Does Decoherence and Entropy Relate to the Second Law of Thermodynamics?

[Bockhorst]

Back in August I asked a question on this forum about Zurek's paper "Decoherence and the Transition from Quantum to Classical—Revisited" and got no response.

I am sure many of the folks on this list have read this paper in which Zurek states that entropy increases upon decoherence (that's how what I interpret equation 12).

Does anyone have an idea how this relates to the second law of thermodynamics?

I would like to know if this is a good question or a stupid question.

Thanks for any response.

 

[Ken G]

I cannot get access to the paper, but I think I get the gist from the abstract, and it all sounds pretty reasonable to me. Yes, your question about the second law is at the heart of this. There are three basic ideas behind the second law, which are simply (1) more likely states tend to be manifested preferentially over less likely ones, (2) this is dramatically true when there a vast number of possibilities and the less likely things are vastly unlikely, and (3) the truth of this tends to grow with time elapsed as the system gains better and better access to the more likely states. So I interpret Zurek as saying, when you couple a macro apparatus to a quantum state, the quantum state becomes entangled with a dizzying array of macro states that will tend toward the more likely configuations. It then becomes vastly more likely that the quantum state will lose correlations between the different eigenstates that are singled out by that apparatus, by virtue of the correlations lost by the vastly more likely states of the macro apparatus. If I'm right, that doesn't adjudicate between Bohr's and Everett's ways of looking at it, but it does give a consistent description of why "collapse" occurs in either interpretation.

 

[Bockhorst]

Ken,

Thanks for the reply.

You can get Zurek's paper at http://arxiv.org/abs/quant-ph/0306072.

In this paper, Zurek rejects both Bohr's and Everett's ways of looking at the measurement problem. He gives a much more plausible description of the process.

But that’s a different discussion.

According to EQ 12, entropy increases when a coherent system de-coheres – when the system interacts with the rest of the universe.

My question is; does EQ 12 represent a new definition of entropy?

Rhea

 

[Andy Resnick]

No- not a new definition of entropy. It's a statistical mechanical type of expression, the concept of 'density of states' is treated quantum-mechanically via the density matrix. This paper discusses how to separate the total (system+environment) matrix into (system) and (environment) matrices, and the consequences of that.

Zurek and his coworkers, IMHO, really revolutionized specifically the field of quantum mechanics, but their ideas have really spread into many other areas of physics, including quantum optics and optical trapping of single/small numbers of atoms.

 

[Ken G]

In this paper, Zurek rejects both Bohr's and Everett's ways of looking at the measurement problem. He gives a much more plausible description of the process.

OK, thanks, I have the paper now and it is indeed an impressive survey of the epistemological accomplishments of decoherence and einselection. I don't think I would say that Zurek rejects Bohr and Everett, indeed he says at one point:
"Decoherence is of use within the framework of either of the two interpretations: It can
supply a definition of the branches in Everett’s Many Worlds Interpretation, but it can also delineate the border that is so central to Bohr’s point of view."

But he does say that Bohr is focused on epistemology of the wave function, and Everett on its ontology, whereas Zurek's approach allows for a kind of taking the best of both worlds while not getting caught up in Bohr's firewall between the classical and quantum worlds, nor in Everett's seemingly bizarre requirement that "everything happens, we merely perceive only one outcome". In other words, Zurek allows us to apply some of the ontological thinking that our minds crave, without requiring that we accept the existence of things we can never verify or test in any way. But fundamentally, it is still consistent with both interpretations, because it is the same quantum mechanics, and I actually see a lot of agreement between Zurek and Bohr-- Bohr was just content to accept the barrier between the quantum and the classical world, whereas Zurek has gone a long way to inquire about that boundary and determine its features. But it ends up working pretty much just like Bohr imagined it would, and I interpret Zurek's results as consistent with Bohr's way of thinking of things, it really just goes deeper to show why Bohr is right about how we do science.

According to EQ 12, entropy increases when a coherent system de-coheres – when the system interacts with the rest of the universe.

Yes, that is natural to occur, and this is indeed the standard meaning of entropy. Basically, what entropy does is to characterize the likelihood of a given class of outcomes based on counting how many ways they can be actualized. If there are more ways of actualizing a class of outcomes, then that is what will happen-- that's the second law in a nutshell. So that's why coupling quantum systems to classical ones results spontaneously in the "collapse" of the wave function-- there are more ways for it to happen such that the coherences are destroyed and "einselection" occurs. That's the "probability sieve", as I understand it-- counting likelihoods is basically what we mean by a measurement. There may be several outcomes that are quite likely, which is why we cannot be completely deterministic, but those outcomes will all be vastly more likely than outcomes that preserve some level of coherence and quantum superposition such as existed in the quantum system before it was opened up to coupling with the environment. I agree with Andy Resnick, it's a very convincing position, I'm glad you pointed to it.

 

[vanesch]

OK, thanks, I have the paper now and it is indeed an impressive survey of the epistemological accomplishments of decoherence and einselection. I don't think I would say that Zurek rejects Bohr and Everett, indeed he says at one point:
"Decoherence is of use within the framework of either of the two interpretations: It can
supply a definition of the branches in Everett’s Many Worlds Interpretation, but it can also delineate the border that is so central to Bohr’s point of view."

But he does say that Bohr is focused on epistemology of the wave function, and Everett on its ontology, whereas Zurek's approach allows for a kind of taking the best of both worlds while not getting caught up in Bohr's firewall between the classical and quantum worlds, nor in Everett's seemingly bizarre requirement that "everything happens, we merely perceive only one outcome". In other words, Zurek allows us to apply some of the ontological thinking that our minds crave, without requiring that we accept the existence of things we can never verify or test in any way.

