Delayed Choice Quantum Eraser

[Schneibster]

Well, dang it, I went and analyzed that experiment, and it turns out that the residual interference is because they used a liquid crystal-based variable delay, and it takes non-zero time to transition between states. This risetime creates the residual interference, not any quantum effect.

Oh, well.

 

[vanesch]

Well, I have a different view. My view is that science is the activity of coming up with descriptions of what happens, and then trying to construct explanations of the facts in those descriptions.

You use different words, but in essence we agree: "a description of what happens" can, to me, be completely mathematical. Only I call that "a theory". It can, for instance, be, that the state of "the world" is a vector in Hilbert space, and that "my eyes" are hermitean operators. What's inherently wrong with that ?
The thing I call my car is then a shorthand for a subspace in that Hilbertspace. A bit abstract, but a perfectly good "explanation", no ?

What is experimentally evident, on the other hand, is not a matter of opinion. It is a matter of fact. And so this has no relevance to the creation of a scientific hypothesis or its testing to see if it is a valid theory.

Here, we differ fundamentally. I don't think that there is anything "experimentally evident". There are just "observations", and it is us who make up a story out of that. That story can change with the wind, and they only make sense within the framework of a theory. Without theory, there's no link between observations, they are just raw impressions, colors, sounds...

Hmmm, well now, I have used Maxwell's Equations (though not recently) and they seemed relatively basic to me. Charge, permittivity, space, time, and the electric and magnetic fields themselves which are defined by the equations.

I was talking about these fields themselves E, and B. They are "vectors in each point in space", and that was inconceivable for people in the 19th century, because vectors, that had only a sense as material displacements. So some matter had to displace, and then you had vectors.
What is this crazy idea of an abstract function from R^3 to R^3 ?? What was the E-field made of ?

I'm not at all sure what you mean when you speak of "classical fields with no mechanistic explanation." What would you describe the field of quantum field theory as?

An operator over Fock space.

Again, I say you are tilting at windmills. Of course one cannot explain quantum theory in terms of classical field theory; it is ridiculous on the face of it to think that you can. The only reason I can come up with for you including this statement in this post is that you think somehow, despite all of my previous statements to the contrary, that that is what I am trying to do.

No, I'm not doing that. I'm only wondering what you call "an explanation", and I thought that you wanted to base that on something "intuitively clear", such as an underlying mechanism or so, because it is only that which is given by our intuition.

I don't know what's wrong in saying that the real universe, out there, is a vector in a Hilbert space. It has been an Euclidean space with points in it, it has been 4-dim manifold and its associated fibre bundle (that's classical field theory), so why for a change can't it be a vector in a Hilbert space ?

Now, you are going to say that that is the MATHEMATICAL FORMALISM, but not the "story". I'm trying to point out that I don't know what's the difference between the story and the formalism. That the essence IS the mathematical formalism, and that you can then invent a few stories that can go with it. Of course, every century or so, the formalism changes, and the story changes. It will change again. That's the progress of science. It also tells you that your story isn't worth a ****, because it will not be around anymore in 100 years.
So Newton's dust points in Euclidean space were not right. The 4-dim manifold isn't right. And the hilbert space vector will not be right. But for the moment, that's what's working, so that's the story I tell myself.

I have stated repeatedly that it is not; I have made explanations and descriptions based on well-known and well-accepted interpretations of quantum mechanics. But you keep saying this. What is your problem with this? How can I help you get over this conceptual barrier?

Let me be more clear: this is a strawman argument, in which you misrepresent my position so that you can attack the misrepresentation and claim to have successfully attacked my position.

I'm not attacking any position. It is just that you are complaining that quantum theory is a "formalism" but that it lacks an "explanation". Naively, I don't see what can be an explanation outside of the classical realm, because we have no intuition outside of that realm. So what's wrong with taking the formalism as the explanation ?
That's btw exactly what I do: my personal "interpretation" is that the universe IS a vector in hilbert space which evolves according to a unitary transformation, and that the Born rule must be applied when I observe something.

The only inherently missing explanatory power in quantum mechanics is due to its assumptions about the structure of spacetime and about the base characteristics of the charges, and the particles that carry them. As a result of these assumptions, quantum mechanics cannot make definitive statements about the origin of the dimensions, nor about the reasons for the particle masses. Worst of all, it cannot be used to construct a theory of gravity.

You apparently didn't see my message in another thread where I told you exactly that: these are indeed the big questions theoretical physicists are working on for the last 2 or 3 decennia. And out of it will come (or not) the next theory (in vogue are superstring theory and loop quantum gravity).
Of course that will "explain" our current theories. But we don't have them yet. Probably it will radically alter the interpretation I give now to QM. Just as QM radically alters the interpretation that is given to Newton's theory.

First of all, prove that they all are of equal utility in every situation. It is common to find that there are multiple different descriptions of events, but that one particular description fits a particular set of events better than another, and to find other situations where that particular description is almost useless. Thermodynamics, electronics, and chemistry are places where this is glaringly obvious, and common enough to be a cliche.

Now let me ask you something: proving that these multiple, equally valid descriptions are in fact equivalent, is that a scientific activity?

It is a word's game: if they are equivalent in all their predictions, then they are called an "interpretation" of the same theory. If they are not, they are called different theories. By definition, distinguishing interpretations is not science per se. What can of course be the case, is that certain interpretations give rise, by induction and extrapolation, to new theories, which CAN differ. If these new theories are successful, then you can in a way "keep" that explanation, and it probably will become the favored interpretation of the former theory.

