Quantum Interpretations history

[vanesch]

Yeah I agree, but I don't agree there exist other universes.
It's too science fiction brink of losing my sanity to me.
Thats not a good "scientific arguement" but there is other interpretations of the formalism, could you (since your a PhD) lead me to a more rational single universe independant of observer interpretation?

There's only one I know of, and that's Bohmian mechanics. However, in order to accept that, you have to give up the principles of relativity... and you won't be able to do a lot with it if you want to understand quantum field theory (which is understandable, QFT is strongly mixed with special relativity).

You accept MWI(beyond my capabilities), to me accepting MWI would be accept life is utterly meaningless and life is impossible to live (for me).
Luckily, MWI might not be true at all, so as long as it's not proven at all, I will cling to proven science and the one observeable universe and hope it'll be confirmed even at the quantum world.

My only motivation to stick to MWI is that it is in fact a non-interpretation. It says that the mathematical entities you manipulate in the quantum formalism are "really out there", and that ALL happenings are quantum interactions, the way they are described in the quantum formalism. In other words, MWI is nothing else but applying strictly the axioms of quantum theory to the whole world, and give a status of reality to the mathematical objects that these axioms claim, give the state of the system.
So it is in fact nothing else but "picturing for real" the mathematical entities of the quantum formalism (hence you will have a hard time finding an experiment that "violates MWI" but is "in agreement with QM": this is why I'm so sure about this!).

The "many worlds" are then just a natural consequence of the axioms of quantum theory. Indeed, a fundamental axiom (the superposition principle) of quantum theory tells you that

"if a system can be in state A and can be in state B, then it can be in any state x |A> + y |B> with x and y complex numbers, and in as much as these states aren't multiples of one another, they represent physically distinct states".

It is this statement which is crazy ! But it is a fundamental axiom of the quantum formalism.

So, apply this to a guy in his lab: "the guy seeing a green light flashing" as a possible state, right ? "the guy seeing a red light flashing" is another possible state, right ?

Well, apply bluntly the axiom of the superposition principle, and you will find that the guy can be in states which correspond to superpositions of "seeing a green light flashing" and "seeing a red light flashing".

And it turns out that - under the assumption of strict applicability of quantum theory - that if the lights flashing are a result of a quantum experiment on a small system, that these superpositions are unavoidable, and moreover, give the correct OBSERVATIONS if we re-interpret the complex numbers by squaring them, and giving them the probability of observation.

So, you say AAAH, easy. These "superpositions" are just probabilities, right ?
Well, wrong. Because if you do that on the *microscopic* scale, the complex coefficients don't behave as probabilities.

Let's apply the superposition principle to our photon. The axiom of the superposition tells us that |slit1> + |slit2> is a different physical state, distinguishable from slit 1 or from slit 2. And indeed, in a 2-slit experiment, the |slit1> + |slit 2> state gives rise (using the formalism of quantum theory) to an interference pattern. This is NOT compatible with saying that |slit1> + |slit 2> represents 50% chance of |slit1> and 50% chance of slit 2, because that would give you two bumps, each with a weight of 0.5. That's what I mean with "the complex coefficients don't behave as probabilities".

Now, the CI tells us that somehow, on a "classical scale", we have to see these coefficients as probabilities, but not on a microscopic scale.
MWI tells us that the "state" continues to have these complex coefficients, but that they represent "probabilities to be experienced".

Hence, the "many" worlds are just the other terms in the wavefunction. In CI, we "put them to 0", in MWI we tell you that we "don't experience them although they are still there".

The formal advantage of MWI over CI is that it can be mathematically shown that "putting the coefficients to 0" cannot happen within the strict quantum formalism, and moreover, that if ever there were such a mechanism, that it would be strictly non-local (and would violate the principles of relativity). So MWI simply doesn't put them to 0.

MWI sounds crazy ? Sure ! But it only ILLUSTRATES the crazyness of the axioms of quantum theory. Nevertheless, these axioms do give rise to a highly successful formalism, as I guess you know. So in order to get a "feel" for this crazy formalism, it can be good to have a faithful (crazy) PICTURE of it.