I agree with you concerning the compatibility with several interpretational schemes. However, I would say that decoherence is most of help to MWI - it is the explanation, or at least an important part of the explanation - that helps MWI, as it gives it a scheme to go from "many ontological worlds" to "one single observed world". Also, decoherence "needs" in a way part of the MWI viewpoint, in that in order for the calculations of decoherence even to make sense, one needs the "macroscopically evolving wavefunction" viewpoint. If, as is the case with Bohr, the physics, and its laws, *change* between the microscopic and the macroscopic, then using the formal tools of quantum mechanics on macroscopic systems would simply be out of the question: we would be using a formalism where it isn't considered valid. Decoherence is based upon the unitary quantum formalism, and if one tries to explain the effect of the Heisenberg cut (the transition between the domain where quantum mechanics is valid, and where classical mechanics is valid) by using the formalism of quantum mechanics, then one is, by definition, not using the right formal context. It would mean that there where we think (according to Bohr) that the classical laws are valid, we *nevertheless* can use the quantum formalism, and *explain* why things happen *as if* the classical laws are valid. But that's nothing else but the MWI viewpoint, and not the Bohr viewpoint which considers explicitly that in the macroworld, classical physics (and hence not quantum physics) is valid.

So I'd say that Bohr doesn't *need* decoherence, and moreover removes decoherence from its formal basis (the use of the quantum formalism). However, what decoherence does bring to Bohr, is that it demonstrates the arbitrariness of the Heisenberg cut, once decoherence has set in.

On the other hand, MWI justifies the formal basis of decoherence (unitary evolution valid universally), and on the other hand, decoherence justifies the "split into worlds" of MWI.

So although it is entirely correct to say that decoherence (a property of complex systems evolving under unitary quantum theory) is independent of any interpretational scheme, I would say that it is in any way "closer" to the needs and frame of MWI than it is to the Copenhagen view.

 

[Ken G]

I agree with you concerning the compatibility with several interpretational schemes. However, I would say that decoherence is most of help to MWI - it is the explanation, or at least an important part of the explanation - that helps MWI, as it gives it a scheme to go from "many ontological worlds" to "one single observed world".

True enough-- I guess it can be said that it adds understanding, so can be used to inform either interpretation. It can also be used to inform objections to each interpretation. For example, my beef with MWI is that it is pure ontology-- it is much like the aether in relativity, a purely ontological construct that cannot be revealed in any test. Decoherence plays the role of the Lorentz transformation-- it reveals why those tests cannot be performed.

Also, decoherence "needs" in a way part of the MWI viewpoint, in that in order for the calculations of decoherence even to make sense, one needs the "macroscopically evolving wavefunction" viewpoint.

Yes, that is the sense to which those inclined to want to use MWI, like those who would want to use an aether in relativity, are equipped with the means to do it.

If, as is the case with Bohr, the physics, and its laws, *change* between the microscopic and the macroscopic, then using the formal tools of quantum mechanics on macroscopic systems would simply be out of the question: we would be using a formalism where it isn't considered valid.

But Bohr does not actually say that the laws change between the domains, that would be an awkward and undesirable (and unnecessary) world view. Bohr does not say the laws change-- Bohr says that we choose to construct them differently because we are asking different kinds of questions. This is quite common in physics-- just look at thermodynamics compared to classical mechanics. All that is required, when we change the questions of interest, is correspondence. That doesn't make the laws different, it makes them concern different questions.

It would mean that there where we think (according to Bohr) that the classical laws are valid, we *nevertheless* can use the quantum formalism, and *explain* why things happen *as if* the classical laws are valid. But that's nothing else but the MWI viewpoint, and not the Bohr viewpoint which considers explicitly that in the macroworld, classical physics (and hence not quantum physics) is valid.

I would expect that Bohr would confer to the word "valid" no other meaning than "succeeds in its predictions", so I do not agree with that claim about Bohr, but I do agree that it allows one to imagine that MWI is somehow still happening "in the background" as one is applying the laws of quantum mechanics to explain classical phenomena. Nevertheless, the claim that MWI is going on in some untestable realm is still inherently untestable-- even with decoherence.

Again, here decoherence plays exactly the same role as the Lorentz transformation in relativity-- it "covers the tracks" of a chosen ontology. Why is it, I wonder, that in relativity we use that to say there is no aether because don't need it in any of our predictions, yet in quantum mechanics, there's a tendency to retain the extraneous ontology anyway? We have the same core idea either way-- that information we have no means nor desire to track should not be imagined to exist all the same. In other words, information is not an ontological entity, it is an epistemological one, and that is the basis of the Bohr approach.

So I'd say that Bohr doesn't *need* decoherence, and moreover removes decoherence from its formal basis (the use of the quantum formalism). However, what decoherence does bring to Bohr, is that it demonstrates the arbitrariness of the Heisenberg cut, once decoherence has set in.

Right, and that is of value to Bohr-- people often object to the arbitrariness of the Heisenberg cut, and ask about gray areas.

On the other hand, MWI justifies the formal basis of decoherence (unitary evolution valid universally), and on the other hand, decoherence justifies the "split into worlds" of MWI.

But it does not justify what has always been the key objection-- how we perceive one thing happening and not the others. I would tend to see that purely probabilistically-- when mixed states are created, there is no need for us to imagine they are all actualized, one is enough.

So although it is entirely correct to say that decoherence (a property of complex systems evolving under unitary quantum theory) is independent of any interpretational scheme, I would say that it is in any way "closer" to the needs and frame of MWI than it is to the Copenhagen view.

And I would say it informs either one-- but does not remove my core objection to MWI. Indeed, when I first heard about decoherence, I thought "that explains the Heisenberg cut", which is tantamount to explaining why we don't need MWI to do physics.

 

[Bockhorst]

No- not a new definition of entropy. It's a statistical mechanical type of expression, the concept of 'density of states' is treated quantum-mechanically via the density matrix. This paper discusses how to separate the total (system+environment) matrix into (system) and (environment) matrices, and the consequences of that.

Zurek and his coworkers, IMHO, really revolutionized specifically the field of quantum mechanics, but their ideas have really spread into many other areas of physics, including quantum optics and optical trapping of single/small numbers of atoms.

Andy,

Thanks, your reply gives me a better idea of what's going on. Now I see that I didn't pose my question very well. Entropy increases because the number of possible states increases.

With better understanding, I will re-formulate my question:

Is EQ 12 the "root cause" of entropy increase in the universe? IOW is decoherence involved in any physical "real world" process where entropy increases?

Rhea

 

[Ken G]

Is EQ 12 the "root cause" of entropy increase in the universe?

