PaulAlmond comments on Welcome to Less Wrong! (2010-2011) - Less Wrong

42 Post author: orthonormal 12 August 2010 01:08AM

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Comment author: PaulAlmond 21 August 2010 02:37:35PM * 1 point [-]

Agreed - MWI (many-worlds interpretation) does not have any "collapse": Instead parts of the wavefunction merely become decoherent with each other which might have the appearance of a collapse locally to observers. I know this is controversial, but I think the evidence is overwhelmingly in favor of MWI because it is much more parsimonious than competing models in the sense that really matters - and the only sense in which the parsimony of a model could really be coherently described. (It is kind of funny that both sides of the MWI or !MWI debate tend to refer to parsimony.)

I find it somewhat strange that people who have problems with "all those huge numbers of worlds in MWI" don't have much of a problem with "all those huge numbers of stars and galaxies" in our conventional view of the cosmos - and it doesn't cause them to reach for a theory which has a more complicated basic description but gets rid of all that huge amount of stuff. When did any of us last meet anyone who claimed that "the backs of objects don't exist, except those being observed directly or indirectly by humans because it is more parsimonious not to have them there, even if you need a contrived theory to do away with them"? That’s the problem with arguing against MWI: To reduce the "amount of stuff in reality" - which never normally bothers us with theories, and shouldn't now, you have to introduce contrivance where it is really a bad idea - into the basic theory itself - by introducing some mechanism for "collapse".

Somehow, with all this, there is some kind of cognitive illusion going on. As I don't experience it, I can't identify with it and have no idea what it is.

Comment author: Saladin comment score below threshold [+] (17 children)

Comment author: prase 23 August 2010 03:52:33PM * 2 points [-]

And my problem is that questions like this are heavily downvoted. This isn't a bad question per se, even if it may be a little bit confused. As I understand, only a minority of people here are physicists, and quite a lot of people on LW haven't technical understanding of quantum theory. So the parent comment can't be perceived as ignorant of some already shared standard of rationality. Also, MWI is still not a broad scientific consensus today, even if some portray it such. So why does the parent stand at -5? Do we punish questioning the MWI? If so, why?

Now on topic. MWI doesn't violate thermodynamics any more than the Copenhagen interpretation. In the CI one can have a superposition of states of different energy collapsing into one of the involved energies; the estimated (mean) energy of the state is not conserved through the measurement.

The energy is conserved in two senses: first, it is conserved during the evolution of a closed system (without measurement), and second, it is conserved completely when using statistical mixed states to model the system - in this case, the collapse puts the system into a mixed state, and the mean value of any observable survives the collapse without change. Of course, the energy conservation requires time-independent dynamics (it means time-independence of the laws governing the system and all physical constants) in both cases.

An important technical point is that measurements always transfer the energy to the apparatus and therefore there is little sense to demand conservation of energy of the measured system during a measurement. To model a realistic measurement, the apparatus has to be described by a non-self-adjoint Hamiltonian to effectively describe dissipation, or at least it has to have a time-dependent Hamiltonian, or both; else, the apparatus will not remember the results. In both cases, energy conservation is trivially broken.

As for the (implicit) first question how the worlds are created: There is one Hilbert space consisting of all possible state vectors of the world. The state of the world can be, in a rough idealisation, decomposed into a tensor-product of smaller states of individual observers and non-observer subsystem (whether a subsystem is or isn't an observer is not particularly important, and it is probably related to the problem of consciousness). In a subspace of a particular observer, some states are specific, while most of the states aren't. The specific states correspond to certain thoughts. In an idealisation of an observer who cares only about one particular physical system, the observer's specific states all correspond to states of the system, which are said to have a sharp value of certain observables.

Now, in the Schrödinger picture, all state vectors evolve. Interaction between the observer and the observed system takes the state vectors into correlation. After that, the overall state vector of the observer+system compound can't be written as a tensor product of a observer-vector and a system-vector, and thus talking about the state of the observer alone doesn't make sense any more.

The consciousness of the observer works in such a way, that it decomposes the state of the observer+system into sum of vectors, each of which can be written as a tensor product of an observer-vector and a system-vector (although entire the sum can't), and lives a separate instance on each summand. Each of this instances forms what is called a world in the MWI jargon.

These worlds thus aren't created from void by some physical action. It's perhaps better to say that they are "interpreted into existence" by individual observers' consciousnesses. The division of the whole universe into individual worlds is observer dependent.

