Many Worlds Interpretation: Does Quantum Mechanics Work This Way?

[reilly]

When we look at cloud or bubble chamber measurements, we see trajectories. And these trajectories, say in a magnetic field, are governed by normal temporal unitary transformations -- in scattering theory we should use wave packets, cf. Goldberger and Watson, Scattering Theory. And so, initial and final states are asymptotic to localized trajectories with reasonably sharp momentum; and the whole process of scattering or particle production is governed by QM.

We make a measurement by examining the trajectories; and clearly under these particular circumstances our measurements can only modify the observer's information; the trajectories are written in stone - or bubbles, as you wish. Our knowledge changes; collapses from a set of possibilities to a single outcome, and that collapse is indeed governed by a unitary transformation, that describes the rods and cones,neurons.

Why, in such a case, invent an MWI-type interpretation that, necessairily requires an uncountable number of possibilities, hence apparently, an uncountable number of universes. Keep this up and you will get to ALEPH1 to the ALEPH1 universes(and on an on), a very nasty number. That is, MWI seems to ascribe a reality to QM derived probability trees; and these grow big real fast, and to the point where it is not at all clear that we have the mathematics, nor any language to describe such a situation.

I just don't see any advantage to building a highly complex structure, particularly when , in my opinion, there are vastly more simple interpretative approaches, some of which have survived for several hundred years, and are still used extensively in practical probability and statistics.

As I think about this, I'm curious to see an example of a "non-unitary" measurement -- all measuring devices are governed by the physics we all know and love.

I do not get MWI at all, it makes no sense to me. I would appreciate a simple minded explanation, that could give some understanding. MWI is an approach to which some very bright and able people have subscribed. Even though I tend to discount all of MWI, there must be things that if I get them will reduce my lack of comprehension.

Regards,
Reilly Atkinson

 

[confusedashell]

Reilly, if I don't remember wrong your a copenhagenist right?

I reject MWI, but agree with it's objectivism and realism so I support Bohm's interpretation, you might want to check that out.

As for MWI: it simply states wave functions are all that exists. Makes no sense.

 

[peter0302]

There is definitely no consensus on what the probabilities mean, but I would look at it this way.

Let's say you start out with two possible spin states for a particle A, + or -. Say the wavefunction is

|Psi A>=.436|+> + .9|->

Now as we all know, the universe continues to evolve after the split, and particle A will continue to interact with other things. Well, the amplitude of the different probabilities of + or - for A will carry through with the rest of the universe as the universe evolves. So when the next experiment comes along:

|Psi B>=.8|+> + .6|->

And A and B eventually interact, the continued universal wavefunction of the system becomes:

|Psi A,B> = .3488|A+,B+> + .2616|A+,B-> + .72|A-,B+> + .54|A-,B->

So with the wavefunction continually evolving, the odds from the original experiment (the odds of A being + or -) carry through as well, and, after a long while, will be reflected in the number of universes in which A is + and the number in which it is -.

I think a good way of looking at it is imagine that you're randomly jumping into all the different quantum realities like Mr. Worf did in one episode of Star Trek. If you had a quantum experiment whose outcome was 75% + and 25% -, 75% of the time you jumped you'd be in a universe where the outcome was +, and 25% 0f the time you'd jump into a universe where the outcome was -, and those odds will be determined by the original wavefunction describing that experiment.

Does that help or make sense to anyone besides me?

 

[JesseM]

As I think about this, I'm curious to see an example of a "non-unitary" measurement -- all measuring devices are governed by the physics we all know and love.

Don't you assume that when you make a measurement, it projects the quantum state of the system onto an eigenstate of whatever you're measuring? And unlike in classical probability you can't assume that this just represents a change in your knowledge rather than a physical change, that would suggest a hidden-variables theory where the system already had a definite value for that variable even before you measured it.

 

[Ken G]

And unlike in classical probability you can't assume that this just represents a change in your knowledge rather than a physical change, that would suggest a hidden-variables theory where the system already had a definite value for that variable even before you measured it.

I would say that measurement represents both a physical change, and a change in our knowledge (the latter change being different if we look or not, the former being the same either way), because the process involves both elements and a great deal of confusion stems from requiring it to be one or the other. To me it makes sense to say that the part that is a physical change involves whatever is the physical coupling to the measurement (say, the interactions that make the bubbles), and the part that is a change in information is when the physicist interprets those bubbles in terms of a solution of some equation involving a wave function. Why can't the measurement be physical but the wave function changes be changes in information? The fact that two people, with different information, can use two different wave functions and still conclude that quantum mechanics is working perfectly is a very telling fact, in my view.

