Problems with Many Worlds Interpretation

[psypher]

i don't claim to know much about this stuff, but i do understand the many worlds theory to a degree.

your flipping coin explanation doesn't really make sense because the coin only generates 2 possible outcomes. i think you would have to consider that in one world you would flip a coin and it would land on heads. in another you may flip the coin a little higher and it will land on heads. in another world it hits a table and lands on heads with all the worlds generating alternate realities and alternate worlds also. worlds being created exponentially. and sloppily you could say with your example 99% more worlds exponentially on the heads side and 1% worlds exponentially on the tails side.

 

[Hurkyl]

then the empiricist takes it as a law of nature that what nature renders invisible, does not exist. That's what happened in relativity, the rationalist-motivated expectation that there should be an aether lost to the empiricist recognition that what cannot be detected should not be said to exist.

Empiricism is the method of using experience to gain knowledge. If you can't gain experience about a thing, then you have no knowledge regarding it. In particular, you don't have knowledge of its non-existence.

You mis-describe relativity. The recognition that a choice of reference frame is invisible did not lead to reject the use of reference frames, nor did it cause people to start insisting that a good empiricist should only use a self-centered reference frame. Instead, it just meant that people stopped attaching any significance to the choice.

A heliocentric reference frame is just as good (arguably better) for studying the solar system as a geocentric reference frame.

(Incidentally, the thing in 1905 was the proposition that special relativity would match observation better than Galilean relativity)

By the way, reference frames have things like origins and axes. Things that cannot be detected. Does your radical empiricist reject making use of them?

Given this, I can't possibly see how any CI-user, or indeed any empiricist, would see any difficulty in having a state that is "mixed" for one physicist be "just as good" for their needs, and "collapsed" for another, being "just as good" for theirs.

But I'm further arguing that the mixed state is just as good my own needs. If I saw heads, then any mixed state with the corresponding heads component will make the same predictions when conditioned on me seeing heads.

Zero empirical content, not at all like relativity.

If there's zero empirical content, then by definition empiricism has nothing to say on the issue.

But it's not zero -- in principle, I could lock you in a laboratory, seal it away from the surrounding environment, and measure in a basis for which the partial traces of basis elements contain both "you saw heads" and "you saw tails" components. It's just the experiment is too hard to do with human-sized components. (it is, of course, not too hard to do with qubit-sized components)

Then the "notion of collapse" only enters our minds in the sense that collapse defines the very nature of what we mean by unitary evolution in the first place.

I didn't really expect your admittance to last; you had already previously been equating an unobservable bird's-eye (or god's eye) assertion about reality with the notion of experience.

Although, your particular phrasing here seems self-contradictory.

 

[dm4b]

Empiricism is the method of using experience to gain knowledge. If you can't gain experience about a thing, then you have no knowledge regarding it. In particular, you don't have knowledge of its non-existence.

I don't think it's quite that simple, as it applies to science today. It's a bit broader meaning derived from experience OR experiment, and science applies more to the experiment part, than it does to the experience part. If you cannot detect something via experiment, THEN it does not exist, EVEN IF an individual may have experienced it.

It's a reason many people don't consider psychology a "real" science, even though it deals with what people are directlty experiencing.

The most controversial example I can think of falls under the study of consciousness - Yoga.

Yoga (specifically raja Yoga, as outline by Patanjali in the Yoga Sutras) traditionally was basically a step-by-step procedure for obtaining a direct experience of higher states of consciousness in a predictable, repeatable and verifiable way, achieved by many folks over the past 1000's of years. This is why many practioners of yoga have considered it to be "scientific."

Yet modern day science hardly acknowledges it, even though it is knowledge of a thing derived through (conscious) experience, in other words "empirical".

Why? For one, science doesn't understand consiousness, pretty much doesn't acknowledge "higher states of consciousness" and sometimes disregards consiousness all together, even though we experience it on a daily basis. But, mainly because we don't know how to quantify it, or measure it in a lab, or rather, you cannot derive knowledge about it through an experimental setup under the currently accepted materialistic paradigm. And, the mere mention of things like Yoga can make people shudder because they're taboo, for the very reasons mentioned.

So, mainly empiricism, as it manifests under modern science, is knowledge gained through experiment performed under a materialistic paradigm . Direct experience is put under a vastly inferior role to that.

So, yeah, that's a controversial example, becuase, well I like to be controversial sometimes, but you can think of many other simple examples of how "direct experience" is given much less credence in modern science to "experimental verification".

 

[Hurkyl]

But it's not zero -- in principle, I could lock you in a laboratory

More than this. A subsystem approximate in a mixture state of "classical" states is not a subsystem exactly in a mixture of "classical" states. I don't actually know what the difference would look like, though -- but if we are serious about decoherence-based interpretation it warrants looking into.


Also, a subsystem is not a whole. It may also be possible to detect and make inferences about the whole that have real, observable effects, in direct contrast to the case of statistical classical mechanics where the components of a mixed state are eternally and perfectly independent of one another no matter how inclusive your analysis is.

Again, this is another aspect I don't know much about, but one IMO warrants the research -- and it's a question that, as far as I can tell, the CI of quantum mechanics rejects as not even making sense.

 

[Ken G]

Empiricism is the method of using experience to gain knowledge. If you can't gain experience about a thing, then you have no knowledge regarding it. In particular, you don't have knowledge of its non-existence.

You mis-describe relativity. The recognition that a choice of reference frame is invisible did not lead to reject the use of reference frames, nor did it cause people to start insisting that a good empiricist should only use a self-centered reference frame. Instead, it just meant that people stopped attaching any significance to the choice.

OK, that entire point was one long straw man. Let's take it straw by straw. First of all, empiricism is not the statement that you can gain knowledge by experience, it is the statement that knowledge comes fundamentally from experience. Hence, empiricism is certainly not agnostic on the issue of knowledge about things you cannot perceive, it regards them all as angels on a pin. So you are not talking about empiricism here, but I am.

Second, I do not mis-describe relativity, you simply reinvent what I said. I have no idea how you got the idea that I said relativity "rejects" reference frames! Empiricism requires reference frames, because it requires observers, and all observers have reference frames. What relativity actually does, and what I said it did, was to provide the lexicon that translates between the reference frames. Having this lexicon unifies empiricism into a single description, instead of a disunion of different experiences, so relativity is crucial to empiricism-- there is no empirical need to unify some imagined class of experiences that cannot be detected even in principle by the observer in question. That's why empiricism must always view MWI as an inquiry into the "angels on the pin". I would have thought that would be obvious to anyone who understands empiricism, so again you just keep establishing that you do not. So what, you don't need to understand empiricism, you're a rationalist-- but that's what I'm trying to get you to understand.

The point is, your analogy between relativity and MWI fails completely for any empiricist. The empiricist can explicitly demonstrate that the lexicon provided by relativity does indeed unify the reference frames of observers who are in communication, at least in principle, and that's why they are not angels on a pin. We can demonstrate that by querying observers in the other reference frames, as we did in the Michelson-Morely experiment as the Earth passed between different frames and communicated outcomes between them. When Michelson-Morely was envisaged as a thought experiment under Galilean relativity, it got the wrong answer-- but the "right" answer could only be obtained by actual communication between the reference frames. Try that in your analogy with many worlds!

A heliocentric reference frame is just as good (arguably better) for studying the solar system as a geocentric reference frame.

Obvious to any empiricist.

By the way, reference frames have things like origins and axes. Things that cannot be detected. Does your radical empiricist reject making use of them?

What would make you think that a radical empiricist would reject using mathematical tools in physics? You just don't seem to get empiricism at all. Empiricists love mathematical tools, they love how they simplify the making of predictions and forming of pictures and models that help us understand the reality of our observations. They especially love it when the mathematical tools come with postulates that say "only invariants are real", when combinations like |observer A><observation a| are what the invariants are. Given all this, they are perfectly fine when a mapping from these "raw" invariants into rationalistic 4-vector norm invariants is discovered-- they hoped such a thing would have to exist, because that is the union of objectivism and empiricism, and so they are glad when it is found.

Once again: empiricism is the statement that reality is what you observe, and theories exist in your mind to make sense of what you observe. That observations require a mind to say what constitutes an observation is the core inconsistency of empiricism, but it lives with it. The core inconsistency of rationalism is that theories keep changing, but observations don't. In the history of science, the latter has been a much larger issue than the former.

But I'm further arguing that the mixed state is just as good my own needs. If I saw heads, then any mixed state with the corresponding heads component will make the same predictions when conditioned on me seeing heads.

Yes I know it is just as good for your needs. That's because "your needs" are purely rationalistic. "Your needs" start by rejecting what you actually experience as the actual reality, which is what forces you to "condition on what you see." For most people, "conditioning on what they experience" is a perfectly redundant step of science, it doesn't require any "if.. then" in front of it. Your approach needs the "if ... then" or it doesn't work. That's exactly why it is so radically un-empiricist, as I keep saying. For some reason, you seem to keep arguing that you are not being un-empiricist by making more and more un-empiricist statements.