Comment author: PaulAlmond 21 August 2010 04:18:32PM * 2 points [-]

These worlds aren't being "created out of nowhere" as people imagine it. They are only called worlds because they are regions of the wavefunction which don't interact with other regions. It is the same wavefunction, and it is just being "sliced more thinly". To an observer, able to look at this from outside, there would just be the wavefunction, with parts that have decohered from each other, and that is it. To put it another way, when a world "splits" into two worlds, it makes sense to think of it as meaning that the "stuff" (actually the wavefunction) making up that world is divided up and used to make two new, slightly different worlds. There is no new "stuff" being created. Both worlds actually co-exist in the same space even: It is only their decoherence from each other that prevents interaction. You said that your problem is "how they (the worlds) are created" but there isn't anything really anything new being created. Rather, parts of reality are ceasing interaction with each other and there is no mystery about why this should be the case: Decoherence causes it.

Comment author: Mitchell_Porter 22 August 2010 05:17:49AM 1 point [-]

It is the same wavefunction, and it is just being "sliced more thinly".

Do you think the number of worlds is a definite and objective fact, or that it depends on how you slice the wavefunction?

Comment author: PaulAlmond 22 August 2010 05:53:12AM 1 point [-]

Well, it isn't really about what I think, but about what MWI is understood to say.

According to MWI, the worlds are being "sliced more thinly" in the sense that the total energy of each depends on its probability measure, and when a world splits its probability measure, and therefore energy, is shared out among the worlds into which it splits. The answer to your question is a "sort of yes" but I will qualify that shortly.

For practical purposes, it is a definite and objective fact. When two parts of the wavefunction have become decoherent from each other there is no interaction and each part is regarded as a separate world.

Now, to qualify this: Branches may actually interfere with each other in ways that aren't really meaningful, so there isn't really a point where you get total decoherence. You do get to a stage though where decoherence has occurred for practical purposes.

To all intents and purposes, it should be regarded as definite and objective.

Comment author: Mitchell_Porter 22 August 2010 07:26:02AM 1 point [-]

the total energy of each [world] depends on its probability measure

Please check your sources on MWI. I think you must be misreading them.

Branches may actually interfere with each other in ways that aren't really meaningful, so there isn't really a point where you get total decoherence.

So in reality, decoherence is a matter of degree. But I thought that the existence of one world or many worlds depended on whether decoherence had occurred. Is there a threshold value, a special amount of decoherence which marks the transition?

Comment author: PaulAlmond 22 August 2010 01:19:48PM 0 points [-]

it sounds like you might have issues with what looks like a violation of conservation of energy over a single universe's history. If a world splits, the energy of each split-off world would have to be less than the original world. That doesn't change the fact that conservation of energy appears to apply in each world: Observers in a world aren't directly measuring the energy of the wavefunction, but instead they are measuring the energy of things like particles which appear to exist as a result of the wavefunction.

Advocates of MWI generally say that a split has occurred when a measurement is performed indicating that it has observed. It should also be noted that when it is said that "interference has stopped occurring" it really means "meaningful" interference - the interference still occurs but is just random noise, so you can't notice it. (To use an extreme example, that's supposed to be why you can't see anyone in a world where the Nazis won WWII: That part of the wavefunction is so decoherent from yours that any interference is just random noise and there is therefore no meaningful interference. This should answer the question: As decoherence increases, the interaction gets more and more towards randomness and eventually becomes of no relevance to you.)

I suggest these resources.

Orze, C., 2008. Many-Worlds and Decoherence: There Are No Other Universes. [Online] ScienceBlogs. Available at: http://scienceblogs.com/principles/2008/11./manyworlds_and_decoherence.php [Accessed 22 August 2010].

Price, M,C., 1995. The Everett FAQ. [Online] The Hedonistic Imperative. Available at: http://www.hedweb.com/manworld.htm [Accessed 22 August 2010].

Comment author: Mitchell_Porter 23 August 2010 06:17:27AM 2 points [-]

If a world splits, the energy of each split-off world would have to be less than the original world.

