Many-Worlds Interpretation Issue

[Farsight]

I can not remember that David Deutsch used this experiment as a "proof of MWI".

Sorry to suggest that Hans, no he didn't. It was setAI being bullish.

 

[CarlB]

MWI needs Dirac's over sited old claim that particles can only interfere with them self and do never interfere with other ones.

It was 26 years ago that I was taught QM and my memory of the learning process is fuzzy, but as long ago as I can remember I have always believed that identical particles do interfere with each other. So I'm kind of surprised that this would be up for debate. Was I jumping to conclusions unwarranted in 1979 or something? I guess that I thought it was obvious that this would happen because of the fact that one had to symmetrize or antisymmetrize multi particle wave functions, IF the multiple particles described were identical.

This means that the number of distinguishable fields that the vacuum has to support, at each point in space time, reduces from 10⁸⁰ (The number of particles in the universe) to a more physical 17 (The number of different elementary particles) and unitarity is caused by something different than by distinguishable wavefunctions.

By the way, there is a subtle argument here on the nature of particles, and the way that we should try to unify them.

It is very obvious that two particles that differ in their spin cannot interfere with each other and therefore must require two different sorts of wave functions. But it's not so obvious why it is that nature created more than one "spin-1/2" particle.

In other words, why is it that electrons don't interfere with neutrinos?

On the other hand, spin up electrons do NOT interfere with spin down electrons, so it would seem that nature treats different particle types in a way that is very analogous to that of spin. Which is why I work on classifying preons with Clifford algebra.

Getting back to your observation, I also think that it is great evidence that of the wave particle duality, the wave part is the more important. Of course waves are indistinguishable. What is unusual about quantum mechanics is that upon measurement, the waves collapse down to particles.

But if you remove the measurement from quantum mechanics, then one can rewrite multiparticle wave functions into a pure wave format. It is only in the measurement that we have to do all the complicated manipulation.

This is an argument I remember from a very long time ago. Let $$\psi(x_1,x_2,t)$$ be a two particle wave function, for two identical scalar particles (spin-0 bosons). By symmetry, we have that
$$\psi(x_1,x_2,t) = \psi(x_2,x_1,t)$$. Schroedinger's wave equation for two non interacting particles (in one dimensions) is something like:

$$i\hbar \partial_t\; \psi(x_1,x_2,t) = \partial_{x1}\psi(x_1,x_2,t) + \partial_{x2}\psi(x_1,x_2,t).$$

Define
$$\psi(x,t) = \int \psi(x,x_2,t)\; d_{x2}$$

Then the above is a solution of Schroedinger's wave equation for one particle. Thus we can always convert a two particle wave function into a one particle wave function.

Similarly it is possible to go the opposite direction, but in doing so, there is more than one possible choice of solution. That is, for anyone particle wave equation there is a two particle wave function that maps to that one particle wave function, but that two particle wave function is not unique.

Now the only way you can distinguish between a one particle wave function and a two particle wave function is by counting particles, which is a measurement. This is what I mean when I say that if you eliminate measurement from quantum mechanics, the need for phase space also goes away. In short, the mystery of QM is in the measurement, without that, it's only classical wave equations.

And as far as classical wave equations go, there is plenty of room in them for all the complication seen in the quantum theory of measurement. In other words, the argument for MWI in terms of counting degrees of freedom only applies on the particle side of the interpretation.

Carl

 

[Hans de Vries]

It was 26 years ago that I was taught QM and my memory of the learning process is fuzzy, but as long ago as I can remember I have always believed that identical particles do interfere with each other. So I'm kind of surprised that this would be up for debate.

Well, You're certainly not alone here. It surprised me as well. I suppose
unitarity may be the main argument behind distinguishable wave functions.

This is an argument I remember from a very long time ago. Let $$\psi(x_1,x_2,t)$$ be a two particle wave function, for two identical scalar particles (spin-0 bosons). By symmetry, we have that
$$\psi(x_1,x_2,t) = \psi(x_2,x_1,t)$$. Schroedinger's wave equation for two non interacting particles (in one dimensions) is something like:

$$i\hbar \partial_t\; \psi(x_1,x_2,t) = \partial_{x1}\psi(x_1,x_2,t) + \partial_{x2}\psi(x_1,x_2,t).$$

Define
$$\psi(x,t) = \int \psi(x,x_2,t)\; d_{x2}$$

Then the above is a solution of Schroedinger's wave equation for one particle. Thus we can always convert a two particle wave function into a one particle wave function.