If there's zero empirical content, then by definition empiricism has nothing to say on the issue.

Again, no. That would be like saying that science has nothing to say about the existence of invisible unicorns. Instead, science is not agnostic about invisible unicorns, it says that if you have zero evidence for something, it is silly to claim it exists. We see this all the time-- a scientific claim that is made on reality requires some evidence be produced that there is an influence on reality. If you want to instead say that MWI makes non-scientific claims on reality, then we have no dispute, that is exactly how I see MWI.

But it's not zero -- in principle, I could lock you in a laboratory, seal it away from the surrounding environment, and measure in a basis for which the partial traces of basis elements contain both "you saw heads" and "you saw tails" components. It's just the experiment is too hard to do with human-sized components. (it is, of course, not too hard to do with qubit-sized components)

You have no idea that this is true. Indeed, in my opinion, the fact that I am sentient is the reason that your experiment would never succeed, not even in principle. But since you cannot produce on your claim, your speculation is irrelevant.

I didn't really expect your admittance to last; you had already previously been equating an unobservable bird's-eye (or god's eye) assertion about reality with the notion of experience.

Although, your particular phrasing here seems self-contradictory.

Then you have not understood. I introduced the "god's eye" view expressly to contrast it with the notion of experience. The "god's eye" view is the unitary evolution of the wave function, and we never experience that. Instead, we experience observable eigenvalues, and we invent the intervening unitary evolution to correctly predict (statistically) what we observe. That is quite demonstrably just exactly what physics did, pick up any history book. The rationalist can claim that it means something else than that, but that's what actually happened. I have no idea what you think I am now "admitting."

 

[kith]

So there's a bijective correspondence between rays and pure state operators.

Ok, they are mathematically equivalent. But whether they mean the same thing physically, is a matter of interpretation. In CI, I would say they don't. A ray describes the state of a single system, a pure state operator an ensemble of such systems. Else, the evolution from pure to mixed states makes no sense.

I don't understand what you're saying here.

Don't you agree that mixed states describe two fundamentally different things in CI and MWI? If we have an electron beam with density operator ϱ ~ |+><+| + |-><-|, this is an ensemble where 50% of the electrons are in state |+> and 50% in state |-> in CI. In MWI, ϱ is the "real" state of a single electron (disregarding issues with indistinguishability). There exist two distinct universes and in one of them, the electron has definite spin +h/2 wrt to the quantization axis and in the other -h/2 .

This is my (possibly flawed) understanding of MWI and decoherence: The state of the universe is always pure. If we decompose the universe into subsystems, say "specimen+everything else", and choose to express the state of the universe in a basis that's consists of eigenvectors of an operator that commutes with the part of the Hamiltonian of the universe that describes the interaction between the specimen and the rest of the universe, then the state operator will be approximately diagonal (after the interaction). So even though it's still pure, it will be practically indistinguishable from a mixed state.

I find it odd to speak of decoherence in the context of the state of the universe, because this state evolves coherently and all you do is to change the basis. Decoherence usually refers to the decay of the off-diagonal elements of density matrices describing open subsystems like our specimen, transferring an initially pure state into a mixed one due to interactions with the environment. I'm not sure what you mean by saying that the density matrix of the universe gets 'approximately' diagonal. What gets diagonal is the density matrix of the specimen. I don't see how this diagonality translates into an approximate diagonality of the whole density matrix. Can you please elaborate?

 

[Hurkyl]

Second, I do not mis-describe relativity, you simply reinvent what I said. I have no idea how you got the idea that I said relativity "rejects" reference frames!

I take the words you say and follow them to the logical conclusion.

Empiricists love mathematical tools, they love how they simplify the making of predictions and forming of pictures and models that help us understand the reality of our observations.

Except for mixed states (as corresponding to observation), apparently.

They especially love it when the mathematical tools come with postulates that say "only invariants are real"

Except when they are conditional probabilities, apparently.

Again, no. That would be like saying that science has nothing to say about the existence of invisible unicorns.

It doesn't. Asserting the non-existence of things you have no evidence against is pure dogma.

Eliminating IPU's is an application of Occam's razor, and nothing more -- when faced with two observationally equivalent alternatives, all that matters are non-empirical concerns (such as simplicity) so recognize science has nothing to say and make your choice based on the non-empirical ones.





How a state is mixed in classical statistical mechanics is unobservable. For most purposes, applying Occam's razor and only bothering with pure states is a reasonable thing to do.

But when the point is to understand how mixed states do just as good of a job as pure ones -- that even the very language used by "internal" observers is agnostic on the issue -- applying Occam's razor to eliminate the mixture is wholly inappropriate.



When we look at QM, the way the state of a subsystem is mixed does have an influence on the dynamics. Occam's razor no longer applies.

You have no idea that this is true. Indeed, in my opinion, the fact that I am sentient is the reason that your experiment would never succeed, not even in principle. But since you cannot produce on your claim, your speculation is irrelevant.

I have some idea.

However, I do recognize that the fantastic successes of QM might falter when pushed to these scale. Or maybe there's an odd theoretical quirk that would prevent such a thing even in principle.

But "it can't work because I'm a human being?" Seriously?

 

[BruceW]

I agree with Hurkyl that just because someone is human, it doesn't mean that it wouldn't be possible to do some kind of quantum experiment with them (for example interference or quantum teleportation). They've done quantum teleportation with atoms, and they've had a superconductor with currents going in a superposition of different directions, so it seems like they will keep making experiments with bigger and bigger systems.

A human is of course an incredibly complex system, so its unlikely they will ever quantum teleport a human. But this doesn't mean it couldn't be done in principle.

Hurkyl raises another good point that there may be some other theory that takes over from QM when we have gotten to such scales. This is why the debate of MWI against CI is very premature.

 

[Ken G]

I take the words you say and follow them to the logical conclusion.

Actually, I explained in detail why that is exactly what you did not do. I guess you are just set in your opinions though.

Except for mixed states (as corresponding to observation), apparently.
Except when they are conditional probabilities, apparently.

No one both counts, empiricists like those situations too. Hard though this may be for you to quite get, empiricists see mathematical tools of all kinds as essential to science. They just see them as tools-- the maps, not the territories. I've no doubt Sir Edmund Hillary was quite fond of his map of Mount Everest, but that doesn't mean he could have just stayed home and climbed the map.

Asserting the non-existence of things you have no evidence against is pure dogma.

Here I fear you have a rather nonstandard understanding of the word "dogma." Most people, when they use that word, mean believing in something purely on the basis of having been told it enough times, or in an authoritative enough setting, without any actual evidence for it being supplied. It is often repeated by rote, rather than paraphrased to express an individual understanding of the ideas. By contract, the rejection of believing in something, on the grounds that there is no evidence for it, is actually much closer to the opposite of dogma. Here I think you have even left the fold of the rationalists.

Now, while I might agree with you that no one has a right to tell someone else they are wrong unless they can produce evidence, it is certainly incorrect to label the skeptical stance as "dogmatic." That's just what the people who believe in ghosts say. Instead, a skeptical stance is a personal choice to accept a certain standard of belief, a standard that requires evidence rather than just desire to believe. In that spirit, I would never tell you that there aren't many worlds, I would merely say that you have not adopted the skeptical stance that scientists normally include in their repertoire of tools. Doubting what has not been verified has proven vastly useful in the history of science.

Eliminating IPU's is an application of Occam's razor, and nothing more -- when faced with two observationally equivalent alternatives, all that matters are non-empirical concerns (such as simplicity) so recognize science has nothing to say and make your choice based on the non-empirical ones.

The issues between MWI and CI were never issues involving Occam's Razor. O.R. is a widely valued principle of science, it just says that if the goal is to understand, then choose a description that is easiest to understand. But as I've said, MWI vs. CI invokes much deeper metaphysical priorities, to wit, rationalism vs. empiricism. The rationalist and the empiricist will encounter their disagreement long before they even get to O.R., indeed O.R. would only be used to adjudicate between various versions of MWI and CI, it is never used to adjudicate between fundamental epistemological priorities. (It would be like telling Sir Edmund Hillary that he should have just climbed his map, because it's "much simpler.")

How a state is mixed in classical statistical mechanics is unobservable. For most purposes, applying Occam's razor and only bothering with pure states is a reasonable thing to do.

But when the point is to understand how mixed states do just as good of a job as pure ones -- that even the very language used by "internal" observers is agnostic on the issue -- applying Occam's razor to eliminate the mixture is wholly inappropriate.

I don't think Occam's razor is ever invoked to eliminate the mixture. The mixture is eliminated directly by observation, that's empiricism. However, as I said above, it is only eliminated for the physicist with access to that observation-- any that do not will still invoke the mixture, so the mixture has not been "eliminated" in some absolute way. The whole concept of mixture vs. pure state never existed anywhere except in the heads of the people who are using the concepts effectively.

When we look at QM, the way the state of a subsystem is mixed does have an influence on the dynamics. Occam's razor no longer applies.