But this didn't happen in the past. The "spacetime" manifold in GR wasn't the extention of some older interpretation of classical physics, but a new idea, and the Hilbert space stuff wasn't really an extension from a former idea either: it was radically different.

Last but not least, if you are speaking of the interpretations, we do not yet know that they are not differentiable. Certainly it is worth examining them closely in the light of new facts to see whether something has taken place that has rendered one or another more probable, or one or another less probable. And if you are telling me that that is not a scientific activity, then I'm going to ask you to rigorously define what you think a scientific activity is, because it has nothing to do with what I think of as such nor with the dictionary definitions of "scientific" or "activity."

By definition, interpretations of a theory don't change anything to the formalism of the theory, and hence to the quantitative predictions of outcomes of measurements. So what could possibly render one more probable than another ?

Let me give you a silly example:
Consider Newtonian mechanics, and it is stated that space is 3-dimensional and Euclidean. Now, imagine that I give you an alternative interpretation in which space is actually 5-dimensional, Riemanian (3+,2-) but that the two coordinates which aren't Euclidean are always equal to 0, for everything.
This interpretation is different from the standard interpretation: indeed, space around us is 5-dimensional and not 3-dim, and on top of that there seems to be a funny thing that constrains us to have these 4th and 5th coordinate equal to 0. What a strange world view !
Now tell me, shall we go and do experiments to see which one is favored ? Or is there little chance to distinguish both interpretations by experiment ?

First, this is unproven, and second, you have been arguing against an interpretation of the DCQE that is firmly based on one of these interpretations! And it isn't even an interpretation I wrote; it's the one in the paper.

It is only because in order to have this DCQE, you have to do violence to strict quantum theory. Indeed, nowhere in the strict sense of quantum theory it is stated that you can apply Born's rule in the middle of your experiment. You normally only apply Born's rule at the end.
Now, you CAN interpret the DCQE the way they do it. I wanted to point out that you don't have to do it that way, and that you are not obliged to think that things here change because you there decide, or not, to measure something or not. I found that remark, by itself, enlightening. That was maybe pretentious on my part.

Ahhhhhh, but you see, you have failed to state that some of these interpretations make statements about physical facts that may or may not become observable in the future;

If that's the case, you're not talking about two interpretations of a same theory, but about two different theories.

not only that, but we already know that things we cannot in principle ever observe can have profound effects on the behavior of the world around us. Vacuum fluctuations are a perfect example; they lead to the Lamb shift and the Casimir effect, but even though we can detect the shift and the effect, we still cannot detect zero point energy directly.

I'm not talking about things which are "directly observable", I'm talking about modifying, or not, the mathematical machinery that cranks out predictions for measurements: if you do not change that formalism, clearly, you'll get out, in all circumstances, the same numbers, so the same predictions. You're dealing with an interpretation.
If you change the formalism, you have a different theory. It is open to scientific enquiry now.

Analogously, we may be able to make predictions about things we can find physical consequences for in some of these interpretations as a result of those consequences and their being observed or not observed. As a result of this, one or another could be bolstered or denied.

No, because if that's the case, you're dealing with different theories.

Shall we have more examples? How about the twin paradox in SRT? What about the sensitivity of the predicted characteristics of the universe to the exact value of the fine structure constant? What about the precise and interrelated values of the permittivity of the vacuum, and the speed of light? There are many more of these extremely constrained behaviors. So it comes naturally and intuitively to me to believe that nature generally behaves in this way, constraining things that have much wider-ranging implications to a very small part of the "possible" behavior, and only expressing the wider behavior under special circumstances.

Yes, of course. So what you are saying is that there must be a deeper theory beyond what we have today. Big deal. OF COURSE ! That's what theorists try to do all day, since about 20 years ! But you can hardly say, that, say, superstring theory is an interpretation of quantum mechanics :-)

Our feelings on the first subject are nearly identical. However, I have taken an additional step: I assume that what I sense is real, and that the other creatures that surround me are real as well. From this postulate comes not only my stance on the reality of experimental results, but my ethics as well.

I didn't say that the world out there is not "real" in a certain sense. But its reality may be much stranger than our familiar perception of it indicates. Think about it: it is quite difficult to argue that the state of the "real" world IS NOT a vector in Hilbert space! In its full Platonic sense. Until the next theory comes along.

cheers,
Patrick.

 

[Schneibster]

We're awfully close. This is almost an argument about how many angels can dance on the head of a pin.

 

[vanesch]

We're awfully close. This is almost an argument about how many angels can dance on the head of a pin.

In a way you are right that discussing about different interpretations or explanations of a mathematical formalism comes down to this

But do YOU know how many angels can danse on the head of a pin ? I always wondered if that didn't depend exactly on what is a pin ? :tongue:

cheers,
Patrick.

 

[Schneibster]

You use different words, but in essence we agree: "a description of what happens" can, to me, be completely mathematical. Only I call that "a theory".

I'm not sure we're talking in quite the same terms of "description." For instance, it is a description to say that the rock falls at 32 feet per second per second. This is not theory; it is observable, measureable fact. That is what I mean by "description of what happens." Our first theory is Newton's Second Law; F=ma. We then postulate a force that makes the rock fall that way. Next, we make another theory: TUG, where we have this "force of gravitation" thingie that works as F(g) = gmm'/d^2. Now we have not only described the experimental behavior of the rock, but also the behavior of this "force" thingie. Finally (so far), we wind up with GRT, which describes the "force of gravity" thingie as a result of curvature of spacetime. To get beyond that level of description, and describe the cause of the curvature, we will need a quantum field theory of gravity, which is a little difficult considering we have a field theory of gravity but no quantum theory of gravity.