 

[peter0302]

I would say that measurement represents both a physical change, and a change in our knowledge

Well, when you measure the state of an entangled particle, information about the twin certainly changes, but is there a physical change in the twin as well? That's why I find great difficulty saying that a measurement is always a physical change.

 

[JesseM]

I would say that measurement represents both a physical change, and a change in our knowledge (the latter change being different if we look or not, the former being the same either way), because the process involves both elements and a great deal of confusion stems from requiring it to be one or the other.

Well, perhaps I should have said that the projection onto an eigenstate cannot be imagined to be purely a change in knowledge in exactly the same manner as changes in subjective probability due to measurement in classical probability. If it were, that would imply that even when the particle is not being measured, it is "really" in one eigenstate or another at all times, with probability equal to the square of the amplitude that its current state assigns to each eigenstate, and measurement just reveals this preexisting truth (if that were the case, why would measurement of which slit the particle goes through in the double-slit experiment affect the probability distribution on the screen?)

 

[Ken G]

Well, when you measure the state of an entangled particle, information about the twin certainly changes, but is there a physical change in the twin as well?

No, there is no physical change in the twin, because there is no interaction with it. That's why someone who does not know about your measurement will never find any contradictions in their quantum mechanics, as a result of not knowing that information.

 

[Ken G]

Well, perhaps I should have said that the projection onto an eigenstate cannot be imagined to be purely a change in knowledge in exactly the same manner as changes in subjective probability due to measurement in classical probability.

Had you said that, it would be true, but all it would be saying is that classical systems respond in a more robust way to couplings to classical measuring devices than do delicate and fragile quantum systems-- a fact that should hardly surprise anyone with the hindsight of quantum mechanics yet seems to continually do so.

 

[JesseM]

Had you said that, it would be true, but all it would be saying is that classical systems respond in a more robust way to couplings to classical measuring devices than do delicate and fragile quantum systems-- a fact that should hardly surprise anyone with the hindsight of quantum mechanics yet seems to continually do so.

But here you have to draw a boundary between "classical systems" and "quantum systems", rather than treating everything using the same quantum laws as reilly was suggesting when he said 'As I think about this, I'm curious to see an example of a "non-unitary" measurement -- all measuring devices are governed by the physics we all know and love.' If you do try to assign a wavefunction to the combined system of the measuring device and the particle being measured, then although you can assign amplitudes to various outcomes after the measuring device does its stuff, if you assume this system is just like any other quantum system then you can't assume the measuring device has "really" found one outcome or another and that if you later measure the measuring device's records, you are merely discovering a preexisting truth. This is just another way of stating the Schroedinger's cat paradox of course, replacing the cat with the measuring device and replacing the fact of the cat being alive or dead with the measuring device's recordings.

Basically, I think the motivation for the MWI is just to treat all systems with a uniform set of laws at all times, without the need for any external observer to measure the system, and to try to make these uniform laws differ as little from the standard textbook laws as possible.

 

[Ken G]

But here you have to draw a boundary between "classical systems" and "quantum systems"

Not in any "real" sense I don't, it's all in how I choose to treat them. I can treat a quantum system classically, if I'm willing to get lots of wrong results along with the right ones, and I can treat a classical system quantum mechanically, if I'm willing to squint my eyes and pretend a bowling ball is a "particle". It's all up to me and my objectives.

If you do try to assign a wavefunction to the combined system of the measuring device and the particle being measured, then although you can assign amplitudes to various outcomes after the measuring device does its stuff, if you assume this system is just like any other quantum system then you can't assume the measuring device has "really" found one outcome or another and that if you later measure the measuring device's records, you are merely discovering a preexisting truth.

Actually, you can assume that, because you cannot be derailed by coherences in classical systems (that's what defines classical systems). You make no errors at all, in the sense that none of your predictions prove false. You just don't surround it with such a formal exoskeleton of untestable axioms.

This is just another way of stating the Schroedinger's cat paradox of course, replacing the cat with the measuring device and replacing the fact of the cat being alive or dead with the measuring device's recordings.