There's no such thing as "the dynamics" of a system, there's only the way our information about the system, and our expectations of that system, are changing. CI has no difficulty tracking how that information and expectations evolve, invoking Occam's Razor in the usual ways.

I have some idea.

No, you don't, you have none at all. Any plausible reason you can give for why that experiment, if possible to do, would come out that way, can be countered by an equally plausible reason why it would not.

However, I do recognize that the fantastic successes of QM might falter when pushed to these scale. Or maybe there's an odd theoretical quirk that would prevent such a thing even in principle.

Yes, maybe this time we got it exactly right, let's just ignore the history of our discipline and pretend it is something now that it has never been before but was always thought to be before by rationalists like you.

But "it can't work because I'm a human being?" Seriously?

Human? I'm not sure how humanity enters the picture. I was referring to sentience, by which I mean, "able to process information and do physics with it." And yes, I am quite serious when I suggest that physics might be fundamentally affected by having the ability to do it. Never a concept that rationalists are terribly comfortable with, I know that.

 

[Ken G]

I agree with Hurkyl that just because someone is human, it doesn't mean that it wouldn't be possible to do some kind of quantum experiment with them (for example interference or quantum teleportation).

Importantly, that was not quite all that Hurkyl claimed. The claim was "- in principle, I could lock you in a laboratory, seal it away from the surrounding environment, and measure in a basis for which the partial traces of basis elements contain both "you saw heads" and "you saw tails" components. It's just the experiment is too hard to do with human-sized components." The statement is internally inconsistent-- I have an enclosure that is sealed away, yet I'm doing measurements on it. That's just not logically possible.

Also, it was not a statement that we don't know how the experiment would come out if we could do it, no MWI proponent could really be happy with that, their world view is too radical for that. It is a statement that we do know, or the MWIers do anyway, we just can't do the experiment. I think that's an unscientific claim-- my claim is that we simply don't know how that experiment would come out unless we could do it, and we can't even talk about the outcome of an experiment that is internally inconsistent. Now the key question is-- which interpretation, CI or MWI, is more comfortable with not knowing the outcome of that experiment?

They've done quantum teleportation with atoms, and they've had a superconductor with currents going in a superposition of different directions, so it seems like they will keep making experiments with bigger and bigger systems.

Actually, there is something much bigger than that in those experiments-- the experimenters.

A human is of course an incredibly complex system, so its unlikely they will ever quantum teleport a human. But this doesn't mean it couldn't be done in principle.

It also doesn't mean it could be done in principle. We simply don't know if quantum mechanics still works when the processor applying the quantum mechanics is part of the system that the quantum mechanics is being applied to. We know it works to predict elements of such a system that are not treated as having processing ability, but that wouldn't foot the bill for teleporting humans. It's all about not pretending that we know our theories will work in situations that are fundamentally different from those the theory was built for.

Hurkyl raises another good point that there may be some other theory that takes over from QM when we have gotten to such scales. This is why the debate of MWI against CI is very premature.

Actually that has been a central theme I've raised all along. CI does not construct a world view, so it will have no problem if QM is shown wrong by the next theory-- empiricism says theories are to understand reality, not to dictate to reality. It is actually MWI that would end up looking pretty darn silly if unitary evolution is discovered to not be a universal principle, as treating it as a universal principle is the whole basis of the MWI. That's the problem with rationalism, that's why it hasn't worked yet when used to create world views (instead of what it should be used for-- to inspire new tools).

 

[Hurkyl]

No one both counts, empiricists like those situations too.

So, you've changed your mind? Even "empiricists" and not just "radical rationalists" are interested in describing their observations with mixed states?

They just see them as tools-- the maps, not the territories.

Wonderful. I bet they even use the maps to help them understand they lie of the land.

But your "empiricist" is rejecting the map where the island of experience is in the sea of mixed states -- even though everywhere he's looked, the map has given the correct information.

Here I fear you have a rather nonstandard understanding of the word "dogma." Most people, when they use that word, mean believing in something purely on the basis of having been told it enough times, or in an authoritative enough setting, without any actual evidence for it being supplied. It is often repeated by rote, rather than paraphrased to express an individual understanding of the ideas.

Yes, that's how I was using it.

By contract, the rejection of believing in something, on the grounds that there is no evidence for it, is actually much closer to the opposite of dogma.

Again, accurate. But irrelevant: you are denying something -- actively asserting a belief that it doesn't exist.

Doubting what has not been verified has proven vastly useful in the history of science.

Agreed. And, incidentally, nobody has verified that experiences are "pure" -- and not just that nobody has verified it: I've never even seen someone propose an experiment that could tell the difference between pure and mixed.

But as I've said, MWI vs. CI invokes much deeper metaphysical priorities, to wit, rationalism vs. empiricism.

Yes, you've said it -- and in the very same breath that you are equate the notion of experience with an unobservable philosophical notion nonetheless.

I don't think Occam's razor is ever invoked to eliminate the mixture. The mixture is eliminated directly by observation, that's empiricism.

This is nonsense until you can propose how to distinguish between observations being mixed and pure.

However, as I said above, it is only eliminated for the physicist with access to that observation

I'm not talking about using the mixture to express ignorance, I'm talking about using the mixture to express "what is" -- e.g. what is observed.

There's no such thing as "the dynamics" of a system, there's only the way our information about the system, and our expectations of that system, are changing.

CI has no difficulty tracking how that information and expectations evolve, invoking Occam's Razor in the usual ways.

Where "usual way" means "the way we did things before we started digesting the ramifications of relative states and decoherence to the question of whether quantum mechanical descriptions could be extended to include observers".

No, you don't, you have none at all.

QM works. Measurements can be done in bases.

Any plausible reason you can give for why that experiment, if possible to do, would come out that way, can be countered by an equally plausible reason why it would not.

I find "QM won't work" to be less plausible than "QM will work".

Yes, maybe this time we got it exactly right, let's just ignore the history of our discipline and pretend it is something now that it has never been before but was always thought to be before by rationalists like you.

I don't know why you are so interested in absolutely certain knowledge. I'm quite content with merely knowing that QM has a lot of empirical evidence going for it, and a good track record for survived challenges of the "reality can't possibly work that way!" sort.

Given the alternatives "QM will work" and "QM won't work", the former seems to be a good bet except on the most ridiculously extreme scales when it starts butting heads with GR. (and in my outsider's opinion, I think the better money is on a quantum mechanical theory of cosmology than a purely classical theory of the microscopic).

Human? I'm not sure how humanity enters the picture. I was referring to sentience, by which I mean, "able to process information and do physics with it."

Surely by this point you are gratuitously looking for reasons to disagree.

And yes, I am quite serious when I suggest that physics might be fundamentally affected by having the ability to do it. Never a concept that rationalists are terribly comfortable with, I know that.

I don't know what "rationalists" have to do with it. Or why you seemingly think you aren't engaging in it with your claim.

 

[Ken G]

So, you've changed your mind? Even "empiricists" and not just "radical rationalists" are interested in describing their observations with mixed states?

No I have not changed my mind, I never for one instant thought that an empiricist who hasn't yet seen the outcome of a coin flip will not want to treat that coin in a mixed state. But if the observer becomes privy to the observation, the mixed state description is no longer needed. "Describing observations" has nothing to do with CI or MWI, they both "describe" the system in the exact same ways because the mathematics of both are exactly the same to the smallest detail and the observations are the same observations. What is different is how they interpret the state. This is the point that needs to be stressed until it takes:
When an empiricist describes a system as being in a mixed state, they are like the person who sees that the coin has flipped, but has not seen the coin. They do not "really think" the coin is in a mixed state, because they never think their "descriptions of states" are the true reality. Also, they can imagine that another observer may have already seen the coin, and they understand how the environment of the coin has decohered the "heads" and "tails" eigenstates. All the same, they will still find considerable value in describing the coin as being in a mixed state, indeed this is just what mixed states are for to the empiricist. The big thing the empiricist is doing here is they are not taking their theoretical description of the coin literally, they are taking it as a useful mathematical tool. That is why empiricists can be just as good at poker as rationalists.

The rationalist, on the other hand, does not have access to the liberating tool of not taking their mathematical tools literally. If the math is the truth, they have to build entire world views around their mathematical postulates. So a rationalist like yourself cannot just describe the coin as being in a mixed state, they are forced to believe, devoutly it would seem, that the coin really is in a mixed state.

But your "empiricist" is rejecting the map where the island of experience is in the sea of mixed states -- even though everywhere he's looked, the map has given the correct information.

The empiricist is happy when the map gives correct information, yes. Yet they still know that it is a map.

Again, accurate. But irrelevant: you are denying something -- actively asserting a belief that it doesn't exist.