It can, for instance, be, that the state of "the world" is a vector in Hilbert space, and that "my eyes" are hermitean operators. What's inherently wrong with that ?
The thing I call my car is then a shorthand for a subspace in that Hilbertspace. A bit abstract, but a perfectly good "explanation", no ?

Heh, sure. Pretty damn big Hilbert space, though.

Here, we differ fundamentally. I don't think that there is anything "experimentally evident". There are just "observations", and it is us who make up a story out of that. That story can change with the wind, and they only make sense within the framework of a theory. Without theory, there's no link between observations, they are just raw impressions, colors, sounds...

How about that rock? Everybody's observation better have it accelerating at 32 feet per second per second, or we're going to start questioning some basic assumptions. "Were you in orbit? On another planet?" So, how is it not "experimentally evident" from some pretty basic experiments that the force of gravity is quantified as 9.8m/s? Given some basic assumptions, like on the surface of earth, etc., we are all going to observe the same things.

I was talking about these fields themselves E, and B. They are "vectors in each point in space", and that was inconceivable for people in the 19th century, because vectors, that had only a sense as material displacements. So some matter had to displace, and then you had vectors.
What is this crazy idea of an abstract function from R^3 to R^3 ?? What was the E-field made of ?

I get your point, but I have to point out that I myself do not believe that a field itself has an independent physical existence. The exchange of virtual quanta causes the change in the action that we generalize as a "field." So it is not "action at a distance" after all, is it?

Now, you are going to say that that is the MATHEMATICAL FORMALISM, but not the "story". I'm trying to point out that I don't know what's the difference between the story and the formalism.

This is a very slippery point, isn't it?

Let's see if we can get some guidance on these matters from where we started. Well, what do you know- I told you that your description was about the beginning and end, not about the middle. And that a description need only tell about the beginning and end, but that an explanation needs to tell what is happening in the middle. The basis of this argument was your first maintaining that the only true information that is available is the correlations at the end of the experiment, and second that the projection postulate must not be applied until after the end of the experiment. Both of which, by the way, I still disagree with.

That the essence IS the mathematical formalism, and that you can then invent a few stories that can go with it.

Nope- the math is just another language to describe it with!

Of course, every century or so, the formalism changes, and the story changes. It will change again. That's the progress of science. It also tells you that your story isn't worth a ****, because it will not be around anymore in 100 years.

I disagree, and present the story of the rock as evidence.

I'm not attacking any position. It is just that you are complaining that quantum theory is a "formalism" but that it lacks an "explanation".

No, that is the box you have been trying to stuff me into. I never said that it is a formalism, and I also never said it lacks an explanation; I said you are trying to treat any explanation as "not physics" when in fact it is physics.

Naively, I don't see what can be an explanation outside of the classical realm, because we have no intuition outside of that realm. So what's wrong with taking the formalism as the explanation ?

That's because you have excluded from "explanation" any description whose story does not agree with classical causality and therefore any and all descriptions of quantum mechanics. QM does not always behave according to classical causality, and so a proper explanation of it cannot either.

I am very much against the (IMO) pure fiction that it is impossible to understand quantum physics. Feynman started that in the 1960s, and it was no more true then than it is now. It is possible to tell a complete and consistent story about what happens in quantum mechanics; you just have to allow what would ordinarily be considered inconsistencies if it were a story of a classical event.

You apparently didn't see my message in another thread where I told you exactly that: these are indeed the big questions theoretical physicists are working on for the last 2 or 3 decennia. And out of it will come (or not) the next theory (in vogue are superstring theory and loop quantum gravity).
Of course that will "explain" our current theories. But we don't have them yet. Probably it will radically alter the interpretation I give now to QM. Just as QM radically alters the interpretation that is given to Newton's theory.

See, when you stay stuff like this, I don't really think you have thought it all the way through. QM doesn't alter the motions of macroscopic objects. Relativity does- but only has a measurable effect on objects that are moving very fast. So Newtonian mechanics are still applicable.

It is a word's game: if they are equivalent in all their predictions, then they are called an "interpretation" of the same theory. If they are not, they are called different theories. By definition, distinguishing interpretations is not science per se. What can of course be the case, is that certain interpretations give rise, by induction and extrapolation, to new theories, which CAN differ. If these new theories are successful, then you can in a way "keep" that explanation, and it probably will become the favored interpretation of the former theory.

As our knowledge pushes forward, formerly indistinguishable interpretations may become distinguishable. Worthwhile to keep an eye on things IMO.

Furthermore, you did not answer the question I actually asked; look at it again, and look at your answer. The question you answered was, "is distinguishing interpretations science?" but the question I asked was, "is proving that different interpretations are equivalent science?"

But this didn't happen in the past. The "spacetime" manifold in GR wasn't the extention of some older interpretation of classical physics, but a new idea, and the Hilbert space stuff wasn't really an extension from a former idea either: it was radically different.

Actually, it has happened often in the past. Proving that the new theory gives the same results as the old theory in most areas is generally a major industry once the new theory is established. GRT may be different in its methods from Newton's Laws; but the results are mostly the same unless you go fast or deal with gravity. There's always a startling and generally unheralded new idea at the core, but it has to agree with all the old experiments. And if you look at the crop of interpretations, you'll find that many of them contain just these sorts of elements.

For another example, how about matrix mechanics and wave mechanics? It doesn't make sense to say that one or the other is "correct," so it is not an example in that regard; but it does make sense to say that proving that the two are the same is science. In fact, that proof was a major accomplishment of Schroedinger's.