No, that would be saying it backwards-- entropy increase is the root cause of decoherence! You can tell because entropy increase is the more automatic principle, it merely says that things that have more ways of happening are what will happen.

IOW is decoherence involved in any physical "real world" process where entropy increases?

That is actually a different question, because it does not specify a particular causal connection between entropy and decoherence. If one is a "quantum realist", one thinks that quantum mechanics rules everything that happens in the universe, and so one would say yes, anything that involves entropy increase is ruled by quantum mechanics, and decoherence is the description in quantum mechanical language of entropy increase. However, if you are, like me, someone who simply looks on quantum mechanics the same way as all other science (an artifice for fashioning testable hypotheses and assembling their outcomes into a unifying framework), then you would say no, theory is never "involved in" anything that "happens" in the universe-- it is merely our way of picturing what is happening, and only when convenient to do so. So take your pick, it is a philosophy question not a physics question.

 

[Hurkyl]

For example, my beef with MWI is that it is pure ontology-- it is much like the aether in relativity, a purely ontological construct that cannot be revealed in any test.

I don't understand -- if I understand the analogy you're trying to set up, MWI's relation to quantum mechanics is exactly the opposite of the Aether's relation to relativity.

The use of the aether was as an addition to the dynamics of special relativity in order to make it more palatable. The aether was supposed to have a more classical foundation, and still manage to give the laws of special relativity as an emergent property.

In the analogy, we would be considering things like wavefunction collapse or pilot waves as the analogue to the Aether: they represent additions / changes to the dynamics of quantum mechanics (unitary evolution) in order to make it more palatable. MWI is the position that one should study unitary evolution as is; one shouldn't add any extra gadgets to the theory. In the analogy, it's the antithesis of the aether.

 

[Ken G]

That's not how I see it, I see it as just the same as the aether-- they are both untestable efforts to describe an ontology that underpins the epistemology of quantum mechanics and relativity respectively. The reason aether provides an ontology to relativity is that it allows light to propagate through a physical medium, making the propagation of light a physical mechanism. Light exists because aether exists, it's ontological. No observations preclude that, because the moment we accepted Lorentz transformations as the way to transform between inertial frames, we also accepted that there would never be any way to sense the presence or absence of an aether. We only chose not to include it, in favor of the epistemological postulate that all observers should be able to do physics the same way, adding nothing that is special to one frame or another. A clear example of a streamlined epistemology trumping an extraneous ontology.

Enter MWI. The wave function is there considered to be an ontological entity, not purely an epistemological one like the way Bohr treated it. The trouble is, as soon as you accept that decoherence in macro systems will be involved in every measurement you ever do to test your theory, you have lost any ability to sense the wave function's ontology. So again we have an extraneous ontology vs. a streamlined epistemology (no "extra worlds" to worry about), yet for some reason, the oft-favored approach now is to take the ontological road. That seems inconsistent. (By the way, pilot waves would be going even farther down the road of extraneous ontology, I don't equate that with wavefunction collapse at all because Bohr's view is that the collapse is an epistemological happening that requires no explanation. Decoherence provides an explanation, but it's just what Bohr anticipated-- I suspect Bohr would just say "I knew that viscerally, I just didn't have a mathematically formal way to say it").

 

[Hurkyl]

streamlined epistemology (no "extra worlds" to worry about),

There are always "extra worlds" to worry about -- they are a consequence of unitary evolution, e.g. via the Schrödinger equation.

And an interpretation that includes an extra mechanism whose properties are ill-defined and whose timing is ill-defined, all for the sake of making an undetectable change to the theory so that you can diminish the cognative dissonance of trying to use incompatable theoretical frameworks to describe reality is hardly something I would call "streamlined". (Okay, I admit I'm exaggerating. But only a little. )


As for the rest of your comments, your use of 'epistemological' and 'ontological' is mystifying. Not only does your example not make sense (an aether is not a prerequisite for light being 'real') -- your insistence on attaching them to theories is, IMHO, incorrect. MWI doesn't require that the wave function be a 'real object', nor does Copenhagen require that wave functions be mental fictions.

Furthermore, even if you wish to refrain from making assertions about 'reality' -- it is still reasonable (and, dare I say, preferable, from a pedagogical standpoint) to base an ontology in a mathematical structure. Denying an attempt at ontology is, in effect, a refusal to try and understand the subject matter.

 

[Ken G]

There are always "extra worlds" to worry about -- they are a consequence of unitary evolution, e.g. via the Schrödinger equation.

That is not necessarily true, it is an example of the kind of backward logic we often see in regard to MWI. It is never the role of a theory to tell reality what to do, that is always backward thinking. Reality does whatever it wants, the theory tries to describe it. Thus, it is simply nonscientific to claim that "the Schrödinger equation" causes there to be "extra worlds"-- equations don't do that, they just don't. Show me the extra worlds, and then show me the equation that describes them-- never the other way around.

And an interpretation that includes an extra mechanism whose properties are ill-defined and whose timing is ill-defined, all for the sake of making an undetectable change to the theory so that you can diminish the cognative dissonance of trying to use incompatable theoretical frameworks to describe reality is hardly something I would call "streamlined". (Okay, I admit I'm exaggerating. But only a little. )

I think those remarks stem more from a misunderstanding about Bohr's approach that from that approach itself. The key is the level of realism involved, i.e., whether one thinks physics is an epistemology or an ontology. All of your criticisms assume it is an ontology, but Bohr never intended it to be that. So there is no "extra mechanism", there's no mechanism at all-- there is the mathematics of making a prediction, that's all "collapse" ever was in the Bohr epistemology. Yes, as ontology, the Bohr approach is not effective-- it is not trying to do that. Show Bohr what observation needs to be predicted, and he will predict it-- never anything more, the scheme for making predictions does not dictate the presence of untestable phenomenon. That would be what I say is "extraneous ontology", and is just what the aether is in relativity.

Now, I do not say it is terrible to have extraneous ontology, we as scientists like ontology, it makes us feel like we are really seeing the truth rather than just a simulacrum of the truth. I merely point out that we are uneven in what extraneous ontologies we tolerate.

