Will quantum computers ever be possible?

[confusedashell]

Will David Deutsch's famous quantum computers ever be realized?
I personally look at MWI as a fairytale sciencefiction hypothesis, so in my opinion other universes DO NOT exist, but can still quantum computers become a reality in single universe terms?

 

[olgranpappy]

quantum computers already do exist.

Here's a snippet from a news article about using quantum computers to factor numbers [emphasis added]:

"...One team is led by Andrew White at the University of Queensland in Brisbane, Australia, and the other by Chao-Yang Lu of the University of Science and Technology of China, in Hefei. Both groups have built rudimentary laser-based quantum computers that can implement Shor’s algorithm - a mathematical routine capable of defeating today’s most common encryption systems, such as RSA."

 

[Tanja]

I suspect: No!
As someone from the "Institute of Quantum Computing" in Waterloo/Canada said: " The opportunity is there!".
If human beings would be able to use this opportunity, one could simulate the universe in each detail (I mean: simulating all particles with its quantum behaviours subject to all kind of potentials . Right now, it's not even possible to simulate a single molecule, correctely)

If it would be possible to realize a quantum computer, no doubt, the possibility to simulate Quantum systems would be great. But before using this opportunity, Quantum systems have to be understood and one have to be able to control them. Isn't that a circular reasoning?

I really love the thought to have applications of quantum physics and a quantum computing is the most interesting subject I can imagine. But there are so many difficulties:
relaxation and decoherence, noise, scalability, quantum algorithms using the super postion of quantum systems...

There should be done a lot more research. Even if it wouldn't be possible to realize it, there will be a lot of useful "wast-products". It's research on the basis on quantum physics and results can be used in many applications, like e.g. in the classical computer industry: Transistors become smaller and smaller and one day quantum effects have be taken into account. Quantum Computing allready has done this research.

Btw: wasn't it Feynman who brought up the thought of a Quantum Computer the first time?

 

[Sojourner01]

I don't think they're intended to 'compute' in the conventional sense - getting an answer out of them comes in a rather roundabout way and there's no guarantee that any given problem will be any more tractable on a quantum computer than on an electronic. I know very little about how they're supposed to work, however.

 

[vanesch]

This statement illustrates a misconception of what quantum theory is about, and what interpretational schemes are about.
An interpretational scheme can normally not have any influence on anything observable, which is predicted by the theory. As such, the observation "quantum computers are possible" is a prediction of quantum theory, not of the interpretational scheme of MWI.

MWI, as an interpretational scheme, can *facilitate* one's intuitive understanding of the workings of the theory (that is btw the manner I see MWI, and the reason why I like it: it gives a more tangible *picture* of what the theory predicts).

So whether quantum computers are possible or not has nothing to do whether "MWI is true or not", but rather:
1) whether quantum theory is true on a large enough scale
2) whether quantum theory allows a practical quantum computer (because decoherence is going to be a nasty problem to solve).

This is totally independent of one's interpretation.

Personally, I think that 2) is going to be a hell of a challenge...

 

[confusedashell]

I see, so it's just deluded deutsch who thinks quantum computers is ultimate proof that MWI is real?
What I don't get is why so many is in favour of a interpretation who has been emperically proven wrong by Afshar experiment (yeye live in denial) + accepting it is accepting that everyone around u is around u for a split second and there is no "real you".
Luckily it has been disproven :)

What are the purpose of quantum computers anyway?

 

[vanesch]

I see, so it's just deluded deutsch who thinks quantum computers is ultimate proof that MWI is real?

Deutsch is indeed misguided IMO that one can prove (or disprove) an interpretation!

What I don't get is why so many is in favour of a interpretation who has been emperically proven wrong by Afshar experiment (yeye live in denial) + accepting it is accepting that everyone around u is around u for a split second and there is no "real you".
Luckily it has been disproven :)

That Afshar experiment didn't disprove quantum theory either ! It is delusion, but in the other direction. The Afshar experiment was a dumb application of classical Fourier optics.

Repeat after me: one cannot prove or disprove an interpretation of a theory. One can only prove or disprove the theory itself.

What are the purpose of quantum computers anyway?

To use the superposition principle to apply classically logical operators massively parallel to a certain problem, in a way that this would have to be done by multiplying hardware, or by serialising in time on a classical computer.

Simple example:
suppose that you have 3 bits, and you want to find out the "and" of the first two, "ored" with the third one:
(a,b,c) -> ( (a & b) | c )

Now, in a classical circuitry, if you'd wire up the things such that if you apply:
(1,1,0), you'd find a 1, for instance.

Now imagine that you want to apply a (1,1,0), and also a (0,1,1). In a classical machine, you'd have to build two identical circuits, or use two clock pulses to do so.

But a quantum computer with the same wiring can do something different.
You can apply the state:
|1>|1>|0>|b> + |0>|1>|1>|a> to the circuit, and out pops directly the state:
|1>|b> + |0>|a>, which can serve as the input to the next circuit etc...

In other words, superposition allows you to "do classically logical operations in parallel", and one sees the advantage of the MWI view in this:
in the "b" world, we applied (1,1,0) to the computer (now seen classically), and it computed 1 ; in the parallel "a" world, we applied (0,1,1) and the computer, in that world, computed 0.

But if you don't like it, you just work with the wavefunctions and that's all. In fact, "just working with the wavefunctions" is exactly what MWI tells you to do...

 

[confusedashell]

I disagree, if a interpretation make certain claims and predictions and these predictions and claims are disproven by experiment, they are no longer valid. THAT'S SCIENCE, a process of advancing.
Clinging to a theory cause it appeals you is religion, would you say ID's "interpretation" of how life came to be cannot be "disproven" either, when it claims Earth is 6000-10000 years old and we got fossil records who disprove this?
I never said Afshar Experiment disproved QUANTUM THEORY, only CI and MWI.
Now those who love and have spent countless hours reading learning accepting and put faith in either of this interpretations won't "let it go" just like that, it's a process, either advance or denial.
That's my opinion, not that Afshar experiment is the only thing that refutes and bring problems to MWI in the first place, preferred basis problem, probability problem etc. not to mention: ITS INSANE:P

No offense, you make up your mind, I make up my mind, I just think we should follow the evidence not our personal convictions.
If nature speaks up, you better listen, cause that's truth, not what some scientist says.

 

[christianjb]

CAH: I think you're misinterpreting V's POV and running the risk of sounding a little pompous. (Sorry, but writing 'science' in capital letters doesn't convince me of your argument.)

Everyone has different interpretations of QM, but we're all using the same equations. (I think that was V's point.)

 

[confusedashell]

Your free to disagree with my opinions by all matters, I'm just saying simply.
If you get TOO caught up in a interpretation and deny to even listen to the arguements against them, you'll get nowhere closer to "the truth".
I'm not saying I got the answer at all, hell, I don't even know which quantum interpretation is more likely to be true or not, I just know it's not CI and MWI for obvious reasons.

 

[vanesch]

CAH, as christianjb pointed out, you miss my point - but it is a common mistake, btw. Even Deutsch falls into it.