By definition, interpretations of a theory don't change anything to the formalism of the theory, and hence to the quantitative predictions of outcomes of measurements. So what could possibly render one more probable than another ?

New information or new ways of looking at the problem. After all, Bell didn't invent his inequality the day after EPR proposed their experiment- it took a couple decades, didn't it?

It is only because in order to have this DCQE, you have to do violence to strict quantum theory. Indeed, nowhere in the strict sense of quantum theory it is stated that you can apply Born's rule in the middle of your experiment. You normally only apply Born's rule at the end.

No, you normally apply Born's rule at any time where there is an emission or absorption of a quantum. This is a central error in your analysis.

I have come across your analysis in the thread "how com my shoes where I left em last night," and I disagree with your analysis there; I will quote from The Infamous Boundary, David Wick, 1995, Copernicus, chapter 4, page 35: "Although Schroedinger's wave evolves continuously and deterministically for most of the time, during the emission or absorption of light Bohr's 'quantum jumps' nevertheless occur." In an SPDC, the mechanism by which the idler and signal photons are created involves emission and absorption of the photon. Thus, we apply Born's rule at that point, and then go on calculating probabilities from there.

Now, you CAN interpret the DCQE the way they do it. I wanted to point out that you don't have to do it that way, and that you are not obliged to think that things here change because you there decide, or not, to measure something or not. I found that remark, by itself, enlightening. That was maybe pretentious on my part.

Well, that clears a lot of things up. Your statements didn't sound to me like you admitted the possibility that there was any valid interpretation but the one you were using, and I simply didn't buy that.

If that's the case, you're not talking about two interpretations of a same theory, but about two different theories.

We don't yet know that; it depends on experimental results and analyses that are not yet available. In fact, we could conceivably complete an analysis ourselves and come to a conclusion that no one else has (although I admit it is unlikely), and based on that an experiment might be performed. In other words, right now some of these interpretations are hypotheses; some formally, some informally, and some not really anything but rationalizations. In the light of further information, it is possible that one or another might become more or less probable.

I think that your thinking is incomplete; you have a tendency to cut off valid avenues of inquiry for the sake of clarity, and this is a bad habit because as a result there are many potentially fruitful avenues you will not explore. I think that you should not be so dogmatic.

I'm not talking about things which are "directly observable", I'm talking about modifying, or not, the mathematical machinery that cranks out predictions for measurements: if you do not change that formalism, clearly, you'll get out, in all circumstances, the same numbers, so the same predictions. You're dealing with an interpretation.
If you change the formalism, you have a different theory. It is open to scientific enquiry now.

Well, without wishing to be rude, merely forthright, I have to ask who the hell told you? Because if it wasn't God himself, then you just plain flat DO NOT KNOW THAT!

Take a look at Jack Cramer's Transactional Interpretation. It seems a bit dense and carefully crafted, not to mention kind of a little bit mathematical and connected with existing mathematical physics, to be an "interpretation" the way you mean it. While it is not falsifiable given our current state of knowledge, I can see several ways in which it could become falsifiable. Other interpretations share these characteristics, though not all of them. My tendency is to dismiss the ones that do not, since I cannot see circumstances under which they could become falsifiable.

I think you have "collapsed the wave function of the interpretations" too early! ;)

No, because if that's the case, you're dealing with different theories.

And once again, you cannot possibly know that.

 

[vanesch]

This discussion is not going to have an end. So I think I'll stop here...

 

[vanesch]

I will quote from The Infamous Boundary, David Wick, 1995, Copernicus, chapter 4, page 35: "Although Schroedinger's wave evolves continuously and deterministically for most of the time, during the emission or absorption of light Bohr's 'quantum jumps' nevertheless occur."

Well, I said I was going to stop, but I cannot let this pass :-)
Wick is of course bluntly wrong here. If he were right, then lasers wouldn't work, for instance. But also, mirrors, lenses etc... There wouldn't be coherent phonon-photon scattering (or, what we do here, phonon-neutron scattering).


cheers,
Patrick.

 

[Schneibster]

Wick is of course bluntly wrong here. If he were right, then lasers wouldn't work, for instance. But also, mirrors, lenses etc... There wouldn't be coherent phonon-photon scattering (or, what we do here, phonon-neutron scattering).

I'm not sure I follow that at all. Why would lasers not work? Not to mention mirrors and lenses.

I should point out that phonons are an epiphenomenon that arises from analysis of pressure waves in solids; they have as much and as little real existence as "holes" in a semiconductor. I do not know enough to do the analysis myself, but I am confident that a quantum-mechanical interaction between the members of the crystal via their van der Waals forces is responsible for periodic changes in the probability distributions of the electrons in the shells of the atoms, and the interaction and its periodicity are due to the pressure waves.

To put this another way, the scattering matrix of a photon from an atom at the peak of the pressure wave is different from the scattering matrix of a photon from an atom at the trough, and we can mathematically represent this difference using the contrivance called the phonon. It is then possible to account for "photon-phonon scattering" as this difference in the matrix. But the phonon has no real existence, just as the "hole" does not.

 

[Schneibster]

And, to top it all off, I still haven't any answers to my questions!

 

[vanesch]

I'm not sure I follow that at all. Why would lasers not work?

Because in a laser, the "quantum jump" when an atom emits a photon, has to be "in phase" with the incoming photon (that's stimulated emission). If, at that moment, you apply the Born rule, there's no way to preserve this phase relationship between the incoming and the emitted photon.


cheers,
patrick.

