MWI for the layperson:
In classical mechanics, each particle has a position and velocity. If there are N particles, the state of a physical system at a given time is given by a list of the positions (a configuration, or point in 3N-dimensional configuration space) and of the velocities for each particle:
X1 = (x1,y1,z1)
classical state: (X1(t), V1(t)), (X2(t),V2(t)), (X3(t),V3(t)), ...
In QM, there is instead the wavefunction, psi, which is a complex-number-valued function on what would classically be configuration space plus the space of spin configurations, and is a function of time:
quantum state: psi(X1,S1, X2,S2, X3,S3, ... , t)
(Spin, Si, takes on a small set of discrete values.)
This is a classic way of generalizing something: instead of a point in a space, there is a function on that space. It must be emphasized that the wavefunction is not a function on regular 3-dimensional space, but on the 3N-dimensional space of configurations. This high-dimensional arena is responsible for many of the counterintuitive properties of quantum mechanics.
If the wavefunction is somewhat sharply peaked near a configuration, though with a wavelength small compared to the width of the peak, it will behave a lot like a classical system; the peak will follow a nearly classical trajectory as a function of time. It is natural to conclude that any interesting things done by such a classical system, such as performing computations, will be done by the wavefunction. It is just like a classical world, only a little 'fuzzy' due to the finite width of the peak. Indeed, roughly this picture is probably how most people think of QM, including chemists - a classical world except that electrons and similar particles are spread out instead of being concentrated at a point.
But that is obviously not a complete picture, because the wavefunction is not concentrated around a single peak. Roughly speaking, there are many peaks, representing quite different classical configurations (e.g. the alive or dead configurations of Shrodinger's cat), and many places even away from the peaks where the wavefunction is nonzero. Yet the world we see resembles a classical, single-configuration world. How can we explain that?There are three main approaches. The first is some modification of QM in which only one peak remains, while the others vanish - this is called 'collapse of the wavefunction'. There are three main problems with this: 1) it introduces a lot of complexity to the model which might be avoided by another approach; 2) it violates things physicists like such as conservation laws; and most importantly 3) it doesn't work because generally speaking, in proposed models that give mathematical details of 'collapse', small residues remain in the other parts of the wavefunction. Small or not, these residues still go through trajectories that should give rise to computations and thus observers - unless we have reason to believe that probability is higher in high amplitude regions; but if we do, we might as well just go with the simpler MWI since deriving that is its main problem.
The second main approach is hidden variables. As we have seen, local hidden variable models are ruled out by Bell's theorem, but nonlocal models exist that don't have that problem - most famously, the Pilot Wave Interpretation (PWI). In the PWI, a classical-like configuration point 'surfs' along the wavefunction. It has been shown that under quite general conditions, the probability distribution for the point evolves in time to match the Born Rule of QM.
Two main problems have been raised for the PWI and similar models. 1) It is nonlocal, and has a preferred reference frame contrary to the spirit of relativity. This is really a matter of taste, and I don't consider it a fatal problem at all, though I do think the nonlocality is an undesirable feature if other models can avoid it. 2) More importantly, it doesn't get rid of the other peaks in the wavefunction at all; it just adds a new trajectory of the hidden configuration point. The wavefunction is still there and should still perform all of the interesting computations as it would in the MWI. Thus, the PWI has been called 'Everett in denial'. Valentini [http://arxiv.org/abs/0811.0810] has denied that charge but his straw-like arguments are easily demolished as Brown has done [http://arxiv.org/abs/0901.1278].
I must note an important exception to the many-worlds property of the PWI: In some versions of what is proposed for quantum gravity, the wavefunction of the universe does not evolve as a function of time; this is known as the Wheeler-DeWitt equation. That would seem at first glance to rule out observers in those models (that remains to be seen even for just a wavefunction). However, the PWI hidden variables would evolve in time even though the wavefunction doesn't, making a single-world model out of it. While interesting, I find it implausible that something as complex as the wavefunction of the universe would have to be in such a model could be an initial condition.