As for the rest of your comments, your use of 'epistemological' and 'ontological' is mystifying.

I think they are quite the normal applications of those terms, actually. Perhaps you are missing my point.

Not only does your example not make sense (an aether is not a prerequisite for light being 'real') -- your insistence on attaching them to theories is, IMHO, incorrect.[

What I meant about the tersely assembled analogy with the aether was simply that imagining an aether makes real a mechanism by which light propagates as a wave. You can imagine something physical, not just mathematical, whereby light propagates. I suspect you think of the wave function that way-- not just a mathematical object, but something really there. For if it is a mathematical object, it exists only in our minds, and has no power to generate "many worlds" or anything else.

MWI doesn't require that the wave function be a 'real object', nor does Copenhagen require that wave functions be mental fictions.

If you don't see the Bohr interpretation as fundamentally epistemological, and the MWI as fundamentally ontological, maybe it is you who do not understand those concepts-- I view this as not at all a controversial interpretation of the situation. For example, at http://books.google.com/books?id=Er...=X&oi=book_result&resnum=1&ct=result#PPA18,M1 we find the statement

Bohr would never allow the type of language that admitted the independent existence of any kind of object which could be said to be in a certain state. That is to say he would not regard it as meaningful to talk about, for example, a particle existing between quantum measurements even if the same results were obtained for a given observable in a sequence of such measurements. Rather, as we have seen, he considered the experimental arrangement and the content (meaning) of the result to be a single unanalysable whole. To talk of a state in abstraction of such an experimental arrangement would, for Bohr, make no sense.

I think the pretty clear, and valid, translation of that is that for Bohr, "ontology is epistemology and nothing more". Which is what I said. Seek other references if you think this is controversial.

As for the MWI, my claim is that it does not say ontology is no more than epistemology, instead, it says that the epistemology springs from the underlying ontology. Your own comments also reveal in every case that you think the same way. Again, MWI is inherently an ontological description, that is pretty much obvious. If you don't want the wave function itself to be the underlying ontology, fine, pick something else (like unitarity, though I don't know how you have that without the wave function it acts upon)-- my claim is only that if you have no underlying ontology from which the epistemology is thought to spring, then you simply have no MWI.

Furthermore, even if you wish to refrain from making assertions about 'reality' -- it is still reasonable (and, dare I say, preferable, from a pedagogical standpoint) to base an ontology in a mathematical structure.

Now you seem to recognize what I've been saying-- your approach requires that we view ontology as fundamental to epistemology (note, for example, that you equate mathematics with ontology, instead of epistemology, despite the fact that mathematics is an operation that occurs in the mind so clearly deals with knowledge not existence), which is precisely what Bohr rejected. It is also what is rejected when we reject the aether-- relativity uses no ontology that goes beyond the epistemology of the observer. The laws of physics are the ultimate authority, not the state of the matter, that is the crux of the standard epistemological interpretation of relativity. It's just like Bohr: no ontology beyond what is evident in the epistemology. First show me the many worlds, then explain them with the mathematics-- the other way around is just magical thinking.

Denying an attempt at ontology is, in effect, a refusal to try and understand the subject matter.

Thank you for that perfectly clear statement of your own prejudices about ontology in science. But it's just prejudice, because in philosophy, there is no such assumption that ontology can be equated with understanding. This is the fundamental flaw in everything you say about MWI-- you always equate ontology with understanding, missing that Bohr is completely justified, if he chooses, to equate epistemology with understanding instead. Indeed, that's generally what science does: epistemology is the route to understanding, ontology is just a kind of convenient crutch to help us get the all-important epistemology right.

 

[Hurkyl]

I suspect you think of the wave function that way-- not just a mathematical object, but something really there.

I think discussions about what is or is not 'really there' are generally nothing more than an expression of personal biases.

It is never the role of a theory to tell reality what to do, that is always backward thinking.

However, it is the role of a theory to make predictions, and every theory that makes use of unitary evolution is going to predict the existence of "other worlds". And given that there are over 100 years of experiments confirming the predictions of unitary evolution -- including experiments involving exactly those effects the methods of many worlds are meant to describe (e.g. Bell tests, quantum erasure) -- I find it rather disingenious to dismiss them without consideration.

Furthermore, it is the role of scientific theories to shape our understanding of the natural world. If our best scientific theories indicate that "other worlds" are worthy of serious consideration, it is not the place of our personal prejudices to say otherwise.

Thank you for that perfectly clear statement of your own prejudices about ontology in science. But it's just prejudice, because in philosophy, there is no such assumption that ontology can be equated with understanding

I assert that ontology is a necessary condition for understanding, but not a sufficient one. If I have an understanding of a theory, then I do have an ontology (or possibly several!) that maps the aspects of that theory onto the mental concepts that make up my understanding. On the other hand, if I refuse to allow myself to build such mental concepts, then I cannot effectively formulate an understanding of the subject.

But yes, I will admit I am not a behavioral scientist, so I don't have the expertise to back up this claim. (But, I speculate that you also don't have the expertise to assert that one can understand without forming mental concepts related to the theory)

 

[Ken G]

I think discussions about what is or is not 'really there' are generally nothing more than an expression of personal biases.

That sounds like a much softer stance on ontology than your previous "Denying an attempt at ontology is, in effect, a refusal to try and understand the subject matter." But the new position will bring us closer into agreement.

However, it is the role of a theory to make predictions, and every theory that makes use of unitary evolution is going to predict the existence of "other worlds".

I think you meant that it is the role of a theory to make testable predictions. Is it not? Note how insertion of that key word invalidates the rest of the statement. When a scientific theory makes predictions that can be tested, and others that cannot, does verification of the testable predictions offer evidence in favor of the untestable ones? Why? Doesn't sound much like science to me, it sounds like the backward logic I was talking about.

And given that there are over 100 years of experiments confirming the predictions of unitary evolution -- including experiments involving exactly those effects the methods of many worlds are meant to describe (e.g. Bell tests, quantum erasure) -- I find it rather disingenious to dismiss them without consideration.

I fear you are constructing straw men and missing my point. Nothing I'm saying has anything to do with anything that is experimentally verifiable, that's the whole point. Or are you going to claim that purely epistemological formulations of quantum mechanics, like Bohr's, cannot correctly predict the result of a Bell-type experiment?