 

[Schneibster]

Because in a laser, the "quantum jump" when an atom emits a photon, has to be "in phase" with the incoming photon (that's stimulated emission).

OK, yes, I'm familiar with that.

If, at that moment, you apply the Born rule, there's no way to preserve this phase relationship between the incoming and the emitted photon.

This I don't get.

The phase of the outgoing photon is determined by the phase of the emitting electron- and that phase is a probability function. If the phase of the electron at the point of the application of Born's rule decoheres into the right phase to match the phase of the incoming photon which also has decohered and exhibited a phase due to interaction with the electron, then the probability of creating an outgoing photon is much higher than it normally is; if not, then it is the normal probability. The photon so emitted is in phase with the triggering photon. At least, that was my understanding of the effect of stimulated emission.

As the pulse bounces back and forth along the material between the silvered ends, many individual photons pass many electrons in many different phases- and whenever they match, this higher probability exists. Thus, as the pulse bounces, it gathers more and more photons, as more and more electrons give up their excited states. Eventually, the probability of passing the half-silvered end of the laser grows high enough that the pulse exits.

So I don't see how you can say that applying Born's rule at the point where the incoming photon makes a measurement of the phase of the electron would cause the laser not to work.

 

[vanesch]

The phase of the outgoing photon is determined by the phase of the emitting electron- and that phase is a probability function.

Can you explain me what you mean by "the phase of the outgoing photon" outside of a superposition ?? Normally, it is the (relative) complex factor in a superposition, but I don't know what it means outside of it (once you have probabilities). Keeping these phase relations is what superposition is all about (and which is eliminated by the Born rule).

cheers,
Patrick.

 

[Schneibster]

Can you explain me what you mean by "the phase of the outgoing photon" outside of a superposition ?? Normally, it is the (relative) complex factor in a superposition, but I don't know what it means outside of it (once you have probabilities). Keeping these phase relations is what superposition is all about (and which is eliminated by the Born rule).

cheers,
Patrick.

Phase means the relationship of two waves to one another. "In phase" means that the phase angle of the waves in time is zero; "out of phase" means it is not. "Opposite phase" means that the phase angle is 180 degrees (or if you prefer, pi radians), and the waves cancel.

An electron and photon that are not interacting cannot have an actual phase, because they do not have actual positions, which means that the times of the peaks and troughs of their waves cannot be determined; this is the meaning of the energy/time uncertainty conjugation. (Yes, yes, I know, they are both actually not plane waves, but that is the best way to describe it intuitively; the math works out the same in any case, and in phase is in phase whether it is a toy plane wave or a real-world elliptical wave.) However, at the point where they interact, they must have a definite position so that they can have a definite phase. This phase is essential to the outcome of the interaction. We normally think in terms of the probability distribution, and use a scattering matrix, but there is a real phase in there between the photon and electron.

At the point where the Born rule is applied, rather than having a probability distribution that describes the possible phases between the electron and incoming photon, the photon and the electron have actual positions, which means that their waves also have an actual phase relationship between them, rather than a probability distribution of phases. If that phase relationship is that they are making a peak at the same time, then they are in phase. If this is the case, then the probability of the electron to release a photon is altered, that is, increased; and if the electron emits a photon, that photon will be in phase with the incoming photon. The fact that the electron and photon have different wavelengths makes this phase relationship a fleeting thing; and the fact that it must happen "on the fly" as the incoming photon breezes by makes it even more ephemeral; nevertheless, it happens, as we well know because lasers work.

One of the characteristics of laser light is that it is coherent; from the optical point of view this means that it is not only monochromatic, but monophasic. This is implicit in the term "coherent," and in the Law of Spin and Statistics for bosons which are occupying the same quantum state. The addition in probabilities under this law that makes bosons more likely to occupy the same quantum state is (if I understand stimulated emission correctly) the factor that causes the electron to be more likely to emit a photon if it will be in phase with the incoming photon. How exactly did you expect that laser light got monophasic?

What you are talking about is the "phase" of the mixing angles of the eigenvalues in two eigenstates (or at least that is how I have understood this use of phase when speaking of superpositions). What I am talking about is the actual, real, physical phase angle between the wave of the electron and the wave of the photon; and since neither position can have an actual value unless they interact, and therefore they cannot have an actual, real, physical phase, I had thought that you would understand that the Born rule must be applied at that point in order that their phase can be definite and have the observed physical consequence of stimulated emission if it is zero.

 

[vanesch]

Phase means the relationship of two waves to one another. "In phase" means that the phase angle of the waves in time is zero; "out of phase" means it is not. "Opposite phase" means that the phase angle is 180 degrees (or if you prefer, pi radians), and the waves cancel.
[...]

You are mixing up semiclassical and quantum descriptions, which do not allow to show when Born's rule can be applied. But I came to realize that the issue is much more complicated than I thought of.
I quickly tried to work it out, and then I realized that there is only one way to make sense to the "coherent emission of a photon by stimulated emission", and that is by throwing the full machinery of QED on it, and see how an incoming coherent state (that's the only way to make a link between the classical phase of an EM wave and the photon description) interacts with an excited model atom (a 2-level system please, not a real atom!)
You feel in your bones that it will be full of superpositions , but I got stuck trying to work it out, and I'm now reading up on it in Mandel and Wolf.
I'll come back to the issue when I cleared it out myself.

cheers,
Patrick.

