Problems with Many Worlds Interpretation

[mitchell porter]

Well, presumably there is a non-"arbitrary" part of the multiverse which actually corresponds to me-here-now, having the specific experience I seem to be having?

Well, yes and no. I'd say there is a whole bunch of you in the multiverse, having all sorts of experiences simultaneously. I would say that your experiences are macroscopic and the boundaries between them, between you-here-now and another-you-there-then are kind of fuzzy.

What you just said basically denies that there are any facts about what gets observed. The problem is not when you say there are duplicates or near-duplicates of me. The problem is when you say that the difference between one copy of me and another copy of me isn't absolute. I know some MWI fans are in love with the continuity of the wavefunction and consider it a virtue to talk about everything blending into everything else, but this is just incompatible with the specificity of observed reality.

Again, the problem is not when you say, you-here-now are observing one thing, but you-in-the-universe-next-door are observing something else; the problem is when you say that there is no objective difference between me-here-now and me-in-the-universe-next-door, that whether there is one person or two is a matter of convention, and that the facts about what happens to me here are not definite. This is a perfect example of a metaphysical belief (a "block multiverse" with no objective boundaries) overriding a basic fact about reality - the definiteness and particularity of anything that exists.

From experience :-) I find it extremely hard to get this point across to someone who has decided that they can think about themselves (or is it just about other people?) in this vague way. For example, sometimes there's a slippage between the incomplete and uncertain knowledge that one has of one's own conscious state, and the fundamental vagueness that is supposed to characterize the different branches of the wavefunction. That is, I might want to argue that you are definitely in a particular conscious state, and so, if this corresponds to a particular quantum state of your brain, then MWI must, with no ambiguity, say that that exact state is one of the substructures of the wavefunction which corresponds to a "world" or a "branch". But then I will be told that I don't know all the details of my conscious state, or that not all the physical details of my brain state matter for my conscious state, and this then provides the MWI advocate with an excuse for insisting that their theory doesn't have to have definite, exactly bounded branches, not even in principle.

So: what you are saying is ridiculous, because you are denying that there are definite facts at any level about what is happening to you. Everything blends into everything else, no quantum basis or state factorization is objectively preferred, and your theory (MWI) contains nothing that corresponds to specific realities.

At every moment, all sorts of quantum superpositions get decohered around you one way or the other. Say if a photon just landed on your forehead, it won't matter that much to you whether it was horizontally or vertically polarized, your experiences will not be affected and you-here-now branch will include both alternatives. On the other hand if a stray cosmic ray hit a cell in a DRAM chip and crashed your computer, one of you would never read this message so you-here-now branch would split and diverge at that point. But between these two extremes there would be a gray area where it would be very hard to tell whether your experiences are sufficiently different to count it as a split.

My point is that, whether or not it is "hard" to use, MWI must contain an objective criterion which (even if only in principle) tells exactly what the different "observer substructures" are in any given wavefunction, because that is the bottom line when it comes to relating reality to MWI. MWI isn't supposed to be just a holy dogma, it's supposed to be a theory of the physical world, and as such, the entities appearing in the theory have to have some relationship to the entities appearing in reality. You tell me that I can't take the appearances of external reality for granted, that this is just a brain state which is in a tensor product with a superposition of external states, some of which don't match what the brain state says? Fine. But then you tell me that MWI does not provide, not even in principle, a definite decomposition of the quantum state of my brain into basis states corresponding to distinct observer states? At that point, the last contact between reality and the ontology of the theory has been broken, and we are dealing with some sort of muddled dogma that doesn't even make comprehensible statements.

Hopefully I have made my point by now: FOR MWI TO WORK, THERE MUST AT SOME LEVEL BE AN EXACT AND OBJECTIVE WAY TO ANALYSE THE WAVEFUNCTION OF THE UNIVERSE INTO A PREFERRED SET OF SUBSTRUCTURES. And of course this is precisely what people who don't like the idea of splitting with respect to a preferred basis, etc, are trying to avoid. You don't have to have splitting - you can keep your transcendently unified wavefunction if you insist - but then you must specify definite substructures. I don't know what. Local maxima in configuration space. Some more abstract notion from fiber-bundle theory. They don't even have to be something whose details you can exactly specify in practice. It is often possible to prove that an equation has solutions, even if the exact solutions cannot be exhibited in detail. In the same way, all we need is something that is conceptually exact. You must be able to state precisely what sort of thing in the wavefunction corresponds to the specific realities which make up the whole of experience. Is it a tensor factor? Is it an infinite-dimensional wavelet? I don't know; this is your problem, not mine.

Yes, I agree, this is a very good question to ask. I also admit that current answer is not entirely satisfactory: some people dismiss it by saying since it is the same old formalism it produces the same answers and doesn't require a separate proof, other people say they have proved it and yet other people say that all those proofs rely on circular arguments and are therefore invalid. I tried to follow these arguments and got seriously bogged down, so I don't have an opinion one way or the other but my gut feeling is that such proof should be possible.

It's not the same formalism, since the Born rule has been removed. Obviously it's a cheat if MWI can only work by "postulating" the Born rule; if there are many worlds, there should be a natural way of counting them, or a natural measure on them, and the Born-rule probabilities should descend from that. But the insistence that it's OK to be vague about what a world or a branch is, insulates MWI from ever having to face this test: we can't count the branches, if there's no objective notion of what a branch is!

 

[xts]

From camera film perspective - when the camera set on timer took a picture of the cat, from gun powder perspective - when it was ignited (or not) and from atom perspective - when it has decayed (or not). What's so special about consciousness, apart form inflated ego?

What is special in my consciousness is that I always perceive only collapsed states and never see mixed states. It makes no difference (except of some troubles with complicated calculations) for me to treat cat as an observer, or to continue thinking about him in terms of superposition of dead and alive. Both approaches lead to the same result at the moment when I open the cage.
I cannot however allow single atom to be an observer. Some experiments show that atoms evolve sometimes like they are in mixed states. So atoms must be on the quantum side of the border.
So I must set a boundary somewhere in this large span of complexity: between my consciousness and single atoms. Everett chose anyone's consciousness as that level of complexity, which is safe. Personally I prefer solipsistic view - not because I am a solipsist, but as it reflects my treating the collapse as an information process rather than physical reality.

 

[haael]

What is special in my consciousness is that I always perceive only collapsed states and never see mixed states.

Of course you can see mixed states, if you set up a proper experiment.

Rather, out senses are special since they always measure position and time observables. We need special devices that convert other observables into our sensory signals. However, there might be some space aliens that live in a momentum-energy space and the concept of being in one point at a time is so wild for them as being in 2 different points for us.

What I mean: it might be our construction that give us illusion of the world having collapsed wavefunction.

There are several people in this thread saying "MWI gives the same predictions as Copenhagen Interpretation". This is a very questionable proposition. The reason is that if you get your MWI probabilities the obvious way, by counting the branches, you typically get the wrong predictions. To get the right predictions, you have to reproduce the Born rule, and that means that branches have to "count" in proportion to the square of their amplitude. But if all branches are equally real, the defining claim of MWI, why would some count for more than others?

To answer this, we need one more assumption: that we, posting on this forum, for some reason live in the largest branch of the multiverse, or one of the largest. Maybe there is some multiverse analogue of the second law of thermodynamics, that all systems are in the largest cell of the configuration space most of the time.

 

[K^2]

Doesn't matter. If the state you are measuring is not in the eigen state of the operator you are measuring, there will be a collapse or world splitting, depending on interpretation.

 

[xts]

Doesn't matter. If the state you are measuring is not in the eigen state of the operator you are measuring, there will be a collapse or world splitting, depending on interpretation.

Here you just use different words to push the problem out: what do you mean by 'measurement', especially when it happens? Does Cat measure the killing machine, or do I measure the box containing Cat and the machine?

 

[Delta Kilo]

What is special in my consciousness is that I always perceive only collapsed states and never see mixed states.