Furthermore, it is the role of scientific theories to shape our understanding of the natural world.

Where "natural world" is defined by our experiments, or our mental constructs inspired by predictions that are only mathematically contiguous to that which can actually be tested?

If our best scientific theories indicate that "other worlds" are worthy of serious consideration, it is not the place of our personal prejudices to say otherwise.

It is a rather amazing argument to claim that it is "prejudice" to assert that you need to show me the extra worlds before science has any need to explain them. Again, that is simply backward to the true charge we give science. When science feels a need to explain that which shows up in no experiment, then it joins with a bunch of other subjective pursuits and opens itself to the same criticisms often leveled at those other pursuits. Now, if instead you mean that you have a suggestion for an experiment that can actually detect those "other worlds", then that's very different and I am all ears. Do you?

I assert that ontology is a necessary condition for understanding, but not a sufficient one.

Now that assertion is prejudice, it is the one I have already identified in you. How could you ever agree with Bohr if you start from a different set of assumptions about what understanding is? Bohr saw no need for any ontology beyond epistemology-- to him, the only ontology science has is its epistemology. I would say this is precisely the spirit of relativity, which was my "mysterious" point from before. I don't necessarily disagree that ontology is nice, I merely recognize that science has a very conflicted relationship with it. I view it as more of a subjective picture we can take or leave as we do what really matters in science-- its epistemology.

If I have an understanding of a theory, then I do have an ontology (or possibly several!) that maps the aspects of that theory onto the mental concepts that make up my understanding.

But here you are misapplying the term ontology. A map onto mental concepts never refers to anything but mental concepts, whereas an ontology must assert the existence of something outside of your mental concepts. That's the whole sticky problem with it, and with many worlds. If you will assert that "many worlds" are nothing but a mental concept that you use to help you understand quantum mechanics, I have no beef with it at all. The normal way it is described, however, is in ontological terms-- the many worlds are really there, because they are implied by a mental construct that overlaps with the same testable predictions as purely epistemological approaches like Bohr's (by "purely", I just mean the ontology extends not one iota past the epistemology).

I'm saying, with Bohr, that nothing ontological should be implied by a theory, it is the proper role of theory to describe only what ontology has been established by direct observation independently of the mathematical specifics of some theory. The rest is no more than "handy mnemonic". It would be like thinking the square root of minus one is somewhere in the real world, simply because it spawns a useful algebra for simplifying quantum mechanical calculations.

On the other hand, if I refuse to allow myself to build such mental concepts, then I cannot effectively formulate an understanding of the subject.

Goodness, no one is suggesting we not build mental concepts! That's what theoretical physics is all about. The issue is, what is the role of those concepts-- to understand what we have evidence exists, or to establish what exists independent from any direct observation of said existence. To me, using pure theory to decide what exists is the ultimate act of human hubris, along the lines of the rational philosophies of the early natural philosophers. Although science owes its existence to those early philosophies, it didn't start to really make progress on its own until it distanced itself from that mode of thinking.

 

[Hurkyl]

Or are you going to claim that purely epistemological formulations of quantum mechanics, like Bohr's, cannot correctly predict the result of a Bell-type experiment?

Of course the Copenhagen interpretation can predict^* the result of a Bell-type experiment. Just like the MWI, it would say that multiple worlds were formed when the photon-pair is created, and those worlds may or may not interfere, based upon the settings of Alice's and Bob's measuring devices. The only difference is that the argument according to the CI wouldn't use those particular words. (And, of course, it would throw in a collapse or two, so as to get a definite outcome)

*: I'm ignoring, for the sake of argument, that I don't see how CI would predict that there wasn't a wavefunction collapse involved that spoils the entanglement. But due to thermodynamics this may be a non-issue.



I did mean to reply to this part earlier, but forgot:

So there is no "extra mechanism", there's no mechanism at all-- there is the mathematics of making a prediction, that's all "collapse" ever was in the Bohr epistemology.

CI asserts that wavefunctions evolve according to the Schrödinger equation, except that they occasionally collapse to. The CI doesn't describe collapse as merely a mathematical technique for computing conditional probabilities -- the CI describe collapse as an actual change in the wavefunction: it was once something, and now it's something else.

(It doesn't matter if you think of the wavefunction as a real object, a proxy for a real object or objects, a collection of information, or even purely a figment of your imagination)

 

[Ken G]

Just like the MWI, it would say that multiple worlds were formed when the photon-pair is created, and those worlds may or may not interfere, based upon the settings of Alice's and Bob's measuring devices.

That is patently untrue, the CI never asserts that "multiple worlds" are formed, as that is a clearly ontological statement. It says that the projection onto the measurement is a mixed state, and that's it-- there's nothing that is being projected, the science is the projection. That dovetails with the simple fact that the projection is the only thing we can do science on, it is in fact the result of the measurement. No multiple worlds at all, no more than mulitiple worlds are created every time you check today's weather in classical physics. I think you misunderstand the CI rather completely, at least Bohr's mature version.

The only difference is that the argument according to the CI wouldn't use those particular words.

Wrong, read Bohr. If it doesn't use the same words, that's not the "only difference", the only difference it is a completely different interpretation of what is happening-- no multiple worlds, ever. It's not me that is saying this, it is both Heisenberg and Bohr, but I particularly point to Bohr-- Heisenberg had a tendency to want to stir in some extraneous ontology of his own.

CI asserts that wavefunctions evolve according to the Schrödinger equation, except that they occasionally collapse to.

The "collapse" in the CI happens when you decide, as the physicist, that you don't want to track certain information. You recognize the epistemological fact that you simply do not have, nor will you ever have, the capability of tracking that information, and so you simply build a model that knows it is not tracking that. Physics does that sort of thing all the time, it's basically what thermodynamics is all about.

The CI doesn't describe collapse as merely a mathematical technique for computing conditional probabilities -- the CI describe collapse as an actual change in the wavefunction: it was once something, and now it's something else.