A *theory* is a formal description of nature (meaning, a mathematical frameset with a link to lab stuff) which can make predictions of observations. We can verify these predictions by doing experiments, and comparing what the theory says about its outcomes, and what we really measure. This is often not as simple as it sounds, as often the observations are somehow indirect, and instrumentation (with their own theory of functioning) is needed, also simplifications are often needed to work out the results and so on... that's why experimental science is not as simple as it sounds in schoolbooks. This is why some experimental "observations" can be disputed too. But at the end of the day, if there is a clear difference between what a *theory* predicts and what is unambiguously experimentally observed, the theory has a problem.

However, an *interpretation* of a theory is the act of giving an ontological meaning to the elements of a theory. It is a way of "looking at the meaning of the mathematical concepts of a theory". As such, an interpretation of a theory doesn't make any predictions different from the theory.
If you have two rivaling interpretations of the same theory, then normally they make exactly the same observational predictions. As such, NO EXPERIMENT EVER can make a distinction between two different interpretations of the same theory.

As such, the orthodox Copenhagen interpretation MAKES EXACTLY THE SAME experimental predictions as does the MWI interpretation of the same theory, quantum theory. So "saying that an experiment favors this or that interpretation" is fundamentally flawed. An experiment can suggest the validity of a theory, or can falsify a theory. But it cannot distinguish between two interpretations of the same theory.

Interpretations have to be judged on more philosophical grounds.

However, certain interpretations can suggest, or be more robust with respect to, MODIFICATIONS OR LIMITATIONS OF A THEORY than others.
For instance, for the MWI interpretation to continue to hold, it is necessary that quantum theory is applicable on human scale (which is unverified). It breaks down if ever quantum theory is falsified on that scale (which hasn't happened either).
On the other hand, the Copenhagen interpretation is more flexible, as there is an undefined "transition zone" between the "quantum realm" and the "classical realm", and hence could accommodate a falsification of quantum theory on a mesoscopic scale (which hasn't happened).

So as long as quantum theory is strictly valid, MWI and CI are indistinguishable. If quantum theory is falsified at a mesoscopic scale, then it will probably be difficult to have an MWI-like interpretation of the NEW theory that will replace quantum theory, while it might still be possible to have a CI-like interpretation of the NEW theory that will replace quantum theory on the mesoscopic scale.

But again, predictions of experiments belongs to the realm of a theory, not to its interpretation. Hence, only a theory can be falsified, and not one of its interpretations.

Saying that an experiment doesn't falsify quantum theory, but does falsify (or support) MWI or CI, or whatever, is an oxymoron.

 

[Tanja]

Why should the excistance of a quantum computer proove MWI? It would only proove that the process of super position can be physically used (I should be careful: I never understood Shor's algorithm and the Quantum Fourier Transfrom, which are based on the super postion states, in detail.).

I imagine the cat state as something that is not physical, but a good mathematical explanation for the system. Like \Psi is nothing that really exists , but has to be there for calculating further physical quantities.

Thinking about a quantum computer, I don't even come to interpretations of the super positioning state , may it be MWI or the "Koppenhagen" interpretation, or whatever.
I already got stuck with the question: Is the cat state something physical, we can manipulate and use without resulting in a collapse?

 

[confusedashell]

vanesch I get your point completely now, but then it is completely retarded for ANYONE to take a stance, ecspecially promote their interpretation and out loud ridicule other interpretations such as Deutsch does in his book.
You too, have picked a "side", so that's kinda being a hypocrite.
Anyway, Afshar experiment changed one of the fundamental things in quantum theory which in return falsified both MWI and CI, do you suggest that he falsified the whole concept of quantum theory or just a "part" of it?

 

[vanesch]

I would like to comment on that famous Afshar experiment, btw.
I had looked at it a long time ago, and I think that the Wiki entry on it is quite well done:
http://en.wikipedia.org/wiki/Afshar_experiment
especially the description of the setup.

What's the idea ? The idea of this experiment is suggested by some handwaving mumbo-jumbo which is unfortunately common in intro quantum courses, the so-called "wave-particle" duality, and other ill-defined concepts.
It's based upon the rather naive "picture" of a photon putting up the hat of a particle sometimes, and the hat of a wave at other times, and this is usually illustrated in intro quantum courses by variations on the 2-slit experiment.

In a 2-slit experiment, it is said (and that's really mumbo-jumbo) that when the two slits are open, and we make no attempt at detecting "which way" the photon went, that it puts up its wave hat, and makes an interference pattern. However, from the moment that we try to trick it into telling us which slit it went through, it puts on its particle hat, and the interference pattern disappears.

This is, IMO, a very naive and very misguiding way of looking at quantum theory, but it is very common to start quantum courses that way, probably to try to make a *didactical* connection with former knowledge by the students, which are acquainted with classical systems of particles (Newtonian mechanics) and of waves (classical EM).

What really happens formally, is that the photon statevector evolves through the setup, and according to changes in the setup, the evolution equation (schroedinger equation) of the statevector is different.

So what happens when one slit is open, is that the state vector takes on the form of a spatial distribution of a "blob" which evolves through the lens onto D1 if slit 1 was open, and on D2 if slit 2 was open. This simply follows from the evolution of the wavefunction, which, in this particular case, is IDENTICAL TO THE MAXWELL EQUATIONS because it is one of those properties that single-photon evolution is identical to classical EM evolution.
This is why this experiment is actually CLASSICAL OPTICS.
If we open both slits, then the wavefunction takes on an interference pattern just before the lens, and refocusses on the two detectors after it.

We have, in this setup, the evolution:
|slit 1> --> |blob1> --> |det1>
|slit 2> --> |blob2> --> |det2>

where the first --> is the evolution through space to just before the lens, and the second --> is the evolution through the lens.

From the superposition principle follows:

1/sqrt(2)(|slit1> + |slit2>) --> 1/sqrt(2)(|blob1>+|blob2>) --> 1/sqrt(2)(|det1> + |det2>)

|blob1> + |blob2> is an interference pattern.

We hence see that if only slit 1 is open, then only det1 will count, if only slit 2 is open, then only det 2 will count, and if slit 1 and slit 2 are open, then we have 50% chance that det 1 will count, and 50% chance that det 2 will count.

Now, let us place the grid. The grid is a projector which let's through entirely the interference pattern:

|blob1> + |blob2> gets through.

But which scatters PARTLY the complementary pattern (with the "peaks" on the wires):

|blob1> - |blob2> is reduced to a (|blob1> - |blob2>) + sqrt(1-a^2) |other>
where |other> stands for a scattering of the light that will not be focussed, nor on detector 1 nor on detector 2 and hence is orthogonal to the |blob1> and |blob2> states.

so its matrix representation in the
|i+> = 1/sqrt(2)(|blob1> + |blob2>) ;
|i-> = 1/sqrt(2)(|blob1> - |blob2>) ;
|other>
basis

is

1 0 0
0 a -sqrt(1-a^2)
0 sqrt(1-a^2) a


Note that because of unitarity, it is impossible for the scattering to scatter into the |i+> state (which is normal, because the i+ state has "darkness" on all the scattering wires).

The coefficient a determines how much of the light of the complementary pattern is actually scattered by the wires and depends on their thickness and so on. If there's not much scattering, then a is pretty close to 1.