 

[JesseM]

An electron and photon that are not interacting cannot have an actual phase, because they do not have actual positions, which means that the times of the peaks and troughs of their waves cannot be determined; this is the meaning of the energy/time uncertainty conjugation.

Are you sure about this? I had thought the peaks and troughs were attributes of the wavefunction, not actual observable quantities like position and momentum, so there wouldn't be any uncertainty in the positions of maximum and minimum amplitude. But that's just how it works in nonrelativistic QM, it's possible things could work differently in quantum field theory. But if you think they do, are you basing this on any source or is it just your own inference?

 

[Schneibster]

You are mixing up semiclassical and quantum descriptions, which do not allow to show when Born's rule can be applied.

Hrrmmm, well, I had thought that anything with a wavelength pretty much had to have a phase. But OK, you know a lot more of the formal stuff than I do, I'll take your word for it.

But I came to realize that the issue is much more complicated than I thought of.

I quickly tried to work it out, and then I realized that there is only one way to make sense to the "coherent emission of a photon by stimulated emission", and that is by throwing the full machinery of QED on it, and see how an incoming coherent state (that's the only way to make a link between the classical phase of an EM wave and the photon description) interacts with an excited model atom (a 2-level system please, not a real atom!)
You feel in your bones that it will be full of superpositions , but I got stuck trying to work it out, and I'm now reading up on it in Mandel and Wolf.
I'll come back to the issue when I cleared it out myself.

cheers,
Patrick.

You know, I have a question. I had thought that all of the talk about electrons being waves, and the phase angle, and all of that, linked right up with classical wave mechanics, and that that was one of the links between QM and CM. From what I'm seeing here, though, it sounds like the phase being used in the probability calculations is a highly abstract entity that has nothing to do with the classical phase of the wave. So I got a question- what determines the phase of the electron wave? I don't mean around the atom, I mean in an electron beam. I'm sure if you put it in an atom, it gets a lot more complex- and IIRC, the classical wavelength is really important, because the shells are resonant whole numbers of classical wavelengths, right?

 

[Schneibster]

Are you sure about this? I had thought the peaks and troughs were attributes of the wavefunction, not actual observable quantities like position and momentum, so there wouldn't be any uncertainty in the positions of maximum and minimum amplitude. But that's just how it works in nonrelativistic QM, it's possible things could work differently in quantum field theory. But if you think they do, are you basing this on any source or is it just your own inference?

No, it's my own inference. And probably wrong, judging by what I just got back from V.

 

[vanesch]

You know, I have a question. I had thought that all of the talk about electrons being waves, and the phase angle, and all of that, linked right up with classical wave mechanics, and that that was one of the links between QM and CM. From what I'm seeing here, though, it sounds like the phase being used in the probability calculations is a highly abstract entity that has nothing to do with the classical phase of the wave.

There are several issues here, and it all comes down to different aspects of quantum field theory. But no panic, you don't need to study that in all detail with all the renormalization and everything to come clear of it.

First, there is the "non-relativistic" quantum particle, with mass (it is trickier to treat a zero-mass particle non-relativistically, and that's where I got myself in a mess by giving that laser example ! But I promise you that I will try to put my "money" (time and posts) where my mouth is :-), such as an electron, or a neutron.

You have to choose a basis, such as the position basis or the momentum basis, to work in. If you work in the "position" basis, there is ONE possible quantum state corresponding to each position (x,y,z) ; and we denote that state by |x,y,z> (or by |x> or something, doesn't matter).
Applying the Born rule in that basis means that you assign a probability to find the particle to each position.
If you choose to work in the momentum basis, then to each momentum vector, (kx, ky, kz) there corresponds ONE quantum state |kx,ky,kz> or for short |k>.

Note that in quantum mechanics, a state |u> and exp(i a) |u> represent exactly the same state.

It turns out that the position state |x> is a superposition of momentum states, namely the integral over all k of exp(i k x) |k> and vice versa:

A momentum state |k> is a superposition of position states:
Integral over all x of exp(- i k x) |x>.

When you write a momentum state IN THE POSITION BASE, then you CALL THE WAVE FUNCTION this exp(- i k x) : they are the coefficients in the superposition of the position state |x> in the considered state, namely the momentum state |k>.
The absolute square of that coefficient gives you the probability, at that moment, if you measure the position, to find the particle in state |x> (in position x) ; this is an application of the Born rule at that point.

You also see that, because |k> and exp(i a) |k> represent the same state, that the wave function exp(- i k x) or the wave function exp( - i k x + i a) describe the same physical state.

So there is no meaning attached to "the phase of the electron wave function".

What can happen, however, such as in a double slit experiment, is that we reason "as if it were a classical wave" (because the unitary evolution equations will be very similar), and we calculate "optical path differences" with "partial waves that interfere". That's a shortcut, which is in fact meant to calculate the final wave function (on the screen) of the electron. Indeed, "interference effects" will then cause you to have a wave function of which the amplitude will not be a constant. This is, as I said, using "classical wave theory" to calculate THE QUANTUMMECHANICAL UNITARY EVOLUTION as expressed in superpositions of position states.
So what seems to be a "classical calculation" when you use a classical field to do quantum mechanics of particles, comes actually down to applying unitary quantum mechanical evolution. But it is a mathematical trick, that can only be applied when talking about the same particle.
If you apply the Born rule somewhere, you do not "switch to the classical wave" but you would switch to "the classical intensities" and your wave is dead. You only do that when you project on a screen (and it is for all practical purposes - thanks to decoherence theory).