 

[confusedashell]

Thanks, obviously your way into this than me.
To me, I go wit William Occam and cut the other universes out of existence, they are not needed.
You agree that it's a way to "picture" quantum world.

People like Weinberg and Hawking agree with the mathemathical formalism, yet they do not believe other universes really exist, only as "abstractions".
Like the number 10 is a abstraction, but not real like "10 onions".
Which interpretation would this be? still MWI math, but a different variant which saves single universe?

I've favoure the Bohmian mechanics for a while, as it's the most rational philosophically and fits our EXPERIENCE of the world, what we have to go by.
So your saying bohmian mechanics CANNOT be right?

 

[vanesch]

Thanks, obviously your way into this than me.
To me, I go wit William Occam and cut the other universes out of existence, they are not needed.
You agree that it's a way to "picture" quantum world.

The problem with using Occam that way is that in order to do away with the worlds, you have to INTRODUCE a new, unknown mechanism (which might, btw, very well given by gravity! That's Penrose's idea, and I like it a lot,... only, as far as I know, it just remains a vague idea and has never been worked out).

People like Weinberg and Hawking agree with the mathemathical formalism, yet they do not believe oter universes really eist, only as "abstractions".

Well, I'm slightly more careful about this. I'm *agnostic* about whether this is "real" or not. I'm even agnostic about whether the world I perceive is really real, the way I intuitively perceive it ! And that's where we enter philosophy...

Like the number 10 is a abstraction, but nto real like "10 onions".
Which interpretation would this be? still MWI, but a different variant which saves single universe?

I think personally, that these considerations are premature. As long as we haven't any clue as to the quantum nature of gravity we haven't any scientific argument one way or another, and it might take a long time (maybe forever!) to find out experimentally. However, given that Hawking himself has used SUPERPOSITIONS of black hole states over times of billions of years, and found agreement with some thermodynamic predictions, we shouldn't go so lightly over the superposition principle on macroscopic (REALLY macroscopic) scales. And if the superposition principle is true on macroscopic scales, I really don't see how you can escape any MWI-like flavor.

I've favoure the Bohmian mechanics for a while, as it's the most rational philosophically and fits our EXPERIENCE of the world, what we have to go by.
So your saying bohmian mechanics CANNOT be right?

No, no, not at all. But Bohmian mechanics has fundamental difficulties integrating the PRINCIPLES of relativity (for very obvious reasons). In fact, the path to Bohmian mechanics is:

Newtonian mechanics ---> ether theory (equivalent to relativity, but without its principles, and a lot of ad hoc concepts) --> quantum potential.

In other words, Bohmian mechanics is obtained by sticking to Newtonian mechanics, and introducing all the necessary machinery each time to save Newtonian mechanics in the light of relativity and quantum theory. But the problem with that approach IMO is that these concepts were each time "introduced after the fact". That is, in relativity, the whole theory is built up on a few principles (speed of light constant, ... ), from these principles you derive a lot of results, and then you IMPLEMENT these results as "god given" directly in the Newtonian frame "length changes", "clocks slow down"... while denying the principles that were at its basis. Of course, you can build an observationally identical theory that way. But you would never have "found it" without having used the principles which you deny after the fact.

In the same way, the quantum-mechanical wavefunction is used to calculate "quantum forces" on the particles such that they deviate exactly as to arrive where they have to to be in agreement with the statistical predictions of QM. But the principles of QM (superposition principle, unitary evolution...) are then relegated to the background once they have given the "quantum potential" (which you would, again, never have found without genuine quantum mechanics).

So although this can be made working, it looks nevertheless a lot like "using a principle, taking the results, and then denying the principle".

And although one can say that Bohmian mechanics does have some elegance in non-relativistic quantum theory, it becomes a genuine mess when trying to do QFT. It is not impossible, but the constructions that have to be invented to "keep agreement with QFT" become rather big and ugly. And you would never have invented it without first looking at QFT.