Right-- and recall that Schroedinger introduced that paradox on the grounds that you could treat the cat as alive or dead, to discredit the idea that you could not-- quite the irony.

Basically, I think the motivation for the MWI is just to treat all systems with a uniform set of laws at all times, without the need for any external observer to measure the system, and to try to make these uniform laws differ as little from the standard textbook laws as possible.

I agree, that is what is behind it. But to me, that's taking science outside its own definitions, and telling reality that it must be the way we like to imagine it. Countless times we have ended up with egg on our faces doing precisely that, so why pretend we know it now? Just treat it like an optional and untestable picture, that admits certain mathematical niceties but does not reflect some of our most basic perceptions of reality. Until we have a working model of what a "self" is, we should expect surprises.

 

[JesseM]

Not in any "real" sense I don't, it's all in how I choose to treat them. I can treat a quantum system classically, if I'm willing to get lots of wrong results along with the right ones, and I can treat a classical system quantum mechanically, if I'm willing to squint my eyes and pretend a bowling ball is a "particle". It's all up to me and my objectives.

But you're talking about what you can do in practice, I'm talking about the more theoretical problem of picking a set of laws such that we can imagine a universe described exactly by those laws, such that what would be seen by an observer in that model universe would look no different than anything we see in actual experiments.

Actually, you can assume that, because you cannot be derailed by coherences in classical systems (that's what defines classical systems). You make no errors at all, in the sense that none of your predictions prove false. You just don't surround it with such a formal exoskeleton of untestable axioms.

You can assume it in practice, but only because in practice you have an informal understanding of the difference between "classical" and "quantum" systems, although no such boundary follows directly from quantum laws themselves. The quantum laws don't give you a basis for saying that for some quantum systems, the square of the amplitudes just represents a probability that the system was in that state before measurement, while for others the square of the amplitudes does not represent any preexisting probabilities.

Right-- and recall that Schroedinger introduced that paradox on the grounds that you could treat the cat as alive or dead, to discredit the idea that you could not-- quite the irony.

In principle QM predicts that you could still see interference effects here, if the cat was perfectly isolated from the external environment and "opening the box" involved measuring every single particle that makes up the cat and the rest of the stuff inside the box that was interacting with it. In practice this would be too difficult, although if quantum computing goes anywhere we might eventually be able to simulate some simplified version of a multiparticle "cat" system which is isolated from the external environment and therefore behaves in a quantum manner before it's measured.

I agree, that is what is behind it. But to me, that's taking science outside its own definitions, and telling reality that it must be the way we like to imagine it. Countless times we have ended up with egg on our faces doing precisely that, so why pretend we know it now? Just treat it like an optional and untestable picture.

Maybe it depends if you see physics more as a set of recipes for making predictions, or as an attempt to create a self-contained mathematical model of the universe whose predictions can be compared with the real world around us. Certainly taking any given successful model too seriously has left scientists with egg on their faces, but at the same time, I think a lot of good theoretical insights have been inspired by physicists who try to go beyond merely predicting the results of current experiments, and who instead try to find elegant mathematical models that give them a "bird's eye view" of a complete universe described by the model's laws, with experimenters and measuring devices just being part of the model (take Einstein's work on general relativity, for example). And I think if you want to do quantum cosmology you're really forced to think about what it would mean to describe an entire self-contained universe using quantum laws, with no external measuring-devices.

Anyway, my main point was just to respond to reilly's comment that 'As I think about this, I'm curious to see an example of a "non-unitary" measurement -- all measuring devices are governed by the physics we all know and love.' Do you agree with this comment? Can we make sensible predictions if we assume measuring devices are governed by precisely the same laws as quantum ones, without adopting some MWI type viewpoint?

 

[Hurkyl]

I do not get MWI at all, it makes no sense to me. I would appreciate a simple minded explanation, that could give some understanding.

I will try to restate a short description of how I understand it.

QM gives us a state space (which is usually presented as a Hilbert space), and the dynamics of how a state evolves over time. MWI says "that's it". All this talk about worlds and splitting universes is just an attempt to make a qualitative description of elements in a Hilbert space, and of how they evolve over time.