It was never something other than a wavefunction, so of course when you couple it to new constraints, you will have new information about it. The crux of the CI is that you choose the information you want to track, and that forms the wave function. In fact, in the CI, there is really no such thing as "the" wave function, any more than there is any such thing as "the" probability that a classical event will happen. Probability, and wave functions, are entirely contingent on the information you choose to include. That's why we can do quantum mechanics in the first place, given the impossibility of finding a perfectly unentangled particle to do experiments on.

(It doesn't matter if you think of the wavefunction as a real object, a proxy for a real object or objects, a collection of information, or even purely a figment of your imagination)

It matters a great deal, actually. As I said above, if you think of "many worlds" as just a kind of picture that helps you do calculations, no one can have an objection to that. But you claim the existence of the many worlds, and you claim it springs from the theory, so that invalidates the claim you just made.

 

[Hurkyl]

That is patently untrue, the CI never asserts that "multiple worlds" are formed, as that is a clearly ontological statement.

That multiple worlds are formed is a qualitative description of the wavefunction, and thus falls in the realm of pure syntax.

 

[Ken G]

That multiple worlds are formed is a qualitative description of the wavefunction, and thus falls in the realm of pure syntax.

If that's all the MWI was saying, it would have no ontological significance at all, and I would have no objection to it as a subjective choice by some physicists about how they like to picture their own calculations. But that is not, at all, what the interpretation is taken to mean, as any quick google on the topic will demonstrate. I guarantee that you will encounter ontological language within about the first three seconds of such an exercise.

For example, the first paragraph of the Wiki entry on the topic concludes " In layman's terms, this means that there is a very large, perhaps infinite, number of universes and that everything that could possibly happen in our universe (but doesn't) does happen in some other universes."

Or this quote (from http://plato.stanford.edu/entries/qm-everett/#5) of De Witt and Graham, credited with the most commonly accepted description of what the MWI entails:"This reality, which is described jointly by the dynamical variables and the state vector, is not the reality we customarily think of, but is a reality composed of many worlds."

Do any of those statements sound like "syntax" to you, or do they sound like completely serious efforts at ontology?

 

[vanesch]

That's not how I see it, I see it as just the same as the aether-- they are both untestable efforts to describe an ontology that underpins the epistemology of quantum mechanics and relativity respectively.

I agree with you that in MWI one takes the wavefunction "for real" (attach an ontological significance to it), and there is a ressemblance to a kind of "ether" in relativity - however, certainly NOT the ether you are referring to.

The "ether" that would correspond, in relativity, to the wavefunction in MWI, would be the four-dimensional manifold "ether", not the 3-dimensional "space" ether which was initially postulated to justify the "electromagnetic vibrations". Now, not all relativists do this, but I think that many of them do give some kind of "ontological" status to the 4-dim spacetime manifold, even though the *observable* part is only a 3-dim slice through it.

Well, I see the wavefunction in MWI in the same way: there is some ontology to the entire wavefunction which is the result of the unitary evolution, but there is only ONE TERM which is an observable part.

The "old" space-ether would in that respect more ressemble to the projection postulate which wants to "cut away" the extra, though unobservable, part of the 4-dim spacetime manifold, and rigidly consider a specific 3-dim slice, in the same way as the projection postulate "cuts away" all those terms in the wavefunction which will turn out not to be observable.

And indeed, the Lorentz transformations indicate why we cannot distinguish between both views (in other words, why such a weird 4-dim spacetime manifold will act "as if" we were living in a kind of 3-dim ether) in the same way as decoherence indicates why we cannot distinguish between a true MWI world, and one in which the extra terms generated by the Schroedinger equation have been cut away.

Of course, the analogy has its limits, but nevertheless, I thought it was interesting to point this out.

Of course, you're not obliged to do this. You can stick to a strictly positivist viewpoint in which science is just there to crank out mathematical descriptions which help us predict how experiments will evolve. But our human mind sometimes craves for a "picture" ; something we like to think is "real" out there. My personal opinion is that in that case, you're best suited with a picture that sticks to the formula, instead of to the intuition. Other people can have other opinions.

 

[Ken G]

And indeed, the Lorentz transformations indicate why we cannot distinguish between both views (in other words, why such a weird 4-dim spacetime manifold will act "as if" we were living in a kind of 3-dim ether) in the same way as decoherence indicates why we cannot distinguish between a true MWI world, and one in which the extra terms generated by the Schroedinger equation have been cut away.

Yes, I see the analogy you make there as well. No analogy is perfect, and I was focusing on one aspect-- the tendency to reject ontologies whose tracks do not appear in the observations. But you make the point that the rejection might actually be on the grounds of the Copernican principle, that giving a special ontology to a frame simply because it appears to be special to us, but has nothing special demonstrable in the theory, is the offending element in relativity. That does put the choice of conferring "realness" to the full 4-D spacetime manifold on a par with doing that for the "many worlds".

Yes, that is probably an even stronger analogy, and explains a certain consistency in the standard approaches, but I would point out that treating the spacetime manifold ontologically requires fewer assumptions because it is like a more sophisticated model to understand the scenery of the play that the actors can interact with directly, whereas MWI is more like an ontology of what is backstage that neither the audience nor the actors ever see. We actually use the 4D manifold in our calculations, but the same is not true for the MWI (even "believers" in it never actually use it in any calculations, it is entirely extraneous to the way quantum mechanics is actually done).

To me, what all this says is that there is a considerable level of Aristotelian rationalism still alive and well in modern physics. It is fashionable these days to sacrifice at the altar of empiricism, and bash natural philosophers like Aristotle who thought they could discover physical law via force of intellect, but then when you look more closely you see that we still do the same thing all the time. The 4D spacetime manifold and the many-worlds are both, when taken ontologically, purely rationalist constructions-- but at least the former actually gets used.

Of course, you're not obliged to do this. You can stick to a strictly positivist viewpoint in which science is just there to crank out mathematical descriptions which help us predict how experiments will evolve. But our human mind sometimes craves for a "picture" ; something we like to think is "real" out there. My personal opinion is that in that case, you're best suited with a picture that sticks to the formula, instead of to the intuition. Other people can have other opinions.