Finally, there is the MWI itself, as first proposed by Everett and in various forms by others. In its basic form, this has the simplest mechanics as it just lets the wavefunction evolve over time, adding no hidden variables or collapse-inducing modifications to the dynamics. There are many peaks in the wavefunction which follow various trajectories and implement various computations. [Much more to be said on that rough sketch.] Each individual observer only notices a single classical-like world because that is the one associated with the motion of the peak giving rise to the computations of his own brain; the others don't have any effect on him.This appealingly simple picture, however, raises a problem of its own: In order for our observations to be at all typical, the Born Rule (which relates probabilities to the square of the wavefunction) must hold, at least to some approximation. This means that small amplitude peaks are less probable than large amplitude peaks. Since the trajectory of a peak (which makes it perform computations and so on) does not depend on amplitude, why would that be the case in the MWI?
The possibility of derivation of the Born Rule in the MWI is the central problem in interpretation of QM. If the Born Rule does follow from the MWI, then the case for the MWI is made beyond a reasonable doubt. I will discuss in other posts various attempts to derive it.
If it does not follow, then the problem remains - what interpretations could work? Continuous collapse models and the PWI would still not work because they would still be the MWI in disguise due to having the wavefunction (with its wrong probabilities) as part of their ontology.
One possibility that looks like it should work in any case is making an honest Many-Worlds version of the PWI: having infinitely many sets of the hidden variables. The simplest version, that of having every point in configuration space sporting a wave-surfing hidden variable, is called Continuum Bohmian Mechanics (CBM). These hidden variable worlds could then outnumber the ones in the wavefunction, producing the Born Rule for typical observers. Of course, this model is more complex than the standard MWI. Also, it still would leave the question of what observers are and how to count them.
Quantum gravity remains an unsolved problem, and the solution may play a role in interpretation of QM, perhaps providing a new set of variables to work with.
Another problem is that in the long term, long after normal observers have died out, spontaneously assembled bits of random matter (which a cosmological constant would produce) would eventually include short-lived observers who would outnumber the normal ones over the history of the universe by perhaps an infinite factor. These Boltzmann Brains, and the necessity of getting rid of them in terms of their effect on typical observations, provide important constraints on what the real answers could possibly be. This deserves a post of its own, at least.
Another (and not unrelated) topic that will get its own post is the Everything Hypothesis, which postulates that every possible thing must exist as an explanation for why things are how they are.
Very interesting blog - Do keep it going, and don't be discouraged by an initial shortage of worthwhile feedback.
ReplyDeleteFor what it's worth, I also think that when considered in the right way, the MWI is a lot more plausible than many assume.
A postage stamp sized comment box (in which the arrow keys and copy and paste don't work - a major PITA!) isn't the best place to expand on this. But I wonder if the term "collapse" applied to a wave function is not misleading, and that it might be more illuminating instead to think of it as almost the opposite - a runaway expansion, albeit of course with the same effect.
The snag is that to be any use it seems this would somehow have to work at superluminal speed without violating the basic tenets of Relativity. All the same, space itself can expand faster then light speed. So perhaps there is some way to interpret a runaway expansion as the same without allowing information to be conveyed faster than light speed.
For example, one could envisage that so-called dark matter is a kind of energy "backscatter", along the lines sketched above, from within a black hole. Likewise, dark energy could be considered much the same - as the ghost of "collapsed" (and hence spread out) energy quanta randomly combining via non-linear effects to produce new energy.
Well, food for thought perhaps (but do delete this comment if your only thought on reading it is "how hopelessly naive"!
Regards
John Ramsden (jhnrmsdn@yahooo.co.uk) remove one o
Me again. Sorry - couldn't resist ;-)
ReplyDeleteThis expansion of a "collapsing" wave function could even provide an ontological explanation of how a universe might split, assuming (as I gather MWI adherents do) that a split is caused by each such expansion.
Is it possible that, despite obviously being very much attenuated, an energy quantum expanding through a wave function with many peaks (as you described) can somehow, by interacting with the wave packet in some vanishingly small non-linear way, influence those peaks to have the effect of splitting the wave function?
I know this must sound utterly absurd, and wouldn't blame anyone for assuming I'm as mad as a mongoose. But it gets better (or worse, depending on your viewpoint!).
Once one thinks of a "collapsing" energy quantum as really undergoing runaway expansion, it starts to sound strangely familiar - Isn't our universe destined to do the same, by all accounts?
So perhaps there's a simple answer to the first question that occurs to most laypersons (and many physicists) in relation to MWI - Where do all these universes go?
The answer is that they are each one of the energy quanta comprising ours. Conversely our universe is no more than one energy quantum within any other universes related to it, with our intrinsic time scale of course shrunk to a scale below what can be measured even in principle within any other such universe.