In the famous entangled photon thought experiment, once Alice measures her photon as spin up, MWI says that if you try to compute "the probability that Bob measures spin down", it will be 50%. However, MWI says that's probably not what you meant to compute -- you probability meant to compute "the probability that Bob measures spin down, given that Alice measured spin up", which will be 100%.

Our knowledge changes; collapses from a set of possibilities to a single outcome, and that collapse is indeed governed by a unitary transformation

To the best of my knowledge, this is (generally) wrong -- collapsing to a single outcome is an honest-to-goodness irreversible process (it's not merely a process statistically unlikely to reverse), even when you take the environment into account. Therefore, it cannot be described by a unitary transformation. To get an actual unitary transformation, you have to invoke decoherence -- the relative state of the system evolves into a statistical mixture of all outcomes. (The state of the system+environment is still pure, though, assuming it started pure) (Decoherence is not possible without interacting with the environment)

 

[Hurkyl]

That sure doesn't sound like "an ontology" to me, a "model" does that fine. Do you think a model is the same as an ontology? If so, we have no disagreement on the physics, though a bit of a disagreement on the language.

That sounds right -- in every context I've cared about where I've seen the word "ontology" used (and given a coherent description), it has appeared operationally equivalent to the notion of an "interpretation" from model theory.

 

[Hurkyl]

Countless times we have ended up with egg on our faces doing precisely that, so why pretend we know it now?

We shouldn't pretend we "know it now" in the absolute sense. We should pretend we "know it now" in the empirical sense -- it is the theory (and interpretation) best supported by the results of our experiments. (except, of course, we don't have to pretend)

 

[Ken G]

That sounds right -- in every context I've cared about where I've seen the word "ontology" used (and given a coherent description), it has appeared operationally equivalent to the notion of an "interpretation" from model theory.

Then I propose we simply stick to the word "model", a well known concept in science, rather than introduce extraneous philosophical notions like "existence" and "ontology". According to what you are saying here, the latter adds nothing to the well-known use in science of models, and it certainly is easily mistaken for making claims about existence.

 

[Ken G]

We shouldn't pretend we "know it now" in the absolute sense. We should pretend we "know it now" in the empirical sense -- it is the theory (and interpretation) best supported by the results of our experiments. (except, of course, we don't have to pretend)

Again, then let's just agree to say "we have a model or a theory"-- the lack of any pretense is more obvious in that statement than in any other I can imagine. This all relates to MWI, because MWI is not a model, nor a theory-- the model or the theory does not require the additional postulate you mentioned above (the "that's it" postulate). The model or theory is perfectly satisfied with "we have no idea if a wave function is appropriate for a system when we cannot use that wave function to do science". Indeed, had I said to a Newtonian-era physicist that "we need not assert that a particle has a location to any greater precision than we can actually do science on", they would likely have accused me of being too lazy or obstinate to accept that an obvious aspect of sensible axioms is that particles do have exact positions even if we can't do science on them. Indeed, that's precisely the mindset that caused such a stir in the 1920s. The lesson still isn't learned.

For example, in the empirical definition you state here, the term "interpretation" has no place, because there is no basis for saying an interpretation is "best supported" by experiment-- other than the interpretation that says what you are interpreting is what you are experimenting on (i.e., CI). MWI extends the interpretation to include things that are not being experimented on (analogous to the exact position of a particle in Newtonian physics), blithely assuming it can account for that which is not being accounted for, and settling for consistency when it should be striving for demonstrability.

Of course, any individual can say "MWI is just an interpretation, a picture I use when I set up the equations, I'm not claiming any of these things actually exist outside my head", but that is not generally how people talk about it, and indeed there are some people in the "quantum myth 1: wave/particle duality" thread who very much seem to view that general type of scientifically responsible approach as "mere memorization" exhibiting "positivist tunnel vision". I don't really blame them-- there is a tremendous lure to take our physics more seriously than is really responsible, and history has shown that over and over.

 

[Hurkyl]

Again, then let's just agree to say "we have a model or a theory"

Now I remember why I don't use the word "model" -- it has multiple meanings. In the model theoretic sense: a theory is simply a collection of statements made in an abstract language (i.e. a theory is pure syntax), a structure is some 'thing' in which the abstract language can be interpreted (i.e. it gives the semantics), and a model is simply a structure that satisfies (the interpretations of) axioms of the theory.