If both slits are open, then we have:

1/sqrt(2)(|slit1> + |slit2>) --> |i+> --> |i+> --> 1/sqrt(2)(|det1> + |det2>)

Here the first --> is the evolution through free space, the second --> is the effect of the wires, and the third is the effect of the lens.

If we have only slit 1 open, then we can write this as:

|slit1> =1/sqrt(2) ( 1/sqrt(2)(|slit1> + |slit2>) + 1/sqrt(2)(|slit1> - |slit2>))

using superposition, this becomes:

|slit1> --> 1/sqrt(2) (|i+> + |i->) --> 1/sqrt(2) (|i+> + a |i-> + sqrt(1-a^2) |other>)
--> 1/sqrt(2)(1/sqrt(2) (|det1> + |det2> )+ a/sqrt(2) (|det1> - |det2>) + sqrt(1-a^2) |nodet>)

So we see that we expect to have as end state:

1/2 (1+a) |det1> + 1/2 (1-a) |det2> + sqrt(1-a^2)/sqrt(2) |nodet>

If there is not much scattering (fine wires), then a is close to 1, and we have that we have almost 100% chance to have |det1>, a very small chance to have |det2> and a small chance to have the light scattered elsewhere.
If there is more scattering, then the chances to hit detector 1 are smaller, and the chances to have detector 2 become higher.
At "perfect" scattering (a=0) then detector 1 and 2 have equal chances to click.

So we see here the error in reasoning:
in as much as the wires have an effect (a smaller than 1), the detectors are less and less "reliable" to "tell us through which slit the light came" in the case of a single slit opening.

This remains so when the double slit is open. Even though one would *THINK* that a click in detector 2 means that the light came through slit 2, and a click of detector 1 means that the light came from slit 1, this is not true. The detectors do not indicate reliably anymore from which slit came the light (in as much as the wires do something). Hence there non-scattering effect in the case of the two open slits (symbolised by the perfect transmission of state |i+>) is NOT in conflict with a so-called "which-way" measurement.

But this experiment has a much more classical interpretation.

Indeed, it is simply "mode-coupling". The optical system without grid is simply "2 waveguides": one that goes from slit 1 to detector 1, and one that goes from slit 2 to detector 2. The insertion of the grid couples these two waveguides, and allows for an exchange. The strength of the coupling is given by the scattering intensity of the wires (here written by "a").

 

[vanesch]

vanesch I get your point completely now, but then it is completely retarded for ANYONE to take a stance, ecspecially promote their interpretation and out loud ridicule other interpretations such as Deutsch does in his book.
You too, have picked a "side", so that's kinda being a hypocrite.
Anyway, Afshar experiment changed one of the fundamental things in quantum theory which in return falsified both MWI and CI, do you suggest that he falsified the whole concept of quantum theory or just a "part" of it?

Our posts "crossed".

1) you CAN have a preference for an interpretation. I have a clear preference for MWI. But not on scientific grounds, but on philosophical grounds.

2) Afshar didn't do anything special !

 

[colorSpace]

That Afshar experiment didn't disprove quantum theory either ! It is delusion, but in the other direction. The Afshar experiment was a dumb application of classical Fourier optics.

Please explain. :) (Or is there a link to a thread or website discussing this?)

(I'm just trying to wrap my head around this experiment, which doesn't look really convincing, for example the reasoning why he thinks diffraction would be excluded. I think the photons could bend around the grid (in a way determined by the interference), and there destroy the path information, for example. Also some physicists don't seem to be convinced there really is an interference pattern where it is assumed, so that doesn't seem to be clear either).

 

[confusedashell]

Your "crossed" post became too complicated for a layman like myself.
Although I think I understand the basics of it.
I respect your view that MWI is what you believe is true, does that include splitting or do you go with the classical view of Everett that splitting is not occurring?

On Afshar experiment: what he did was simple, in terms he showed Einstein was right, Bohr was wrong.

On "philosophical grounds" I would not see how anyone believing that their loved ones constnatly split and are really not original and just bunch of copies could even lead normal ives...

In other manner: do you trust MWI to the point where you dare to take the famous Quantum suicide tests? are you so sure of MWI?:P

 

[vanesch]

Your "crossed" post became too complicated for a layman like myself.
Although I think I understand the basics of it.

In fact, I came to think of it (that was another discussion here a while ago), the Afshar experiment falls in the trap of "assigning probabilities to non-measured wavefunctions". This is something that is at the basis of about all quantum paradoxes (a bit like implicitly assuming conservation of simultaneity is at the basis of most SR paradoxes).

The Afshar "paradox" is that "detecting through which hole came the photon" is supposed to make the photon have a particle hat, while the fact that the grid doesn't seem to perturb the light when both holes are open, seems to indicate that the photon has put up the "wave hat".

But that's entirely misunderstanding how quantum mechanics works - although this kind of handwave talk is common in many intro texts (and many people kind of integrated it through their later education).

What is REALLY true in quantum theory is that "wavefunctions become probability distributions at the act of irreversible observation". Call it "particle behaviour" if you like. In between, wavefunctions do NOT HAVE A CONSISTENT probability distribution interpretation.

So Afshar makes a double mistake. First of all, he makes a mistake by thinking that the link (hole1 - det1) and (hole2 - det2), which is true in the no-wire setup, remains true in the wire setup. It is not because det1 clicks, that the photon "came from hole 1", because there is a transformation of the wavefunction by the wires.

But the most important mistake he makes is the following: he thinks that "being more or less able to tell from which hole the photon came, turns it into a particle" , implicitly thinking: once we are in this situation, I can use the wavefunction EVERYWHERE as a probability density, even when I don't measure, such as at the grid - this because that would be the expected "particle" behaviour. In fact, no. The wavefunction propagates from the slitset through the wires to the detectors, according to the schroedinger equation. It is only through the act of observation by the detector that we are allowed to consider this wavefunction generate a probability density.

Now, the superposition principle is such, that the scattered contribution from hole 1 is exactly canceled by the scattered contribution from hole 2. If we have only hole 1, we have scattering (some clicks in detector 2, and some stuff elsewhere (blurring of the image). If we only have hole 2, we have the same effect (but with opposite phase). If we have both, then both scattering effects cancel, and we get out an image as if the wires weren't there. This is due to the fact that the scattering function acts only on the piece of wavefunction at the wires, and if the wires are there where the contributions from hole 1 and hole 2 are equal and opposite, their scatterings will be equal and opposite to. That's what it means to put the wires at the nodes of the interference pattern.

Afterwards, the superposition of hole 1 and hole 2 will evolve in 50% chance to hit detector 1 and detector 2... but there is NO GUARANTEE AT ALL that a hit on detector 1 means that the photon came from hole 1! This is testified by the fact that if there's only hole 1, there is scattering (and hence also a chance to hit detector 2). This chance doesn't have to be 50% of course, it can be only 1%. That means that the wires don't scatter much, and hence that the effect is "small". But if the wires scatter a lot, then this chance will also be quite high, and the "certainty of which way" drops consequently.

I respect your view that MWI is what you believe is true, does that include splitting or do you go with the classical view of Everett that splitting is not occurring?

I don't believe MWI is "true". I don't believe it to be false either ; I'm agnostic about it. I think MWI is a very useful mental picture to help one understand the workings of quantum theory.