Regards
John R Ramsden
John:
ReplyDeleteThanks for your comments.
The idea of an actual collapse-like 'splitting' of universes is exactly the kind of misconception about the MWI that I was hoping my description of it would dispel. The basic Everett MWI is nothing but the Shrodinger equation - the wave equation of QM in configuration space.
There is no precise definition for a measurement, so there is no precise condition for a 'split'; that's one reason the 'Copenhagen Interpretation', the old collapse idea, failed. The MWI needs no such thing. For practical purposes (negligable intereference between alternate observed outcomes), entanglement and decoherence give the illusion of collapse if the Born Rule holds.
As for 'where the other universes go', it is not a problem at all: they are simply waves in other parts of the configuration space.
Regards,
Jack
With some trepidation, but reassured by the thought that feedback by a layperson on an article intended for one may not be unwelcome, I'll add another 2 cents worth if I may.
ReplyDeleteFirstly, if you don't mind my saying, the second paragraph isn't entirely clear. With a bit of digging elsewhere, I have now taken on board the basic point about the wave function being defined on configuration space rather than physical space, and that of course makes the final line clear in your preceding reply.
Although there's no denying your summary states this, and I feel a bit dumb for not fully taking it in immediately, the average layman (perhaps not familiar with linear algebra for example) might well fall into the same trap of seeing the word "space" and identifying this with physical space.
Also, I presume the spin is the second function. But it might be worth spelling out each function. (Incidently, a post on the topic of spin and how, if at all, this relates to energy and momentum would be very useful.)
Next, you refer to the Born Rule early on, but don't define this until much later where it turns out to be a major consideration. In view of that, and the fact that it won't be familiar to most laypeople, I would include a summary description where it first appears. Same goes for other QM concepts brought into the discussion.
I think your posts would also profit from more links, and in due course these might raise your
score in search engine rankings. For example, I found a wonderful and bang up to date account of the Collapse Problem at the Stanford Encyclopedia of Philosophy site, and there are many other fascinating artices there.
(There's every chance the comment formatter will make a complete pig's ass of the above link; but it should be clear what I was *trying* to achieve! In case the URL is dropped, it is http://plato.stanford.edu/entries/qm-collapse )
So often in discussions of physics, like anything else, misunderstandings arise on account of different unstated assumptions.
For example, in Bohmian QM (as I understand it) and even more so in the model I sketched there is an assumption of hidden levels of structure which influence the evolution of systems even though they may not themselves be measurable even in principle.
But how do physicists who dogmatically deny the existence of these deal with what seems the inescapable logical conclusion of that stance namely that QM and reality itself must be in a sense "finite" in its levels of structure? That has always seemed to me far *less* intuitive, in fact untenable and ridiculous, compared with the idea of a reality "infinite in all directions" as Dyson expressed it.
In parting, I would say the main point I was trying to convey was that the "tails" of collapsed wave functions are not pesky embarrassments, to be swept under the carpet, but are probably the causal factor underlying the initial "random" uncertainty of other wave packets in Bohm's model (as described on page 119 of "Quantum Non-locality and Relativity" by Tim Maudlin - sorry the Google Books link is too long to type, and pasting doesn't work here!).
Furthermore, it seems very likely that collectively an accumulation of these tails, each limited somehow from simply spreading indefinitely and flattening to zero, could also readily explain dark matter and dark energy.
Regards
John R Ramsden (jhnrmsdn@yahooo.co.uk) remove one o
P.S. When typing my second reply, the arrow keys and copy and paste worked (in Firefox). But now unaccountably they are back to being disabled, which makes typing replies diabolically difficult. It seems as if one is constantly fighting some rogue keystroke-suppressing javascript code!
The main issue is that being able to copy the text is vital as a backup, in case the "post reply" fails and one returns to the screen with a blank comment box having lost all the text typed!
John,
ReplyDeleteThanks again for your comments.
There's a lot of ground to cover here! First, some posts will be appropriate for the layperson (so far they have been) but I hope some should be more technical. I think I want my blog to be for both physicists and non-physicists, but what I had in mind was more that other physicists could get good ideas on how to explain things to non-physicists from it :)
I will edit the blog post to try to clarify it by adding a few equations, though a blog is not ideal for that. I can see that I should make a post which will just be "basics of QM" so that a layperson might follow the blog.
John, what did you think of my post on Bell's theorem?