For non-relativistic QM, Bohmian mechanics is again experimentally identical to quantum theory, so it can be seen as an "interpretation". I'm not so sure about the QFT case, whether it is "mostly in agreement" or "perfectly in agreement". I'm simply not knowledgeable about it.

 

[confusedashell]

Thanks again, you got a big intellect vanesch... Thank you for your input and help in solving some questions I've had...

You seriously doubt perception?
Ofcourse the world infront of us is the way the world is, doubting that is leading to solipsism and if that's a position you could take in anycase, your mentality is not very healthy.
NO OFFENSE:P

 

[colorSpace]

And if the superposition principle is true on macroscopic scales, I really don't see how you can escape any MWI-like flavor.

Well, in the double-slit experiment, where you definitely have superposition and interference, you still eventually measure each photon at a specific location on the screen. So finally, at the point of measurement, you still have the phenomenon of either a collapse, or a "split", or something else, that has to explain why the photon eventually shows up in a specific place. (Or why it appears to do so.)

 

[peter0302]

They could only prove that the Heisenberg cut is "higher up" than one might first think.

I dunno, to me it would prove there is no "Heisenberg cut" at all, because if the "cut" happens at a higher level than the elementary particles then where it happens is just chosen at the whim of the experimenter depending on the goal of the experiment, which means the cut has no meaning except on paper. Unless you adhere to the view that the human observer somehow is responsible for the very existence of the particle, which I'm not even going to begin to get into...

But I don't understand how one can even IMAGINE thinking that one is going to find an experiment that distinguishes IDENTICAL SETS of numbers to which one has given different STORIES ?

That's just my point. Just labeling it a "story" is nothing but a way to marginalize it. It becomes more than a "story" the moment someone divines an experiment that would produce different results. And we already agree that MWI could be decisively disproven if spacetime and gravity were not quantized, so I don't know what more you want of it before you would accept it as a theory.

 

[peter0302]

peter0302, what about afshar's experiment? doesn't it do exactly what your saying?

The jury's still out on Afshar. Some say there's really no way of knowing that the photon that exited a particular slit wound up at a particular detector because the lens may have served to re-randomize the EM field.

I for one think this is a stretch but a lot of people much smarter than me believe it so I am not really in a position to argue with them. :)

 

[colorSpace]

The jury's still out on Afshar. Some say there's really no way of knowing that the photon that exited a particular slit wound up at a particular detector because the lens may have served to re-randomize the EM field.

I for one think this is a stretch but a lot of people much smarter than me believe it so I am not really in a position to argue with them. :)

Or the "wires" placed in the interference positions (causing a similar effect as the slits).

 

[peter0302]

Or the "wires" placed in the interference positions (causing a similar effect as the slits

Isn't that even more of a stretch? The wires don't block any photons (the slits do!). That's what the experiment shows. As I often say, a photon is not a magic bullet.

 

[colorSpace]

Isn't that even more of a stretch? The wires don't block any photons (the slits do!). That's what the experiment shows. As I often say, a photon is not a magic bullet.

I'm not talking about blocking. Just like slits, they may cause more uncertainty in the momentum. The slits also alter the path of those photons that go through, otherwise you would only see two narrow stripes on the screen [Edit: in the case of the double slit experiment]. The photons have the option of "bending" around them.

 

[peter0302]

The slits also alter the path of those photons that go through, otherwise you would only see two narrow stripes on the screen

Yes, the presence of the slits determines the state vector of the photons that go through them, but the slits only allow a small % of the photons to actually pass through - the rest are blocked. By contrast, the number of photons going through the Afshar grid is virtually unchanged. That's the whole point.

So the difference is, with the slits, most are being blocked, and the ones that aren't come out in a superpositioned state. Whether the slits merely isolated those photons in that state, or caused them to be in that state, is a matter of interpretation. But either way, with the Afshar grid - NONE of the photons are blocked. Yet you still want to say hat their state vectors are changed by the presence of a device which otherwise doesn't seem to interact with the photons at all? Again, I think this is a stretch.