But consciousness is not required for that. It is sufficient for an observer to be macroscopic and to interact strongly with the environment. A photo camera or a computer connected to particle detector would be good examples of such observers. There is every reason to believe they never 'perceive' (make redords of) superimposed states either and no evidence to the contrary.

Besides you say your consciousness is special, do you have any reason at all to suspect that other people's consciousness is different in this respect? How is this not solipsism?

 

[fleem]

I've no strong opinion on which is the most useful way to look at things (MWI, CI, or maybe a form of non-local hidden variables), and this post is not to refute anyone here, but I've a few comments/questions:

1. 'I think, therefore I am', is the only deductive proof, and therefore the only 100% proven thing. All other things are "proven" inductively and therefore not quite 100% proven. So solipsism (unfortunately) can't be discounted. However, IMO its extremely improbable. I think we're agreed on this.

2. I think one reason some embrace MW is that we are trying to make QM events consistent with classical probability theory so that we can "understand" QM events. But note that we learned classical probability theory by studying strictly classical phenomena. (like creating axioms to describe a swarm of bees and then trying to apply those axioms to a single bee)

3. Isn't CI just "shut up and calculate" and the word "superposition" without a rigorous definition? (This is an honest question). If so, then embracing that view will never allow us to answer the important philosophical question (IMO), "Is there true randomness (pure chaos) in the universe, or is there only pseudo-randomness and no chaos?". Frankly I've vacillated between the two over the years. My latest guess is that the simplest reality is one in which all events are possible (chaos)--but then perhaps only non-paradoxical events were able to evolve to higher order, like conservation of number, etc. So maybe the randomness we see in low-energy events is a glimpse of that chaos.

 

[xts]

It is sufficient for an observer to be macroscopic and to interact strongly with the environment.

Sure! That is a common-sense-Copenhagen approach. It has one more strong point against consciousness based interpretation - it is practical - calculations are feasible.

Besides you say your consciousness is special, do you have any reason at all to suspect that other people's consciousness is different in this respect? How is this not solipsism?

It would be a solipsism, if I assign some real physical meaning to collapse. It is rather subjectivism. For me consciousness of mine is special. Fortunately, if for you your one is equally special, we may still talk and understand each other and we predict the same outcomes of the experiments we do. As in my understanding the collapse is nothing 'real' - it just reflects knowledge about the experiment outcome, there is nothing solipsistic if I make no difference between 'I measured something', 'I may used collapsed wavefunction for further description of the word' and 'I learned the experiment outcome'

 

[Delta Kilo]

What you just said basically denies that there are any facts about what gets observed. ...

Well, I see that I'm not getting my point across. It' s ok, happens from time to time :) I also see that either you confused me with someone else or otherwise put a lot of words in my mouth that I didn't say.

I guess the term MWI has evolved and means different things to different people. To me it means basically:
a) The same quantum laws apply from micro all the way to the entire universe.
b) The evolution is unitary, there is no collapse.
c) The wavefunction describes the reality. (all parts of the wavefunction are equally real)

As I said, I find the notions of 'splits' and 'branches' less than helpful. These were introduced to illustrate some concepts in a handwavy sort of way.So what is a branch, how does it come to be? Say you have a bunch of systems (observers) A,B,C interacting with common environment E. Say the current state is described as |A>|B>|C>|E>. Say at some point you introduce a particle P in a state of superposition |P1>+|P2>. Decoherence tells us that the system quickly evolves from (|P1>+|P2>)|A>|B>|C>|D>|E> into something like (|P1>|A1>|B1>|C1> +|P2>|A2>|B2>|C2>)|E>, where Ai,Bi,Ci, are new states of A,B,C after interacting with Pi in the preferred basis dictated by the the environment, the environment E has 'soaked up' all the off-diagonal terms, but it is so big that it appears unchanged for all practical purposes. Once this happens the two parts evolve independently and do not affect each other in any way. So we just say they represent two separate branches that he world around us has split into.

Contrary to what is usually assumed, branches do not span the entire multiverse. No matter how many systems are split, there is always a bigger environment out there that 'does not care'. And the change is gradual, the branch just 'fades away' sort of, the information about the event that has caused a split becomes more and more thinly spread and less and less relevant. We never actually look at the exact details of it, we just assume it happens somewhere in the environment which is too big and complex to be analyzed in details.

These kind if things (observations of particles in superposition by macroscopic observers) are happening all the time which causes the world to be constantly split every which way. The question "which branch does this point belongs to" does not make sense, one has to specify the event that has caused a split. Similarly, the notion of you-here-now branch does not make sense because as a system, you-here-now does not have well-defined boundaries. Presumably it includes your present state of mind including all the events that have influenced it up until now, which is quite a lot to ask about. You would have to define carefully which events and branches are relevant to the definition of you-here-now and which are not.

NEVERTHELESS, having said all that, if you ask the right questions you will most certainly get definite answers. If you ask about the outcome of a particular quantum measurement, as evidenced by the state of a particular macroscopic observer, you will find the boundaries between the branches to be pretty sharp and well-defined, and what's more, the branches defined by different observers will line up, that is the observers will generally agree on what they saw. Also they won't change if you move the boundary between the system and the environment back and forth. And if you perform a number of experiments you can then define intersections and unions of the branches etc. You can then use the set of perceived outcomes to label the branches, and the branch labeled with outcomes that you yourself perceived will be the branch containing that elusive you-here-now.

To sum up, branches are just non-interfering terms in a wavefunction (or chunks of reality described by those terms if you wish). They only make sense when the wavefunction can be written in a particular way with the understanding that they are statistical approximations of the real thing. They are just tools to be used when appropriate.

Regarding the Born rule, as I understand, the derivation aims to show that: a) equally probable branches have the same magnitude and b) the sum of magnitudes squared after the split equals magnitude squared before the split. Posing that some branches are 'equally probable' is what usually raises questions, and the jury appears to be still out on whether or not they were answered satisfactory.

 

[mitchell porter]

Well, I see that I'm not getting my point across. It' s ok, happens from time to time :) I also see that either you confused me with someone else or otherwise put a lot of words in my mouth that I didn't say.

You didn't say them, but they are implied by your position. For example, you say

the notion of you-here-now branch does not make sense because as a system, you-here-now does not have well-defined boundaries.

and I interpret that as a denial

that there are any facts about what gets observed

I mean, what I observe here and now is a property of me-here-now, right? And you say that there is no me-here-now. There's just a continuum of "me"s, that can be coarse-grained in different ways, and there is no canonical coarse-graining that produces a canonical "branch" that corresponds to the existence of this copy of me. That means the answer to the question, "exactly what am I observing" comes back as "undefined, you must specify your coarse-graining". Or in other words: there are no absolute facts about what gets observed. There are just "relative facts", relative to a coarse-graining.

For confused readers who might not follow what's happening this discussion, I want to emphasize that I am not just saying "I see one thing in one universe and another thing in another universe". That is not the "relativeness" that I am talking about. Delta is confirming that MWI does not offer a unique division of the multiverse into universes, or even a unique division of the 'local multiverse' into copies of me. You can chop things up however you like and they are all equally valid. You can take the quantum density matrix of the left hemisphere of my brain, treat it in terms of the position basis, and then you can still think about my right hemisphere as being in a superposition, or you can look at it in terms of the position basis, or the momentum basis, or any basis you like; and every one of these decompositions of the local part of the wavefunction of the universe is apparently equally valid. The consequence is that there is no answer to the question 'in this branch, what is my brain doing?', because there are multiple choices of quantum basis for different parts of my brain.

Would it be a better world if there was a wider appreciation, among fans of physics, of just how absurd MWI is? It's hard to say, because the true absurdity depends on mildly technical details like those I mention above, and yet the standard understanding of what MWI says is just, 'there are parallel worlds', and that's not an intrinsically absurd notion. Somehow it needs to be conveyed that MWI is a nice idea, or at least a superficially valid idea, but the attempt to develop the details of that idea, within the actual context of QM, produces reams of nonsense.

