather than the entire universe -- and so we get a restriction of the full state space, much as in my example of the qubit.

The second kind of locality says that if the region V is causally determined by the region U (e.g. the past light-code of every point in V has a cross-section lying entirely in U), then the quantum state local to V is completely determined by the state local to U -- time evolution is local.

In particular, this means that if the quantum state local to U is a statistical mixture of some pure states, then time-evolving to V is required to preserve this mixture!

I understand even less of this, but maybe I'll have to wait until I get around to reading Haag's book. It's been on my bookshelf for a year, and it's on the list of the next ten books I'd like to read.

 

[Hurkyl]

It's interesting, but I'm not sure it's relevant here. I was talking about decomposing a physical system into subsystems, and you chose a system that can't be decomposed.

That was half out of convenience, and half intentional -- I think decomposition is a special case.

I don't quite follow you here. Can you post some details?

I'm not sure what part specifically you're asking about. But I do notice I fibbed (kinda) at one place!

(IIRC) In the Bloch sphere picture, the quantum state \rho corresponds to the point (\rho(S_x), \rho(S_y), \rho(S_z)) whose coordinates are the 'expectation' values (where I use S_x as the operator with eigenvalues \pm 1 for spin about the x direction).

So when projected onto the interval, then, \rho gets mapped to \rho(S_x) -- the (mixed) state representing

Spin up with weight (1 + \rho(S_x)) / 2
Spin down with weight (1 - \rho(S_x)) / 2​

The part I fibbed about is the Born rule doesn't appear when projecting; it appears in the correspondence between the Bloch sphere and the more usual kets-in-a-Hilbert space representation of the pure quantum states.

I think the point I wanted to make was that one doesn't need to make any reference to the Born rule to analyze how the quantum state projects from the Bloch sphere down to the interval.

 

[Fredrik]

I'll start with a quick summary of some of the technicalities. The most general qubit state is

|\psi\rangle=\cos\frac\theta 2|0\rangle+e^{i\varphi}\sin\frac\theta 2|1\rangle

The corresponding density matrix, in the |0>, |1> basis, is

\frac 1 2(I+\vec r\cdot\vec \sigma)

where \vec r=(\sin\theta\cos\varphi,\sin\theta\sin\varphi,\cos\theta). By "projecting", I assume that you mean e.g. to replace \vec r by (0,0,\cos\theta). This is a projection onto the z axis. The density matrix becomes

\frac 1 2(I+\cos\theta\ \sigma_3)=\frac 1 2\begin{pmatrix}1+\cos\theta & 0\\ 0 & 1-\cos\theta\end{pmatrix}=\begin{pmatrix}\cos^2\frac\theta 2 & 0\\ 0 & \sin^2\frac\theta 2\end{pmatrix}

and the corresponding density operator is

\cos^2\frac\theta 2|0\rangle\langle 0|+\sin^2\frac\theta 2|1\rangle\langle 1|=|\langle 0|\psi\rangle|^2\ |0\rangle\langle 0|+|\langle 1|\psi\rangle|^2\ |1\rangle\langle 1|

It took me a while to work out these technical details, but I understand them now. What I still don't understand is how you interpret results of this kind, and why you think they're relevant to the MWI. These are some of my thoughts:

The Born rule says that \langle A\rangle_\rho=\mbox{Tr }(\rho A) when \rho is a pure state. From this we can easily show that when \rho=\sum_n a_n|n\rangle\langle n|, with \sum_n a_n=1, \mbox{Tr }(\rho A) takes the form \sum_n a_n\langle n|A|n\rangle. This is a weighted average of pure state expectation values, so this result is what tells us to interpret \sum_n a_n|n\rangle\langle n| as a representation of an ensemble with a_n of the systems in state |n>.

What does the qubit calculation really tell us? It tells us that a projection onto an axis will change the state in exactly the same way that the Born rule tells us the state will change. So it tells us that a measurement is a projection onto an axis. But there's one important detail that we must not forget. The reason why we can interpret the projected state as the statistical mixture that the Born rule predicts...is the Born rule! So it's not like we can derive the Born rule from an axiom that says that a measurement projects a point in the geometrical representation of a state onto an axis. We need the Born rule to interpret the result of the projection.