On Afshar experiment: what he did was simple, in terms he showed Einstein was right, Bohr was wrong.

No, Afshar showed that the naive "wave-particle" duality, and the erroneous interpretation of a non-measured wavefunction as being a particle density, runs into troubles. But that's no news :-)

On "philosophical grounds" I would not see how anyone believing that their loved ones constnatly split and are really not original and just bunch of copies could even lead normal ives...

First of all, I think MWI should be used to help you solve conceptual problems with quantum theory, and not for any moral view on human society. That said, I don't have problems personally with those considerations, as they don't really would affect my social behaviour (except maybe for the fact that it helps one put "important events" in perspective: I would indeed never think of doing grandiose things that would only benefit others).

In other manner: do you trust MWI to the point where you dare to take the famous Quantum suicide tests? are you so sure of MWI?:P

The way I look upon MWI doesn't guarantee quantum survival at all. I think that if you "branch" into the "dead" branch, that you (as a subjective experience) are dead (and you don't really care that a copy of you lives on do you ?). That's a bit as the following: imagine that it would be possible to clone you just before you die. Would you now think that you won't die ? I wouldn't. I would think that I'd still die, and that another person would look a lot like me. It's not because your twin survives a car accident, that you didn't die in it.

But again, I look upon such considerations a bit tongue-in-cheek. Although it might be finally "true", it is IMO also very well possible that quantum theory will have to be changed one day into something totally different. After all, MWI needs a very strong extrapolation of the domain of validity of quantum theory from the microscopic into the macroscopic, where it hasn't been tested extensively. I think that gravity might be one of the reasons for a need of a change of theory. As such, MWI is then just the "interpretation that goes with current-day quantum theory" and will maybe loose all of its significance in any follow-up theory. Then, maybe not.

In the mean time, I still find it the view that gives me the best intuition on quantum theory and that it allows a very clear intuitive understanding of a lot of fuzzy stuff in other interpretations (i'm thinking of EPR experiments, delayed quantum eraser experiments, and so on).

 

[vanesch]

Just to add something more:

How can we say in quantum theory "whether a particle went through slit 1 or slit 2", say ?

In fact, we can't, and the statement doesn't even have any intrinsic meaning.

Even in the non-grid experiment, it is *convention* to say that a hit in detector 1 means that the "particle came through slit 1", although classically, that should be true.

However, there is a way in which this can be seen as useful.

If we have a particle in a state |hole1> + |hole2> and it results in an end state |det1> + |det2>, then that doesn't mean anything. But the initial state (prepared state) |hole1> + |hole2> is linked to the end state |det1> + |det2> by a unitary transformation, which is given by the Schroedinger equation of the setup, and which we will represent by U.

So we have U(|hole1> + |hole2>) = |det1> + |det2>.

If this unitary operation now splits into two "independent" parts,
U(|hole1>) = |det1>
and
U(|hole2>) = |det2>

(which is a property of U, which in its turn, depends on the setup)
then we don't make an ERROR by saying that upon hitting |det1> we can say that the particle came through hole1.

In fact, from an MWI viewpoint, we've simply applied a projection, which is allowed for, because any subsequent measurement will be in fact nothing else but a *correlation* measurement with the observed outcome.

Imagine that we have an entangled system:

|a> |hole1> + |b> |hole2>

We can interpret this as "a or b testifying "through which hole" the second system went. We can say that the first system has performed a measurement on the second one, in the "hole" basis.

Now, in as much as U only acts on the second system, we will have that the outcome is:

|a> U(|hole1>) + |b> U(|det2>)

or
|a>|det1> + |b> |hole2>

(that's what an MWI-er would do).

But if we detected "det1" clicking, then we will be entangled with "a", while if we detected det2 clicking, then we'd be entangled with "b", and we took this as "indicating which hole the particle went through" already.

So we see that if the unitary evolution assigns the |hole1> state to |det1> and assigns the |hole2> state to |det2> that, upon detection of det 1, saying that from the original |hole1>+|hole2> state, we now know that the particle went through hole 1, doesn't lead to any inconsistensies.

But strictly speaking, it is not correct. Because if we say that "the particle went through hole 1" upon detecting det1, then we shouldn't have said earlier that it was in the state |hole1> + |hole2> but rather in the state |hole1>.

But it wasn't. It was really in the quantum state |hole1> + |hole2>, and our colloquially saying that "after all, it came through hole 1" looks a lot like INTERPRETING THE STATE |hole1> + |hole2> as a statistical mixture instead of a pure quantum state although it was not a state that was directly measured.

But again, we won't find any inconsistencies that way if U is totally separated.

But we WILL run into troubles if we apply that same reasoning to intermediate states which are not entirely separated by the unitary evolution, and that's exactly the kind of mistake used in the interpretation of the Afshar experiment.

Intermediate quantum states are NOT statistical mixtures.

It is again one of the many formal advantages that MWI gives a clear view on this: at no point we say that "the particle came through hole 1", but rather that we now have a superposition of states with which we got entangled, and as such we got a number of correlated observations (like the a and the det1 observation in one "world" and the b and det2 observation in another "world").

 

[colorSpace]

Thank you, Vanesh, for the explanation. As far as I can tell, this is very much (yet in a much more sophisticated and detailed way) what I was thinking (here and more so in the other thread) about the grid and its influence.

 

[Demystifier]

I think MWI is a very useful mental picture to help one understand the workings of quantum theory ...
I still find it the view that gives me the best intuition on quantum theory and that it allows a very clear intuitive understanding of a lot of fuzzy stuff in other interpretations (i'm thinking of EPR experiments, delayed quantum eraser experiments, and so on).

I would say the same for the Bohmian interpretation.
But consider the following: if all possible worlds are real (as MWI asserts), then a world in which particles move along the Bohmian trajectories is also one of real worlds. Hence, if one would find an experimental proof that particles really do move along the Bohmian trajectories, this would not exclude MWI. Funny, isn't it?

 

[peter0302]

Deutsch is indeed misguided IMO that one can prove (or disprove) an interpretation!

MWI makes some predictions about quantum gravity which can theoretically be disproven. There's also an idea that an intelligent quantum computer could prove the collapse of worlds by observing an electron spin and erasing all memory of it. That'd at least _disprove_ naive Copenhaginsim.

 

[vanesch]

MWI makes some predictions about quantum gravity which can theoretically be disproven.

You will have noted my caveat for gravity !

However, not having a serious consistent quantum THEORY for gravity (note that NEWTONIAN gravity has no problem with unitary QM), I would refrain from giving an INTERPRETATION of an as of yet non-existing theory !

Gravity is a problem for quantum theory, not for a specific interpretation.

 

[peter0302]

Sorry I didn't see your caveat for gravity. Anyway. point is MWI requires gravity to be quantised; so if gravity isn't quantised, MWI is disproven.

 

[colorSpace]

Also, I'd think that any attempt to sell MWI as a local theory could be disproven. ;)

 

[f95toli]

Will David Deutsch's famous quantum computers ever be realized?
I personally look at MWI as a fairytale sciencefiction hypothesis, so in my opinion other universes DO NOT exist, but can still quantum computers become a reality in single universe terms?