However, working with the classical electromagnetic field is a lot trickier. In fact, the mapping between the classical EM field and the QM representation requires the full machinery of QED. The EM field is not really "the field of the photon", although you MAY use it that way if you work with a one-photon state, in the same way as we did above. But then this is just a mathematical trick, not a correspondence with a real EM field.
The reason is exactly the one you are struggling with:
a real EM field has a definite phase, while a one-photon state hasn't.
So if you want to relate to the "real phase" of a classical EM field, you need to construct, what is called "coherent states".
QED sees the quantum EM field in several states, but now the number of photons (it is in fact the DEFINITION of what is a photon...) is variable. So the different possible quantum states of the quantum EM field are:

|0> Nothing, the vacuum
|k> One - photon state with momentum k (for all vectors k)
|k1,k2> 2 - photon states ; one with momentum k1 and one with momentum k2.
|k1,k2,k3>
|k1,k2,k3,k4>
...
|n-photon state>
...
(I dropped the 2 possible polarisations for each photon).

Note again that there is no "phase" attached to each photon, or to each state. Each state is just a bucket saying that there are 7 photons, one with momentum k1, one with momentum k2... No position, no phase.
It is only if we limit ourselves to one-photon states that we can play the trick with the "wave function".

What corresponds now to a classical EM field WITH phase ?

It is the state, described by the following superposition:

$$|\alpha,k> = N \sum_{n} \frac{\alpha^n}{n!}|k,k,k..(n)..k>$$

Here, we have the coherent state which corresponds to a plane wave with wave vector k, intensity given by |alpha|^2 and phase (this time the real, classical phase of the corresponding classical EM field) by the phase of alpha.
You see that we can, as usual, change the quantum phase of the state, it doesn't change the "classical phase" which is encoded in the relative phases of the terms in the superposition.
You also see that a well-defined classical wave consists of superpositions of quantum states with different photon numbers. In fact, this state can also be shown to give rise to the Poisson statistics if we will count photons with a photon detector (applying Born's rule to this state in this basis).

I was trying to work out the effect of stimulated emission, in which I tried to show that this transforms a coherent state in another coherent state with slightly more amplitude, but my calculation screwed up and I have to find out where it did.

cheers,
patrick.

 

[Schneibster]

Thank you, Patrick; that hardly says enough to cover the effort you went to, so, let me say also: I really appreciate it.

I have a question: What is denoted by exp(- i k x)? I am not familiar with this notation.

I will make some comments on your post shortly, not to dispute but to make sure I understand it properly. This is a question that I have not received an answer to before, and I have asked others. So again, I really do appreciate your effort here.

 

[vanesch]

What is denoted by exp(- i k x)? I am not familiar with this notation.

It is $$e^{- i k x}$$

e is the neperian logarithm base (2.78...)
i is the imaginary unit

In real and imaginary components, we have:

$$e^{- i k x} = \cos(k x) - i \sin(k x)$$

I hope this is somehow familiar ?

cheers,
patrick.

 

[vanesch]

I will outline what I tried to do in my calculation, and where it screws up.

In the following, |n> will denote an n-photon state, all with the same momentum k.

A simple (too simple) way to describe emission by an excited atom is:

$$|excited atom> |n> \rightarrow a |excited atom> |n> + b \sqrt{n+1} |desexcited atom>|n+>$$

If you naively apply this to a coherent state:

$$\sum_n \alpha^n/n! |n>$$

then you find something that takes on the appearance of:

$$a \sum_n \alpha^n/n! |n>|excited> + \sum_n \alpha^n/n! b \sqrt{n} |n+1>|desexcited>$$

But this cannot be right. First of all, I don't manage to get the second term in the right form of a coherent state. And that would still leave me with a superposition between excited and unexcited atoms.

What is wrong of course is that there is not only emission, but also absorption, and that will retransform back the |n+1> state into an |n> state. So one should really solve the evolution equation completely, and not separate absorption and emission. And that's where I'm stuck for the moment.

cheers,
patrick.

 

[Schneibster]

It is $$e^{- i k x}$$

e is the neperian logarithm base (2.78...)
i is the imaginary unit

In real and imaginary components, we have:

$$e^{- i k x} = \cos(k x) - i \sin(k x)$$

I hope this is somehow familiar ?

cheers,
patrick.

Sure, I get it; is there some reason you couldn't have put it that way in the first place?

 

[selfAdjoint]

Sure, I get it; is there some reason you couldn't have put it that way in the first place?

Sigh, the exponential notation exp( X) is entirely equivalent to the power notation $$e^X$$. They are used interchangeably throughout math and physics.

 

[Schneibster]

Sigh, the exponential notation exp( X) is entirely equivalent to the power notation $$e^X$$. They are used interchangeably throughout math and physics.

Gee, that's two smartass comments in a row! What, has everybody got a stick up their ass today?

Sorry, son, I hadn't come across that notation before. Do you want me to bow down before your splenderiferous awesomeness now, or can I wait until next Tuesday?

 

[vanesch]

Sure, I get it; is there some reason you couldn't have put it that way in the first place?

ASCII laziness. exp(a) types easier than the power notation, and moreover you don't have to lower font size, which makes "a" usually more readable.
And, as SA pointed out, it is standard notation, so I didn't realize it would confuse anybody.

cheers,
Patrick.

 

[Schneibster]

ASCII laziness. exp(a) types easier than the power notation, and moreover you don't have to lower font size, which makes "a" usually more readable.
And, as SA pointed out, it is standard notation, so I didn't realize it would confuse anybody.

cheers,
Patrick.