Regarding the Born rule, as I understand, the derivation aims to show that: a) equally probable branches have the same magnitude and b) the sum of magnitudes squared after the split equals magnitude squared before the split. Posing that some branches are 'equally probable' is what usually raises questions, and the jury appears to be still out on whether or not they were answered satisfactory.

I think the problem is just, what does probability mean if all branches exist? If there are three outcomes and there is one branch for each of them, then the three outcomes are equally frequent in the multiverse and so they ought to be equally probable. But in QM, probabilities are not uniform. OK, so now in MWI we talk about the 'magnitude' of a branch. But what does that mean? If we want one outcome to be more common in the multiverse than the others, then common sense says it needs to occur more often than the others. We need duplicate or near-duplicate branches, more of them for the higher-probability outcomes. You can't just say, 'that single branch has a bigger "magnitude", therefore it shall count as having higher probability', it makes no sense. You might as well flip a coin twice, get heads once and tails once, but say that tails "have a bigger amplitude" than heads, so tails have a greater probability. Once you decide to be a realist about the existence of other branches / worlds / whatever, you can no longer treat probability in this way, it has to be linked to the frequencies with which events actually occur in the multiverse.

P.S. I want to add a remark, distinct from the debate about MWI, for readers who just want to know what QM says about reality. My advice is to start with the attitude that the wavefunction is not real, that it is just a calculating device, like a probability distribution. I see far too many discussions on the net in which people start out by assuming that wavefunctions are real, and then proceed to debate whether the wavefunction collapses - and if so, when, how, and why - or whether it doesn't collapse, leading to many worlds.

In quantum mechanics, the things which can definitely exist are called "observables". For example, position of a particle, or energy density of a field. Wavefunctions offer a way to calculate probabilities for the possible values of those quantities. Quantum mechanics does not tell you which observables take values; this is why we can say the theory is incomplete.

Now from here you can go in many directions. In my opinion, the path to discovering the truth about QM lies through the most advanced theories, like quantum field theory and quantum gravity, because those are the forms of quantum mechanics we are using to describe the real world. This doesn't tell you whether Bohm or Bohr or Everett or none of the above offers the best clue to the final truth; I just mean that extra knowledge about the details of advanced physics is far more important for your understanding than the usual "interpretational debates" that don't even take into account the novelties that come from QFT, such as the role of relativity.

Of course, QFT is hard, and quantum gravity even more so, so this is not easy advice to follow. Unfortunately I don't already know "the answer" and can't tell it to you. But my best advice is this: you will not go wrong, in trying to understand QM and these more advanced theories, if you always make your starting point, and your fallback position, the view I described, i.e., the observables are real, the wavefunction is not. If you want to know what a particular super-duper-unified theory is about, try to find out what its observables are - those are what it is about. The wavefunctions for those observables will be highly abstract constructs living in infinite-dimensional abstract spaces, dependent on particular "gauge fixings", and so on through many other details. But the observables are where reality is at in such a theory, and it's the behavior of the observables which an "interpretation" of QM, or a theory beyond QM, has to explain or reproduce.

 

[Delta Kilo]

You seem to have this picture-book version of MWI where you have these parallel universes which are all cleanly separated and self-contained and we-here-now live in one of them. And when an atom decays (or not), an entire copy of the whole universe is made and the only difference between it and the original is that atom decays in one and stays put in the other. And then we (-here-now) go along with one of the copies and the other is populated with our doppelgangers.
In this picture you-here-now copy of you is sharply defined (as a single point of measure 0, as a perfect delta-function in phase space) and distinct from all other points. The evolution in time is then represented by a tree (in graph theory sense) where the edges representing parallel universes are all sharply defined and have zero thickness. And there is one path through the graph that corresponds exactly to you-here-now experiences. And you just coast along this path like a train along the tracks taking random turns at every junction.

Well, this picture is wrong. It breaks down on micro level where the buckyball somehow goes through both slits and it doesn't work on a grand scale where we assume the evolution is unitary and superposition is maintained. It also has problems with assigning labels (coordinates) and probability measures to individual branches. But the biggest problem of all is that this picture is not what MWI is all about.

I already told you what (as I understand it) MWI is all about:

a) The same quantum laws apply from micro all the way to the entire universe.
b) The evolution is unitary, there is no collapse.
c) The wavefunction describes the reality.

Each point is plausible enough.
a) Introducing different laws at different scales has run into problems of actually finding the boundary and explaining what's so special about it.
b) The only alternative is to modify Schroedinger equation to add explicit collapse. That's just plain ugly, not to mention a whole lot of other issues. Besides we already have decoherence which demonstrates how an appearance of wavefunction collapse happens to an observer coupled with its environment.
c) Well, if not the wavefunction, then what? This is getting a bit metaphysical, but if we agree that wavefunction indeed describes the reality, then how could we single out just one term of this function and say well, this term is real and the rest are just figments of our imagination?

Now, assuming for a moment the points a),b),c), where does it lead us?
Again, we see that under certain conditions (more often than not) the wavefunction of a subsystem coupled with environment tend to evolve into a shape which can be approximated by a sum of independent terms where each term seems to describe particular state consistent with one of the outcomes. This is where all the splitting and branching come from.

A few points I'd like to address (skipping obvious rant):

And you say that there is no me-here-now. There's just a continuum of "me"s, that can be coarse-grained in different ways, and there is no canonical coarse-graining that produces a canonical "branch" that corresponds to the existence of this copy of me.

That's right, there is no "canonical" precisely defined, unique you. Why does it come as a surprise? We are talking about QM after all. We already know there is no sharply defined picture on the micro level and we are working under the defining assumption that the same laws apply all the way up. Besides, even if there was such a well-defined you-here-now, how do you tell it from the whole bunch of other you which all look pretty much the same?

That means the answer to the question, "exactly what am I observing" comes back as "undefined, you must specify your coarse-graining". Or in other words: there are no absolute facts about what gets observed. There are just "relative facts", relative to a coarse-graining.

Well, yes. The facts are relative. When you say "X is true absolutely" you mean "X is true for me-here-now". But "you-here-now" tells me exactly nothing at all. I already gave you a procedure which can be used to narrow down the position of you-here-now by supplying more and more facts. So "X is true" becomes "X is true in those universes where A,B,C is true" or simply "X is true given A,B,C".

You can chop things up however you like and they are all equally valid.

No, this is incorrect. The boundaries are not arbitrary but defined by the (macroscopic) facts which hold true for a given branch. Most of these facts correlate strongly between each other and so the emergent boundaries are stable with respect to choosing a subset. Eg. there are lots os factual evidence supporting the proposition that Earth has a moon. All this evidence is strongly correlated, so you can take different subsets of it and they will still define pretty much the same branch where the Earth has a moon. Basically, as decoherence takes its place and the off-diagonal terms get ''soaked up' by the environment, you get sort of clusters of self-consistent cross-corroborated macroscopic facts emerging dynamically.

You can take the quantum density matrix of the left hemisphere of my brain, treat it in terms of the position basis, and then you can still think about my right hemisphere as being in a superposition, or you can look at it in terms of the position basis, or the momentum basis, or any basis you like; and every one of these decompositions of the local part of the wavefunction of the universe is apparently equally valid. The consequence is that there is no answer to the question 'in this branch, what is my brain doing?', because there are multiple choices of quantum basis for different parts of my brain.

Sorrry, but this just does not make sense. And the last bit is incorrect. The brain is macroscopic and tightly coupled within itself and with the environment. There will be a strong environmentally-selected basis. Any quantum disturbance would quickly decohere, producing many redundant copies of the same outcome throughout the entire brain and its environment. As a result the brain as a whole will be entirely consistent with one outcome in one branch and with another outcome in another.