What I am actually doing is asserting a doubt that it is correct, a skepticism that its reality has been established well enough to include it in the body of scientific knowledge. That is enough to justify CI-- if one doubts the many worlds, one cannot hold to MWI. It is only the devout believer in what they cannot perceive that can accept the MWI, and that is the dogma here. CI has no interest in saying anything about the quantum realm, other than that there is a big "no trespassing to empirical evidence" sign placed right on it, leading the empiricist to doubt that a quantum realm even exists in an empirically demonstrable way.

That's not a world view, it is the avoidance of a world view that extends beyond our instruments. MWI is the world view based on quantum postulates, CI is the stance of basic skepticism. CI asserts only the outcome of the observation, it asserts that physics happens after we interact with the physical system, not before. That's CI, pure and simple.

Agreed. And, incidentally, nobody has verified that experiences are "pure" -- and not just that nobody has verified it: I've never even seen someone propose an experiment that could tell the difference between pure and mixed.

We've covered this already-- there is no such thing as pure experience, yes. All the same, people have little difficulty with the basic concept. All that empiricism needs is a meaning for what a "measurement" is. Note there is no such thing as a "pure measurement" either, and no doubt the deconstructionists have a field day with that one, yet all the same, physicists seem to have little difficulty with that concept either. If you are going to base your plea for rationalism on the difficulty in finding a rigorous definition of a "pure measurement", you are going to face a fleeing of your followers.

This is nonsense until you can propose how to distinguish between observations being mixed and pure.

Huh? I have no idea what you mean by a mixed observation. The whole point of empiricism is that observations are pure. What I actually said is that observations eliminate mixed states when the observer perceives the result. I also said that mixed states are descriptions used as tools prior to perceiving the results, or when individual results are not perceivable (as for some ensembles).

I'm not talking about using the mixture to express ignorance, I'm talking about using the mixture to express "what is" -- e.g. what is observed.

No you aren't, you are talking about using the mixture to express "what is" in your head. The mixture is not observed for a single event, ever. If quantum mechanics did not call for unitary evolution, no one would ever talk about mixed states as if they were real. Do you doubt that? If not, your argument falls to pieces-- for you are claiming that a theory is what allows mixtures to be observed. That's nonsense, observations are the reading of a pointer, the setting up of an apparatus to ask a question. The observation can be motivated by a theory, and it can invoke theory A in order to test theory B, but the observation itself could not test a theory if it required that theory.

QM works. Measurements can be done in bases.

No, again, measurements are just measurements. That they are "in bases" is a purely theoretical construct in the head of the physicist who is choosing to frame them that way. It's an effective construct, of course, but the measurement is just a measurement, and can be (and often is) done by a technician who doesn't know a whit about "bases," but they know how to read a pointer. The difference between what you need to know, and what you need to do to get a measurement, is crucial in empiricism-- indeed it's crucial in science, because otherwise no consensus would ever be possible if different ideas in our heads led us to different measurement outcomes.

I find "QM won't work" to be less plausible than "QM will work".

It is completely unnecessary for me to believe that QM won't work to reject a world view that falls to pieces if QM doesn't work-- all that matters is I am capable of doubting that it will work. Hence I doubt the validity of your world view. Whether or not I believe QM could work in any given situation where nothing like it has ever been done is utterly irrelevant-- why would anyone care what anyone believes in a situation like that, is this religion or science we are doing? CI has nothing like that to doubt-- it is empirical, it says we observe a collapse, so there's a collapse. You have to doubt the observations to doubt CI, which is exactly why you have to talk about hypothetical observations that give mixed-state outcomes on single systems, even though no observations ever actually do that.

I don't know why you are so interested in absolutely certain knowledge. I'm quite content with merely knowing that QM has a lot of empirical evidence going for it, and a good track record for survived challenges of the "reality can't possibly work that way!" sort.

And I don't know why you aren't. It's like you think physics just appeared yesterday, and it always works. Don't you think Newtonians in 1850 thought exactly like you do? Don't you think they made statements just like that? It is different this time because we have greater accuracy now, is that your whole stance here?

Given the alternatives "QM will work" and "QM won't work", the former seems to be a good bet except on the most ridiculously extreme scales when it starts butting heads with GR. (and in my outsider's opinion, I think the better money is on a quantum mechanical theory of cosmology than a purely classical theory of the microscopic).

I agree that in any isolated instance of observations we can actually do, I'd bet on QM. But MWI asserts hypothetical outcomes of observations that we cannot actually do. The empiricist in me is very suspicious of that requirement-- I think there may be a pretty good reason we can't do the observations that would actually be needed to demonstrate that MWI was correct, just as Einstein felt there was a pretty good reason we can't find any observations that detect Lorentz's aether.

Surely by this point you are gratuitously looking for reasons to disagree.

Perhaps a little, but I do think it's an important distinction-- many people who don't understand CI think it is some kind of humanist philosophy, but the key is simply the recognition that we need to do a heck of a lot of intelligent processing before we can do physics. What kind of fingerprints are we leaving on the crime scene after doing all that processing? I believe that physics is like a telephone call to nature, and there is very much a speaker at both ends of the line. That's not because we're human, it's because we're physicists, and I suspect that nonhuman physicists would face a similar quandary.

I don't know what "rationalists" have to do with it. Or why you seemingly think you aren't engaging in it with your claim.

I agree that making theories requires rational thought. One has to basically pretend one is a rationalist long enough to come up with the theory, then go back to being an empiricist to decide if the theory has anything to do with reality.

But the problem I was referring to is that rationalists have to believe that mathematical truth applied to physics works just like mathematical truth applied to mathematics-- it transcends their own intelligence and perception, it's true "outside them." That's why rationalists have such a hard time understanding that the experimenter is included in every experiment, and that might be important. If the mathematics is the truth, there is no place for the brain that has decided what axioms to use in that mathematics (witness Godel) and the postulates to use in that theory. The theory is true, the math is true, the brain is just the oracle. I think that mode of thought is getting pretty close to its swan song in physics, even at the brink of some of its greatest accomplishments-- and I think the outlandish world view of the MWI is a symptom of exactly that.

 

[Hurkyl]

No I have not changed my mind, I never for one instant thought that an empiricist who hasn't yet seen the outcome of a coin flip will not want to treat that coin in a mixed state. But if the observer becomes privy to the observation, the mixed state description is no longer needed.

Again, I am not talking about using mixed states to represent ignorance. I am talking about mixed states to represent the result of observation.

Yet they still know that it is a map.

Yes, a map is a map. That fact is completely irrelevant to the question of which map to use.

CI has no interest in saying anything about the quantum realm. What I am actually doing is asserting a doubt that it is correct, a skepticism that its reality has been established well enough to include it in the body of scientific knowledge.

Eh? I thought QM was the best tested and most precisely accurate theory in the history of mankind. Surely it's come time to at least entertain the thought it might have something worth listening to?

I often get the feeling that many adopt CI as an ostrich interpretation -- just bury our heads in the sand for a century or so and hope that QM gets replaced with a more palatable theory.

The mixture is not observed for a single event, ever.

Eh? How can you tell? What experiment has ever been done that can tell the difference between mixtures being observed and not?

If you can't provide such an experiment, then empiricism has absolutely nothing to do with your claim.

for you are claiming that a theory is what allows mixtures to be observed.

No, you just observe mixtures. Any theory, interpretation, or philosophy about the observational results of testing a proposition that posits the only answers are "true" and "false" can be replaced with an observationally identical theory, interpretation, or philosophy where the answers take values in an arbitrary Boolean algebra.


But the point is that in QM, mixtures don't appear because of a trivial swap like the above -- they appear because of physical laws, and play a part in those laws. QM makes the topic relevant.

all that matters is I am capable of doubting that it will work.

No, it really matters how your doubt that it will work compares to your doubt that it won't, and if your doubts are actually justifiable.

CI has nothing like that to doubt-- it is empirical, it says we observe a collapse, so there's a collapse.

You're dictating to reality again.

You have to doubt the observations to doubt CI

No, I just have to doubt its dictation to reality. The empirical evidence supporting quantum mechanics along with the way mixtures appear give me good reason to doubt the dictation to reality.

And I don't know why you aren't.

Because I'm not the cartoon straw-man you enjoy attacking. And didn't you just get finished criticizing me because you claimed I thought my knowledge certain? I think you've misinterpreted me.

Observation gives evidence for propositions. Reason gives evidence to the conclusion of an argument based on the evidence for the hypothesis. The more evidence we have for a claim, the more we favor it. That's the core mechanic to how knowledge operates in science.

 

[Ken G]

Again, I am not talking about using mixed states to represent ignorance. I am talking about mixed states to represent the result of observation.

I am all ears as to what you mean by using a mixed state to represent the result of an observation, that preserves the basic empirical connection between the observer and the observed, and is not just an expression of incomplete information. How are you labeling the transformations between these observers?

Yes, a map is a map. That fact is completely irrelevant to the question of which map to use.

There was never any question as to which map to use. The exact same map is always used by every interpretation, that's why they are all the same theory. Had there been any question of which map, there would be a question of which theory.

Eh? I thought QM was the best tested and most precisely accurate theory in the history of mankind. Surely it's come time to at least entertain the thought it might have something worth listening to?

