# Will quantum computers ever be possible?

1. Jan 9, 2008

### 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?

2. Jan 9, 2008

### olgranpappy

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."

3. Jan 9, 2008

### 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?

4. Jan 9, 2008

### 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.

5. Jan 9, 2008

### vanesch

Staff Emeritus
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...

6. Jan 9, 2008

### confusedashell

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

7. Jan 9, 2008

### vanesch

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

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.

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...

8. Jan 9, 2008

### 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.

9. Jan 9, 2008

### 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.)

10. Jan 9, 2008

### 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.

11. Jan 9, 2008

### vanesch

Staff Emeritus
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 accomodate 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.

12. Jan 9, 2008

### 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?

13. Jan 9, 2008

### 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 thats 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?

14. Jan 9, 2008

### vanesch

Staff Emeritus
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 lets 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").

15. Jan 9, 2008

### vanesch

Staff Emeritus
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 !

16. Jan 9, 2008

### colorSpace

(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).

17. Jan 9, 2008

### 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 occuring?

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

18. Jan 9, 2008

### vanesch

Staff Emeritus
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 cancelled 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 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.

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 :-)

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).

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).

19. Jan 9, 2008

### vanesch

Staff Emeritus

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").

Last edited: Jan 9, 2008
20. Jan 9, 2008

### 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.