But in QM, probabilities are not uniform. OK, so now in MWI we talk about the 'magnitude' of a branch. But what does that mean? If we want one outcome to be more common in the multiverse than the others, then common sense says it needs to occur more often than the others. We need duplicate or near-duplicate branches, more of them for the higher-probability outcomes. You can't just say, 'that single branch has a bigger "magnitude", therefore it shall count as having higher probability', it makes no sense.

Well of course it does not make sense to talk about probability measure for an isolated delta-function, but it makes perfect sense for a sharply peaked but finite distribution.

But my best advice is this: you will not go wrong, in trying to understand QM and these more advanced theories, if you always make your starting point, and your fallback position, the view I described, i.e., the observables are real, the wavefunction is not.

Yes, and please take these complimentary blindfolds. Use them whenever the sight of an elephant in the room [wavefunction collapse] makes you uncomfortable.

 

[Hurkyl]

for readers who just want to know what QM says about reality. My advice is to start with the attitude that the wavefunction is not real, that it is just a calculating device, like a probability distribution.

I've never seen anyone argue this position effectively. Your version reeks of double-think -- you are accepting QM as a good theory of reality while at the same time rejecting its description of reality.

In quantum mechanics, the things which can definitely exist are called "observables".

Now this is clearly wrong -- an observation is a description of reality, not reality itself. The observable related to the observation is an even more abstract object.

Now, it would be fair to suggest that reality is made up of things that can be observed in ways described by observables, in an effort to avoid trying to impose any additional preconceptions upon reality.

But it turns out that if you pursue this route, you pretty much wind up right back at the existing quantum mechanical description of states.

 

[mitchell porter]

You seem to have this picture-book version of MWI where you have these parallel universes which are all cleanly separated and self-contained and we-here-now live in one of them. And when an atom decays (or not), an entire copy of the whole universe is made and the only difference between it and the original is that atom decays in one and stays put in the other. And then we (-here-now) go along with one of the copies and the other is populated with our doppelgangers.
In this picture you-here-now copy of you is sharply defined (as a single point of measure 0, as a perfect delta-function in phase space) and distinct from all other points. The evolution in time is then represented by a tree (in graph theory sense) where the edges representing parallel universes are all sharply defined and have zero thickness. And there is one path through the graph that corresponds exactly to you-here-now experiences. And you just coast along this path like a train along the tracks taking random turns at every junction.

Well, this picture is wrong.

I know that's not how most MWI insiders see it. But that is how outsiders see it. It's a good thing for curious onlookers to hear explicitly that that is not how it's supposed to work.

The question now is whether there is an alternative picture that makes any sense, or whether your three principles...

a) The same quantum laws apply from micro all the way to the entire universe.
b) The evolution is unitary, there is no collapse.
c) The wavefunction describes the reality. (all parts of the wavefunction are equally real)

...just don't make sense in combination.

This is a bad start, if the objective is for MWI to be plausible:

That's right, there is no "canonical" precisely defined, unique you.

It seems we are in total agreement here about what MWI says: There is no canonical division of the wavefunction into worlds, there is no canonical set of parallel "me"s, there are multiple ways to chop up the wavefunction into basis functions, corresponding to noncommuting sets of observables, and thus noncommuting sets of "me"s. The difference is that I regard this as a reductio ad absurdum of MWI, whereas you regard it as a fact about reality revealed by MWI.

even if there was such a well-defined you-here-now, how do you tell it from the whole bunch of other you which all look pretty much the same?

This is similar to the epistemological dodge sometimes used by Copenhagenists who want to say that the electron doesn't have a definite state before we measure it: We can't know it if we don't measure it, so what does it matter if I say nonsense things about the unmeasured electron, wah wah wah. In this case, you're saying: Even if there was such a thing as a definite set of parallel "you"s, you couldn't know exactly which one you were, therefore it's OK for me to have an ontology in which there is no such thing. In both cases, the epistemic difficulty (of knowing anything about an unmeasured electron; of knowing all the exact details of your momentary conscious experience) is used as an excuse for the ontological nonsense (the unmeasured electron has a position but doesn't have a definite position; I exist but I don't have a definite set of properties).

Well, yes. The facts are relative. When you say "X is true absolutely" you mean "X is true for me-here-now". But "you-here-now" tells me exactly nothing at all. I already gave you a procedure which can be used to narrow down the position of you-here-now by supplying more and more facts. So "X is true" becomes "X is true in those universes where A,B,C is true" or simply "X is true given A,B,C".

Let me emphasize - again more for the understanding of third parties to this discussion - that you are not talking about selecting universes from a multiverse of "cleanly separated and self-contained" parallel universes. Specifying A, B, C involves making a choice between noncommuting observables - and therefore about which slicing, out of many mutually incompatible possibilities, to use in dividing up the local multiverse - and we are also leaving unspecified properties in superposition.

No, this is incorrect. The boundaries are not arbitrary but defined by the (macroscopic) facts which hold true for a given branch. Most of these facts correlate strongly between each other and so the emergent boundaries are stable with respect to choosing a subset. Eg. there are lots os factual evidence supporting the proposition that Earth has a moon. All this evidence is strongly correlated, so you can take different subsets of it and they will still define pretty much the same branch where the Earth has a moon. Basically, as decoherence takes its place and the off-diagonal terms get ''soaked up' by the environment, you get sort of clusters of self-consistent cross-corroborated macroscopic facts emerging dynamically.

Still, doesn't MWI imply that it's not an absolute fact that the Earth has a moon in this branch? There is some very small but nonzero amplitude for a moonless Earth to nonetheless have had a persistent appearance of a moon, and since branches are only a local phenomenon, there is no ontological difference between 'earth that actually had a moon' and 'earth that had an appearance of a moon generated by other causes'. The local present does not have a unique past (because multiverse histories, amplitude currents in the multiverse, split and join); another MWI feature that I regard as a bug.

Sorrry, but this just does not make sense. And the last bit is incorrect. The brain is macroscopic and tightly coupled within itself and with the environment. There will be a strong environmentally-selected basis. Any quantum disturbance would quickly decohere, producing many redundant copies of the same outcome throughout the entire brain and its environment. As a result the brain as a whole will be entirely consistent with one outcome in one branch and with another outcome in another.

Well, this is interesting. Suddenly we have a preferred basis after all.

This is another unresolved contradiction in MWI thought. After being told so many times that it's wrong to think in terms of a unique set of self-contained parallel universes, one might have supposed that any local basis is as good as any other, ontologically. But no, we are only supposed to consider a basis in which the local density matrix is nearly diagonal, or as diagonal as possible? Please make up your mind. Why am I not allowed to think about my left hemisphere in the position basis and the right hemisphere in the momentum basis? Is there some maximum size for the off-diagonal elements, beyond which a particular basis must be rejected as not allowed?

Yes, and please take these complimentary blindfolds. Use them whenever the sight of an elephant in the room [wavefunction collapse] makes you uncomfortable.

Wavefunction collapse is a problem only if you insist on thinking of the wavefunction of the universe as the actual state of the universe. If you think of it as a prior, as in probability theory, then 'collapse' is just updating of the prior in response to new information. Of course this leaves unresolved the question of why quantum mechanics works. But the discussion so far provides ample reason to think about alternatives to wavefunction realism.

 

[mitchell porter]

I've never seen anyone argue this position effectively. Your version reeks of double-think -- you are accepting QM as a good theory of reality while at the same time rejecting its description of reality.

I'm just saying it's incomplete, that's all. And the attempt to view it as complete, by subtracting the Born rule and attributing reality to the wavefunction of the universe, is not going very well. By losing the Born rule, the theory loses all predictive power, and by saying that the wavefunction is all and doesn't even have a preferred basis, the theory also ceases to make any comprehensible statement about the nature of reality, as my discussion with Delta Kilo is showing.