There are plenty of quantum computers around. They have been implemented using NMR, optics (photons), superconducting qubits, ion traps, semiconductors and a few other systems.
No existing quantum computer is PRACTICAL (of them have between 3 and 11 bits), i.e. they are simply no small to be of any use in applications. However, all of the key algorithms (sorting, factorization etc) have been experimentally tested.
It is thought that about 20 bits is needed before we can do anything useful (with 20 bits you can simulate certain quantum systems that are too complicated to handle on ordinary computers).
With a few hundred bits we can start using error correcting algorithsm that -at least in principle- can then be used to scale up the systems to large scale practical computers.
It is still not known whether or not this will ever be possible but coherence times of solid state QCs are slowly going up (solid state systems are probably the only ones that can be realisticaly scaled up to hundreds of bits). A few years ago T1 and T3 were on the order of tens on nanoseconds for a single qubit; now they are at a few microseconds.

 

[vanesch]

Sorry I didn't see your caveat for gravity. Anyway. point is MWI requires gravity to be quantised; so if gravity isn't quantised, MWI is disproven.

Well, *quantum theory* requires gravity to be quantized, so if gravity isn't quantized, quantum theory is "disproven"

 

[vanesch]

Also, I'd think that any attempt to sell MWI as a local theory could be disproven. ;)

That depends on what exactly you understand by "local theory", because the unitary evolution of the wavefunction can be formulated in a way that satisfies certain definitions of "local". This is not very visible in the Schroedinger picture, but in the Heisenberg picture, you can show that no operator A(x,y,z) is influenced by anything outside of its past lightcone (there are a few papers on that on the arxiv, I think by Hansen).

 

[colorSpace]

That depends on what exactly you understand by "local theory", because the unitary evolution of the wavefunction can be formulated in a way that satisfies certain definitions of "local". This is not very visible in the Schroedinger picture, but in the Heisenberg picture, you can show that no operator A(x,y,z) is influenced by anything outside of its past lightcone (there are a few papers on that on the arxiv, I think by Hansen).

I can't discuss on the mathematical level, but maybe this can be done in english.

A local theory would be one that can explain the influence of measurement angles in entanglement without an instant or superluminal 'connection' from "A" to "B" and vice versa. It would also have to do this for experiments using GHZ entanglement and entanglement swapping, which use entanglement of more than two particles and so have three (or more) locations, possibly arranged in a triangle (see other thread: https://www.physicsforums.com/showthread.php?t=206291 ).

 

[MaverickMenzies]

Well, *quantum theory* requires gravity to be quantized, so if gravity isn't quantized, quantum theory is "disproven"

How so? The MWI requires that the axioms of quantum mechanics be taken as fundamental - we live in quantum universe and everything has a fundamental quantum description. In contrast, (as I understand it) the CI splits reality into classical and quantum systems and doesn't advance the view of fundamental quantum description for everything. So the motivation to quantize gravity is tied to the idea that QM is a fundamental description. Surely, the possibility exists that gravity simply does not have a quantum description?

 

[vanesch]

How so? The MWI requires that the axioms of quantum mechanics be taken as fundamental - we live in quantum universe and everything has a fundamental quantum description. In contrast, (as I understand it) the CI splits reality into classical and quantum systems and doesn't advance the view of fundamental quantum description for everything. So the motivation to quantize gravity is tied to the idea that QM is a fundamental description. Surely, the possibility exists that gravity simply does not have a quantum description?

Let's say that the CI "ducks the problem". The transition quantum-classical is never described in the CI. Consider for instance two neutrons, for instance in a bound state on a perfect mirror. This quantum state has been demonstrated by a colleague of mine btw. How do you describe their (tiny) gravitational interaction ? Of course, I know that this doesn't matter in practice, because of the smallness of the effect in general, but the question can be asked, and quantum theory has a serious problem here. Note that we don't "measure" the position of the neutrons here (we leave them on their own for a while), which would give a CI-style classical position to the neutrons. So no observation, no classical state according to CI. What do we fill in as a distance for the Newtonian gravitational interaction then, if we have no position ?

 

[confusedashell]

Vanesch a simple question: you said you wouldn't do BIG THINGS for another person because you accept MWI and believe people split all the time.
Wouldn't it be sad if reality as we experience it, is how reality is, there is no splitting and there is only one universe and you "hold back" and act less "giving" all because of some interpretation of things the human brain NEVER ever evolved to even ponder?Another thing with the MWI i never got either was why the **** "splitting" was fantasized up anyway, just because the nature of light is being both particles and wave at the same time has NOTHING to do with macrosopic things.
Occam prolly made a tunnel in his grave

 

[vanesch]

Vanesch a simple question: you said you wouldn't do BIG THINGS for another person because you accept MWI and believe people split all the time.

No. I said I wouldn't do big things which wouldn't profit (or of which I would expect - even wrongly) at least also a tiny bit myself, in one way or another, but this is NOT in any relationship with MWI :-) I already defended this position when I was a teenager - to the big dismayal of the guy (the priest) who tried to make a good catholic out of me :-) I'm just such a bad character. I don't believe in self-sacrificing heros (although I would of course try to convince anybody else to try to be a self-sacrificing hero if I think that would benefit myself )

As such - that was my point - my "morality" is not influenced by any MWI stance.

Also, MWI is not the only "philosophical stance" that would "corrupt morality". In fact, solipsism, which is as old as philosophy itself, would already justify such a "moral corruption". Or the view that all people except yourself are zombies. Or the view of determinism (fatality). Or the view of an infinitely extended universe (even a more classical one), because in an infinitely extended universe ALSO all variants of all possibilities happen. So even if I blow up THIS earth, there is somewhere else far far away an almost identical Earth with an almost identical "me" around which didn't blow it up... and vice versa... there are soo many excuses for not getting up and sacrificing your bloody arse

Wouldn't it be sad if reality as we experience it, is how reality is, there is no splitting and there is only one universe and you "hold back" and act less "giving" all because of some interpretation of things the human brain NEVER ever evolved to even ponder?

No, not really, because that wouldn't benefit me any more so I don't see the advantage of that viewpoint...

Also, I am entirely with you to think of MWI as "speculation on the correctness of a theory far beyond its frame of proven applicability". As I said already many times before: you should look upon MWI as a way to try to understand (current-day) quantum theory. Not as a "philosophy of life".

Another thing with the MWI i never got either was why the **** "splitting" was fantasized up anyway, just because the nature of light is being both particles and wave at the same time has NOTHING to do with macrosopic things.
Occam prolly made a tunnel in his grave

Well, look upon it this way. Your reaction is a bit like that of the Pythagoreans, when they discovered the irrational numbers. Imagine someone propose that space is described by a 3-dimensional REAL space, which maps upon a Euclidean space, instead of a 3-dimensional RATIONAL space.
Then this Occam argument you use would sound like:
"Do you realize how many unidentifiable points you've now added to space, just because of this silly property of diagonals of a square ?"