External links can be very useful, and thanks for the tips, but there is one problem: There is liable to be something I disagree with at most links. For example, while the article on collapse interpretations that you gave a link for is good, it casts them in a more favorable light than I would. I mentioned collapse in my blog only to say why it is wrong, get it out of the way, and move on to the more interesting stuff :)
Your idea that there ought to be hidden levels of structure seems to turn Occam's Razor (the idea, used in science, that the simplest explanation is more likely) on its head! But perhaps you will like the Everything Hypothesis, when it comes time to discuss that ...
Re: the tails of collapsed wavefunctions: Not sure what you mean but I think you will have to learn more physics before thinking it properly; nothing wrong with that! For one thing, there is no collapse in Bohmian mechanics, any more than in the MWI. The linearity of QM guarantees that there could be no dark-matter-like effects from "the tails". Dark matter/dark energy have far more plausible explanations such as axions and scalar fields.
Regards,
Jack
P.S. I agree about copying text as a backup before hitting post! I've lost posts and it's not fun. In Explorer, Edit/Select All and and Edit/Copy works for me, as do arrow keys. You could also try composing posts in Notepad.
Hi,
ReplyDeleteI like the idea of your pages, and, as a proponent of PWI, I hope for some interesting discussions.
What is IMHO clearly wrong is the claim that
"If it does not follow, then the problem remains - what interpretations could work? Continuous collapse models and the PWI would still not work because they would still be the MWI in disguise due to having the wavefunction (with its wrong probabilities) as part of their ontology."
First, the denial-argument has never been even proposed for physical collapse interpretations, and cannot, because they have modified the Schrödinger equation.
Second, the PWI clearly works. If the denial-argument would be valid, it would not prevent the PWI from working, it would only define a simplicity argument in favour of MWI. But the PWI would not remain working, there would be simply appear different things which look similar and can have similar experiences, like flies around us, or (even better) clouds which sometime
remember human faces: If these clouds would be stable enough, one could argue that we are something like these clouds as well.
The disagreement starts earlier: I certainly disagree about your opinion that
"If the Born Rule does follow from the MWI, then the case for the MWI is made
beyond a reasonable doubt."
Instead, it could at least become a well-defined interpretation. Now it is only a hope that, in some future, it may become a well-defined interpretation. Everything else is wishful thinking.
But even this is too much, in the light of a non-uniqueness result I have found in
arXiv:0901.3262 and
arXiv:0903.4657 MWI in it's current form
simply becomes invalid, with or without Born rule, because it does not have an additional structure which is necessary to fix the preferred basis: The papers prove that different choices are possible, and lead to different physics. The Copenhagen intepretation solves this problem with its association of the operators p, q with classical experimental arrangements, but this solution is not available in the Everett interpretation.
Thus, to make MWI a (viable) intepretation, you not only have to derive the Born rule, but
also have to add some new structure to fix the canonical preferred basis. After this is done,
we can start to reevaluate the denial-argument, which will be, with high probability, invalid
because the new structure will not be part of PWI.
There is a lot more to criticize in MWI, in particular its unprofessional vagueness, but it makes no sense to beat an already dead theory.
In hope for an interesting discussion, sincerely yours,
Ilja.
Ilja, thanks for the comments.
ReplyDeleteYou wrote "First, the denial-argument has never been even proposed for physical collapse interpretations, and cannot, because they have modified the Schrödinger equation."
For the continuous collapse models, it is known as the problem of tails. These models have "collapse" that leaves a lump of wavefunction in a random area, but with very small nonzero 'tails' all over configuration space.
If we can say that small amplitudes are associated with small probabilities, as in the Born Rule, then the tails are not a problem - but in that case we can just use the regular MWI. If, however - as opponents of the MWI allege - probability is independent of amplitude, then these continuous collapse models would be a sort of MWI, with most worlds in the tails, and would be stuck with the wrong probabilities like the standard MWI.
You wrote "If the denial-argument would be valid, it would not prevent the PWI from working, it would only define a simplicity argument in favour of MWI."
That is again false in the case that the Born Rule would not follow from the MWI. With both the wavefunction and the hidden variables being real, _almost all_ observers _would_ be implemented by the wavefunction - _not_ the hidden variables the PWI wants to add - so, if the wavefunction gives the wrong probabilities, then so must the PWI.