No, you are misunderstanding the argument. I am a MWI opponent but I know you are getting this wrong. If we switch to orthodox QM for a moment, and ask what the energy of a generic superposition is, the closest thing to an answer is to talk about the expectation value of the energy observable for that wavefunction. This is a weighted average of the energy eigenvalues appearing in the superposition. For example, for the superposition 1/sqrt(2) |E=E1> + 1/sqrt(2) |E=E2>, the expectation value is E1/2 + E2/2. What Q22 in the Everett FAQ is saying is that the expectation value won't apriori increase, even if new worlds are being created within the wavefunction, because the expectation value is the weighted average of the energies of the individual worlds; and in fact the expectation value will not change at all (something you can prove in a variety of ways).

To use an extreme example, that's supposed to be why you can't see anyone in a world where the Nazis won WWII: That part of the wavefunction is so decoherent from yours that any interference is just random noise and there is therefore no meaningful interference.

Well, this is another issue where, if I was talking to a skilled MWI advocate, I might be able to ask some probing questions, because there is a potential inconsistency in the application of these concepts. Usually when we talk about interference between branches of the wavefunction, it means that there are two regions in (say) configuration space, each of which has some amplitude, and there is some flow of probability amplitude from one region into the other. But this flow does not exist at the level of configurations, it only occurs at the level of configuration amplitudes. So if "my world", "this world", where the Nazis lost, is one configuration, and the world where the Nazis won is another configuration, there is no way for our configuration to suddenly resemble the other configuration on account of such a flow - that is a confusion of levels.

For me to observe interference phenomena, I have to be outside the superposition. But I wasn't even born when WWII was decided, so I am intrinsically stuck in one branch. Maybe this is a quibble; we could talk about something that happened after my birth, like the 2000 US election. I live in a world where Bush won; but in principle could I see interference from a world where Gore won? I still don't think it makes sense; the fact that I remember Bush winning means that I'm in that branch; I would have to lose the memory for the probability flow here to come into contact with the probability flow in a branch where Gore won. More importantly, the whole world configuration would have to morph until it came to resemble a world where Gore won, for some portion of the probability flow "here" to combine with the probability flow there.

I'll try to explain what I'm talking about. The wavefunction consists of a complex-valued function defined throughout configuration space. Configuration space consists of static total configurations of the universe. Change exists only at the level of the complex numbers; where they are large, you have a "peak" in the wavefunction, and these peaks move around in configuration space, split and join, and so on. So really, it ought to be a mistake to think of configurations per se as the worlds; instead, you should perhaps be thinking about the "peaks", the local wavepackets in configuration space, as worlds. Except, a peak can have a spread in configuration space. A single peak can be more like a "ridge" stretching between configurations which are classically inconsistent. This already poses problems of interpretation, as does the lack of clear boundaries to a peak... Are we going to say that a world consists of any portion of the wavefunction centered on a peak - a local maximum - and bounded by regions where the gradient is flat??

But here I can only throw up my hands and express my chronic exasperation with the fuzzy thinking behind many worlds. It is impossible to intelligently critique an idea when the exponent of the idea hasn't finished specifying it and doesn't even realize that they need to do more work. And then you have laypeople who take up the unfinished idea and advocate it, who are even more oblivious to the problems, and certainly incapable of answering them.

Paul, if I could convey to you one perspective on MWI, it would be as follows: Most people who talk about MWI do not have an exact definition of what a world is. Instead, it's really an ideology, or a way of speaking: QM has superpositions in it, and the slogan is that everything in the superposition is real. But if this is to be an actual theory of the world, and not just an idea for a theory, you have to be more concrete. You have to say exactly what parts of a wavefunction are the worlds. And when you do this, you face new problems, e.g. to do with relativity and probability. The exact nature of the problems depends on how the MWI idea is concretized. But if you give me any concrete, detailed version of MWI, I can tell you what's wrong with it.

Comment author: wnoise 23 August 2010 02:10:03PM 0 points [-]

First, let me say beautifully clear explanation of what MWI is and especially what questions it needs to answer.

Except, a peak can have a spread in configuration space. A single peak can be more like a "ridge" stretching between configurations which are classically inconsistent. This already poses problems of interpretation, as does the lack of clear boundaries to a peak... Are we going to say that a world consists of any portion of the wavefunction centered on a peak - a local maximum - and bounded by regions where the gradient is flat??