 

[colorSpace]

Yes, the presence of the slits determines the state vector of the photons that go through them, but the slits only allow a small % of the photons to actually pass through - the rest are blocked. By contrast, the number of photons going through the Afshar grid is virtually unchanged. That's the whole point.

So the difference is, with the slits, most are being blocked, and the ones that aren't come out in a superpositioned state. Whether the slits merely isolated those photons in that state, or caused them to be in that state, is a matter of interpretation. But either way, with the Afshar grid - NONE of the photons are blocked. Yet you still want to say hat their state vectors are changed by the presence of a device which otherwise doesn't seem to interact with the photons at all? Again, I think this is a stretch.

Yes of course I want to say that. Diffraction applies to photons which pass the slits, or the wires, in any case, not to those which would be blocked (if any). And when you have diffraction, then you can't tell anymore which way the photon came. The which-way-information is lost for the path prior to the grid. Too simple to be true?

http://en.wikipedia.org/wiki/Diffraction

 

[peter0302]

But the slits don't cause diffraction like a lens or prism does. The slits merely pick out photons in such a way as to make it ambiguous which slit they went through. But I still say they only went through one slit or another, as evidenced by the fact that if you put detectors immediately beyond the slits before any interference pattern can show up, you only see one detector or the other go off.

 

[colorSpace]

But the slits don't cause diffraction like a lens or prism does. The slits merely pick out photons in such a way as to make it ambiguous which slit they went through. But I still say they only went through one slit or another, as evidenced by the fact that if you put detectors immediately beyond the slits before any interference pattern can show up, you only see one detector or the other go off.

Did Vanesh tell you that?

 

[colorSpace]

BTW, there will always just one detector be hit. Photons just don't spread out like butter, even when they interfere. Even in a tunneling situation, you won't be able to quickly insert a bigger separator and then find the photon in both places. Which reminds me that I wanted to find out more about Bose-Einstein Condensates.

 

[Fra]

Ofcourse the world infront of us is the way the world is, doubting that is leading to solipsism and if that's a position you could take in anycase, your mentality is not very healthy.

I didn't follow the last development of this thread, but if we by solipsism mean the idea of subjective or relative information that is not as silly as it might seem. It has some depth that I find very plausible.

I can't speak for Vanesch opinion but to a certain extent I think I share his solipsism-like view and I see no problem at all with this mentality.

From my point of view, any question asked must be formulate and defined relative to a questioner. And this same questioner is also the one who must verify any possible answer.

So solipsism in this context can be thought of - IMHO - as taking the concept of "intrinsic information" seriously. This can even be a plausible abstracted generalisation of the principle of locality - the idea that remote things will not affect local things.

The generalisation also needs to updat the concept of "will not", because clearly nothing KNOWS the future. All we can do is to have _expectations_ of the future, and this expectations MAYBE rules our choices, and interaction properties.

A possible generalisation of "locality" in the flavour of solipsism, that I like is therefore something like that

The _expected_ influence of extrinsic information is 0. That is, we have no reasong to _except_ that factors that is outside of our knowledge _will_ impact us. This is exactly what should lead to _expected_ unitary time evolution.

This however does NOT MEAN, that these factors wont' show up! and that unitarity is true! Because the whole point is that it is impossible to know. We can guess all we want, but that never gets more than guesses no matter how eduated!

That is the whole trick with the expectation, it's a subjective expectation that governs our actions - up until the point when we receive new information that now becomes part of the to us intrinsic information, and then our expectations are obviously updated. This solipsist thinking can IMO lead to quite interesting group dynamics. The concept of intertia enters this picture naturally, since the expectations are of course updated respecting the expected confidence in the new information vs the existing information.

Solipsism isn't about thinking that "I am the world" and what I don't know doesn't exists. It's rather IMO connected to the concept of limiting information and capacity issues.

We are all walking in darkness, interacting with each other, and doing so we learn... and interactions evolve, but there is a limit to our learning capability. Because I don't think that information about the universe can possible encode in a local system. Thus, there are questions that the local systems are simply unable to ask, because he lacks the complexity required. Thus there are answers he will never get because he doesn't even understand the questions.