 

[confusedashell]

Well solipsism is so flawed I don't even understand why people throw it up in discussions(and those who believe in it should seriously get help professionally and mentally).
Zombie arguement, well read Daniel Dennetts explanation of such complex "zombies", they would by definition BE conscious humans.
Consciousness is not some special thing(as I bet you know)
Infinite universe = doubt it, i think it's finite and doubt there's another "identical planet"(thats Max tegmark retardedness at its fullest).
Parallel universes = doubt it, it's science fiction(which I see most quantum physicist have a strong fetish for which might explain why such absurd hypothesies arise from otherwise intellectual and bright people) and don't even understand how a bright physicist like Deutsch could ever believe in it(tho he believes in virtual reality and supercomputers godlike alien **** too so...well, he's insane:P).

I agree self sacriefice is stupid, but egomeganomaliac is no better, ofcourse, yourself is most important in your life, but others are important in my view too, we got a part in our brain for altrurism, even ants got it, so being a selfish retard would mean ur dumber than a ant:p

I think I'll view quantum mechanics realistically, as Einstein did, not be a arrogant idiot, it's unsolved and not the final answer, atleast not indicating other universes, and my personal opinion and that of others is that Afshar experiment proves this.
Single universe is what we observe and have emperical evidence for, for me the consequences of such a bizarre thing would be devastating so since there's "infinite" evidence for single universe and zero for multiple I'll just ignore the issue and go on about life in the single universe present for us.

I doubt you really think deep down that this conversation you've been speaking to several different splitted me's in differnt universes.

Thanks for helping me realize what quantum computers was though and showing me that they have nothing to do with MWI really, Deutsch is just full of himself and he wouldn't change his mind on his pet theory of parallel universe if all the emperical evidence in the cosmos of their nonexistance showed up, so... **** it:P

Thanks again;)

 

[colorSpace]

That depends on what exactly you understand by "local theory", because the unitary evolution of the wavefunction can be formulated in a way that satisfies certain definitions of "local". This is not very visible in the Schroedinger picture, but in the Heisenberg picture, you can show that no operator A(x,y,z) is influenced by anything outside of its past lightcone (there are a few papers on that on the arxiv, I think by Hansen).

So is this a joke, like this "philosophical stance", or supposed to mean that MWI gives you a way to disentangle the wavefunctions of multiple entangled photons?

 

[colorSpace]

...Zombie arguement, well read Daniel Dennetts explanation of such complex "zombies", they would by definition BE conscious humans.
Consciousness is not some special thing(as I bet you know)

There is no working definition of consciousness which would include the subjective experience of seeing colors. Nothing is consciousness "by definition".

Consciously seeing colors, hearings sounds, etc, is indeed a special thing, that even Daniel Dennett knows nothing about.

Just as a side note, I'm not going to discuss this here.

 

[confusedashell]

Nah ofcourse we don't know all about consciousness, but do we really need to?
All we know is that it's ALL related to the brain and not some mystical dualistic immaterial soul

 

[vanesch]

So is this a joke, like this "philosophical stance", or supposed to mean that MWI gives you a way to disentangle the wavefunctions of multiple entangled photons?

The crux of the "local" explanation of EPR situations is that the correlation only happens upon the meeting of the protagonists, and not "when they did their measurement at spacelike intervals".

As both outcomes (at both sides) take place, there is no "spooky action at a distance". The observers simply get entangled with the received entangled particles (and doing so, "split" into different contributions, or different "observed measurements"). It is only when they MEET, that the correlations (which have been inherited through the original entangled pair of particles) show: that is to say, that the right "Alice measurement state" pairs up with the right "Bob measurement state", so that they both seem to observe correlations. But at that point, they are LOCAL to each other.

EDIT:

I've written this out at least 10 times on PF here, so I just picked out one random version of it. Here it is:
https://www.physicsforums.com/showpost.php?p=937905&postcount=10

 

[vanesch]

Well, look upon it this way. Your reaction is a bit like that of the Pythagoreans, when they discovered the irrational numbers. Imagine someone propose that space is described by a 3-dimensional REAL space, which maps upon a Euclidean space, instead of a 3-dimensional RATIONAL space.
Then this Occam argument you use would sound like:
"Do you realize how many unidentifiable points you've now added to space, just because of this silly property of diagonals of a square ?"

I want to add something to this. I wanted to edit this post already yesterday, but the server went down. I think that this "switch from rational to real numbers" has many properties which are similar to the switch from one universe to many in MWI, and illustrate my stance on it.

For the Pythagoreans, the "rational" numbers had some clear meaning, and the discovery of irrationality was shear horror. We are now used to the real number system (or at least we think so), but we seem to forget how horribly big it is! MOST real numbers cannot even be defined (written down). No measurement ever can result in a real number (it is always a rational number). As such there is no ounce of "evidence" of the existence of "points in space" which correspond to elements of R^3 which are not in Q^3. For practical things, at no point we need really "real numbers", and when we do numerical calculations, we always use rational numbers.

So why do we even consider these in physics ? If ever there is one or other form of discreteness of spacetime, then the real numbers are also physical nonsense. So the introduction of real numbers in the description of (Euclidean) space has the following properties:
- it blows up the "number of space points" incredibly
- it has no measurable basis, no observation has ever "confirmed" the existence of real number coordinates
- it might even be fundamentally wrong (if space turns out to be discretized)

Why consider such "nonsense" ? Shouldn't Occam's rasor do away very quickly with such horror ?

Well, when doing NEWTONIAN MECHANICS, we need real numbers. We need to postulate that space is Euclidean with real numbers, because otherwise the concept of derivative wouldn't make mathematical sense. It would be very difficult to formulate Newtonian mechanics if space was made up of Q^3, because limits wouldn't exist (and hence, derivatives wouldn't exist, and Newton's law F = m.a wouldn't be possible).

So the "natural way" of looking at space in Newtonian mechanics is to consider that space is a Euclidean space, isomorphic to R^3. Despite the huge amount of "useless" spacepoints. Despite the fact that it might be fundamentally wrong, and observationally impossible. The *theoretical* construction is simpler this way. So Occam works on the conceptual side, not on the "number of space points".

Well, I see MWI in the same way. It is, to me, the natural way to look upon quantum theory. Quantum theory postulates the superposition principle, well, we apply it to everything. Whether this is physically "true" or not. And this simplifies the conceptual side of quantum theory. No "spooky action at a distance", no "collapse upon observation", no "dichotomy between physical interaction and observation". Occam doesn't count the number of states, but the number of different concepts.

Is space "really" made out of R^3 points, or not ? I don't know. Could be, couldn't be.
Does the superposition principle apply to humans ? I don't know. Could be, couldn't be.

 

[colorSpace]

The crux of the "local" explanation of EPR situations is that the correlation only happens upon the meeting of the protagonists, and not "when they did their measurement at spacelike intervals".

As both outcomes (at both sides) take place, there is no "spooky action at a distance". The observers simply get entangled with the received entangled particles (and doing so, "split" into different contributions, or different "observed measurements"). It is only when they MEET, that the correlations (which have been inherited through the original entangled pair of particles) show: that is to say, that the right "Alice measurement state" pairs up with the right "Bob measurement state", so that they both seem to observe correlations. But at that point, they are LOCAL to each other.

EDIT:

I've written this out at least 10 times on PF here, so I just picked out one random version of it. Here it is:
https://www.physicsforums.com/showpost.php?p=937905&postcount=10

Thanks for the link.