There is really only one nontrivial counterargument that someone could try to be make to the charge that the PWI "is the MWI in denial". That one invokes the static wavefunction of the Wheller-DeWitt equation of quantum gravity. But I don't like that on Occam's razor grounds. Other than that, the PWI really is dead. Wallace is doing a service in making that fact better known.
Now, the standard MWI may _also_ fail, but in that case the PWI can _not_ come to the rescue. It would have to be something else.
I will evetually discuss all this in more detail when I explain the computationalist approach in this blog. My MCI paper, though being revised, also explains it (perhaps not yet clearly enough).
http://arxiv.org/abs/0709.0544
I wrote "If the Born Rule does follow from the MWI, then the case for the MWI is made beyond a reasonable doubt."
Emphasis on "reasonable" ;) Of course there will always be doubters (just look at how many still doubt Darwin) but _my firm prediction_ is that _if_ the Born Rule is truly derived - and I must also say, _if_ religious objections to the MWI are not a big factor - then the vast majority of people would come to accept the MWI.
Now, Ilja, there are actually a number of things that we do agree on.
Yes, there must be a preferred basis, although the equivalent must be true in any mathematical model (for computationalism to work), so it's not unique to QM.
We agree (I take it) that the attempts by Wallace and Zurek to derive the Born Rule in the MWI fail. Perhaps you will enjoy reading my attacks on them :) As you know, I have my own attempts, that I think may be better.
We agree also that the standard MWI is too vague, but I would say the same about _any_ approach that does not explicitly deal with modelling (and enumerating) observers. The MCI attempts to make it precise; decoherence plays an important emergent role, but no fundamental role.
Regards,
Jack
Hi Jack
ReplyDeleteYou wrote "That is again false in the case that the Born Rule
would not follow from the MWI. With both the wavefunction and the
hidden variables being real, _almost all_ observers _would_ be
implemented by the wavefunction
Sorry, but PWI postulates that our configuration is
described by the "hidden variables", and not by the wave function.
Whatever happens to "exist" inside the wave function is completely
irrelevant, and the number of universes which "exists" in the
wave function is much less relevant than the already completely
irrelevant number of microbes in other galaxies.
The only point of the "denial"-argument is a simplicity
argument: Assumed everything works fine in many worlds, there would
be no good reason to introduce an additional entity - the configuration
q(t) - into the theory. But if something fails in MWI, this certainly
doesn't work.
And with my non-uniqueness argument (0901.3262, 0903.4657v2)
the denial argument is dead anyway. Because to save MWI one has to
introduce additional structure, with sufficient physical importance,
to remove the non-uniqueness, and after this the denial-argument,
which works only if all MWI elements of reality are also PW elements
of reality, no longer works.
You write "Now, the standard MWI may _also_ fail, but in that case
the PWI can _not_ come to the rescue. It would have to be something
else."
Sorry, but a working MWI which is really simpler in some aspect than PWI would be an argument against PWI, but it would not be based on a problem of PWI, but on the advantages of MWI. Certainly this completely disappears if MWI somehow fails. Which is probable, because it is, at the current moment, not a valid proposal, given first the problem with probability (recognized) and second my non-uniqueness problem (not yet recognized, AFAIU).
You wrote "If the Born Rule does follow from the MWI, then the case for the MWI is made beyond a reasonable doubt." Emphasis
on "reasonable" ;) Of course there will always be doubters (just look
at how many still doubt Darwin) but _my firm prediction_ is that _if_
the Born Rule is truly derived ... then the vast majority of
people would come to accept the MWI."
I certainly don't care about what the vast majority accepts (else, I would adopt some religion) but about rational arguments. Ockham's razor in form of the denial-argument is a rational argument. But there are lot's of other things I don't consider to be sound in MWI. Valentini's anti-denial paper describes some of them: The simple picture with "localized wave-packets" seems unreasonable. MWI has to solve my non-uniqueness problem. There is indirect evidence: PWI has nice mathematics, MWI is only philosophical speculation, with the only math involved being that of decoherence, but if this nice part of MWI survives my non-uniqueness argument remains to be seen.
You write: "Now, Ilja, there are actually a number of things that we do agree on. Yes, there must be a preferred basis, although the equivalent must be true
in any mathematical model (for computationalism to work), so it's not
unique to QM."
This sounds like you have not understood the point of my non-uniqueness argument: It is not that we need a preferred basis. It is that the preferred basis cannot be derived, by decoherence, as proposed by Wallace, Zurek and co., but that it has to be postulated. Or some other additional physical structure has to be postulated.