So now your argument requires that you be able to equate a theory that "contains something worth listening to" with one that "justifies a complete overhaul of one's entire world view based on taking its postulates as absolute literal truth." I'm sorry, it sounds illogical to equate those, the first is what the scientific do, the second is what the devoted do.

I often get the feeling that many adopt CI as an ostrich interpretation -- just bury our heads in the sand for a century or so and hope that QM gets replaced with a more palatable theory.

On the contrary, CI is entirely complete in what it accomplishes, indeed it is more complete than MWI. The coup de grace of CI is that it recognizes there is nothing empirical that is left to explain once one is done with CI, it is only if one wants a theory to be more than that, if one wants the theory to dictate to reality beyond what can be observed, that CI seems incomplete. So no CI proponent needs any other theory, it is a fully finished theory-- except for the usual problems if observations crop up that don't agree with the theory (as we expect at the Planck level, but maybe somewhere else too). MWI, on the other hand, is not complete, because it postulates the existence of many worlds, which can never be tested or checked in any way. So MWI does work on all our observations, just as CI does, but CI leaves nothing at all hanging-- whereas MWI leaves hanging the very existence of those many worlds. Hence, it is the MWI camp that must wait for the next observational surprise-- the one that allows us to actually detect those other worlds. CI doesn't expect that will ever happen, so there's nothing to wait for.

Eh? How can you tell? What experiment has ever been done that can tell the difference between mixtures being observed and not?

What experiments have ever been done that can tell the difference between red invisible unicorns and green ones? Empiricism sees no need to tell that difference, there is no difference-- mixtures are make believe from the perspective of empiricism, all observations are pure results in empiricism, by definition. If there is no way to detect an impure result, the empiricist is happy with the definition they are using, they see it as silly to even ask "but how can you tell your observations aren't mixed?" The observations are just the observations, that is the starting point of empiricism, not some kind of conclusion that requires verification. You may as well ask a mathematician how they can tell that geometric points don't have compacted dimensions in there somewhere.

If you can't provide such an experiment, then empiricism has absolutely nothing to do with your claim.

Wrong. Empiricism has axioms, and here's the main one: observations are taken literally, theories are taken figuratively. So if a theory suggests you take your observations as "impure", the empiricist says "no."

No, you just observe mixtures. Any theory, interpretation, or philosophy about the observational results of testing a proposition that posits the only answers are "true" and "false" can be replaced with an observationally identical theory, interpretation, or philosophy where the answers take values in an arbitrary Boolean algebra.

And any geometry that invokes points can be replaced by one with undetectable compacted dimensions inside those points. So what?

But the point is that in QM, mixtures don't appear because of a trivial swap like the above -- they appear because of physical laws, and play a part in those laws. QM makes the topic relevant.

No, mixtures appear in QM entirely because of lack of information. That's the CI approach anyway, and it works just fine. So your claim is only true if you already assume it is true.

No, it really matters how your doubt that it will work compares to your doubt that it won't, and if your doubts are actually justifiable.

Now we have to justify doubt? Can rationalism really be so anathema to skepticism? Here's what I doubt: I doubt that the postulates of QM are exactly true. Hence, I doubt any radical world view that requires those postulates be exactly true.

Because I'm not the cartoon straw-man you enjoy attacking.

There's only one thing in your stance that I am attacking, it is the crux of the whole matter: you seem to feel that your attitude is not one of die-hard rationalism, but rather is just doing good science. Everything I've said has been an effort to get you to see two things:
1) your approach is indeed radically rationalistic, so much so that you almost cannot even conceive of empiricism or skepticism about the rationalistic axioms you have accepted in your world view, and
2) although there are no logical inconsistencies in your approach, it suffers the historical weakness that when it is used to generate a nonskeptical world view, it is really only relevant while the theory in question is regarded as our best description of the empirical data available.
As yet, I have seen no significant dents made by you against either of those positions, your arguments just seem to reiterate point #1 while dodging point #2.

Observation gives evidence for propositions. Reason gives evidence to the conclusion of an argument based on the evidence for the hypothesis. The more evidence we have for a claim, the more we favor it. That's the core mechanic to how knowledge operates in science.

And not a single thing you just said adjudicates in the least way between CI and MWI, so it is true but quite irrelevant.

 

[jensa]

Hurkyl, I am curious to hear how the concept of experiments fits into your view of science. You seem to reject the notion that we can even perceive a definite outcome of measurements so where does this leave experimental physics?

For example: In your worldview, is it even possible to disprove unitary evolution? Clearly you do not consider the experimental data, which suggests a (perceived) collapse, to be evidence on the basis that we can construct an interpretation consisting of multiple worlds where every possible outcome is observed. By this construction, even though we perceive non-unitary evolution, "reality" is still unitary. To some this would seem as a way of bypassing experimental evidence. What I am trying to say is; can you think of a scenario where you would accept experimental evidence for non-unitary evolution? If not then it seems as though unitary evolution, according to your worldview, is true by construction.

 

[Hurkyl]

You seem to reject the notion that we can even perceive a definite outcome of measurements so where does this leave experimental physics?

The same place it's always been.

From the rationalist point of view, our math, language, and logic have no way to distinguish whether they are talking about definite outcomes or not.

From the empirical point of view, my knowledge of having seen an outcome is always conditioned on having seen that outcome. When I make a claim about what I saw, my particular claim depends on what I saw. When I make predictions about what I will see in the future, those predictions involve what I saw in the past.


When you look at it externally it looks a little weird -- e.g. if outcomes aren't definite, then how does an observer "get" the outcome he bases everything on? The thing that finally straightened it out for me is that I spent some time seriously considering the question "if that's how things are, then how would the internal observer know?" So while the external analysis has to use an indeterminate variable (or condition on a hypothesis), what the internal observer sees looks perfectly normal.

For example: In your worldview, is it even possible to disprove unitary evolution?

Sure -- at least for individual quantum theories. You could, for example:

• find an experiment that QM gives the wrong result for.
• work out quantum thermodynamics and show that it makes the wrong predictions about the macroscopic world.
• find some aspect of the whole that remains observable despite the subsystem being in a mixed state, and see that QM gets it wrong
• find some aspect of the "approximately" in "approximately a mixed state of classical definite outcomes" that could be tested, and see that QM gets it wrong

 

[Travis_King]

It's a good thing there are definite outcomes then.

 

[Ken G]

When you look at it externally it looks a little weird -- e.g. if outcomes aren't definite, then how does an observer "get" the outcome he bases everything on? The thing that finally straightened it out for me is that I spent some time seriously considering the question "if that's how things are, then how would the internal observer know?" So while the external analysis has to use an indeterminate variable (or condition on a hypothesis), what the internal observer sees looks perfectly normal.

Yes, that is exactly what I meant by a "god's eye" view. It is not a bird's eye view, because the bird only sees the entirety of the pieces seen by all the frogs on the ground, and the bird can communicate to all those frogs. The "god" sees what even the bird cannot, and this vision cannot be empirically perceived by the bird or any of the frogs, it can only be conceived by them when they imagine such a god.

Sure -- at least for individual quantum theories.

And that is just entirely the rub here-- it is only a given quantum theory that could be falsified, never the notion of unitary evolution. That's what I was driving at earlier when I said that some highly anti-empiricist classical philosopher at some point probably pointed out that when we flip a coin, we don't actually know that a heads or a tails "really happens." That philosopher might have believed in some kind of unitariness principle (perhaps a variant on the thoughts of Parmenides, one of the earliest of all known philosophers), that says a coin cannot come up either heads or tails-- if it has the capacity to come up either, then it must come up both. This is now the expression of unitariness in purely classical physics, and everything that the MWI says about QM could have been applied to classical physics in 1800 by such a philosopher.

I see nothing any different from that in MWI-- you can certainly falsify any particular theory, but you can never falsify unitariness, or the "many worlds," because I could always invoke precisely the "god's eye" perspective that Hurkyl uses in concert with any theory that recognizes the possibility of multiple outcomes and does not provide the observer the power to predict the precise outcome they will perceive (just like classical themodynamics, for example). I would simply have to violate the core axioms of empiricism to do it, and that's what MWI has to do in concert with QM. That doesn't make it wrong, it's just an important thing to recognize about MWI.

 

[Hurkyl]

This is now the expression of unitariness in purely classical physics, and everything that the MWI says about QM could have been applied to classical physics in 1800 by such a philosopher.

This is flat out wrong.

Yes, a 19th century philosopher could have talked about these parmstates^*. In fact, I think the way math has gone (the formulation of probability theory, the techniques of set theory and logic), I think that even if we never came up with QM it's very likely that some people would start considering it seriously.

But that completely misses the point.

Newton's laws cannot create or destroy parmstates^* -- in fact, they operate completely independently of any parmness^* that may or may not be featured in reality.

The central idea of MWI, when applied to classical mechanics, would never have bothered one way or the other with the idea of parmstates -- they have nothing to do with considering how Newton's laws could be applied to explain the results of observation.