Thanks, Patrick, I appreciate the explanation. I am used to scientific notation for quantities like 4x10E3, or 6.35x10E-6, and I figured exp meant exponent, but what stumped me was exponent of WHAT BASE?

 

[Ontoplankton]

To put this another way, the scattering matrix of a photon from an atom at the peak of the pressure wave is different from the scattering matrix of a photon from an atom at the trough, and we can mathematically represent this difference using the contrivance called the phonon. It is then possible to account for "photon-phonon scattering" as this difference in the matrix. But the phonon has no real existence, just as the "hole" does not.

As I understand it, some people think ordinary particles are just as much a mathematical contrivance as quasiparticles like phonons; the basic entity is the quantum field, and particles are just a convenient way to talk about decoherent trajectories. I think this point of view makes a lot of sense.

See e.g. There is no "first" quantization

 

[Schneibster]

Yes, I have come across that point of view as well. I'm currently trying to sort out what I think about it as opposed to more traditional ideas.

 

[Schneibster]

Patrick, did you ever figure out your problem?

And will we ever get to the point where I can get some answers to the questions I asked in my initial post in this thread?

 

[one_stinky_bum]

Didn't mean to bring the thread back from the dead, but I worked on a QE experiment last summer - maybe our paper would be helpful. We've fixed the problem in the explanation that the earlier version had.

http://marcus.whitman.edu/~beckmk/QM/qe/qe.pdf

Ashifi.

 

[vanesch]

Didn't mean to bring the thread back from the dead, but I worked on a QE experiment last summer - maybe our paper would be helpful. We've fixed the problem in the explanation that the earlier version had.

http://marcus.whitman.edu/~beckmk/QM/qe/qe.pdf

Ashifi.

Nice paper :-)

However, what I find strange in these reasonings is that one insists on ERASING information. Of course, this somehow comes down to the same thing, but I find it more mysterious that "erased" information gives rise to interference. Usually one needs to EXTRACT INCOMPATIBLE information in order to obtain interference.

What I mean is the following. In the "classical" quantum erasure experiment where one can use the idler polarisation "to find out which path the signal photon took" or where one can "erase that information", what one actually needs when "erasing that information" is to extract information of an incompatible variable in order to subselect a sample which does show interference. Of course, when one extracts that information, and because of the incompatibility of that measurement with the "which path" measurement, one has in fact also lost every possibility to recover that which path information, so one can say, with some poetic liberty, that one has "erased" that which path information. But what one really needed was to EXTRACT other information !
A simple way to demonstrate this, is in the interference or not of the two beams obtained from the signal beam. It is not because the idler beam is dumped into a block of hot graphite (which also erases all possibilities of recovering the which path information from that beam), that suddenly an interference pattern appears at the signal side. It is because you need to have a coincident CLICK of the the idler under 45 degrees that you can select one of the two subsamples at the signal side. So I'd say that in this case, it is clear that you *need to extract* information, and that "erasure" is not sufficient (or has in fact anything to do with it). But, as I said, it is true that the extraction of the needed information makes you make an incompatible measurement with the "which path" measurement ; and as such you did erase this information, as a side effect.
The reason you need information extraction is that in ALL these potential "which path" experiments, you have lack of interference, or, what comes down to the same, a superposition of two shifted interference patterns (because sin^2 + cos^2 = 1). In order to separate out one of both subsamples (the cos^2 one, or the sin^2 one), you need extra information. It is the extraction of that extra information which is incompatible with the extraction of the "which path" information.

As you point out in the paper, around equation (2), you need to know whether you will be in the +45 or the -45 branch, because it are these two branches which give rise to the two interference patterns (the cos^2 and the sin^2).

I don't, however agree with the explanation on top of page 9: indeed, if you DUMP the idler beam in a hot graphite block, you erased the information also. That doesn't make the interference pattern appear at the signal side.

I don't agree to what is stated below equation (4) either: both density matrices are equal, and as such, the mixed states are identical. It is an error that is easily made (I've been guilty of that myself and been corrected for it a few times): different statistical compositions of pure states can give rise to identical mixtures. In quantum statistics, if the density matrices are identical, the mixtures are identical, even if you composed them by lumping together different pure states. You have the liberty to write the mixed state in the hh + vv way, or in the ++ + -- (45 degree) way. Both are diagonal density matrices with 1/2 on the diagonal, and as you know, a unitary transformation keeps such a scalar matrix a scalar diagonal matrix.
The reason why these mixtures are physically identical is that ALL expectation values of ALL possible measurements (which constitute all what is observable) are given by Tr(rho A). So if the rho's are identical, there is NO WAY to distinguish the two mixtures, hence they are physically identical.

You are cheating if you look at the "interference of fringes and anti-fringes" because to do that you have to synchronize with your 1 Hz generator. If you want the 1 Hz generator to make a "mixed state", then you shouldn't analyse results on the 1 Hz scale, but you should accumulate data over many cycles ; otherwise you're not working with the mixture, but with the individual |HH> and |VV> states ; now THERE is of course a difference between a |HH> state and a |45 45> state of course. There is no difference between the mixtures. But you didn't really make a mixture because the 1 Hz scale is too remote from the frequency of the light or the time constants of the detectors, and there are many simple techniques to recover the pure states from the data. The reason is that you are working with an analysis that supposes stationary random processes and that your 1 Hz modulated choice is not a stationary process (except if you look onto it on a timescale which is very long compared to 1 second).

cheers,
Patrick.

 

[one_stinky_bum]

I'll run your comments by my prof (Mark) and I'll get back to you. I don't want to say something I'm not 100% sure of.