I don't think this is any more unreasonable than talking about firing two separate localized wave-packets at each other and watching them interfere, even if we don't have a specific fixed idea of what in full generality counts as a "wave-packet". Typically, of course, for linear wave equations we'd use Gaussians as models, but I don't think that's more than a mathematically convenient exemplar. For non-linear models, (e.g. KdV) we have soliton solutions that have rather different properties, such as being self-focusing, rather than spreading out. I guess I don't see why it matters whether you have an exact definition for "world" or not -- so long as you can plausibly exhibit them. The question in my mind is whether evolution on configuration space preserves wave-packet localization, or under what conditions they could develop. I find it hard to even formalize this, but given that we have a linear wave-equation, I would tend to doubt they do.

e.g. to do with relativity

Of course relativity will be an issue. QM is not Einsteinian relativistic, only Galilean (relabeling phases properly gives a Galilean boost), and that's baked into the standard operators and evolution.

Comment author: PaulAlmond 23 August 2010 08:27:26AM 0 points [-]

I do admit to over-generalizing in saying that when a world splits, the split-off worlds each HAVE to have lower energy than the "original world". If we measure the energy associated with the wavefunction for individual worlds, on average, of course, this would have to be the case, due to the proliferation of worlds: However, I do understand, and should have stated, that all that matters is that the total energy for the system remains constant over time, and that probabilities matter.

Regarding the second issue, defining what a world is, I actually do understand your point: I feel that you think I understand less on this than is actually the case. Nevertheless, I would say that getting rid of a need for collapse does mean a lot and removes a lot of issues: more than are added with the "What constitutes a world" issue. However, we probably do need a "more-skilled MWI advocate" to deal with that.

Comment author: Mitchell_Porter 23 August 2010 08:55:53AM * 1 point [-]

I do admit to over-generalizing in saying that when a world splits, the split-off worlds each HAVE to have lower energy than the "original world". If we measure the energy associated with the wavefunction for individual worlds, on average, of course, this would have to be the case, due to the proliferation of worlds

Let me see if I am understanding you. You're now saying that the average energy-per-world goes down, "due to the proliferation of worlds"? Because that still isn't right.

The simplest proof that the average energy is conserved is that energy eigenstates are stationary states: subjected to Hamiltonian evolution, they don't change except for a phase factor. So if your evolving wavefunction is Psi(t), expressed in a basis of energy eigenstates it becomes sum_k c_k exp(-i . E_k . t) |E_k>. I.e. the time dependence is only in the coefficients of the energy eigenstates, and there's no variation in their norm (since the time dependence is only in the phase factor), so the probability weightings of the energy eigenstates also don't change. Therefore, the expectation value of the energy is a constant.

There ought to be a "local" proof of energy conservation as well (at least, if we were working with a field theory), and it might be possible to insightfully connect that with decoherence in some way - that is, in a way which made clear that decoherence, the process which is supposed to be giving rise to world-splits, also conserves energy however you look at it - but that would require a bit more thought on my part.

ETA: Dammit, how do you do subscripts in markdown? :-)

ETA 2: Found the answer.

continue this thread »

Comment author: Perplexed 21 August 2010 04:46:34PM 1 point [-]

How do You reconcile MWI with the 1st Law of thermodynamics?

Why do you see a conflict? You seem to be assuming both that the total energy of the universe is positive (not known!), and that each universe has the same total energy (i.e. that energy is not arbitrarily scalable). Why not assume that a universe with 100 joules of energy splits into two universes - one with 100 zorkmids of energy and the other with 100 arkbarks of energy (where it is understood that 1 zorkmid + 1 arkbark = 1 joule).

Comment author: LucasSloan 21 August 2010 03:56:21PM 1 point [-]

A better question - how does the observed 1st law of thermodynamics arise from the laws of physics underpinning the many worlds?

Comment author: XiXiDu 21 August 2010 04:19:07PM 0 points [-]

Erm, I can tell you less about physics than the creationist museum about evolution but I don't think it applies to open systems.

Anyway, for some interesting information about thermodynamics go here:

Mea Culpa: I was wrong; Eliezer was wrong; Sean Carroll was right.

Comment author: ciphergoth 21 August 2010 04:50:29PM 2 points [-]

I don't understand the argument in that post, even now re-reading it over a year later. Do you? If not, why are you citing it?

Comment author: XiXiDu 21 August 2010 05:25:37PM 0 points [-]

The post shows that even intellectual high-fliers like EY and Hanson can err on this topic (if it is to be believed that they were wrong). In other words, I wouldn't recommend asking questions made up of terms that are themselves poorly understood even by the best minds within this community.

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