The reason the actual MWI wants to describe the classical-seeming world with (approximate) parmstates is because that appears to be a necessity for considering how Schrödinger's equation could be applied to explain the results of observation.


The name "Many Worlds" didn't come from the motivation of the interpretation -- it came from (a description of) a prominent result of the research project.


*: I'm going to coin a word, to make it easier to talk about these things, since there has been so much confusion over phrases like "mixed state", "indefinite outcome" and the like. "Parm" is short for "Parmenides".

 

[Ken G]

This is flat out wrong.

Yes, a 19th century philosopher could have talked about these parmstates^*. In fact, I think the way math has gone (the formulation of probability theory, the techniques of set theory and logic), I think that even if we never came up with QM it's very likely that some people would start considering it seriously.

Well, I'd say that makes it flat out right. (In other words, I agree it would have been very interesting to see what would have happened to classical physics without quantum mechanics, and I think all the MWI issues are already there in classical physics.)

Newton's laws cannot create or destroy parmstates^* -- in fact, they operate completely independently of any parmness^* that may or may not be featured in reality.

In a CI interpretation of Newton's laws, yes. But what about an MWI interpretation? All one needs is an equivalent reformulation of Newton's laws that does refer to parmness. Perhaps a formulation based on the principle of least action. All one needs to do is take the uncertainty in the initial conditions seriously, and consider a Hamiltonian system that exhibits chaos (and imagine that one that doesn't is just a special case that does not reveal the parmness). The equivalent of the quantum mechanical "stationary state" is then an ergodic covering of a fixed energy manifold, which of course remains classically stationary. For that to be a pure state, we merely need to take it seriously, as though a set of observers with their feet in "many worlds" could actually observe every state on the manifold at once.

Unitarity in such a classical context then follows from the time reversibility of the equations of classical physics. The philosopher in 1800 then looks at the second law of thermodynamics and says "what an awful botch those CI-empiricists have made of that law! Clearly, the equations are time reversible, so entropy cannot increase, that would be non-unitary. The empiricists have mistaken the concept of information about reality for the concept of reality itself. What must be happening is that the observers are only seeing part of the ergodic manifold, which leads them to think a pocket of states on the manifold is evolving into an ergodic distribution of higher entropy. If they had the "god's eye view", they would see the manifold is already fully ergodic, and the entropy is not changing at all, as required by unitarity. To see why that must be true, simply run time backward-- all of physics is the same, but the empiricists see something impossible happening, so obviously they see an illusion."

Voila, unitarity comes to classical physics, and all the equations of Hamiltonian dynamics are still exactly the same as the ones we use. We just built the empiricism into the states in classical physics, but that wasn't as straightforward in QM. All the same, the philosopher who wanted a unitary universe could have reframed all of classical mechanics in a unitary form, simply by adjusting our understanding of what an observer is.

The point here is, there is nothing special about QM that allows it to admit to a unitary MWI approach. We just didn't think of it in the classical context, that philosopher either didn't come along or didn't have any converts. QM seems to give us more reason to go that route, but it is not a road that is unique to QM. More importantly, there is nothing about QM that requires that road, as CI proves.

The central idea of MWI, when applied to classical mechanics, would never have bothered one way or the other with the idea of parmstates -- they have nothing to do with considering how Newton's laws could be applied to explain the results of observation.

What I have shown is that they could have, they just didn't. Historical accident, the unitarity philosophy wasn't in place, the classical parmstates weren't seen as aesthetically pleasing.

The reason the actual MWI wants to describe the classical-seeming world with (approximate) parmstates is because that appears to be a necessity for considering how Schrödinger's equation could be applied to explain the results of observation.

Not to the CI, doesn't seem necessary at all. Instead, the parmstates are just mathematical linkages that describe the information we have about the real states, the observed states. CI treats physics as manipulation of incomplete information, MWI treats it as the god's eye view, that's all true classically and could have been discussed prior to quantum mechanics. The CI is an interpretation where there is a second law of thermodynamics for a closed system, the MWI is an interpretation where there isn't. That would all have been there in classical physics too.

 

[Hurkyl]

In a CI interpretation of Newton's laws, yes. But what about an MWI interpretation?

Also yes.

The line of reasoning that historically led to the MWI of QM simply would not have lead to a many-worlds interpretation of classical mechanics.

Of course, other lines of reasoning may have led to a many-worlds interpretation of CM -- for example, your following quote closely relates to one of the ways I had in mind that such a thing may have come about.

All one needs to do is take the uncertainty in the initial conditions seriously,

But taking uncertainty in initial conditions seriously doesn't change Newton's laws, which still operate on individual (time-varying) points of phase space. The extension of Newton's laws to parmstates is simply to act on each point of the parmstate separately.

I do not see a probable path towards a variation on Newtonian mechanics that does not share this property. (whether or not we invented QM)


Going down one of my lines of thought -- if you consider empirical propositions to be the important part of classical mechanics, the most natural associated mathematical notion of "truth" is that the truth value of any particular proposition is simply the set of all points of phase space upon which the proposition is satisfied. (of course, it's all too easy to interpret this mathematical notion of "truth" as quantifying ignorance -- i.e. "possibilities" -- rather than quantifying "actual reality")

And there are neat consequences from the hypothesis that only open sets are allowed. For example, it gives a rigorous foundation to a variety of ad-hoc claims about what is impossible because of precision issues -- e.g. if X is the variable denoting the position of a particle, then "X=3" would become a logical contradiction, since the constraint is just 'too narrow'. (I could actually go into rigorous detail on this paragraph, but I figure it's off-topic and the details are probably uninteresting, so I'm sticking to the vague but suggestive language)

Unitarity in such a classical context then follows from the time reversibility of the equations of classical physics.

In classical mechanics, "unitary evolution" is time-reversibility, no matter what "context" or "interpretation" you have on things.

The point here is, there is nothing special about QM that allows it to admit to a unitary MWI approach.

There is nothing special about QM that allows it to use unitary evolution.

What is special about QM is that it's not immediately obvious that unitary evolution is consistent with observation -- and for a few decades of its early formative years people even thought they had an impossibility proof against that hypothesis. And so as QM was being first developed, a great deal of time and effort was spent trying to formulate and interpret the theory in a way that violated it. (e.g. do unitary evolution for a while, then collapse!)

Not to the CI, doesn't seem necessary at all.

Er, CI isn't even interested in the topic. It is uninterested in applying Schrödinger's equation to explain the results of observation -- instead it is interested in collapsing the state to provide the link to observation, with Schrödinger only being applied 'in-between'.

 

[PAllen]

Following this thread in bits and pieces. The last post by Hurkyl reminded me of an essay I've wanted to write for a long time, but never gotten to. To wit: "The Paradox of Boltzmann's Cat", to wit we pretend Boltzmann had proposed the original cat paradox, strictly classically:

A dice shaker, and optical reader, and a circuit to open a cyanide bottle are in a closed box with a cat. The shaker is shaken every second and read by the reader. When snake eyes appears twice in a row, the cyanide is released.

It appears to me that very little can be said about the Schrodinger case that wouldn't apply to the purported Boltzmann case.

 

[Ken G]

The line of reasoning that historically led to the MWI of QM simply would not have lead to a many-worlds interpretation of classical mechanics.

That's only because that line of reasoning was affected by the QM theory. I am speaking in more general terms, about the whole concept of unitarity, essentially introduced by Parmenides some 2500 years ago. It has always been there, ready to be applied to every theory of physics that came along. It just happened that it took QM for it to come to the fore-- a historical accident.

But taking uncertainty in initial conditions seriously doesn't change Newton's laws, which still operate on individual (time-varying) points of phase space. The extension of Newton's laws to parmstates is simply to act on each point of the parmstate separately.

Yes, the coherences are erased at the classical level, that is true. But my point is that unitarity does not require tracking coherences-- it would just be a different rationalist motivation to include it in the interpretation. You are saying QM has a more convincing motivation for including it, but I'm saying the imaginary philosopher in 1800 could have been completely convinced of the need for unitarity in Newtonian mechanics, for the reasons I mentioned. What is convincing depends on the philosopher, when rationalism is the approach. That's another difference with empiricism-- everyone can agree on what the observations are, but they cannot all agree on what is a convincing reason. Parmenides thought he had a convincing reason for unitarity 25 centuries before Schroedinger! Perhaps he has been right all along, but empiricism remains skeptical that thought can render objective perception illusory. That is the road to "the Matrix."