It is this additional structure, to be postulated by a new version of MWI, which destroys the denial argument immediately if it is not the configuration space itself, because this additional structure is not part of PWI, thus, PWI no longer contains the whole MWI. If one postulates the configuration space, one has to give it a physical meaning.
(There is more I disagree with, but your interface has refused to accept that much.)
Hi, Ilja.
ReplyDeleteYou wrote "Sorry, but PWI postulates that our configuration is described by the "hidden variables", and not by the wave function."
Could you 'postulate' that the human mind resides in the left foot and not in the brain? Sure you could. Of course you would have to be a dualist about consciousness to do so, and also you would have to postulate some far more complex laws of consciousness than mainstream dualists like Chalmers favor. But believing in such a model is obviously foolish, because the brain computes far more than the foot, and such a belief clearly goes against Occam's Razor.
Your postulate about the particles but not the waves giving rise to observers is no different. If you are any sort of computationalist, you must accept that any implementation of the right computation gives rise to consciousness, whether by wave or particle. Or if you are just a dualist, it is simpler to just postulate that the wavefunction is what gives rise to consciousness, and your laws of dualism can give you any probabilities you want (that is Don Page's approach).
You wrote "It is not that we need a preferred basis. It is that the preferred basis cannot be derived, by decoherence, as proposed by Wallace, Zurek and co., but that it has to be postulated. Or some other additional physical structure has to be postulated.
It is this additional structure, to be postulated by a new version of MWI, which destroys the denial argument immediately if it is not the configuration space itself, because this additional structure is not part of PWI, thus, PWI no longer contains the whole MWI. If one postulates the configuration space, one has to give it a physical meaning."
As I told you, the need for a preferred basis or set of physical variables is not unique to QM, but is a feature of any mathematical model including classical mechanics.
The only thing that has to be postulated is that some relatively simple system of physical variables is the actual one to be used by the model. That postulate is needed for any mathematical model, whether it be classical mechanics, QM, or the PWI.
You seem to want to make that assumption for the PWI particles but not for the PWI wavefunction. That's not only a needless complexity; the computations performed by the particles depend on the wavefunction configuration too, so denying a fixed mathematical description for that would seem to ruin any computationalist account of the PWI.
Regards,
Jack
ReplyDeleteYou wrote: Could you 'postulate' that the human mind resides in the left foot
and not in the brain? Sure you could. ... foolish, because the brain computes
far more than the foot, ... Your postulate about the particles but not the
waves giving rise to observers is no different.
It is. The computations possible in a single configuration (even if we forbid
it to use quantum enhancement) is sufficient to explain my mental abilities. If the
number of computations done by my foot would be sufficient in the same sense, your strawman
would be indeed comparable. But this is (at least I think so) not the case. The number
of computations done elsewhere is irrelevant.
You wrote: If you are any sort of computationalist, you must accept that any
implementation of the right computation gives rise to consciousness, whether
by wave or particle.
I have no greater problem to accept that some "computations"
made by wave functions can give some rise to some sort of consciousness (ignoring
for the sake of the argument all the MWI problems) than to accept that flies have
consciousness. It does not follow that I have to accept that I'm a fly, even if there
are much more flies than humans. So, whatever the number of ghosts living and computing
in the wave function, I don't have to accept that I'm such a ghost. Ockham's razor works
only if (1) these ghosts really exist unavoidably if PWI is correct (2) they remain to
exist if we cut away the configuration and (3) their observations are indistinguishable
from our observations. But (3) holds only in some dreams of some many worlders, and if
if (3) fails, PWI is not damaged in any way.
You wrote: "As I told you, the need for a preferred basis or set of
physical variables is not unique to QM, but is a feature of any mathematical
model including classical mechanics. You seem to want to make that assumption
for the PWI particles but not for the PWI wavefunction."
No. I ask for some structure which solves the non-uniqueness
problem I have defined. What is not unique in this problem is the choice of
the canonical observables p and q. This has nothing to do with your computationalism.
...the computations performed by the particles depend on the wavefunction
configuration too, so denying a fixed mathematical description for that would
seem to ruin any computationalist account of the PWI.
First, I do not deny a fixed mathematical description for the wave function,
instead, fixing a preferred q fixes also a representation psi(q) for the wave function.