 

[Fredrik]

I'm starting to come around a little bit about the MWI. For a long time, it just seemed more nonsensical the better I understood it, but it's been going in the other direction while I've been writing my posts in this thread. I still think the terminology is confusing at best and idiotic at worst, and the same goes for the statements that MWI proponents make about the MWI, but I think it's possible to make sense of some of their ideas.

These are some of my thoughts:

There's no way to define the MWI without including the Born rule in some form. The idea that defines the MWI isn't that every system evolves according to the Schrödinger equation. It's that there actually exists a physical system (the omnium) with the properties defined by the Dirac-von Neumann axioms of QM. (The alternative is that QM is just a set of rules that we can use to calculate probabilities of possibilities). It's not a crazy idea, but it's really weird to call it "the many-worlds interpretation". It should be called "realism" or something like that (and it sometimes is). Sure, if we think about the consequences of the defining assumption for a while, taking into account the results of decoherence theory, it's pretty clear that this physical system will include both a dead cat and a living cat at the end of a Schrödinger's cat experiment. But it's really hard to make more specific statements about these things.

I think I made a mistake before when I suggested that the MWI must point out the exact mathematical structures that represent the various worlds. It already does, via the Born rule (which tells us that we must be able to reconstruct the Hilbert space of the omnium as the tensor product of the subsystems). There's no preferred way to decompose the omnium into subsystems, and that means that all of the decompositions are equally valid. If we choose one particular decomposition, we end up with a specific set of worlds. If we choose another decomposition, we get a different set of worlds. This is analogous to how different inertial frames in special relativity disagree about simultaneity and many other things.

Note that the picture of the universe as constantly "branching" into more and more "worlds" doesn't even come close to accurately representing the MWI. The time evolution of the state of the omnium is represented by a curve in its Hilbert space. That curve doesn't have any branches. When we decompose the omnium into "the system" and "the environment", the time evolution is represented by two curves (one in each Hilbert space), but neither of them has any branches. They don't even split during those times when the states of the system develops correlations with macroscopically distinguishable states of the environment.

So what happens when e.g. a physicist measures a spin component of a silver atom, using a Stern-Gerlach apparatus, from the point of view defined by the decomposition of the omnium into "the spin of the atom" and "the environment". The first thing that happens is that the interaction between the atom and the Stern-Gerlach magnet causes a correlation between spin states and position states. This is not a measurement, because the position states are not "pointer states" of the environment, in decoherence theory terminology. The moment after that, correlations will start to form between the position states of the atom, and states of the detectors. These detector states are pointer states, so now we have measured the spin, by allowing these correlations to form.

Nothing funny happens to the curves that represent the time evolution of the omnium in the Hilbert spaces of the subsystems, but as soon as the correlations with the pointer states have formed, we assign a new meaning to their projections onto the subspaces in which the spin and position have definite values. We now think of each of the projections in the atom's Hilbert space as representing the state of the atom as described by an environment in the corresponding pointer state. The worlds in this decomposition are just different projections of the two time evolution curves. There may be other decompositions in which it isn't possible to find anything at that time that resembles these two worlds.

The "environment" can be decomposed further into smaller subsystems. We can take one of them to be the physicist performing the experiment. At some point in time, the environment (that includes the physicist) has developed correlations with the atom, but the information hasn't yet reached the physicist. At this time, the physicist needs both of the projections of the atoms state vector to describe its state from his point of view. To him, the atom is now in a mixed state. This is the type of situation in which one physical system needs a mixed state operator to describe the state of another physical system. At a later time, the memory states of the physicist are correlated with the atom's spin states, and we can now talk about worlds that contain physicists with different memories of what just happened, but only given this decomposition into subsystems.

I still feel that the name "the many-worlds interpretation" should refer to a set of statements about the sort of things I've been talking about here, and not to the simple statement that the omnium is an actual physical system. Instead, people claim that the MWI is defined by statements that can't possibly define an interpretation, and they call the only set of statements I have heard of that's about how subsystems view other subsystems "the relational interpretation".