Interesting, Thanks for bringing it up.

And as far as classical wave equations go, there is plenty of room in them for all the complication seen in the quantum theory of measurement. In other words, the argument for MWI in terms of counting degrees of freedom only applies on the particle side of the interpretation.

Carl

Yes, or in other words. The mystery of unitarity.Experimental two photon interference and EPR tests

This 2-photon interference experiment is an extremely interesting one:

If two different (but equally polarized) photons meet at a beam splitter
then their wave functions combine (interfere) and both photons are
always detected at the same detector even though the wavefunction
is split and goes both ways.There's a very interesting link to EPR tests here. It is always assumed that
the choice of going left or right in a beam splitter is random, that is, it may
have an X% chance of coming out left and a 100-X% chance of coming out
right.

Even the Bell-type hidden variables maintain this randomness (That's
why they fail in the first place to predict the measured correlations)

With this experiment it's for the first time that I see a sign of non-random
behavior (correlation) for two particles which are not "entangled" !

I've always had a suspicion that there might be something in the wave-
function which predetermines somehow at which output the photon
will be detected, and this experiment reinforces that: The combined
wavefunction after interference might have a property which pre-
determines at which output both photons are detected...

It is not that hard to find candidates for such a property. Two apparently
equal photons may have completely different V,A potentials. One always
has to define a gauge, typically the transverse gauge.

However. If you look at the radiation pattern of a charge moving up and
down then its easy to see that the A field propagated is always exactly
vertically and generally not transversal to the direction of motion. That
is, only the horizontally propagated radiation is transversal gauge like
(V=0, A= transversal)

The experiment has several more interesting aspects. It's one of the
most interesting ones I've seen in a long time.

http://arxiv.org/abs/quant-ph/0603048Regards, Hans

 

[koantum]

What about the countless interactions among particles/systems that don't involve "measurements"?

There are no interactions that don't involve measurements. Our description of the quantum world is entirely in terms of correlations between measurement outcomes. If two systems interact, it means that their probability distributions over the possible outcomes of possible measurements get correlated.

 

[koantum]

...in a universe with one particle, there are infinitely many linearly independent observables...

A universe with one particle is no universe at all. All positions, all momenta, are relatively defined. In a universe with only one particle there are neither positions nor momenta. And so there is no space. And so there is no universe. Besides, it is time that we learn to distinguish between

• operators, which are useful in characterizing probability distributions over measurement outcomes, by allowing us to calculate their mean values, standard deviations, and higher moments,
• and observables, which are things that can be measured, and that have values only if, when, and to the extent that they are measured.

So you may have infinitely many operators in your disembodied mind, but you won't have observables in a world without things by which they can be measured.

 

[koantum]

MWI is the rejection of the collapse postulate.

MWI is what you get if you reject the symptom (the collapse postulate) without rejecting the underlying disease, which is the belief that quantum states or wave functions represent evolving instantaneous states of affairs. The time dependence of a quantum state is the dependence of an algorithm on the time of the measurement to the possible outcomes of which it assigns probabilities. (Sorry for this convoluted sentence, but the alternative to many worlds is many words. ) A quantum system has its measured properties at the time, and to the extent that, they are measured.

We ought to have the honesty to admit that any statement about a quantum system between measurements is "not even wrong" (Pauli's famous phrase), inasmuch as such a statement is by definition neither verifiable nor falsifiable experimentally. Such a statement is unscientific by Popper's definition, which requires of a scientific statement that it be at least falsifiable. So the story according to which quantum states evolve (or appear to evolve) unitarily between measurements should be seen for what it is - a story. And it is this story which implies that quantum states "collapse'' (or appear to collapse) at the time of a measurement.

That said, the meaning word "particle" as used in quantum mechanics only vaguely resembles the meaning of the same word as used in classical mechanics.

No resemblence whatsover.

Neither the classical notion of a particle nor the classical notion of a wave is adequate to describe light.

Absolutely right.

Instead you need some new quantum mechanical notion capable of resembling (but not being) both!

And what might that be, given that all we have is correlations between measurement outcomes?

if you take the exact same wavefunction but write it in the momentum representation, it now looks like a superposition of things that look like plane waves.