A wavefunction is not a probability distribution, but it has a lot in common with probability distributions. If we had a classically probabilistic fundamental theory, some of us would be involved in looking for a microscopic causal model of the probabilities - we wouldn't decide that "the probability function is reality itself". There are well-known barriers to the construction of a locally deterministic theory (or even a locally stochastic theory) which reproduces QM; fine, then use a little imagination. The holographic mapping from boundary to bulk introduces a little nonlocality in the bulk; maybe QM can be derived from a local theory on the boundary (this is 't Hooft's idea). Maybe you can get spacelike correlations from closed timelike curves (this is Mark Hadley's idea, and also has something in common with John Cramer's transactional interpretation). Maybe you can have interactions that are local and fundamental objects that are 'multilocal'. And then we have the example of Bohmian mechanics, which, while unacceptable on account of the preferred reference frame, might be modified in one of these other directions. For that matter, I even think MWI's analysis of the wavefunction's structure could be a source of inspiration! But MWI as expounded in this thread, has neither predictive capability nor conceptual coherence.

Now this is clearly wrong -- an observation is a description of reality, not reality itself. The observable related to the observation is an even more abstract object.

I didn't say that "observations are what is real", I said that observables are what is real. The momentum of an electron is an observable. The electromagnetic field density is an observable. "Observable" is just a word that history has left us. In effect, it's short for "observable thing".

Now, it would be fair to suggest that reality is made up of things that can be observed in ways described by observables, in an effort to avoid trying to impose any additional preconceptions upon reality.

But it turns out that if you pursue this route, you pretty much wind up right back at the existing quantum mechanical description of states.

I think your use of the word "observables" is unnecessarily distanced from physical reality. An "observable" is not just an element in a local operator algebra, or whatever. The observables are what QM is about: the predictable properties of the basic physical objects.

Possibly you are referring to eigenstates. Certainly there is a lot of casual slippage, in physics discourse, between "the electron being at point x0" and "the quantum state of the electron being in the position eigenstate with eigenvalue x0". But it's like the difference between "the cat sitting on the mat" and "the probability distribution which says that the cat is sitting on the mat with 100% probability". It's not hard to maintain the distinction.

 

[Jodo Kast]

Hugh Everett was a dedicated hedonist; I honestly can't take his MWI theory seriously. However, I did write something last year in defense of MWI...

"Back in the 1950s, the orthodox explanation of quantum physics was called the 'Copenhagen Interpretation', which was propounded by Niels Bohr. And he was from Copenhagen, hence the name. The Copenhagen Interpretation posits that the observer is somehow separate, while the Many-Worlds Interpretation posits that the observer is not separate. In other words, prior to the 1950s, it was thought that reality could only exist if someone was around to observe it. But now it is thought that everything is being observed and the explanation for that is we continually split into parallel universes, since it is not possible to observe all possible outcomes in just one universe. The greatest problem with the Copenhagen Interpretation is that observers are real, which means they can only be real if they are observed, ad infinitum. It's called an 'infinite regression'."

 

[Fredrik]

for readers who just want to know what QM says about reality. My advice is to start with the attitude that the wavefunction is not real, that it is just a calculating device, like a probability distribution.

I often say this too.

I've never seen anyone argue this position effectively.

Have you seen anyone argue effectively for the opposite position? I would say that it isn't possible to "argue effectively" for either position, because the subject is neither scientific nor purely mathematical. To add the statement "this theory describes reality" or its negation to the list of axioms that defines a theory wouldn't change the theory's predictions. That means that we're not talking about science.

That being said, I still think that the things I said in posts 40-41 here, and the posts I linked to in there, are pretty good reasons to not think of QM as a description of reality. (It may not be an "effective" argument by your standards, but I think those standards may be unreasonably high, considering the unscientific nature of what we're talking about).

Do you have an argument for the opposite position?

Your version reeks of double-think -- you are accepting QM as a good theory of reality while at the same time rejecting its description of reality.

There's nothing contradictory about it if we define a theory as an assignment of probabilities to possible results of experiments.

 

[chaszz]

The aspect of MWI that has always bothered me most is conservation of energy. Where is all the energy coming from to fuel all these new universes that keep popping into existence? There is enough of a problem trying to conceive where the energy came from in our universe without compounding the problem practically to infinity. Am I missing something in MWI which does attempt to account for this?

 

[BruceW]

Some people interpret MWI differently. In the most well-accepted version of MWI, no new universes are literally created. MWI in its most basic simply says that non-unitary collpase of the wavefunction does not happen.

 

[Fyzix]

Some people interpret MWI differently. In the most well-accepted version of MWI, no new universes are literally created. MWI in its most basic simply says that non-unitary collpase of the wavefunction does not happen.

Yes and this is the version that Mitchell Porter has just debunked.
Have you read the thread or did you just decide to jump in and make assumptions?
This is one of the most detailed debates on MWI on this site to date, so unless you got some detailed rebutle for Mitchell Porter's posts, let's not mess the thread up by stating stuff without having read the thread

 

[BruceW]

Yes and this is the version that Mitchell Porter has just debunked.
Have you read the thread or did you just decide to jump in and make assumptions?
This is one of the most detailed debates on MWI on this site to date, so unless you got some detailed rebutle for Mitchell Porter's posts, let's not mess the thread up by stating stuff without having read the thread

You think that Mitchell Porter has just debunked MWI? Well I guess he should be expecting his nobel prize in the post any day now.
Haha, sorry to joke, but seriously, I don't find anything In Mitchell Porter's posts that debunk MWI. He made one good point though: in MWI the Born rule must be one of the postulates.
You might argue that the fact that MWI requires the Born rule postulate makes MWI less likely, but it doesn't mean MWI is wrong.

Edit: As I said earlier in the thread, its all about aesthetical preference. There have been no experiments to distinguish between the two interpretations.

 

[Fyzix]

You think that Mitchell Porter has just debunked MWI? Well I guess he should be expecting his nobel prize in the post any day now.

Are you aware of how many interpretations there are? Do you really think you would win a Nobel Prize by showing how one or many of them are bad? Seriously?
When I say debunk I obviously mean "shows why it doesn't work".
Fact is: if MWI can't get Born rule right, it has infact been falsified...
QM is all about probabilities, if you can't get them right, you have no interpretation that fits reality.

However this thread brings up a lot more interesting problems that MWI has and if you put them all together you could say that a certain interpretation is infact debunked, yes.
Which is why I don't want the thread to side track, I want to see proponents of MWI to respond to Mitchell Porter's posts in a detailed manner, so that the discussion can go on and we might see where MWI fails in other areas etc.

I don't find anything In Mitchell Porter's posts that debunk MWI. He made one good point though: in MWI the Born rule must be one of the postulates.
You might argue that the fact that MWI requires the Born rule postulate makes MWI less likely, but it doesn't mean MWI is wrong.

He has brought up more problems than just the famous Born Rule problem and I think he will bring up more if the debate goes further.
But I may ask you, do you seriously think you can just say "I postulate Born Rule" and *poof* MWI makes sense?

You have to have a mechanism, some sort of explanation for how you postulate the Born Rule.
Is there a God selecting the amount of branches to fit with Born Rule? Are there hidden variables? Are we even talking about MWI anymore ?
If you are going to postulate you need to give a detailed account of HOW.

Edit: As I said earlier in the thread, its all about aesthetical preference. There have been no experiments to distinguish between the two interpretations.

Same goes for consciousness collapse, transactional interpretation, ensemble interpretation, deBroglie Bohm interpretation, many minds interpretation, itacha interpretation and 50 other interpretations.
Just because there are no experiment to distinguish these interpretations, one can still philosophically and technically pick certain interpretations apart and thus debunk them.

Like for instance people can say about Bohm: it violates relativity, how do you claim to fix that without modifying your interpretation or postulating new physics?
Same goes for all the problems in MWI...

 

[Hurkyl]

I'm just saying it's incomplete, that's all.