Yes, I agree that the craving for ontology is strong, and important to recognize. I merely ask that we recognize we are doing it, and that there is an important scientific difference between building theories that explain a physical reality we actually observe, versus imagining a physical reality we do not observe to fit our theories.

 

[Naty1]

Charles Seife in DECODING THE UNIVERSE says

Like entropy, decoherence let's you know which way time is running; decoherence is an arrow of time...Decoherence of a qubit increases the entropy of the system by kLog2...nature is always measuring and disseminating information..

 

[vanesch]

Yes, I see the analogy you make there as well. No analogy is perfect, and I was focusing on one aspect-- the tendency to reject ontologies whose tracks do not appear in the observations. But you make the point that the rejection might actually be on the grounds of the Copernican principle, that giving a special ontology to a frame simply because it appears to be special to us, but has nothing special demonstrable in the theory, is the offending element in relativity. That does put the choice of conferring "realness" to the full 4-D spacetime manifold on a par with doing that for the "many worlds".

Yup.

Yes, that is probably an even stronger analogy, and explains a certain consistency in the standard approaches, but I would point out that treating the spacetime manifold ontologically requires fewer assumptions because it is like a more sophisticated model to understand the scenery of the play that the actors can interact with directly, whereas MWI is more like an ontology of what is backstage that neither the audience nor the actors ever see. We actually use the 4D manifold in our calculations, but the same is not true for the MWI (even "believers" in it never actually use it in any calculations, it is entirely extraneous to the way quantum mechanics is actually done).

I know, and this is true, at least for relatively simple spacetimes. However, when people consider inflation, and "bubble" spacetimes in which there are parts of the spacetime manifold which are causally unconnected to our "bubble", then the ressemblance becomes larger, no ?

Is the part of the spacetime manifold beyond an event horizon "really there" ?

To me, what all this says is that there is a considerable level of Aristotelian rationalism still alive and well in modern physics. It is fashionable these days to sacrifice at the altar of empiricism, and bash natural philosophers like Aristotle who thought they could discover physical law via force of intellect, but then when you look more closely you see that we still do the same thing all the time. The 4D spacetime manifold and the many-worlds are both, when taken ontologically, purely rationalist constructions-- but at least the former actually gets used.

In fact, the MWI approach can also be used. For instance, an "ontological explanation" of the EPR setups is entirely "logical" in an MWI frame (as it is in a Bohmian frame, btw), while it hovers on the verge of illogical magic in "more Copernican" views.

Yes, I agree that the craving for ontology is strong, and important to recognize. I merely ask that we recognize we are doing it, and that there is an important scientific difference between building theories that explain a physical reality we actually observe, versus imagining a physical reality we do not observe to fit our theories.

I think we should always realize that when we ask for an ontology, we are leaving the realm of the pure and hard science. Ontology is not falsifiable in a way.
But, but... is the moon "really there", or is it just a theoretical construct that helps us explain moonshine and tides ? I guess now that people have walked on its surface, it is "really there". And the stars ? Are they theoretical constructs which allow us to predict the light in telescopes, or are they "really there" ? And remote galaxies ? And quasars ? And black holes ? And... In what way are these theoretical constructs "really there" and in what way are they just ways to calculate how our telescopes and radio telescopes and satelites will react ? In other words, in what way are they just constructions modeling a flux of electromagnetic (and other?) radiation impinging on the neighbourhood of the Earth ?

You see, it is entirely arbitrary to consider that certain scientific constructions are "genuinly real" and others are just "there for us to help us make predictions". When do we stick to our intuitive observations (Copernican) or when do we let ourselves be guided by our formal constructions (Aristotelian) ?

 

[atyy]

You see, it is entirely arbitrary to consider that certain scientific constructions are "genuinly real" and others are just "there for us to help us make predictions".

Do you think it is possible to push away "genuinely real" entirely, and self-consistently say that everything is just "there for us to make predictions"? I'm half thinking that at least the experimental data must be real - but on the other hand, you cannot even describe the results of an experiment without language, which necessarily has some theoretical constructs.

 

[Hurkyl]

Do you think it is possible to push away "genuinely real" entirely, and self-consistently say that everything is just "there for us to make predictions"?

Certainly... but that doesn't get eliminate the issues involved. Even if we do get people to adopt the position that Lorentz and Einstein were just talking about methods of making predictions, the core issue still remains. For example...

Special relativity organizes our experiments into the structure of a 3+1 Minkowski universe. Lorentz Ether theory^* organizes our experiments into the structure of a 3+1 Gallilean universe, but whose properties force all experiments to 'live' in an emergent 3+1 Minkowski structure.

Given this, one is compelled to ask the question, "If we are studying the behavior of 'experiments', and they only involve the Minkowski structure, then why would we keep the Gallilean structure around?"

So even though we've gotten rid of that pesky idea of what 'reality' is, we haven't gotten rid of questions like the above.

*: I'm referring to those variations that are observationally equivalent to SR

 

[Ken G]

I know, and this is true, at least for relatively simple spacetimes. However, when people consider inflation, and "bubble" spacetimes in which there are parts of the spacetime manifold which are causally unconnected to our "bubble", then the ressemblance becomes larger, no ?

Yes, that does get into issues of how far successful mathematics can be extrapolated before it loses contact with the empirical evidence that supported it in the first place. If it works, it will be heralded as an amazing anticipation of unseen events, and if it doesn't, it will be forgotten as though it never existed. Winners write history.

Is the part of the spacetime manifold beyond an event horizon "really there" ?

That's a tricky one indeed. I tend to think of what is behind an event horizon as a bit like the fields inside the conductor when "image charges" are being used to calculate the field outside of one. The mathematics can be extended easily enough, but no one really expects the fields to do that in the image-charge example, yet many do when it comes to event horizons. It's not a perfect analogy, but it points to the pitfalls of doing science in regimes where no empirical data exists (or ever will).

In fact, the MWI approach can also be used. For instance, an "ontological explanation" of the EPR setups is entirely "logical" in an MWI frame (as it is in a Bohmian frame, btw), while it hovers on the verge of illogical magic in "more Copernican" views.