I see similarities to the solipsist thinking of MWI here, although I think the language of multiuniverses is strange and I don't share that view but I still depend the solipsism thinking I briefly elaborated above. I should not judge myself, but I can say that it's not because we are mentally disoriented. There is deeper stuff in this.

Edit: In this thinking one can also see "locality" as emergent, and a result of self-organisation of the universe. The mutual interaction leads to structure formation that by design will have a kind of locality builtinto it. But this means that it's also easy to picture violation of locality when we are so to speak "far from equilibrium". Because ultimately locality is a "educated expectation", not a "law". This IMHO at least (probably not agreed upon my others) is all in line with the solipsist argument I had above.

/Fredrik

 

[colorSpace]

To add another thought:

Bohmian Mechanics shows that one doesn't need to make the assumption that the photon traveled through "both" slits in any sense, in order to explain behavior that indicates "knowledge" of both slits.

Similar, in tunneling one doesn't need to assume that the particle will "look around" before it tunnels to another location unreachable by classical explanation.

 

[vanesch]

To add another thought:

Bohmian Mechanics shows that one doesn't need to make the assumption that the photon traveled through "both" slits in any sense, in order to explain behavior that indicates "knowledge" of both slits

Yes, that is correct: in BM, the particle (BM has problems with photons as these are relativistic things, so let us take a massive particle like an electron or so) follows a definite trajectory... However, the associated quantum state (which is identical to the one in normal quantum mechanics!) DID "travel" through both slits, and it is this quantum state which induces the quantum potential acting on the particle to deviate its trajectory in exactly such a way as to be statistically detected in the same way as in standard quantum mechanics. So although the *trajectory* exists and only goes through one slit, its "associated quantum state" did exactly the same thing as in usual quantum theory, and was in a superposition all right.

 

[peter0302]

Did Vanesh tell you that?

Heh, nope.

Put another way. A slit is basically a filter. It filters out any photons that don't go through it. A double slit filters out photons that don't go through either slit. Etc. For phootns that went through a double slit, if they progress far enough away, it becomes completely ambiguous which slit they went through.

The Afshar grid is not a filter because the number of photons going in is equal to the number of photons going out. It is a 100% (in theory) non-perturbative measurement. Or another way to look at it is _passive_ measurement. What the grid did was give us information about the location of the photons without disturbing them. And what we saw is that the photons avoid the interference minima in space. And yet they still always always always hit one detector or the other but not both.

I don't care if we can tell _which slit_ the photons went through. The fact that they only hit one detector or the other is what's remarkable to me.

 

[colorSpace]

Yes, that is correct: in BM, the particle (BM has problems with photons as these are relativistic things, so let us take a massive particle like an electron or so) follows a definite trajectory... However, the associated quantum state (which is identical to the one in normal quantum mechanics!) DID "travel" through both slits, and it is this quantum state which induces the quantum potential acting on the particle to deviate its trajectory in exactly such a way as to be statistically detected in the same way as in standard quantum mechanics. So although the *trajectory* exists and only goes through one slit, its "associated quantum state" did exactly the same thing as in usual quantum theory, and was in a superposition all right.

Yes, and as far as I understand, the quantum potential is created by the experimental configuration (mostly, but also by the photon). So the photon does not have to split up itself, nor "its" wavefunction, since the quantum potential is somewhat like a field in that it is created by all objects jointly, AFAIK.

[And the quantum potential extends in principle through the whole universe, it doesn't have multiple parts.]

 

[colorSpace]

Put another way. A slit is basically a filter. It filters out any photons that don't go through it. A double slit filters out photons that don't go through either slit. Etc. For phootns that went through a double slit, if they progress far enough away, it becomes completely ambiguous which slit they went through.

The slits not only filter out photons that don't go through, they also cause diffraction to the photons which go through, even when only one slit is open. This why you see not only a narrow stripe of equal distribution on a screen behind the slit, but a wider, graduated distribution.

I don't care if we can tell _which slit_ the photons went through. The fact that they only hit one detector or the other is what's remarkable to me.