It sounds like more than that, but let me ask you a question:

You would advise the QM mechanics student not to form an idea about wave-functions corresponding to entities in reality.

Would you also advise the fluid mechanics student not to form an idea about fluids corresponding to entities in reality?

If your answer is yes:

Then I assert that all of this talk about wave-functions not being real and such is a red herring -- it has absolutely nothing to do with the question of how to interpret quantum mechanics. Instead, it is just a reminder that interpretations are merely interpretations. (But then... why do you think we needed a reminder? )​

If your answer is no:

Then what alternative interpretation? If none, how can I interpret your position as anything but a rejection of QM?

If there was no question of interpretations, the quantum mechanics student would absorb QM in the same way as other subjects, and form an interpretation along the lines of

• Wave-functions are real entities
• Wave-functions evolve according to Schrödinger's equation ...
• ... except when they evolve according to collapse
• Measuring devices (with numerical output) loosely correspond to operators
• A measurement somewhere involves a collapse according to the operator describing the measuring device.

and so forth.

I can see why someone would come along and suggest MWI instead -- even though we can't be sure it works out until quantum thermodynamics is more fully developed -- since it unifies the two forms of evolution and has the potential to expand the scope of applicability of QM.

If you are rejecting interpreting wave-functions as reality, and you are not supplying an alternative, what am I supposed to think your motivation is, if it's not a rejecting of using QM to understand reality?​

I really wonder how history would have differed if people figured out decoherence before they figured out the no-go theorem that unitary evolution cannot produce a lossy transformation such as (actual) collapse.

Well, this is interesting. Suddenly we have a preferred basis after all.

I agree with Delta Kilo; you're not really making sense. It's almost like you're determined not to see how things can be made to work out.

Consider, for a moment, a nice simple system: a qubit in a statistical mixture of 60% spin up about the Z axis, and 40% spin down about the Z axis.

Surely, you see that this state can be written as a statistical mixture of Z+ and Z-.

Can you also see that this state cannot be written as a statistical mixture of X+ and X-?

Can you also see that this state can be written as a statistical mixture of Z+, Y+ and Y-? (Specifically, it is 20% Z+, 40% Y+, and 40% Y-)

(P.S. since when did "preferred" come to be applied to descriptions derived from physical information? Do GPS coordintes count as a preferred coordinate system now?)

The observables are what QM is about: the predictable properties of the basic physical objects.

Possibly you are referring to eigenstates.

No, I mean taking the algebraic structure QM describes that contains elements corresponding to those "observables", a description of how they are supposed to relate to physical states, turning the mathematical crank (e.g. this), and *poof* states are wavefunctions.

 

[unusualname]

The MWI interpretation problems occur with the "splitting universes" stuff

There is a much more obvious alternative, that each individual event in the universe is random and results in an evolution at each step ( see http://www.jbg.f2s.com/quantum2.txt )

Now, the Born Rule should be calculable here...

 

[BruceW]

Same goes for consciousness collapse, transactional interpretation, ensemble interpretation, deBroglie Bohm interpretation, many minds interpretation, itacha interpretation and 50 other interpretations.
Just because there are no experiment to distinguish these interpretations, one can still philosophically and technically pick certain interpretations apart and thus debunk them.

Yes, I was trying to make it clear that all the interpretations are scientifically correct. (Since they correctly fit the results of experiments).
I'm guessing by 'debunk', you mean: show that a particular interpretation is not as good (in being a physical theory) as some other interpretation. The problem here is that different people will disagree on what makes a good theory.
I think a good theory has: as few postulates as possible, has as great a generality as possible, and makes predictions on the outcomes of experiments.
Even if we agree on this definition of a good theory, people will still disagree on which interpretation fits this definition the best.
This is why I think a discussion on 'the best interpretation' is kind of premature until physicists find empirical evidence that can be used to distinguish between the various interpretations.

 

[Delta Kilo]

If people insist on equating MWI with this 'the universe splits in half at every moment' comic-strip, I am prepared to abandon the use of term MWI and just say that I subscribe to bare-bones "No-Collapse" interpretation. At least I won't have to argue anymore about branches and splits, which are really just secondary artefacts. I am also willing for the time being to give up arguing about what's real and what's not as it does not change anything at all in the grand scheme of things.

I hope that a simple "Collapse/No Collapse" dichotomy has at least some physical sense behind it.
a) If there is an objective collapse, then Schroedinger equation needs to be modified.
b) If there is no collapse then the emergence of observables and Born rule needs to be demonstrated.
In any case a decent model of measurement process is badly needed because at the moment it is a mess and it sits smack in the middle of otherwise beautiful theory. Anyone approaching QM for the first time is faced straight away with those awkward questions about measurement, and these questions do not go away as you learn more.

 

[dm4b]

Hi jtbell,

from: http://www.anthropic-principle.com/preprints/manyworlds.html

"Political scientist" L David Raub reports a poll of 72 of the "leading
cosmologists and other quantum field theorists" about the "Many-Worlds
Interpretation" and gives the following response breakdown [T].

1) "Yes, I think MWI is true" 58%
2) "No, I don't accept MWI" 18%
3) "Maybe it's true but I'm not yet convinced" 13%
4) "I have no opinion one way or the other" 11%

Amongst the "Yes, I think MWI is true" crowd listed are Stephen Hawking
and Nobel Laureates Murray Gell-Mann and Richard Feynman. Gell-Mann and
Hawking recorded reservations with the name "many-worlds", but not with
the theory's content. Nobel Laureate Steven Weinberg is also mentioned
as a many-worlder, although the suggestion is not when the poll was
conducted, presumably before 1988 (when Feynman died). The only "No,
I don't accept MWI" named is Penrose.

Yet another reason for me to like Roger Penrose ;-)

 

[mitchell porter]

It sounds like more than that, but let me ask you a question:

You would advise the QM mechanics student not to form an idea about wave-functions corresponding to entities in reality.

Would you also advise the fluid mechanics student not to form an idea about fluids corresponding to entities in reality?

...

If your answer is no:

Then what alternative interpretation? If none, how can I interpret your position as anything but a rejection of QM?

If there was no question of interpretations, the quantum mechanics student would absorb QM in the same way as other subjects, and form an interpretation along the lines of

• Wave-functions are real entities
• Wave-functions evolve according to Schrödinger's equation ...
• ... except when they evolve according to collapse
• Measuring devices (with numerical output) loosely correspond to operators
• A measurement somewhere involves a collapse according to the operator describing the measuring device.

and so forth.
​

They don't learn statistical mechanics like this. People don't come away from the study of statistical mechanics thinking that probability distributions correspond to the actual state of anything. A probabilistic description of a physical state provides incomplete but nonetheless useful information about what is actually there. When you acquire new information, you have to update the probability distribution, and it "jumps" or "collapses".

The idea of wavefunction collapse as a physical process, and the idea that maybe wavefunctions don't collapse, both arise from treating wavefunctions as real, in a way that we would never do for probability distributions.

I agree with Delta Kilo; you're not really making sense. It's almost like you're determined not to see how things can be made to work out.

Consider, for a moment, a nice simple system: a qubit in a statistical mixture of 60% spin up about the Z axis, and 40% spin down about the Z axis.

Surely, you see that this state can be written as a statistical mixture of Z+ and Z-.

Can you also see that this state cannot be written as a statistical mixture of X+ and X-?

Can you also see that this state can be written as a statistical mixture of Z+, Y+ and Y-? (Specifically, it is 20% Z+, 40% Y+, and 40% Y-)

I don't know what your point is. My point is that if you believe in wavefunctions but you don't believe in collapse, then you need to explain what parts of the wavefunction correspond to reality. Suppose that we have a qubit whose density matrix is as described. What is the physical reality?

1) Two "branches", one with Z+ spin, one with Z- spin, and nothing else.

2) Two "branches", one with X+ spin, one with X- spin, and nothing else.

3) Three "branches", one with Z+ spin, one with Y+ spin, one with Y- spin, and nothing else.