I should have clarified-- when I said "used", I meant used in the simplest formulation of the calculation being done. I did not mean "used to satisfy an aesthetic ontological craving", which is really all it ever does. Incidentally, I would point out that the CI also provides a logical ontology to EPR experiments-- the information was never anywhere but in the mind of the physicist trying to understand the results of some observation, so of course it is completely local to that mind. (Yes, other minds with the same information will reach the same conclusions, but that is hardly surprising either.)

I think we should always realize that when we ask for an ontology, we are leaving the realm of the pure and hard science. Ontology is not falsifiable in a way.

Indeed, and ontology is probably not one thing, but a continuum of ideas, some pretty "hard", others "soft", and still others downright "magic".

When do we stick to our intuitive observations (Copernican) or when do we let ourselves be guided by our formal constructions (Aristotelian) ?

That's the old "empiricist vs. rationalist" debate, I imagine it will never be resolved nor should it be-- it is just the backdrop against which science happens.

 

[Hurkyl]

Incidentally, I would point out that the CI also provides a logical ontology to EPR experiments-- the information was never anywhere but in the mind of the physicist trying to understand the results of some observation, so of course it is completely local to that mind.

I was under the impression that, generally speaking, when one does try to do ontology, one tries not to reinvent solipsism.

 

[Ken G]

I was under the impression that, generally speaking, when one does try to do ontology, one tries not to reinvent solipsism.

I'm not sure if your impressions, by themselves, can be counted as an argument. Perhaps you just don't understand what I'm saying. In Bohr's interpretation of what quantum mechanics is, there is an ontology there-- it simply does not extend past the epistemology of making predictions based on available information. Bohr asks, what exists outside of our ability to measure it? In other words, we are macroscopic entities, and all observations we will ever be capable of interpreting will have to be passed through that filter. As such, nothing will ever leave any imprint on our minds other than what survives that filter, so what is the point in imagining anything else exists that doesn't survive it? It is a fiction we create for our amusement.

Note this is still an ontology, and not a solipsistic one, for there is no need to state that nothing exists beyond our minds. Instead, the assertion is that we will never know anything about anything except which leaves an imprint in our minds, so to pretend otherwise is false and unnecessary. So if we apply that logic to the EPR, we reach the conclusion that any physicist can use the information at her disposal to predict correlations, and check them, and any other physicist with less knowledge will simply be unaware of those predictions and suffer no flaws in their world view as a result. Indeed, physics would be completely impossible were that not true, as our information is highly limited. Any ontology that cannot embrace these fundamental limits is nothing but a wild guess.

Bohr is saying that reality is whatever is consistent with our own information, and if you compare notes with someone else, you find theirs is too, so there is no difficulty with the premise. Whenever our information overlaps, so does our reality. No problem there either. There is simply no reason for the reality to "come first", and the information to conform to the reality-- they just come together, whenever they come at all. That's precisely how we experience physics measurements, so why would we want to pretend something else was happening? That's the only ontology required in the CI, it's a very minimalist ontology but very true to what science is. And although it recognizes certain inescapable elements of solipsism, it isn't solipsism-- it makes even fewer undemonstrable assertions than that.

 

[vanesch]

I'm not sure if your "impressions" can be counted as an argument. Perhaps you just don't understand what I'm saying. In Bohr's interpretation of what quantum mechanics is, there is an ontology there-- it simply does not extend past the epistemology of making predictions based on available information. Bohr asks, what exists outside of our ability to measure it? In other words, we are macroscopic entities, and all observations we will ever be capable of interpreting will have to be passed through that filter. As such, nothing will ever leave any imprint on our minds other than what survives that filter, so what is the point in imagining anything else exists that doesn't survive it? It is a fiction we create for our amusement.

I wouldn't call such a view an "ontology" ! The "fiction we create for our amusement" is exactly what ontology is about, no ? An ontology is saying what "really exists" (and is, because of that, always up to a point, hypothetical and non-falsifiable). An ontology that doesn't go "past the epistemology of making predictions" is therefor a very strange kind of "ontology". Does it mean that what's past that epistemology "doesn't exist" ? Or "exists in a way but we don't care" ? An ontology needs to answer the question of *what* exactly exists.

Maybe I'm wrong - I never saw two identical descriptions of what *was* Bohr's viewpoint (maybe it exists in a superposition ? ) - but I was under the impression that Bohr claimed that the epistemological world which is accessible to us, is genuinly classical, and that there is then another, inaccessible, world, which is ruled by quantum mechanics and for which it will be impossible to say "what really happens", but that the filter between both is the Heisenberg cut, which doesn't have a well-defined place, but that from the moment we get information about it, we can assume that we're back in the classical world.
In other words, the motion of a tennis ball is purely classical, and classical mechanics is here NOT an extremely good approximation of an underlying quantum process. It is genuinly classical. Quantum mechanics doesn't apply. An electron in an electron gun starts out classically, then "plunges into the quantum world" and "re-emerges" in the classical world after some or other interaction process when we measure it. We can't know what it did when it was taken away from the classical world, before it re-emerged, but we have a mathematical technique of predicting probabilities of how and when it will re-emerge classically. That's how *I* understand Bohr.

 

[Ken G]

Do you think it is possible to push away "genuinely real" entirely, and self-consistently say that everything is just "there for us to make predictions"? I'm half thinking that at least the experimental data must be real - but on the other hand, you cannot even describe the results of an experiment without language, which necessarily has some theoretical constructs.

Your last point is a very important one, I think. There is really no escape from the need for filtering in our minds, there's never a reality that is separate from that. Normally, we don't worry about that-- if we must filter, then we can do no better than using the result of the filter when forming our impressions of what is real. In short, what is real is what passes the filter of our mind's eye (I think you see why that is not the same thing as a claim that nothing exists outside the mind, which would be solipsism).

That seemingly innocuous idea never caused any problems in classical physics, where the mind's eye was not fundamentally separated from what "is" other than by surmountable technical details. But the Copenhagen interpretation starts with the recognition that in quantum mechanics, there is such a fundamental separation, which has to do with our inability to experiment on coherences without coupling them to decohering classical instruments (including our own minds). So the concept of "experimental data" being real, in the context of quantum mechanics, is fraught with new ontological difficulties that motivated the CI (and the other approaches) to navigate them.