Then, I certainly don't care about your computationalist approach. As I have already
explained, I don't think the numbers of flies or alien civilizations even in our world
has any relevance for fundamental physics. Ghosts possibly living in the wave function
are even less relevant.
By the way, while I consider the wave function as real in the sense that it contains some information about real objects, I do not think about it as existing itself, as some wave on some space. Imagine a computer which computes, in each time step, for a given state of the universe, what will be the next state. We can modelize this computer by some function on the space of all states. This function contains all the relevant information about this computer, the computer really exists, so that in this sense this "wave function" is real. But where are, in this picture, all the "empty wave packets" of this "wave function"? They are only hypothetical considerations.
Ilja,
ReplyDeleteYou wrote "If the number of computations done by my foot would be sufficient in the same sense, your strawman would be indeed comparable."
So you do admit that computation is what matters, it seems. The point about the foot is that if you use dualism, which you need to if you want to single out the particles as special, you might as well admit it and go all the way.
The number of computations is not all that matters, it is the type of computations that matter. The number of computations does matter when they are all of the right types since measure (and thus effective probability) is proportional to the number.
You wrote "So, whatever the number of ghosts living and computing in the wave function, I don't have to accept that I'm such a ghost. Ockham's razor works only if (1) these ghosts really exist unavoidably if PWI is correct (2) they remain to exist if we cut away the configuration and (3) their observations are indistinguishable from our observations. But (3) holds only in some dreams of some many worlders, and if if (3) fails, PWI is not damaged in any way."
There are no ghosts. There are things that compute the right things, like the wavefunction for your brain, and things that don't, like your foot.
Your (1), (2), and (3) obviously all hold. As one obvious point in favor of (3), you can not deny that the wavefunction contains structures corresponding to all of the speech and writing (including electronic records) ever produced by humans. Fly-like consciousness could not have produced those. It is clear evidence of human consciousness. To deny that the wavefunction performs the right computations is just ridiculous.
You wrote "I ask for some structure which solves the non-uniqueness problem I have defined. What is not unique in this problem is the choice of the canonical observables p and q. This has nothing to do with your computationalism."
If it has nothing to do with brain computations, then it has no relevance to observation, and thus no relevance to physics.
You wrote "Imagine a computer which computes, in each time step, for a given state of the universe, what will be the next state. ...
But where are, in this picture, all the "empty wave packets" of this "wave function"?"
The same place as the supposed "particle positions" - patterns in your Matrix-computer's memory banks.
Jack
You wrote "So you do admit that computation is what matters, it seems."
ReplyDeleteNo, only for the sake of the argument. My existence is, of course, a proof that there exists something which is able to make a certain type of nontrivial computations. But that's all.
You answer my question about the place of the "empty wave packets" in my computer picture: "The same place as the supposed "particle positions" - patterns in your Matrix-computer's memory banks."
The point is that there may be no such patterns in memory banks, except for the actual computation of the next stage for the actual positions. Computers may have algorithms different from looking for the
result in a large table for all input values.
You write "Your (1), (2), and (3) obviously all hold." I certainly disagree. In my computer picture, which is not obviously wrong, no empty wave packets exist, except mathematically, similar to the existence of
results of computations for input values which which are different from the actual value.
About my non-uniqueness construction you write: "If it has nothing to do with brain computations, then it has no relevance to observation, and thus no relevance to physics."
It has nothing to do with your computationalistic ideology, which is quite different from unobservable by computers.
The differences are observable, for human brains as well as computers, so your arguments fails (beyond the point that it is positivistic ideology).
Ilja:
ReplyDeleteYou wrote "My existence is, of course, a proof that there exists something which is able to make a certain type of nontrivial computations. But that's all."
If your existance is proof of computation, then computation matters. If you are suggesting dualism, so that something else matters too, then my points about Occam's razor and going whole hog with dualism apply.
You wrote "The point is that there may be no such patterns in memory banks, except for the actual computation of the next stage for the actual positions. Computers may have algorithms different from looking for the result in a large table for all input values."
Interference effects show that the wavefunction must be retained to correctly compute the time dependent hidden variable trajectories. If there is a simulated QM universe, it will have to keep track of the wavefunction. That has nothing to do with using a lookup table, and much more resembles using a finite difference method for coupled differential equations.
Of course if the computer uses an approximate alogorithm it may discard info about the wavefunction that has small effect on the trajectories. In that case, in principle, experiments could be done to detect the information loss; it would not be the standard PWI.