4) All of the above and more: all possible basis decompositions of the qubit density matrix correspond to actually existing parallel branches. These noncommuting sets of parallel branches somehow exist in intersection in the wavefunction of the universe.

5) None of the above. Only the density matrix, considered globally and holistically, is the true reality.

6) There is a preferred basis selected by the qubit's environment.

7) Something else.

I would appreciate a straight answer to this question. And it needs an answer, because in the observed world - the one that physics is meant to be explaining - we always see just one possibility realized. If you want a "no-collapse, wavefunction-is-real" interpretation of QM to make sense, your very first step must be to explain what "part" or "aspect" of the wavefunction we should be looking at, in order to find what we see around us. The next step is then to explain where the empirical probabilities come from. But we can't even get to that point if you won't take the first step.​

 

[Hurkyl]

When you acquire new information, you have to update the probability distribution, and it "jumps" or "collapses".

Or, you don't update anything at all, and start asking questions about conditional probabilities (should you actually desire to condition things).

both arise from treating wave-functions as real, in a way that we would never do for probability distributions.

Think about your comment for a minute. Why wouldn't you do that for probability distributions? Interpreting probability distributions as being the actual reality is mathematically and theoretically indistinguishable from interpreting them as being ignorance probabilities.

So what grounds could you possibly have to insist that you would never do things that way?


The only (good) answer I know simply doesn't apply when we start considering collapse based versus decoherence based interpretations of quantum mechanics...

I don't know what your point is. My point is that if you believe in wavefunctions but you don't believe in collapse, then you need to explain what parts of the wavefunction correspond to reality.

If ignorance probabilities about which definite state a system is good enough for corresponding to reality, and that view is theoretically indistinguishable from a system really being in a mixed state, then mixed states are good enough for corresponding to reality.

If you can't agree on that point, then nothing else in the discussion matters.

 

[Delta Kilo]

What is the physical reality?
1)...
2)...
...
7) Something else.
I would appreciate a straight answer to this question.

The answer to this question is of course Forty-Two
Define 'physical reality' and I'll give you a straight answer.

And it needs an answer, because in the observed world - the one that physics is meant to be explaining - we always see just one possibility realized.

Just out of curiosity, do you accept that there might be "physical reality" which is not part of our "observed world"? Like for example inside the event horizon of a black hole or outside of the bubble of our currently observable universe?

This is pure metaphysics anyway, so the answer one way or another does not really change anything.

 

[mitchell porter]

Interpreting probability distributions as being the actual reality is mathematically and theoretically indistinguishable from interpreting them as being ignorance probabilities.

OK, so you flip a coin, I don't see the outcome. I could say that it is actually heads or that it is actually tails, I just don't know which. Or, I could say that the actual reality is 50% heads and 50% tails - but not that there are two worlds, one where it's actually heads and another where it's actually tails; that would be the naive view of well-defined, self-contained parallel worlds that is apparently being rejected by the defenders of MWI here. Instead, I am just to believe that the probability distribution itself is the reality - whatever that could mean.

Doing this with wavefunctions is even worse because of the multiple incompatible choices of basis. In that case it is even harder to defend the practice of "interpreting [the calculational device] as being the actual reality".

If ignorance probabilities about which definite state a system is good enough for corresponding to reality, and that view is theoretically indistinguishable from a system really being in a mixed state, then mixed states are good enough for corresponding to reality.

If you can't agree on that point, then nothing else in the discussion matters.

When I interpret the probability distribution "50% heads, 50% tails" to mean that the coin is actually heads or actually tails, but I don't know which, that is an "ignorance interpretation" of the probability distribution. I am advocating that wavefunctions be interpreted in exactly the same way - as an incomplete statement about the probable values of observables like "the side of the coin that is facing up". Since QM is incomplete, one has reason to speculate about what a more complete description of reality might be, and so maybe you could then try regarding the wavefunctions as real (and then you run into the problems that I have been pointing out) - and I thought this is what you were doing.

So afer all this, are you telling me that you do interpret wavefunctions as incomplete descriptions of reality?

 

[mitchell porter]

The answer to this question is of course Forty-Two
Define 'physical reality' and I'll give you a straight answer.

That which actually exists.

Why on Earth would you need to resort to a dodge like this? Here we are talking about what quantum mechanics means. Apart from "epistemological interpretations" which say, correctly but somewhat unhelpfully, that QM is about making correct predictions of the behavior of physical entities, I thought "interpretations" were supposed to restore to physical ontology the conceptual clarity it had before QM. Before QM, a theory might be right or wrong, but it clearly took a stand on what it is that exists. Although I maintain that the sensible "first intepretation" of QM is to say that the observables define the ontology of the theory, and the wavefunctions are a predictive device for its behavior, it's true that QM's idiosyncrasies give it a less clear-cut status than the classical theories. There is some ambiguity about what is supposed to exist, according to the theory, or else we wouldn't be having these discussions.

I thought the purpose of an interpretation of QM was to resolve that ambiguity by making definite claims about what it is that exists. The claims might be right or wrong, just as a classical theory might be right or wrong, but we would at least have a theory with ontological clarity, which took a stand about what it is that exists. By refusing to answer a simple multiple-choice question - which even included "none of the above" as an option, leaving you license to write your own explanation of the "no collapse" ontology - and by asking for a definition of "physical reality" instead, it begins to appear rather questionable that you even have a theory, in any conventional sense of the word.

Just out of curiosity, do you accept that there might be "physical reality" which is not part of our "observed world"? Like for example inside the event horizon of a black hole or outside of the bubble of our currently observable universe?

I said several times in this thread that I do not have an a-priori problem with the idea of parallel worlds with copies of me experiencing things I don't know about here. I also don't have a problem with the existence of things that no-one is experiencing. My whole problem is with people who say they have a theory and then cannot explain, on even the most basic level, what the theory says.

Hurkyl has just started talking about ignorance interpretations, which makes me wonder if he doesn't intend for wavefunctions to be the actual states of things after all. And your own earlier remarks about choosing to put aside the issue of what's real in the theory lead in the same direction. I have been saying wavefunctions are like probability distributions, and as Hurkyl points out, you can have a "no collapse" interpretation of probability distributions: Instead of changing the probability distribution in response to new information, you keep the distribution but then condition on the information in order to use it. Of course I don't disagree with anything there, but at this point it seems we have wandered far from MWI and even far from "MWI without collapse", and are no longer talking about what a complete description of reality might be like.

If you do settle for an ignorance interpretation of wavefunctions, then the measurement problem can disappear as a separate problem. You can indeed just have a joint wavefunction for measurement device and measured object, evolving according to the physics of the measurement interaction in question, and you then apply the Born rule (or its generalizations) to any observable that you care about - and here by observable I don't just mean observables that get diagonalized by the measurement interaction, I mean any property anywhere in the history of the joint system. The algebra of observables tells you that they cannot all take definite values, but coarse-graining as in decoherent histories let's you specify a set of commuting observables, and you can apply the Born rule to them if you want to ask yourself about their probable values, their correlations, and so on.

Two points: First, while this approach removes the problem of measurement as being a distinct sort of physical process, it does nothing about the incompleteness of quantum mechanics. It doesn't even tell us which observables, in the history of the universe, actually take values - as I said, it can't be all of them because they don't all commute, and yet presumably it is some larger subset of them than the minimalist solipsistic option of "positions on ions around neural membranes in my brain". It's a framework which allows us to be totally consistent with empirical QM, and yet the answer to "what is real" is anything from neuro-solipsism to a maximal set of commuting observables covering most of space-time. This is another way to see that QM is ontologically incomplete.

Second point: In this ignorance interpretation of QM, you still need the Born rule! Otherwise you can't make any statements about probable behavior of observables. So you can have a "no-collapse" ignorance interpretation, but you can't do without the Born rule as an independent postulate.