And if you take the wave function of two particles, it looks like one thing spread out over a 6 dimensional space. And so on ad absurdum.

 

[vanesch]

I also have a question regarding MWI (although I'm not sure if its actually a sensible question!). If I understand the interpretation correctly, then every time a system exists in a superposition of eigenstates with respect to a class of commuting observables then the universe splits into many copies such that when a measurement is performed only one eigenvalue is recovered in each universe?

However, one could equivalently regard the original superposition of states as being a single eigenstate of another set of observables (which don't commute with the first). How does the interpretation handle this fact?

I guess I can repeat that a million times and this question will come still back

The simple observation is that "the universe doesn't split".

"Splitting universes" are not objective properties, they are - as you seem to understand - observer-dependent. In other words, the "different universes" are constructs that depend on how you write down the wavefunction from a specific observer point of view ; in other words, what are the "different states of experience" of the individual observer you're considering, and how they entangle with the rest of the universe. Now, there's some hope that these "different states of experience" emerge naturally from a process of decoherence, but nevertheless, they will be different for different observers ; so the "split" in "different universes" will be different for different observers.
"Different universes" is a colloquially used term which is not precisely defined, and is certainly not an objective property. It is unfortunate that many people think about MWI that way. It would be better to talk about "different states of perception" instead of "different universes", then it would be clear that it is an observer-dependent concept.

Now, these "different worlds" DO obtain some independent existence once all considered observers have interacted amongst themselves (exchanged, say, information, or just thermal radiation, or some air molecules), because then they will have entangled their states in such a way that the split according to observer 1 will be the SAME split as the one according to observer 2 etc... So (a la Rovelli) if we say that what is "objective" is what observers interacting with each other agree upon, these observers will agree upon their splits, and hence these splits become "objective" (but still limited to a group of interacting observers ; and maybe not for another group of interacting observers on Andromeda), and we can call them, "worlds". This grouping together of different observer states, which then remain robust through time evolution and remain together, is the entire program of environmental decoherence. I have to say that I don't know up to what point this is established, and up to what point this is what one hopes to establish: I'm still in the process of understanding the recent work done in the domain, because one has to be careful of over-enthousiastic claims.

That solves then the "preferred basis problem" that you touch upon: they are not a free choice, but they are those observables which have robust eigenspaces throughout time evolution (and which are supposed to correspond to "states of experience" for observers). In other words, they are defined by the interaction hamiltonian between systems and their environment.
Now, if this doesn't work out as hoped for, there's always the uglier but surer way of doing things: by POSTULATING a basis of "states of experience", but it would be nice if this simply *emerged* from the interaction with the environment, as decoherence seems to indicate.

 

[vanesch]

the exponentiating field of quantum computing physically demonstrates every day that the MWI is the only tenable interpretation [that we currently have] because computations can be performed that use far more resources than the number of particles [or 'actions'] in this universe- all the possible states CANNOT be in one universe- there aren't enough observables here to account for the computation

You really should stop saying that. In as much as I'm rather pro-MWI as an interpretation of the quantum formalism, all other empirically equivalent formulations are, well, empirically equivalent, and hence there's no lab experiment that proves MWI right.
Hell, even an interference experiment with humans wouldn't prove MWI! You can still consider Copenhagen, but consider that humans are still microscopic, and that the quantum/classical transition only occurs on the level and size, say, of a galaxy.

 

[CarlB]

MWI is what you get if you reject the symptom (the collapse postulate) without rejecting the underlying disease, which is the belief that quantum states or wave functions represent evolving instantaneous states of affairs. The time dependence of a quantum state is the dependence of an algorithm on the time of the measurement to the possible outcomes of which it assigns probabilities. (Sorry for this convoluted sentence, but the alternative to many worlds is many words. ) A quantum system has its measured properties at the time, and to the extent that, they are measured.

Well said. I say "so too!"

Carl

By the way, am I the only one who can't set up an avatar? If it's because of the incident with the naked picture, hey, I'm sorry, it won't happen again.

 

[vanesch]

Well said. I say "so too!"

The problem I have with all these claims about quantum theory being just an algorithm calculating probabilities, is the following. I'm of course not disputing that quantum theory is an algorithm for calculating probabilities of observation, no more than that classical physics is an algorithm for calculating outcomes of measurements. This is the minimum requirement for all scientific theories: they should *at least* be an algorithm to allow you to calculate something that you can compare to experiment.
But the problem with the claim that quantum theory is "just an algorithm" is: what do you think we learn from such a statement ?