Going down one of my lines of thought -- if you consider empirical propositions to be the important part of classical mechanics, the most natural associated mathematical notion of "truth" is that the truth value of any particular proposition is simply the set of all points of phase space upon which the proposition is satisfied. (of course, it's all too easy to interpret this mathematical notion of "truth" as quantifying ignorance -- i.e. "possibilities" -- rather than quantifying "actual reality")

Exactly, those are the choices. I personally have no issue with taking uncertainty seriously, I think it is pretense to imagine there is a "truth" that transcends uncertainty. But I reject both the imagining that there is a "true" state (unless one throws a wide enough net, like all the states of a coin that get grouped in the "heads" class), and also the imagining that the uncertainty is itself a "true" state. My approach is ever the skeptic-- I don't see any reason to imagine any of these concepts of "truth" are true! They are all just ideas, they are our somewhat desperate and flailing efforts to make sense of a reality that is way out of our depth, yet all the same, we've been amazingly successful-- not so flailing after all, somehow. Yet we are still cheating on the exam-- we ask ourselves the questions we already feel we know the answers to, and ignore the ones we don't. Sometimes we even pretend the questions we don't know the answers to are meaningless questions, we have no shame at all.

And there are neat consequences from the hypothesis that only open sets are allowed. For example, it gives a rigorous foundation to a variety of ad-hoc claims about what is impossible because of precision issues -- e.g. if X is the variable denoting the position of a particle, then "X=3" would become a logical contradiction, since the constraint is just 'too narrow'. (I could actually go into rigorous detail on this paragraph, but I figure it's off-topic and the details are probably uninteresting, so I'm sticking to the vague but suggestive language)

No need on my behalf, I agree completely. Even in Newtonian mechanics, imagining that X=3 meant something more than an idealized language for talking about position was absurdly arrogant. That's kind of my point about rationalism-- it's just great until you take it seriously. You're upping the sophistication of the rationalism, in hopes that adding a layer of flexibility will solve the ultimate impossibility of knowing the nature that gave rise to our intelligence. I say, just accept that we are doing the best we can, and don't make it a world view. I don't claim empiricism has any greater grasp of the truth, it is just the stuff that doesn't change every time we come up with a better way to think about things.

In classical mechanics, "unitary evolution" is time-reversibility, no matter what "context" or "interpretation" you have on things.

Yes, unitary evolution is time reversibility, but interpretation is still extremely important. When we watch a movie, and an explosion returns to a bomb, we know with certainty that someone is showing us that movie backward, even though everything we see obeys the laws of Newtonian mechanics. Where's the time reversibility? It is our interpretation of what we see that there is no time reversibility there. But what we see does have a tiny probability of happening, so we can make it a reasonable thing to see simply by embedding that perception into a "many worlds" of enough things to allow that one. Then all we need is a prescription for saying why we perceived that seemingly unlikely one. Sound like the "landscape"? It was supposed to. Time reversibility can be restored to statistical mechanics with a suitable manipulation of the many worlds, and it could have been done before quantum mechanics, we just weren't willing to deviate that far from empiricism to have unitarity. That many are willing now is just a historical accident, Parmenides would have had us do it thousands of years ago.

What is special about QM is that it's not immediately obvious that unitary evolution is consistent with observation -- and for a few decades of its early formative years people even thought they had an impossibility proof against that hypothesis. And so as QM was being first developed, a great deal of time and effort was spent trying to formulate and interpret the theory in a way that violated it. (e.g. do unitary evolution for a while, then collapse!)

This is where we differ. I would say that no time or effort was speng trying to interpret the theory that way, because that is precisely a description of what we perceive. So the instant one adopts empiricism, poof, it is done, no effort at all. The idea that unitary was rejected because of some rationalist proof is missing the point-- CI is empiricist, it would never need any kind of proofs of anything, it doesn't believe in proofs because proofs are just ways of understanding what a theory asserts, not what reality does.

 

[Fra]

CI isn't even interested in the topic. It is uninterested in applying Schrödinger's equation to explain the results of observation -- instead it is interested in collapsing the state to provide the link to observation, with Schrödinger only being applied 'in-between'.

Given that unitary evolution of SE is simply the "expected evolution" with respect to an observer (real observer, not god's view) I acknowledge this issue, but then the issue we arrive at is I insist a problem of QM itself, not a problem of interpretations.

The way I see it - but consistency of reasoning, this must hold.

Observer A sees it's environment by patches of unitary evolution interrupted by collapses (information updates).

Now an observer B, that observers A and it's environment (ie. B is a big frog) necessarily at any instant of time has en expected eovlution of A+environment. This EXPECTATION contains no collapses.

Thus collapse or not, is a matter of perspective, BUT as I see it that TASK is to understand how the inside view connects ot the outside view. Ie. we should be able to construct the hamiltonians of a big frog view without classical baggage. In it's extreme it should follow from a novel renormalisation program where the "collapses" are simply thte naked actions, and the unitary expectation is the view from far away.

To just find one "master view" where all is unitary, somehow misses the point. If if this master would in some sense might be right, it's useless, because real life decision prolbmes where we need to find the expected evolution always apply to big frogs. There is no decison problem in the master view anyway, because "God/master" is not interacting with the system.

/Fredrik

 

[Ken G]

It appears to me that very little can be said about the Schrodinger case that wouldn't apply to the purported Boltzmann case.

I agree, that's the case I've been making. I've always felt we missed the boat when we decided to stress how "non-classical" quantum mechanics is-- I'd say QM just ushered in a big shift in how we think, but it's not the theory itself that is all that different, it's just the lessons we finally learned from it. The problem is, now we have a dispute over what those lessons were! The rationalist says the lessons were that we have limited ability to perceive what is actually true, and the empiricist says we have limited ability to build theories that work like our perceptions, the latter being the foundation of scientific truth. There's a fundamental disconnect there, lurking all along but it took QM for us to finally notice it. Amazingly, even though the CI and MWI have probably the all-time record different perspectives (even more different than atoms vs. fields, possibly), even so the physics they each motivate is still identical. I think this is telling us something about physics-- it is better than the people who created it.

 

[Ken G]

In it's extreme it should follow from a novel renormalisation program where the "collapses" are simply thte naked actions, and the unitary expectation is the view from far away.

On the surface that sounds to me like decoherence. What we call a measurement is expressly the conscious attempt to cause collapse of the substate, that's the ultimate "information update." The collapse is done on purpose, somehow that is central to the scientific method.

To just find one "master view" where all is unitary, somehow misses the point. If if this master would in some sense might be right, it's useless, because real lif decision prolbmes where we need to find the expected evolution always apply to big frogs

I believe you have your finger on just why Parmenides never caught on. I've always suspected that at some deep level he was right (the all-time coup de grace of logic, coming at essentially the invention of logic), but in a useless way. (For those who don't know Parmenides and don't feel like googling him, he basically said pure logic proves that change is an illusion, simply because if A is A then A cannot become B, for if it were in A to become B, then that would just be more A).

 

[Fra]

On the surface that sounds to me like decoherence. What we call a measurement is expressly the conscious attempt to cause collapse of the substate, that's the ultimate "information update." The collapse is done on purpose, somehow that is central to the scientific method.

There are some important extra things in what I describe. In decoherene the environment is like an information sink. In my view the only "sinks" are big frogs, and these are bounded. This introduces information cutoffs.

I agree that hte collapse can't and shouldn't be removed in a fundamental way, no more than you can "remove the observer". But one can still change perspective, and see that the collapse is observer dependent, meaning that the one observers collapse cna in principle be expected by another observer. Similarly, one observer can observe another observer, and their preconceptions of each other might encode their physical interactions.

However this "receipe" can not be repated infinitly. The reason is that the big frog has limited information capacity. This is also why this works fine for small subsystems only. Where small means small relative to the big frog.

In a unified model of interactions, it's quite possible that once subatomic parts see other parts "collapsing" - ie this is the "inside view", but what we see from the big frog view (laboratory frame) is a unitary evolution.

The exact link here... is missing. And this link is what's needed to make complete sense of what I'm suggesting.

So I think it's correct to say that the collapse is observer dependent. But this does not mean that (like in relativity) there exists deterministic transformations that takes you from one to the other so that equivalence classes cna be defined.

I think that instead of loooking at "observer invariants" (which are impossible to define in an empirical way) I'm focusing on the "democratic PROCESS" where you have observer democracy and where the democratic negotiation process is identified as the regular physical interactions.

/Fredrik

 

[Fra]

But one can still change perspective, and see that the collapse is observer dependent, meaning that the one observers collapse cna in principle be expected by another observer.

With this I don't mean that the specific outcomes are generally expected, but more that the entire "history of information updates" is understood as a random walk.

And the random walker gets a surprise after each step he takes, takes new direction and takes another step in accordance to the intrinsic expectations (which are highly constrained, which is exactly why it's a "random walk").

But from perspective a second observer seeing the first observer as a small subsytem, timeless statistical regularities are emergent and we can call them laws. This is the view we humans have on particle physics. But the actual time evolution of the system is not understood in terms of a random walk seen from perspective, it's coming from inputting classical baggage like hamiltonians. This is a big leap in insight, and gives no clue to unification problems.

The random walk concept also in a deep way has potential to explain couplings, because if we assume that the random walker updates his information in a rational way in terms of counting empirical evidence, and is placing his nexts moves according to the so derived "odds", the behaviour of the random walker by construction decouples with things that he can not perceive. And what she CAN perceive, depends on the complexity scale. So in the observer -> low complexity limit, we have pretty much a complete decoupling between systems since neither of them has the complexity to encode reactions. We are at the most extreme random walk domain.