 

[Hurkyl]

Ugh, this is a lot of words. Sorry.

Hurkyl has just started talking about ignorance interpretations, which makes me wonder if he doesn't intend for wavefunctions to be the actual states of things after all.

That's to describe the way you're thinking about things. An ignorance interpretation is "reality is in one of those states, but I don't know which and I'm assigning probabilities to capture my ignorance". "Probability distributions are real" is not an ignorance interpretation.

OK, so you flip a coin, I don't see the outcome. I could say that it is actually heads or that it is actually tails, I just don't know which. Or, I could say that the actual reality is 50% heads and 50% tails ... I am just to believe that the probability distribution itself is the reality - whatever that could mean.

Right, we start with something like this. And we run with classical mechanics for a while to get used to the shift in perspective.

While before we described the coin with an actual value "Heads" or "Tails", we now describe the coin with a random variable.

We consider the fact that when I observe the coin, I will see one of the two values in the set {heads, tails}. Ah, that's accounted for in the fact the sample space of the random variable is the set {heads, tails}.

The fact that actual observation sees only one outcome? The trivial fact that $P(X=a | X=a) = 1$. We just used to using conditional probabilities with random variables, when before we talked about absolute probabilities involving indeterminate variables.


Happy? The important thing at this point isn't that you think "this is a wonderful way to think about classical mechanics" -- it's that "huh; this is self-consistent and physically indistinguishable to the ordinary way of thinking, even if it seems a little weird."


Now, let's continue applying this to quantum states. Traditionally, we think of results of measurements being classical ignorance probabilities across definite outcomes. But now, we're thinking of probability distributions as reality -- but it's a bit more convenient than the classical case, because it's already built into the mathematical description of quantum state -- e.g. a quantum state could be written as a weighted positive linear combination of density matrices -- rather than us having to layer probability theory on top of the quantum state space. Also, quantum states are somewhat more general.

Now we run into the question you had before:

Suppose that we have a qubit whose density matrix is as described. What is the physical reality?

The answer is: the physical reality is the wave-function. Everything else follows from that. I mentioned a quantum state earlier that was a mixed state that could be written as

60% Z+ and 40% Z-​

Since we made ourselves happy with probability distributions as reality, it's not difficult to understand a quantum particle as really being in this state that is a probability distribution over pure states.

We understand that this is completely indistinguishable from a definite-outcomes interpretation where we view it as an ignorance probability over definite states.

Also, we can understand a quantum particle as really being in the state

20% Z+ and 40% Y+ and 40% Y-​

Now, you were having a problem with the fact these were different sums describing the same quantum state. What is the reality?? But the question was already answered -- reality is the wave-function. A little thought should convince you that the difference between the sums is entirely superficial -- the two decompositions cannot be distinguished by any physical experiment, and therefore we shouldn't be quick to insist that we must interpret them as different.

(and if it doesn't, try computing the expectation of some observable -- say, spin around the axis half-way between the Z+ and Y+ axes)


Are you with me this far? Again, I've not said anything to answer "why should we think this way" (except possibly for comments about things being physically indistinguishable), but instead have discussed "why can we think this way".

We've seen that something we might have thought as classical ignorance probabilities weighted 60% Z+ and 40% Z- give the same results as thinking of a qubit in a certain mixed quantum state. And that classical ignorance probabilities weighted 20% Z+ and 40% Y+ and 40% Y- gives the same results as thinking of the cubit in a certain mixed quantum state.

And we saw the interesting new physics that the two mixed states are the same -- and the interesting result that the two superficially different classical ignorance probabilities actually describe the same physics... something we might not have otherwise noticed if we weren't thinking about mixed states.


The next two major points are the relative state of a subsystem (I was probably going to talk about the entangled photon scenario as an example), and the fact that relative states provide a way around the old no-go theorem -- when a system undergoes unitary evolution, its subsystems can decohere.

Can you see where I'm going with these, or do I need to continue?

Anyways, once we have these points, we have the basic premise behind the family of decoherence-based interpretations of quantum mechanics -- the ignorance probabilities that QM was traditionally thought in terms of work out to be indistinguishable from mixed states. Mixed states can be produced by decoherence of relative states of subsystems. Decoherence of subsystems can occur through unitary evolution ala the Schrödinger equation. We have a framework where unitary evolution at least has the potential to produce the same mathematical descriptions of state that appear in a collapse-with-ignorance-probabilities point of view.



Aside: the "good" reason to use ignorance probabilities I mentioned earlier was Occam's razor -- in classical statistical mechanics, the decomposition of a probability distribution into a weighted combination of individual states is absolute and eternal, unlike the weighted combinations that appear in the framework I described above. For classical mechanics, we lose nothing (except possibly a wider point of view) by deciding to interpret everything as ignorance probabilities, so Occam can be applied. But in QM, we do lose something by insisting on thinking in terms of ignorance probabilities, so Occam doesn't apply anymore.

 

[Delta Kilo]

By refusing to answer a simple multiple-choice question - which even included "none of the above" as an option, leaving you license to write your own explanation of the "no collapse" ontology - and by asking for a definition of "physical reality" instead, it begins to appear rather questionable that you even have a theory, in any conventional sense of the word.

It's not about a theory, its about interpretation. It would become a theory if, for example, someone manages to get Born rule out of unitary evolution, much like normal law appears from random walk. Decoherence does at least part of the job, it shows how complex wavefunction is reduced to a set of choices in environmentally-selected preferred basis, but the last step of getting the actual probabilities, I don't think we are there yet, unfortunately.

Regarding the definition of reality and its connection with the observable world, there is yet another radical alternative: our observable world might not be real. Say, we observe temperature and pressure, would you say they are real or would you say the motion of individual molecules is real and temperature and pressure are just emerging statistical artefacts? What if we are simply unable to perceive the 'real' thing due to us being simply too big, too macroscopic?

As in, what is more real, an object or a picture of it on TV? What if we are unable to leave the room and the only thing we can observe is a picture on TV? Well, we can still develop a good consistent theory explaining (and predicting!) what we see, like colors, shadows, occlusions, etc. Would we then consider our 3D model as more or less real than 2D picture we see on TV?

These are all rhetorical questions, I do not pretend to have answers for them. And it does not matter one way or the other. What matters is to have a good working model.

 

[Fredrik]

Hurkyl,

if I flip a coin and you don't see the result, would you say that the reality of the coin is a probability distribution with roughly equal probabilities for heads and tails? Based on what you said, I don't see how your answer can be anything but "yes". So reality is subjective? It sounds like you have simply redefined the word "reality" to refer to the mathematical object a person uses as a representation of reality.

Consider a wavefunction that's non-zero over a large region. QM tells us how to use it to calculate probabilities of possible results of experiments. QM doesn't say if the graph of the function $|\psi|^2$ describes the particle's current shape, or if particles are actually point-like objects that move in really weird ways. How can QM be said to describe reality when it doesn't even tell us a particle's shape?

Since QM doesn't tell us the shape, we are free to make assumptions about it. I would say that it's these (non-mathematical, non-scientific and unnecessary) assumptions that define descriptions of possible realities. I still don't see a reason to say that the theory describes a possible reality, let alone the actual reality.

I also don't consider this a rejection of QM, as you apparently do. To reject it would be to say that its predictions aren't very accurate (this is certainly not true), or that it doesn't improve our understanding of reality at all. I would say that it does. It just doesn't improve it as much as we want it to.

 

[Fredrik]

It's not about a theory, its about interpretation.

That's exactly why it doesn't make sense to demand a definition of "reality". In the context of interpretations, "reality" must be considered a primitive, a term that's left undefined. How would you define it? No, I'm not asking what definition you would choose. I'm asking what sort of thing you would consider a definition. Do you mean that we should associate the term with something in a theory of physics? Wouldn't the only point of having a definition be that we might be able to derive such an association from it? I would say "yes", and that this means that a definition of this sort would be worse than useless.