I could just as well say that "things happen" in nature, and well, scientific theories are observations of apparent regularities of these things happening, so they are some kind of resume of a catalogue of previously observed regularities and it would be erroneous to try to find any deeper meaning to these observed regularities. So is astrology, btw.

If quantum theory (or for that matter, any scientific theory) is just an algorithm for calculating probabilities (say, regularities) of outcomes, then there's no deeper principle which tells us what form such an algorithm should take on, because the very claim of it being an algorithm which doesn't describe anything underneath means that it can take any form.
As such, there's no reason, nor for the specific form of the algorithm (why this stuff with Hilbert spaces and so on, why a unitary transformation, why Lorentz invariance etc...). All these properties can only leave us wondering, because an algorithm of regularities in a big catalogue of events shouldn't a priori obey any principle.

The power of a good scientific theory has always been that it doesn't ONLY provide an algorithm to calculate outcomes of experiment, but that the algorithm is UNDERSTOOD as following from an underlying ontological description based upon a few fundamental principles. Claiming that scientific theories are now reduced to pure algorithms *without meaning* kills off any explanatory power, or for that matter, any required structure what so ever. So there's no leg to stand on anymore to require whatever principle (like covariance, or superposition, or constancy of the speed of light or whatever), because all these concepts are just applied to "variables in an algorithm with no genuine meaning". So personally, I don't buy the "quantum theory is JUST an algorithm to calculate probabilities of outcomes". Of course it is an algorithm, TOO. But saying that one should think of it as ONLY that is giving up on the essential part of science, because we've switched from investigating the nature of nature, to "stamp collecting".

 

[vanesch]

quantum computations don't even work unless pure superposition is maintained until the output-

Yes, but that would simply mean that the Heisenberg cut has to be applied after you reach the "output". As interpretations of the Copenhagen type don't tell you WHERE and WHAT exactly is a measurement (where the collapse is supposed to occur), you can put it anywhere that fits observation. von Neumann even said that you can put it anywhere *as long as it doesn't make any difference*.

So, again, no amount of experimental result can prove MWI right or wrong over Copenhagen, as Copenhagen can always put the cut AFTER the point where the last visible effect of superposition is observed.

The only thing you could possibly do is the opposite: prove MWI FALSE, by showing an observation where there OUGHT TO BE quantum interference, and where it doesn't happen (after having carefully taken into account all potential sources of decoherence, which is not easy). Copenhagen can accommodate both observations: if no interference is observed, it can tell you that that's normal, because the Heisenberg cut was applied before the interference was supposed to occur ; and if interference is observed, it can tell you that that's normal, because the Heisenberg cut comes in only later. So there's no interference experiment with positive or negative result that is ever going to falsify Copenhagen. However, a negative outcome (where a positive is expected) clearly falsifies MWI.

 

[CarlB]

If quantum theory (or for that matter, any scientific theory) is just an algorithm for calculating probabilities (say, regularities) of outcomes, then there's no deeper principle which tells us what form such an algorithm should take on, because the very claim of it being an algorithm which doesn't describe anything underneath means that it can take any form.

Yes, I agree with you completely here. I think that quantum mechanics points towards the thing that is underneath, but I do not think that quantum mechanics itself is very close to the thing underneath. Quantum mechanics is as good as we've got at this time, but that doesn't mean that it is an accurate description of reality.

As such, there's no reason, nor for the specific form of the algorithm (why this stuff with Hilbert spaces and so on, why a unitary transformation, why Lorentz invariance etc...). All these properties can only leave us wondering, because an algorithm of regularities in a big catalogue of events shouldn't a priori obey any principle.

One can only make one step at a time. The current theory is quantum mechanics. If one tries to interpret QM ontologically, one ends up with inanities like MWI. Instead, what one must do is to walk the cat back one step at a time.

From the point of view of Einstein, QM should all go back to principles of geometry. Thus the next step for understanding QM is to write it in geometric form.