That is remarkable, but not specific to Afshar's experiment. That is always the case. For the argument that Afshar's experiment is making, the which-way-information is critical.

 

[peter0302]

That is remarkable, but not specific to Afshar's experiment. That is always the case. For the argument that Afshar's experiment is making, the which-way-information is critical.

That is always the case, but what Afshar introduced - which, to my knowledge, no one else had before - was the fact that the photons _physically avoid_ the grid like a wave would, but still only hit one detector or the other, like a particle would. As I see it, that's the "duality" being exemplified in toto. True, "which-way" is gone, but it's still "one or the other" and not "both."

 

[colorSpace]

That is always the case, but what Afshar introduced - which, to my knowledge, no one else had before - was the fact that the photons _physically avoid_ the grid like a wave would, but still only hit one detector or the other, like a particle would. As I see it, that's the "duality" being exemplified in toto. True, "which-way" is gone, but it's still "one or the other" and not "both."

Even in the usual double-slit experiment, when there is wave-like interference, each photon will appear on the screen only in one position.

 

[peter0302]

Even in the usual double-slit experiment, when there is wave-like interference, each photon will appear on the screen only in one position.

Who before Afshar has shown evidence of wave-like interference in the _path_ of the photon before measurement? I think Afshar's experiment proves that the question of what path a photon traverses before measurement actually is worth asking.

 

[colorSpace]

I'd say the grid is a partial measurement, since it measures whether or not photons hit those areas. The result of this measurement is apparently, that there is interference at that point (although the images that I have seen show that the grid has an effect easily visible in these images). Then the detectors make a second measurement, but due to the presence of the grid, they cannot anymore make a statement about which path the photon has taken before the grid, since the grid will cause diffraction. The diffraction that it causes on an interference pattern may be very different then the diffraction it causes on a single-slit setup. It seems to me that this difference hasn't been taken into account so far.

 

[vanesch]

I don't care if we can tell _which slit_ the photons went through. The fact that they only hit one detector or the other is what's remarkable to me.

Indeed. But that is already the case in any optical interference. Classically, you have an image. Quantum-mechanically, you have single impact upon single impact. The simple double slit experiment already does this.

 

[vanesch]

That is always the case, but what Afshar introduced - which, to my knowledge, no one else had before - was the fact that the photons _physically avoid_ the grid like a wave would, but still only hit one detector or the other, like a particle would. As I see it, that's the "duality" being exemplified in toto. True, "which-way" is gone, but it's still "one or the other" and not "both."

Or, you can see it differently: the photons don't avoid the wires ! The photon coming from slit 1 scatters on the wires, and the photons coming from slit 2 also scatter on the wires, but it happens that they scatter with opposite phases. So at the detector, these two scattering amplitudes cancel perfectly. That's actually what happens when you apply the evolution operator to:

|slit 1 > + |slit 2> ---> |image1> + |scatter > + |image2> - |scatter>

 

[peter0302]

Indeed. But that is already the case in any optical interference.

"Any optical interference" does not test single photons. Let's try this experiment with single electrons then.

The photon coming from slit 1 scatters on the wires,

Not buying it. The wires are opaque. They absorb photons as shown in the other part of the experiment where one slit is closed. They are not lenses (which would always pass ~100% of the photons but alter their trajectory). They are more akin to the double slits themselves - filters - that happen to filter NO photons when placed in the interference minima.

Unless you're suggesting that the scatter actually does reduce the image quality?

 

[vanesch]

"Any optical interference" does not test single photons. Let's try this experiment with single electrons then.


Not buying it. The wires are opaque. They absorb photons as shown in the other part of the experiment where one slit is closed. They are not lenses (which would always pass ~100% of the photons but alter their trajectory). They are more akin to the double slits themselves - filters - that happen to filter NO photons when placed in the interference minima.

Unless you're suggesting that the scatter actually does reduce the image quality?