Your explanation seems a bit different than the one discussed in the thread I mentioned. In a sense, it is more "solipsistic", since it "postpones" all collapses until a specific observer is confronted with any results. So I am not quite sure yet whether the argument using GHZ entanglement, will also apply to your version.

However, independently, this argument may now become even stronger due to additional requirements:

Postponing the second "collapse" turns it from a 'random' event into a very 'intelligent' event. The second collapse for each observer has "limited choices", it needs to collapse in a way consistent with the rules of entanglement. In your description, you wrote down a 'non-local' state description, but a local universe can't do that.

When Bob meets Alice, each of his worlds (or at least each in which he meets Alice) needs to have access to each of Alice's possible states, which have now developed into complex-ly different branches, and somehow any of Bob's worlds needs to be able to "pick" the corresponding one which matches his own measurement results. That is, it would seem to me, the second collapse now has to be a more Copenhagen-like collapse since it can't realize all possibilities anymore. Furthermore, the information to make this 'choice' needs to be available in a form that some physical process can make such a choice.

I don't yet see how it should be possible:
a) to make this information available in usable form, and
b) where should this physical process of making the correct choice happen? and
c) how should this choice then influence the collapse?

This is where I think the non-locality may now be hidden: In the lack of 'space' for making this choice. (Or in the need to use non-local state-descriptions all the same). The non-locality may now be in this monster-collapse that doesn't fit into physical space anymore.

[Edit added:] And, it seems to me, that now a possibly huge developed state at Alice's side needs to be collapsed either all at once, or in a impossible looking gradual process.

 

[colorSpace]

[Addition to last post.]

I think the GHZ entanglement with its triangular situation will also pose problems to your version. In the thread in which I discussed it, the problem became that copies of two systems needed to be matched up without information from the third location. In your version the problem is perhaps just postponed, such that this match becomes "real" and later on, when meeting with the third location's effects, it will turn out the the situation which has already become real is impossible, meaning something that has in a sense already happened then needs to be erased from history in hindsight, since it runs into a paradox.

However I need to think about this further before describing it in detail.

 

[vanesch]

Your explanation seems a bit different than the one discussed in the thread I mentioned. In a sense, it is more "solipsistic", since it "postpones" all collapses until a specific observer is confronted with any results. So I am not quite sure yet whether the argument using GHZ entanglement, will also apply to your version.

The "collapse" in that link is not physical of course, but is from a single observer's viewpoint. It is what one would have called a collapse in a CI viewpoint. There are as many alternative "collapses" as there are observer versions, and I picked out one single observer "line" in that example. Sorry if that was confusing.

When Bob meets Alice, each of his worlds (or at least each in which he meets Alice) needs to have access to each of Alice's possible states, which have now developed into complex-ly different branches, and somehow any of Bob's worlds needs to be able to "pick" the corresponding one which matches his own measurement results. That is, it would seem to me, the second collapse now has to be a more Copenhagen-like collapse since it can't realize all possibilities anymore.

That is because the "second collapse" is nothing else but a correlation, where we have already a first "known" result (have picked out already a previous "bob" observer amongst the many).

Note also that the "collapse" for a certain "alice" state results in a different outcome for this Alice than the Alice that was in the "collapse" for a certain Bob state. This is because "collapse" is relative, and there's a collapse for each of the terms in fact, I just picked out a single example for bob and a single example for alice, to show how for THAT SPECIFIC ALICE things LOOK AS IF a collapse took place.

 

[vanesch]

[Addition to last post.]

I think the GHZ entanglement with its triangular situation will also pose problems to your version. In the thread in which I discussed it, the problem became that copies of two systems needed to be matched up without information from the third location. In your version the problem is perhaps just postponed, such that this match becomes "real" and later on, when meeting with the third location's effects, it will turn out the the situation which has already become real is impossible, meaning something that has in a sense already happened then needs to be erased from history in hindsight, since it runs into a paradox.

However I need to think about this further before describing it in detail.

I think the situation you describe cannot happen, because it would mean that there is a real macroscopic observation which is reversible (quantum-erased). Normally, something that is macroscopically observed is so much entangled with the environment that the decoherence of it is irreversible.

 

[colorSpace]

The "collapse" in that link is not physical of course, but is from a single observer's viewpoint. It is what one would have called a collapse in a CI viewpoint. There are as many alternative "collapses" as there are observer versions, and I picked out one single observer "line" in that example. Sorry if that was confusing.

Either it wasn't confusing, or it still is. :)
I think that's how I understood it.

That is because the "second collapse" is nothing else but a correlation, where we have already a first "known" result (have picked out already a previous "bob" observer amongst the many).

Note also that the "collapse" for a certain "alice" state results in a different outcome for this Alice than the Alice that was in the "collapse" for a certain Bob state. This is because "collapse" is relative, and there's a collapse for each of the terms in fact, I just picked out a single example for bob and a single example for alice, to show how for THAT SPECIFIC ALICE things LOOK AS IF a collapse took place.

Ok, "correlation" then. My point above, appears to apply all the same.

I have tried to explain it carefully, and I don't see how you addressed the question of how these states are going to be correlated. The question where all the information comes from, which will allow some process to match up exactly those states which are allowed by the entanglements rules. This appears to require either a non-local mechanism, such as hidden in non-local state descriptions, or a lot of information being passed along in the local states, which allows them to be matched up correctly when they meet, as I have explained above.

[Edit added:] It seems in your description, Bob already carries around with him a state description of Alice's superposition, and it's relation to his own, but in a local universe this wouldn't be "allowed" as a mechanism to explain the interaction.

 

[colorSpace]

I think the situation you describe cannot happen, because it would mean that there is a real macroscopic observation which is reversible (quantum-erased). Normally, something that is macroscopically observed is so much entangled with the environment that the decoherence of it is irreversible.

Of course it cannot happen. That's why I say it is not possible.

 

[vanesch]

[Edit added:] It seems in your description, Bob already carries around with him a state description of Alice's superposition, and it's relation to his own, but in a local universe this wouldn't be "allowed" as a mechanism to explain the interaction.

The way this is written in the Schroedinger picture looks a bit non-local indeed. Each "state" (sub-state in fact) carries with it the "phase information" of with which sub-states of other systems it is entangled, as well as the phase relation to its "cousin-substates".

If I write:
|u+> |v-> - |u-> |v+>,

then the "u+" state carries with it the fact that it is entangled with |v->, and also that it has a 180 degree phase shift wrt |u->. This is encoded in the wavefunction.

But the important point to note is that this information is never *changed* at a distance. So you can see it that "u+ and v-" share a kind of "phase tag" that they were in a product state, and that "u- and v+" share also another phase tag that they were in a product state, and that u+ and u- (and, through the sharing of the tags) also share a phase relationship that they have 180 degrees difference (and eventual amplitude differences). If ever v- evolves into something else, say, (|vx> + |vy>) then they inherit this "term tag" so that later on, in an interaction, when they interact with the u-system, they "remember" being in the same term (sharing the same term tag).

This is just a story that is implemented by the algebra of the terms in the wavefunction and the linearity of the interaction operators.