But QM already comes equipped with a geometry, namely the Dirac matrices. Note that I say the Dirac matrices, rather than the Dirac spinors. The reason for distinguishing these is that the Dirac matrices have an immediate geometric interpretation in the Geometric Algebra (Clifford algebra) of David Hestenes. See:
http://modelingnts.la.asu.edu/

So to understand the states in QM, what one must do is to write them in terms of the Dirac matrices. Hestenes wrote the spinors in terms of Dirac matrices (well, Clifford algebra, which amounts to the same thing), and gave a geometric explanation for the imaginary numbers of QM:
http://modelingnts.la.asu.edu/html/GAinQM.html

But there is a much simpler way of attaining the same program. If one wishes to geometrize the states, they are much more easily treated as density matrices then state vectors. For example, let $$S_z$$ be a spin operator for the Dirac algebra in the z direction, and let $$S_e$$ be the charge operator for the Dirac algebra so that electron states satisfy $$S_e|e\rangle = +|e\rangle$$ and positron states satisfy $$S_e|\bar{e}\rangle = -|\bar{e}\rangle$$. These operators are easy to write in geometric form given any particular representation of the Dirac algebra.

Given these two (commuting) operators, it is possible to write the density matrices for the states with the four possible cases of spin and charge as follows:
$$|\pm z\pm e\rangle\langle \pm z\pm e| = \rho_{\pm z\pm e} = (1 \pm S_z)(1 \pm S_e)/4$$

That is, the above is an eigenvector of $$S_z$$ with eigenvalue +-1 according to the S_z +-1, and an eigenvector of $$S_e$$ with eigenvalue +-1 according to the S_e +-1. The "4" is there for normalization.

That's all there is to the density matrix versions of the states (other than the dependence on space and time, which are naturally geometric as well). If you want to read off the spinor state, you can simply take any non zero column out of the matrix $$\rho_{\pm z\pm e}$$. But in replacing the matrix with one of its columns, you must make a choice, and that choice amounts to a choice of a sort of gauge. That is, in addition to the U(1) gauge, your choice of a column also amounts to a geometric gauge (that is hidden in the usual spinor version of QM).

Bt the thing to note here is that the density matrix forms are naturally independent of choice of U(1) gauge. To make them also independent of the non Abelian gauges requires that one go yet farther beyond the scope of this thread. But my point here is that understanding quantum mechanics ontologically is not impossible, it's just very very difficult, and the first steps are not in the direction that spinors would point you. I'm busily typing this up into a paper. Some more stuff along this direction is at the website I started a few weeks ago http:www.DensityMatrix.com .

Carl

 

[setAI]

the exponentiating field of quantum computing physically demonstrates every day that the MWI is the only tenable interpretation [that we currently have] because computations can be performed that use far more resources than the number of particles [or 'actions'] in this universe- all the possible states CANNOT be in one universe- there aren't enough observables here to account for the computation

You really should stop saying that.

but I DIDN'T say it: "there are indeed other, equally real, versions of you in other universes, who chose differently and are now enduring the consequences. Why do I believe this? Mainly because I believe quantum mechanics... Furthermore, the universes affect each other. Though the effects are minute, they are detectable in carefully designed experiments... When a quantum computer solves a problem by dividing it into more sub-problems than there are atoms in the universe, and then solving each sub-problem, it will PROVE to us that those sub-problems were solved somewhere - but not in our universe, for there isn't enough room here. What more do you need to persuade you that other universes exist? "

"The quantum theory of parallel universes is not the problem, it is the solution. It is not some troublesome, optional interpretation emerging from arcane theoretical considerations. It is the explanation—the only one that is tenable—of a remarkable and counter-intuitive reality."

-David Deutsch


so far the only professional scientist that has debated Deutsch's argument [that I have found]- Seth Lloyd- has subsequently conceded and now accepts the MWI as at least trivially true- so if you think the idea that quantum computers physically demonstrate the MWI isn't right then someone should inform the leaders in the field of quantum mechanics that they are wrong and to stop publishing that they do!

-I am just a messenger (^__-)

 

[ttn]

so far the only professional scientist that has debated Deutsch's argument [that I have found]- Seth Lloyd- has subsequently conceded and now accepts the MWI as at least trivially true- so if you think the idea that quantum computers physically demonstrate the MWI isn't right then someone should inform the leaders in the field of quantum mechanics that they are wrong and to stop publishing that they do!