I thought they scattered, because they are metallic wires, but in fact, it doesn't really matter what kind of channels they scatter into. "absorption" is indeed nothing else but another channel (excitation of an electron cloud or whatever). Read in the state "scatter", instead then "excited electron cloud" or something. The opposite slit will put that electron cloud then in the same state, but with a 180 degree phase shift. The story remains the same.

 

[peter0302]

No the story does not remain the same. Let's assume (you may be right about the metal wires - I'm now unsure) that the experiment uses thin strips of glass mirrors at the interference minima that actually reflect back any photons. Do we agree then that no photon that hits the wire should in any way be seen by the detector? Yet in that case the result will still be the same as in Afshar's experiment - but now you can't argue there was scattering of any photons by the grid.

Or another possibility - the metal wires, due to the photoelectric effect, would generate current when a photon strikes, right? Let's measure the current to see if there actually was any excitation of the electrons in the metal. Bet you a steak dinner there wouldn't be any.

 

[vanesch]

No the story does not remain the same. Let's assume (you may be right about the metal wires - I'm now unsure) that the experiment uses thin strips of glass mirrors at the interference minima that actually reflect back any photons. Do we agree then that no photon that hits the wire should in any way be seen by the detector? Yet in that case the result will still be the same as in Afshar's experiment - but now you can't argue there was scattering of any photons by the grid.

Or another possibility - the metal wires, due to the photoelectric effect, would generate current when a photon strikes, right? Let's measure the current to see if there actually was any excitation of the electrons in the metal. Bet you a steak dinner there wouldn't be any.

Of course there won't be any, because that current itself is the result of an interference, so in the end there won't be any!
What I mean is:

unitary evolution of slit 1: |slit 1> ---> |detector 1> + |otherstuff>

that "otherstuff" can be scattering (photons in different directions, emission of an electron, backscattering... whatever: it is another quantum state). It can be a sum of different states (some spatial scattering, some electron emission, some atom excitation, ... whatever: the different channels of interaction with the wire)

unitary evolution of slit 2: |slit 2> ---> |detector 2> - |otherstuff>

It is exactly 180 degrees shifted in phase with the first one, exactly because of the position of the wires (the "empty" interference lines are namely those where both states are 180 degrees out of phase). So this means that the quantum state of, say, the scattered electron will also be 180 degrees out of phase with the quantum state of the scattered electron from the first slit.

Hence, if you make the sum (superposition principle of time evolution):

|slit 1> + |slit 2> evolves into |detector 1> + |otherstuff> + |detector 2> - |otherstuff>

So you get destructive interference in all the "other channels": the emitted electron quantum state from slit 1 interferes with the emitted electron quantum state from slit 2, the excited atom state from slit 1 interferes with the exited atom state from slit 2 etc... and nothing remains (simply due to the 180 degree phase shift of the incoming states).

 

[peter0302]

Where is "otherstuff" coming from in the evoluion of Slit 1 if the photon that went through slit 1 doesn't interact with the grid?

You're _assuming_ what you're trying to prove - that the phtoons interact with the grid. Part of Afshar's experiment was showing that when one slit was closed, the grid blocked photons, but when both slits were open, there was no blockage. Neither you nor colorspace have provided any evidence or argument why that part of the experiment is wrong and, in fact, there is interaction between the photons and the grid.

And you also didn't address my point about using mirror strips instead of metal wires. Or put photon detectors at the interference minima instead of wires. They'll never (or rarely) go off.

 

[vanesch]

Where is "otherstuff" coming from in the evoluion of Slit 1 if the photon that went through slit 1 doesn't interact with the grid?

You're _assuming_ what you're trying to prove - that the phtoons interact with the grid. Part of Afshar's experiment was showing that when one slit was closed, the grid blocked photons, but when both slits were open, there was no blockage. Neither you nor colorspace have provided any evidence or argument why that part of the experiment is wrong and, in fact, there is interaction between the photons and the grid.

And you also didn't address my point about using mirror strips instead of metal wires. Or put photon detectors at the interference minima instead of wires. They'll never (or rarely) go off.