So, yes, if you want to look upon it this way, a specific substate "carries with it" all the "information" of product (term sharing) and phase relationship to its cousins, which is transmitted to its descendants. It's a peculiar way of doing algebra

But this can be worked out much better in the Heisenberg picture, there's a paper on that:
arxiv:quant-ph/0204024v2

 

[colorSpace]

The way this is written in the Schroedinger picture looks a bit non-local indeed. Each "state" (sub-state in fact) carries with it the "phase information" of with which sub-states of other systems it is entangled, as well as the phase relation to its "cousin-substates".

If I write:
|u+> |v-> - |u-> |v+>,

then the "u+" state carries with it the fact that it is entangled with |v->, and also that it has a 180 degree phase shift wrt |u->. This is encoded in the wavefunction.

But the important point to note is that this information is never *changed* at a distance. So you can see it that "u+ and v-" share a kind of "phase tag" that they were in a product state, and that "u- and v+" share also another phase tag that they were in a product state, and that u+ and u- (and, through the sharing of the tags) also share a phase relationship that they have 180 degrees difference (and eventual amplitude differences). If ever v- evolves into something else, say, (|vx> + |vy>) then they inherit this "term tag" so that later on, in an interaction, when they interact with the u-system, they "remember" being in the same term (sharing the same term tag).

This is just a story that is implemented by the algebra of the terms in the wavefunction and the linearity of the interaction operators.

So, yes, if you want to look upon it this way, a specific substate "carries with it" all the "information" of product (term sharing) and phase relationship to its cousins, which is transmitted to its descendants. It's a peculiar way of doing algebra

But this can be worked out much better in the Heisenberg picture, there's a paper on that:
arxiv:quant-ph/0204024v2

I did expect that the "algebra" you suggest (the "Heisenberg picture") would remove the non-local references (at least as one possibility). This would, so far, only mean that my argument above actually applies. You have only confirmed, so far, the problem I've outlined.

 

[colorSpace]

[Continuation from the previous message.]

I just found that the linked PDF does mention the first problem I've described, and calls it the "problem of label proliferation". Apparently this problem hasn't been resolved yet:

On page 2:

The amount of information which even a simple electron carries with it regarding the other particles with which it has interacted is thus enormous. In Ref. 22 I termed this the problem of “label proliferation,” and suggested that the physical question of how all this information is stored might receive an answer in the framework of quantum field theory.

And the whole text ends in addressing this topic once more:

As for the label-proliferation problem, quantum field theory provides no explanation, beyond that provided by first-quantized theory, for the manner in which this information is recorded. The representation of the label information does seems more natural in quantum field theory than in point-particle quantum mechanics. In quantum mechanics, the operators pertaining to each particle acquire tensor-product factors acting in the state spaces of other particles with which the particle in question interacts. In quantum field theory, each operator acts in an infinite-dimensional space (see, e.g., Ref. 49 for an explicit representation) and changes the nature of its action in this space based on the nature of nearby operators. But, be it quantum-mechanical or quantum-field-theoretic, a single quantum operator is capable of carrying an unlimited amount of information regarding past interactions.

I haven't read the whole text yet (much of which is beyond my mathematical level), I just found these passages so far. Yet so far it seems that the problem is still understated. For example it seems to be explained as if this "enormous" information would apply only to the entangled particle and Alice' or Bob's state of mind. However, they need not meet in person, one could send the results in a plain email. Then it would follow that all this "unlimited amount of information regarding past interactions" would have to go through the fingers of the typist into the keyboard, and then over the internet.

In a local universe, it is no trivial problem to store, and transmit everywhere, an "unlimited amount of information".

Unless I'm missing something, this seems absurd. And this would even be just the problem of the information that needs to be available, in addition there needs to be an explanation of how this complex information is going to be evaluated in its mutated form such than when this email arrives, the correct "pairing-up" can happen. (I haven't yet read enough in this PDf to see whether that is mentioned except in a single sentence where it is called "pairing-up".)

And then there is still the triangular challenge I mentioned above (and in the other thread).

 

[colorSpace]

BTW, this is, I think, the text which I mentioned in a different thread that I had read earlier, linked from the old homepage of D.Deutsch, from 1999, and already mentions the "Heisenberg picture", but apparently less developed at that point in time.

http://xxx.lanl.gov/abs/quant-ph/9906007

 

[vanesch]

I haven't read the whole text yet (much of which is beyond my mathematical level), I just found these passages so far. Yet so far it seems that the problem is still understated. For example it seems to be explained as if this "enormous" information would apply only to the entangled particle and Alice' or Bob's state of mind. However, they need not meet in person, one could send the results in a plain email.

Well, the particles in the fingers typing, in the electrons and atoms of the silicon circuits, and of the EM fields used in the wireless transmission (as well as the air molecules etc...) all just entangle with them of course. I don't see why this would be a particular problem. In fact, about all material objects which have the experiments in their past lightcone will - unless one takes great care and pain to avoid this - end up entangled with the particles in the experiment: all the air molecules, the EM field (suppose that a red light flashes if it is "up" and a green if it is "down") etc... So about all subsystems that have an "interaction possibility" with the tested particle will end up "measuring" it and hence entangling with it. So I don't see why you make such a big deal about those fingers and that e-mail.

Then it would follow that all this "unlimited amount of information regarding past interactions" would have to go through the fingers of the typist into the keyboard, and then over the internet.

Yes, of course, but over the "quantum internet" of course ! The "internet" you think about, is just one classical state of the "quantum internet" which can have all thinkable states of the internet, and the different entanglement informations you talk about in the e-mail go with the quantum-email (think q-bits), of which a simple e-mail is just one state.

THIS picture is BTW why Deutsch claims quantum computers are so much more powerful. But MWI just *illustrates* it, it comes just from the *hugeness of hilbertspace*. It is this hugeness which you are discovering here, not "MWI craziness". MWI "craziness" just puts in light what is enclosed in strict quantum theory.

In a local universe, it is no trivial problem to store, and transmit everywhere, an "unlimited amount of information".

It's not unlimited, but it is very big. But you are thinking of a *classical* universe. A *quantum universe* is mindbogglingly bigger, but that's already the case from the start: the quantum states are a HILBERT SPACE spanned over the classical configuration space: with each POINT of classical configuration space corresponds a DIMENSION in Hilbert space. That's not MWI, that's quantum theory.

Unless I'm missing something, this seems absurd. And this would even be just the problem of the information that needs to be available, in addition there needs to be an explanation of how this complex information is going to be evaluated in its mutated form such than when this email arrives, the correct "pairing-up" can happen. (I haven't yet read enough in this PDf to see whether that is mentioned except in a single sentence where it is called "pairing-up".)

Well, that's just how the dynamics in hilbertspace occurs. You see, your surprise is a bit like that of the Pythagoreans again. Imagine they say: yes but that would mean that the position of a point particle is now given by 3 REAL numbers. Where does it store this infinite amount of information (3 real numbers contain indeed an infinite amount of information, as compared to the finite amount of information in 3 rational numbers) ? And on top of that, it even has to store its velocity, which is also 3 real numbers ?

So you see, one of the advantages of an MWI view is to ILLUSTRATE the mindbogglingly huge statespace of quantum theory.

And then there is still the triangular challenge I mentioned above (and in the other thread).

I thought we agreed that the problem you mentioned could not occur ?