-I am just a messenger (^__-)

This is just the kind of bogus argument that advocates of crazy nonsense always use. Can't you just hear the bible-thumping advocates of "intelligent design" saying "so far hardly any professional biologists have been able to refute me"! The fact is, some ideas are so stupid that to positively engage with them (by debating their advocates or whatever) is at best a waste of time, and at worst an irrational sanction. If nobody's willing to publicly debate David Deutsch, maybe it's because his ideas (as vanesch has repeatedly pointed out, and as is obvious to anyone who understands these issues) are so stupid as to not even deserve to be refuted or debated, not because nobody can find anything wrong with them. Ever think of that?

 

[setAI]

This is just the kind of bogus argument that advocates of crazy nonsense always use. Can't you just hear the bible-thumping advocates of "intelligent design" saying "so far hardly any professional biologists have been able to refute me"! The fact is, some ideas are so stupid that to positively engage with them (by debating their advocates or whatever) is at best a waste of time, and at worst an irrational sanction. If nobody's willing to publicly debate David Deutsch, maybe it's because his ideas (as vanesch has repeatedly pointed out, and as is obvious to anyone who understands these issues) are so stupid as to not even deserve to be refuted or debated, not because nobody can find anything wrong with them. Ever think of that?

of course- except that Deutsche's arguments are backed up by one of the largest empirical efforts in history: the field of quantum computing- and many of the greatest physicists of our age have PUBLICALLY ENDORSED him- such as Gell-Mann/ Rees/ Hawking/ Lloyd/ not to mention that David Deutsch is probably the most respected by his peers and best funded quantum physicist on the planet right now- and a good bet for the recipient of the Nobel http://www.edge.org/3rd_culture/prize05/prize05_index.html

there simply is no exscuse for the bias against his ideas I have seen on this forum- [and ONLY this forum- especially by mentors] when his ideas about the MWI are now nearly universally excepted/corroborated/empiracally repeated by the actual scientists in the field- except I guess for certain isolated regions in the United States [rather like foreign policy it seems]

 

[Hans de Vries]

of course- except that Deutsche's arguments are backed up by one of the largest empirical efforts in history: the field of quantum computing- and many of the greatest physicists of our age have PUBLICALLY ENDORSED him- such as Gell-Mann/ Rees/ Hawking/ Lloyd/ not to mention that David Deutsch is probably the most respected by his peers and best funded quantum physicist on the planet right now- and a good bet for the recipient of the Nobel http://www.edge.org/3rd_culture/prize05/prize05_index.html

there simply is no exscuse for the bias against his ideas I have seen on this forum- [and ONLY this forum- especially by mentors] when his ideas about the MWI are now nearly universally excepted/corroborated/empiracally repeated by the actual scientists in the field- except I guess for certain isolated regions in the United States [rather like foreign policy it seems]

You are mixing things up. MWI and qubits haven't anything to do with
each other. The fact that qubits are fashionable nowadays does not mean
at all that all these people buy his QM interpretation.

I have seen fashions coming and going from fifth generation AI computers,
fuzzy logic systems, neural networks, functional languages, dataflow
computers, lisp systems, prolog computers, 1 bit parallel processor
"thinking machines", et-cetera, et-cetera, all interesting academic
exercises, each developing their own mathematical frame work.

Each of them was going to revolutionize the world. Each one was going to
stay for ever and ever. Each time the academic community mastered the
new fashion, they played with it, wrote papers, played, played more,
until the day it became boring and unfashionable and the next fashion
appeared...


Regards, Hans

 

[0rthodontist]

Neural networks, fuzzy logic, functional languages are all in current use.

 

[setAI]

oh- I fully agree that the MWI is at best an incomplete fashionable idea- but it is by far the best we have right now and according to everything I have seen from Deutsch/ Lloyd/ Gel-Mann / Rees suggests that the MWI is curently the only interpretation of QM that we know about that is tenable- and at the moment I accept their overwhleming evidence that the advent of quantum computers has established the MWI and eliminated Copenhagen/hidden Variable interpretations in the same way that Hubble's discovery of the doppler shift established the Big Bang model and eliminated the Steady State- [although this is the realm of interpretations of a single theory- not a competition between different theories- but with just as many implications to the nature of reality]

and so future progress in interpretting QM must proceed from and include the basic postulates of the MWI picture- just as progress in cosmological models has proceeded from and included the Big Bang

 

[Hans de Vries]

Neural networks, fuzzy logic, functional languages are all in current use.