Note that as long as we're talking about a formulation of QM based on the Dirac-von Neumann axioms, there are only two interpretations: The realist interpretation (a.k.a. the MWI) which merely states that the omnium exists, and the anti-realist interpretation (a.k.a. the statistical interpretation or the ensemble interpretation) which states the opposite, i.e. that QM is just a set of rules that tells us how to calculate probabilities of possibilities. Any other interpretation of this axiomatic framework can only be a clarification of what the MWI is about.

There are of course other axioms that we can take as the starting point, e.g. the path integral formulation. There are two mutually exclusive possibilities in this case too. Either the math describes what actually happens or it doesn't. I'm not sure what the realist interpretation says here. Maybe the realist interpretation of these axioms isn't the MWI, but the transactional interpretation? (I only have a rough idea about what the transactional interpretation is aobut, so I can't really tell). In that case, the name of the MWI is justified. We need to call it something other than "realism" because the realist interpretations of different formulations of the theory can be very different.

 

[Dmitry67]

Fredrick, cool
For you, what was a set of axioms of MWI?

Because if you say that there is just unitary evolution of omnium, then it is not takes seriously because 'it does not describe the classical world'

When you explain it, you get into the wordy stuff, and other people complain that 'MWI is just a long blah-blah-blah'

 

[Fredrik]

Fredrick, cool
For you, what was a set of axioms of MWI?

The same as the axioms for the statistical interpretation (Link), plus the additional assumptions that it makes sense to consider the Hilbert space of the universe (even though it includes yourself), and that a state vector in that Hilbert space is a representation of all the properties of a physical system (the omnium). (The statistical interpretation doesn't assume that, and it never includes the observer in the Hilbert space).

Because if you say that there is just unitary evolution of omnium, then it is not takes seriously because 'it does not describe the classical world'

The classical world is explained by what I said about decoherence, correlations between states of subsystems, and how the subsystems describe each other. The reason why we never experience superpositions is that consciousness involves changing memory states. Each pointer state of the environment (which you're a part of) has your brain in a well-defined memory state, not a superposition. Decoherence ensures that the distinguishable memory states of your brain are correlated with the eigenstates of the observable you're measuring. (Hm, I know that there's something called the "many-minds interpretation", but I have no idea what it says. We may be entering its territory here. If that's the case, then "many-minds" is one of the interpretations that can be described as just a clarification of what the MWI is actually saying).

When you explain it, you get into the wordy stuff, and other people complain that 'MWI is just a long blah-blah-blah'

Yes, it gets wordy, but I have never really had a problem with the amount of words required to explain the consequences of the assumptions that define the intepretation. My objections have been against the lack of a clear explanation of what the MWI says, or against really bad explanations like the infamous Everett FAQ. Max Tegmark came pretty close to defining the MWI properly, but he blew it (in my opinion) by failing to realize the significance and importance of the Born rule.

It's of course still possible that I have misunderstood something fundamental, and that I'm wrong about a lot of this. I still don't know decoherence very well for example, so when I talk about pointer states and stuff like that, I only have a rough idea about what they are.

 

[hamster143]

You've correctly grasped the essence of MWI. Once you admit the possibility that the observer is a quantum object that may be in a superposition of states with different sets of memories, you're more than halfway there.

Note that as long as we're talking about a formulation of QM based on the Dirac-von Neumann axioms, there are only two interpretations: The realist interpretation (a.k.a. the MWI) which merely states that the omnium exists, and the anti-realist interpretation (a.k.a. the statistical interpretation or the ensemble interpretation) which states the opposite, i.e. that QM is just a set of rules that tells us how to calculate probabilities of possibilities. Any other interpretation of this axiomatic framework can only be a clarification of what the MWI is about.

There are also varying degrees of positivism/agnosticism and varying points of view. An observer "out of the universe" would be able to tell the difference, but an internal sentient observer would be perfectly able to describe his own history and experience using, say, Copenhagen and wavefunction collapse, and treat everything about splitting of himself as Occam razor violating nonsense.

I wonder if it's possible to set up an experiment that creates a superposition of a human being in different states.

Note that the picture of the universe as constantly "branching" into more and more "worlds" doesn't even come close to accurately representing the MWI.

This all depends on what you mean by "world". There's a definite branching of sentient beings and of classical worlds. There isn't any branching of the whole state of the universe in the big Hilbert space - that one simply evolves according to Schrodinger's equation.