The random walker starts to couple to more an more things in the environment, as it acquires more complexity.

I think this idea, while speculative and an open issues, in a natural way shows the importance of hte "information update" concept. I think the information update it self, is a key to understand coupling or noncoupling between two decision makers for example.

/Fredrik

 

[friend]

It seems to me that the Many Worlds Interpretation is a theory that can not possibly be confirmed. As I understand it, MWI says that the universe splits off into a different reality whenever a superposition of possibilities collapses upon measurement. Then the alternative that we don't measure exist in a universe that has split off from the one that we did measure. But since that alternative reality is not measurable, it's not possible to confirm the MWI of QM.

 

[BruceW]

If you define MWI as 'no non-unitary collapse theory', then the universe never fully splits. (This is the whole point of MWI). You could say that it splits into weakly interacting universes, but the connection is still there.

In fact, you've described something much closer to CI, where one universe is chosen via non-unitary collapse, and the other universes do fully split off. (And are discarded).

 

[Ken G]

No, CI never "discards the other universes," because CI begins with the observations as the reliable witnesses to what "the universe" is doing in the first place. This is perhaps the most important thing to understand about CI-- it is an interpretation of the theory that does not start with the theory. Those who don't understand that really never get CI. If you ask a CI proponent "what is quantum mechanics", they say "it is a theory designed to explain the following observations", and then proceed to tell you those observations. That's what counts to a CI person, so when they get to "discarding", all they are discarding is elements of the theory that don't match their observations. Unitarity in the classical limit is what is discarded, not universes. Very analogous to what the second law of thermodynamics does.

 

[Hurkyl]

That's what counts to a CI person, so when they get to "discarding", all they are discarding is elements of the theory that don't match their observations.

This really needs clarification -- normally when a person ignores that a theory makes wrong predictions, we call them a crackpot.


Also, normally we don't assert a theory makes wrong predictions unless the particular sort of prediction is something testable.

Those who don't understand that really never get CI. If you ask a CI proponent "what is quantum mechanics", they say "it is a theory designed to explain the following observations", and then proceed to tell you those observations.

That is not CI -- that is simply science.

One isn't doing anything novel by constantly reminding themselves and others "it's just a theory". And it seems to do some harm -- some people are so worried about remembering "it's just a theory" that they seem to have forgotten what to do with one.

 

[Ken G]

This really needs clarification -- normally when a person ignores that a theory makes wrong predictions, we call them a crackpot.

The problem is, theories don't make predictions, theorists do. All the theory does is give us a time evolving wave function, what we make of that is up to us. The theory includes a very ad hoc postulate, the Born rule, which tells us how to make a statistical prediction, but it doesn't tell us what we are doing when we apply the Born rule. That's where the theorist comes in, as well as the interpretation.

The CI user says that the purpose of the Born rule is to make statistical predictions of the real outcomes of the experiments. That works just fine when we distribute over many trials of the same experiment, the theory is not falsified. The MWI user says the purpose of the Born rule is to provide some kind of relative weight to the "many worlds", so that when we distribute over not trials of the experiment, but observers throughout those many worlds, we get the correct statistical behavior. That works too, but only to the rationalist-- the empiricist says "if your interpretation of the Born rule is that all outcomes occur in every trial, you need to show me a trial in which more than one outcome occurs." When you fail to do that, the empiricist says your interpretation does not agree with experimental reality. You respond that reality doesn't agree with their experiment.

We cannot say who is right, but we can certainly tell the difference between an empirical fact and a rationalist assertion. Calling it a "fact" doesn't make it true, but noticing the difference between empirical fact and rationalist assertion has actually been quite important over and over in the history of science. When all the rationalists said that Michelson-Morely would detect an aether, and the empiricists said "why don't we just do the experiment and find out-- oops, no it didn't, deal with it." The same will happen if CERN doesn't find the Higgs (or does find fast neutrinos), or if unification of QM throws out unitarity. The empirical facts don't change, but the rationalist assertions are different every century or so. So we need to know the difference there.

That is not CI -- that is simply science.

And yet this is quite testable. Tell 10 empiricists and 10 rationalists that you are a physicist but you would like their take on the question: "how do quantum systems behave?" I'll bet you most of the 10 rationalists will start telling you the postulates of quantum mechanics, because to them, the behavior of quantum systems is a theory about quantum systems (what else could possibly motivate MWI?). The 10 empiricists will think you want to know how quantum systems behave in practice, and will start telling you about the observations, not the theory. A funny thing happens when you describe observations-- you are describing a litany of nonunitary outcomes.

One isn't doing anything novel by constantly reminding themselves and others "it's just a theory".

If the MWI devout really did make a habit of just that, I'd have no objection at all. Unfortunately, they don't mention that at all-- in fact, they really hate to be reminded.

 

[Hurkyl]

If the MWI devout really did make a habit of just that, I'd have no objection at all. Unfortunately, they don't mention that at all-- in fact, they really hate to be reminded.

That's because they aren't being reminded they're doing science -- they're being reminded they're dealing with closed-mindedness.

I don't think I've ever actually seen the words "it's just a theory" used to remind people that science is science. Instead, it's always used to rationalize the dismissal of what a theory says.

You never see an exchange go like:

Alice: Darn it, time is absolute! Our universe is one of classical mechanics!
Bob: Newton's laws were just a theory, and now we have a better one -- special relativity.​

or

Alice: Darn it, electrons are mixed into atoms like plum in pudding!
Bob: Sorry, but the plum puddling model was just a theory that didn't pan out experimentally. You really should try to let go of the idea​

but instead, you see things of the form

Alice: Darn it, the Earth revolves around the sun!
Bob: While the heliocentric model is an elegant way to work out the epicycles, it's just a theory after all. You shouldn't take it so seriously.​

or

Alice: Darn it, objects in motion tend to remain in motion!
Bob: Have you ever seen an object in motion? Newton's laws are useful for making predictions, but it's just a theory, and it clearly doesn't match observation.​

Or, of course

Alice: Darn it, if we study how unitary evolution behaves when an observer is part of the system...
Bob: Pfft, QM is just a theory. You shouldn't really pay attention to what it says!​

A funny thing happens when you describe observations-- you are describing a litany of nonunitary outcomes.

Eh? Tell me again how you can tell the difference between "a litany of nonunitary outcomes" and "a litany of unitary outcomes"?

For such an apparent staunch empiricist, you seem to have difficulty with the basic idea that if hypothesis X predicts we see Z, and hypothesis Y predicts we see Z, then observing Z doesn't give us any information about X versus Y.

 

[Ken G]

I don't think I've ever actually seen the words "it's just a theory" used to remind people that science is science. Instead, it's always used to rationalize the dismissal of what a theory says.

In this case, I'm using it to call into question the use of the theory to justify an elaborate world view of invisible other outcomes to every experiment. That is not at all "what a theory says", so I'm certainly not doing what you claim.

You never see an exchange go like:

Alice: Darn it, time is absolute! Our universe is one of classical mechanics!
Bob: Newton's laws were just a theory, and now we have a better one -- special relativity.​

or

Alice: Darn it, electrons are mixed into atoms like plum in pudding!
Bob: Sorry, but the plum puddling model was just a theory that didn't pan out experimentally. You really should try to let go of the idea​

On the contrary, I see exchanges like that all the time. Are you an educator?

but instead, you see things of the form

Alice: Darn it, the Earth revolves around the sun!
Bob: While the heliocentric model is an elegant way to work out the epicycles, it's just a theory after all. You shouldn't take it so seriously.​

And you see a problem with Bob's position? Sounds fine to me.

or

Alice: Darn it, objects in motion tend to remain in motion!
Bob: Have you ever seen an object in motion? Newton's laws are useful for making predictions, but it's just a theory, and it clearly doesn't match observation.​

Your analogy has unravelled at this point, it bears no resemblance any more.

Eh? Tell me again how you can tell the difference between "a litany of nonunitary outcomes" and "a litany of unitary outcomes"?

Consider this sentence: "I flipped a coin, and it came up heads." Shocking claim that, but quite nonunitary. Now we have your version: "I flipped a coin, and it appeared to come up heads, but I can't really tell that it didn't come up both heads and tails because I'm a radical anti-empiricist and don't believe my senses." Nothing wrong with your stance, but we should see it for what it is. The "litany of nonunitary outcomes" I refer to requires only one thing: a regard for empirical fact. That regard can certainly be relaxed, without fear of contradiction, but it is what it is.

For such an apparent staunch empiricist, you seem to have difficulty with the basic idea that if hypothesis X predicts we see Z, and hypothesis Y predicts we see Z, then observing Z doesn't give us any information about X versus Y.

Trouble is, hypothesis Y includes angels on the pin. What you don't get about empiricism is that it holds that observations don't exist to test theories, they exist to tell us what is true.