I think you're entirely missing my point. I'm not claiming that photons are interacting or not interacting with the wires ; I'm showing you that you can consider it both ways, because of the linearity of the unitary evolution operator.

We know that if we have a photon in state |slit 1> (slit 2 is closed), that we have a certain amplitude of arriving in detector 1, and "other stuff". That other stuff can be: "absorption" (that is: excitation of another system, such as the electron cloud in the wire), or "scattering" (blurring of the image, going elsewhere, or hitting detector 2 or ...), or "ionisation" (that is, the emission of an electron), or whatever.
But all these other channels just give rise, also, to an AMPLITUDE for this to happen. For instance, the emitted electron is a wavefunction of an outgoing electron and so on.

So we have that the "physics of what happens behind the screen" can be written as:

U( |slit 1> ) = |detector 1> + |otherstuff>

In a similar way, if we have a photon in state |slit 2> (slit 1 is closed) we have a similar story. But, and that's the important part, the wires being placed at exactly those points where the wavefunction from slit 1 is in antiphase with the wavefunction from slit 2 (that's what it means to be in the troughs of the interference pattern), we know that the interaction of the |slit2> photon with the grid will be identical but in opposite phase with the interaction of a |slit1> state.

As such, we have that:

U ( |slit 2> ) = |detector 2> - |otherstuff>

For instance, the electron wavefunction of an emitted electron by the slit-2 photon on the wire will be in exact anti-phase with the wavefunction of an emitted electron by a slit-1 electron. As such the emitted electron by the slit1 state will interfere destructively with the emitted electron of the slit 2 state, and in fine, no electron will be emitted.

So, using the superposition principle, we have:

U (|slit1> + |slit2> = |detector1> + |otherstuff> + |detector2> - |otherstuff> =
|detector1> + |detector2>

This is the view that the two components |slit1> and |slit2> each interacted with the slit, but them being in opposite phases there, gave rise to anti-phases in the resulting channels, which hence cancel. (so, in the end, 0 amplitude for an emitted electron, or an excited atom or some scattered photons)

The other view is that we FIRST look at what |slit1> + |slit2> looks like, and then decide that this state has no photon amplitude at the wires, and will hence not scatter.

These two views are equivalent, given the linearity of the time evolution operator U.

 

[peter0302]

I'm not even sure your equation is right though. This only works if the wire grid is capable of directing any photon it absorbs to one or the other detector. If we make the grid out of black rock, or mirror, this will not happen - the vast majority of photons hitting the grid will be absorbed and not re-emitted, or reflected back the directoin they came - either way, no possibility of being detected, regardless of the phase. Thus, the equation should be:

U( |slit 1> ) = |detector 1> + |blocked by grid> + |otherstuff>
U( |slit 2> ) = |detector 2> + |blocked by grid> - |otherstuff>

U( |slit 1> + |slit 2> ) = |detector 1> + |detector 2> + 2*|blocked by grid>

Yet that is not what we see.

 

[colorSpace]

Part of Afshar's experiment was showing that when one slit was closed, the grid blocked photons, but when both slits were open, there was no blockage. Neither you nor colorspace have provided any evidence or argument why that part of the experiment is wrong and, in fact, there is interaction between the photons and the grid.

Not any argument? I've said multiple times that diffraction applies to photons which *pass* the grid, not to any blocked ones. It alters the direction of photons that pass the grid next to it. This argument doesn't depend on whether there are any blocked photons or not. The way the direction is affected depends on the interference at that point, and can be very different from how a single-slit pattern is affected by the grid, since the grid is placed at a location very specific to the interference pattern. On Afshar's website, I couldn't find any indication that he has considered interference-specific diffraction.

Furthermore, Bohm writes in "The Undivided Universe", that even a "negative" measurement causes "collapse"-like effects elsewhere. Such as, in a different experiment, if a counter is *not* triggered, it will still cause a collapse-like effect. This is because the wavefunction is affected even if the particle isn't [directly, so to speak]. It would seem to me this is easier to understand in an interpretation where the wavefunction is non-local, although I wouldn't really know how a local interpretation might handle this, I've read it just in passing.