Qubits will never go away altogether either, most things never will, they
live on with the people who love to use them. However at the end there
are many ways to achieve the same thing. Qubits as a mathematical
framework is not unique either, it's a human invention, not something
which is forced upon us by nature or physics.


Regards, Hans

 

[Hurkyl]

and at the moment I accept their overwhleming evidence that the advent of quantum computers has established the MWI and eliminated Copenhagen

How do you manage to keep saying that without ever addressing the (obvious) objection everyone has been raising?


And I just realized a (fatal?) flaw in your argument based on counting particles in the universe. It is based on the fact that the state-space of a collection of n qubits is (2^n)-dimensional.

But there's a big assumption: that the whole state space is "accessible".

To wit, the state at any intermediate stage of the computation is a deterministic function of the state of the input. It requires exactly as many (classical!) bits to represent any intermediate state of computation as it does to represent the input to the computer. (Of course, certain representations will require more bits than necessary)

In fact, a quick google search turns up this:
http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=694607
which claims that any quantum algorithm that runs in O(s) space can be simulated by a probabilistic classical algorithm that uses no more than O(s) space, or by a deterministic classical algorithm that uses no more than O(s²) space.

 

[Hans de Vries]

oh- I fully agree that the MWI is at best an incomplete fashionable idea- but it is by far the best we have right now and according to everything I have seen from Deutsch/ Lloyd/ Gel-Mann / Rees suggests that the MWI is curently the only interpretation of QM that we know about that is tenable- and at the moment I accept their overwhleming evidence that the advent of quantum computers has established the MWI and eliminated Copenhagen/hidden Variable interpretations in the same way that Hubble's discovery of the doppler shift established the Big Bang model and eliminated the Steady State- [although this is the realm of interpretations of a single theory- not a competition between different theories- but with just as many implications to the nature of reality]

and so future progress in interpretting QM must proceed from and include the basic postulates of the MWI picture- just as progress in cosmological models has proceeded from and included the Big Bang

You, know. I'm all for freedom of religion, the problem is that each religion
always wants to prohibbit all the other ones...

It's bogus to say that quantum computing proves MWI. The examples
shown on the Deutsch video apply just as well to entirely classical
systems based on the superposition of electromagnetic waves!

This means that classical physics would prove MWI Regards, Hans

 

[0rthodontist]

Qubits will never go away altogether either, most things never will, they
live on with the people who love to use them. However at the end there
are many ways to achieve the same thing. Qubits as a mathematical
framework is not unique either, it's a human invention, not something
which is forced upon us by nature or physics.


Regards, Hans

Functional languages, fuzzy logic, and especially neural networks aren't "going away" in any sense of the phrase. They are very popular.

 

[vanesch]

Yes, I agree with you completely here. I think that quantum mechanics points towards the thing that is underneath, but I do not think that quantum mechanics itself is very close to the thing underneath. Quantum mechanics is as good as we've got at this time, but that doesn't mean that it is an accurate description of reality.

Ok, but I always repeated that in order to give an interpretation to *quantum theory* one shouldn't start by saying that it is wrong, and quickly invent a few properties of a non-existing potentially underlying theory that could explain it all. One should stick to the theory that one is trying to interpret, and start by assuming that it is right ; in other words, imagine a toy universe where said theory is to hold strictly.
It is too easy to speculate about the properties an underlying theory (that you still don't have and that is certainly not experimentally tested) to base any interpretation of an actual, working theory on, no ?

So, my claim is that *in a toy universe where quantum theory is strictly true*, it is hard to avoid an MWI kind of ontology. Now, in how much that toy universe corresponds to ours, that's an open question, and this will always remain an open question. But the exercise was not to say how our universe "really is" (as nobody "really knows" and never will), the exercise was to interpret quantum theory.

 

[koantum]

personally, I don't buy the "quantum theory is JUST an algorithm to calculate probabilities of outcomes". Of course it is an algorithm, TOO. But saying that one should think of it as ONLY that is giving up on the essential part of science, because we've switched from investigating the nature of nature, to "stamp collecting".

We had a long discussion about this. You still haven't gotten my point. Of course there is more than the algorithm. How else could there be so much stuff on my website about the ontological implications of the mathematical formalism of the theory? What I object to is the naive transmogrification of an algorithm (which depends on the time of a measurement) into an evolving instantaneous state of affairs. Going beyond probabilities requires a careful analysis of the quantum-mechanical probability assignments.