Of course there is no reason to take seriously such a 'computer simulated universe' scenario.
You wrote "It has nothing to do with your computationalistic ideology, which is quite different fom unobservable by computers.
The differences are observable, for human brains as well as computers, so your arguments fails (beyond the point that it is positivistic ideology)."
You are simply 100% wrong in the above paragraph, by definition. If the differences are observable by computers, then it has everything to do with the measure distribution of computations, which is what I talk about. In reality, you non-uniqueness contruction has no observable effects as long as there is a unique actual basis, which I take to be the position basis. My 'ideology' is nothing but standard computationalism.
As for positivism, if you mean that I deny the existance of a 'real world' or that we might guess its nature, that is obviously a false charge. If something (like hidden variables) has no effect on what we observe, then Occam's Razor is our only guide.
Jack
I think what Ilja is trying to say is that the wavefunction doesn't really create other conscious beings because it is not the same as particles in PWI.
ReplyDeleteKind of like how a equation(in this anology WF) isn't REAL, even if it describes something that is real (particles).
Peter,
ReplyDeleteIf it has real effects, it's real. The WF in the PWI is real. Any other view is doublethink at best, and makes no sense at all.
Jack
Jack, what is your opinion on branching vs divergence in terms of worlds?
ReplyDeleteIt has been argued by Simon Saunders in Many Worlds?(2010) that divergence is more elegant than branching.
Alastair Wilson has written several papers on this the last years, most extensive in 2011 and 2012.
In that paper Saunders seems to be trying to make a distinction between 'branches' and 'worlds' because - IMO - he is very slowly and very haltingly groping towards trying to understand that 'observers' are a different thing altogether, which of course is a fact he would know very well if he read just a little of my blog here :)
DeleteSaunders' specific proposal - observers as consistent histories, basically - is ill-defined nonsense.
Remember, there's no precise definition of "world", and there's no such thing as the "probability of a world" (contrary to what Saunders thinks). Effective probabilities relate to observers, not to worlds. As Albert's fatness measure illustrates, there's no a priori reason to think that "two observers in the same world" (not really two, and not really one world, but you should know what I mean) couldn't have different effective probabilities.
There are four basic types of transitions we can talk about: branching, diverging, merging, and replacement. Actually, by a suitable definition, 'replacement' can cover everything. And I prefer that definition as it eliminates confusion about whether it matters whether something (in particular some person) is "the same person" at a later time: It CAN NOT ever matter for any purpose; as I've explained many times, only the measure distribution matters.
But by using causality-based definitions we can define:
branching: a given structure is the cause of multiple structures (of that kind) at a later time
divergence: each single structure is the cause of a single structure at a later time
merging: multiple structures are the cause of the same structure at a later time
replacement: later structures are not caused by the earlier structures of that kind, but by other dynamical processes
Given these definitions, for "worlds" (e.g. wavepackets) I'd say that branching is the main dynamic. There would be - in some state basis - diverging as well, such as |a>(|b> + |c>) --> |a>|b> + |a>|c>. But many processes - such as a photon hitting a half silvered mirror - are certainly best though of as branching of the wave packets. There's certainly some merging as well; at thermodynamic equilibrium it's of course balanced between diverging and merging.
For observers, such causes can be defined in terms of extended chains of formal state relationships. If my computationalist speculations say with a noise-based cutoff hold then it seems to be a mix of all four, with branching and merging often sort of combined so that A and B are both causes of both C and D, I think. You get spreading out (diverging), from different staring areas, and overlapping of some of the consequences (merging: both branch to the same place). You also get chains that can't be continued any more, and new ones that work (replacement) - depending on the noise, for example.
The bottom line is that it doesn't matter. Once observers exist, with some distribution, that's what determines anything with observable or moral consequences.
Saunders is concerned with questions of the type: What does it mean for Alice to say "I have a 50% chance to see spin up after the experiment"? If there's only branching that statement doesn't make sense, while if there's only divergence, it's true in the standard classical sense of her ignorance of the facts.
So what DOES it mean? Actually, not much, without precise definitions of "I" and "chance".
A much more well-defined statement would be "After the experiment, the effective probability (defined as a measure-of-consciousness ratio) for Alices (defined as certain consequences of her current state, without any implication that they are or are not "the same person" as she currently is, which can never matter) to see spin up is 50%."