What a physicist calls a theory really consists of three parts:
(1) A mathematical theory
(2) An interpretation of that theory in the 'universe'
(3) Empirical evidence supporting the claim that the universe is a model of the mathematical theory

Well, (3) isn't part of the physical theory, but it's a requirement for calling it a physical theory.

 

[Ken G]

What a physicist calls a theory really consists of three parts:
(1) A mathematical theory
(2) An interpretation of that theory in the 'universe'
(3) Empirical evidence supporting the claim that the universe is a model of the mathematical theory

Well, (3) isn't part of the physical theory, but it's a requirement for calling it a physical theory.

I basically agree, but I have a few modifications to that scheme. [2] should not say "an interpretation", it should say "a set of interpretations that are equivalent with respect to application of the theory to the observations, chosen entirely by the preference of the practitioner". One does need that to know how to apply [1], but one does not need to see any particular interpretation as integral to the theory, nor does one need to think that any interpretation describes reality (a problem with how many people talk about MWI). Also, note that in [3] you refer to the universe as a model of the theory, but in fact the theory is a model of the universe. That kind of inversion of what is real, and what is in our heads, is precisely my "beef" with MWI.

 

[Hurkyl]

Also, note that in [3] you refer to the universe as a model of the theory, but in fact the theory is a model of the universe.

Only if you make a fallacy of equivocation. As I said, I am using the word "model" in the model theoretic sense -- a model of a theory is, by definition, an interpretation for which the axioms of the theory are valid. In this sense, nothing can be a model of the universe, because the universe is not a theory. But we can ask if a particular the universe is a model of a theory (under a chosen interpretation). More generally, we can apply statistical inference to experimental results to assign degrees of confidence¹ to statements of the theory, and use the given interpretation to translate back into the universe in order to make predictions.

1: Or, to sidestep the whole 'a priori' issue, we can simply look at the Bayes factors, rather than trying to derive a posteriori confidence.


Incidentally, I note the Wikipedia page on the meaning of the word that you're using (i.e. not the model-theoretic kind) explicity states that models have ontologies.

 

[Ken G]

As I said, I am using the word "model" in the model theoretic sense -- a model of a theory is, by definition, an interpretation for which the axioms of the theory are valid.

You still have it wrong, but I have to amend my language as well. The theory does give rise to a model, in the language you defined, so in that sense we have "models of the theory" not models of the universe. However, the universe is still not a model of the theory. This is the point, everything you listed in your "model theory" definitions are in our heads, and the universe isn't. So when I said the theory is a "model of the universe", in the language you are using, I meant the theory generates a model of the theory which is then tested as a "good" model when confronted with observations of the universe. Separating "the universe" from "what's happening in our heads" is the central concept of objectivity, so it is the very beating heart of the scientific method.

In science, it is more common to use the other meaning of "model" that you also mention, whereby we talk about "a good model of the universe", but I agree that is not precisely correct language within the scheme you have defined. Nevertheless, it carries the spirit much better than the awful "the universe is a model of the theory", which is really what I was objecting to, and indeed which remains the core of my objection to MWI-- I see MWI in exactly that light, people really think the theory is the truth and the universe is some kind of model of that theory. It's right out of Plato. Maybe Plato was right after all, but I see that as turning the scientific clock back thousands of years. Anyone who does not think that will certainly disagree with my assessment, I'll admit I'm being staunchly anti-Platonic.

But we can ask if a particular the universe is a model of a theory (under a chosen interpretation).

Did you really mean "a particular universe"? This is exactly my point-- imagining hypothetical universes to place "model theory" into a larger conceptual context is a mathematical device that can be pedagogically useful to science, but it is quite separate from the process of testing theories on the one universe we can demonstrate a connection with, and on whose back science is built.

Incidentally, I note the Wikipedia page on the meaning of the word that you're using (i.e. not the model-theoretic kind) explicity states that models have ontologies.

I admit that the word "ontology" can be taken to mean "pretending something exists in order to help visualize a model". As I've said many times now, if that's all people are doing when they talk about "many worlds", I have no objection at all. But a simple googling of "many worlds interpretation" generates immediate hits that put the lie to the claim that this is all it is being used for, and I listed them earlier. Furthermore, the same person on that other thread you allude to, who at one point distinguished between "real" ontologies and these more "pretend" flavor of ontologies, is also the person who clearly felt it was intellectually "lazy" to not use ontologies in the real sense of the word.