Photons do not travel in straight lines

[tickle_monste]

By considering interfering fields or probability amplitudes instead of photons the situation becomes much clearer and lots of the ambiguities are avoided.

That makes sense. So before the photon is absorbed by, say, an atom in your eye, it can be considered as "delocalized" across an area? Is this area considered to be a sphere emanating from whatever the photon originated from, expanding at the speed of light, sort of like a bubble? Information must be present everywhere on this (supposed) bubble, does that information suddenly "collapse" when the photon is finally absorbed by that atom in your eye? I would guess that once it is absorbed, you would be able to trace back the (a single) path to the source, that would be the equivalent of a straight line (when you account for lensing, reflection, the curvature of space-time, etc.), is this correct?

 

[Cthugha]

That makes sense. So before the photon is absorbed by, say, an atom in your eye, it can be considered as "delocalized" across an area? Is this area considered to be a sphere emanating from whatever the photon originated from, expanding at the speed of light, sort of like a bubble? Information must be present everywhere on this (supposed) bubble, does that information suddenly "collapse" when the photon is finally absorbed by that atom in your eye?

Well, what the value of some variable is, before it is measured, is one of the great questions in qm. Different interpretations of qm will give different answers to this questions ranging from a simple "the value is not well defined" to a more complicated answer a Bohmian would favor. What one can indeed say, is that the field, which originated from some light source, spreads out as a sphere and so does the probability density to detect a photon. Whether there is some real and localized entity connected with it before the detection of a photon, is again difficult to answer.

I would guess that once it is absorbed, you would be able to trace back the (a single) path to the source, that would be the equivalent of a straight line (when you account for lensing, reflection, the curvature of space-time, etc.), is this correct?

Not necessarily. If you try to find the path to the source in the double slit experiment for example, you will only find out, that one of the slits was the source, but not which one. If you knew, you would not find an interference pattern.

1) Photons, being Bosons, do not and cannot interfer with themselves or each other.

Do photons know that, too?

2) It is only the effects of photons on matter that can show interference. Interference phenomena therefore require intervening media such as slits and biprisms etc. That is why you will never see an interference experiment with only light sources and detectors.

Strange that interference experiments with synchronized and phase locked lasers work completely without a slit or other matter. Michelson interferometers also do not use slits and show interference. 2-photon-interference experiments using consecutive photons from single photon sources also work without a slit, using just a beam splitter. Or is even a beam splitter too much matter for your taste?

3) Photons travel in straight lines until they interact with matter. It is the only way momentum is conserved.

Prior to a measurement the best thing you can do is to consider the coupled system of photon and photon source, which has some well defined momentum. If you measure the measure the momentum of the photon or the emitter after an emission process, you have a photon with well defined momentum. Before that measurement, the momentum is simply not well defined. As said before, attributing real values to unmeasured variables can go pretty wrong. What at last completely kills your argumentation is the problem, that a description using a well defined and localized photon density does not give sensible results for polychromatic fields. If you define a localized photon probability density, its maximum will not be locally connected to the energy density and it will also not be locally connected to the detection probability density (see Mandel and Wolf, Optical Coherence and Quantum Optics, chapter 12.11, around page 637 in my edition). So these 3 distributions will peak at different positions, which renders the concept pointless.

4) Interfernce experiments have been done with photons of different wavelength, therefore it is not true that interference requires the same type of photons.

Sure, if they come from the same source or have some other fixed phase relationship this can work. However, even in this situation the probability amplitudes will still be indistinguishable. After some detection you are not able to tell, which photon is which, even if you could do that beforehand (see for example "Quantum interference with distinguishable photons through indistinguishable pathways" by Kim and Grice, JOSA B, Vol. 22, Issue 2, pp. 493-498 or on arxiv), so it is again not meaningful to talk about different photons, because one has no means to tell them apart. Again, there is no problem, if you use probability amplitudes as the basis of your description in these cases.

 

[bjacoby]

Oh so in the double slit experiment, the interference pattern produced by the two waves is called single photon interference? So the waves that interfere are separate but part of the same photon? That is quite confusing. How can one photon be split into two and then reform?

Well it is confusing. And of course QM standard model is even worse. So instead of reading a freshman textbook describing all the magic, and fairies that go measure the second slit for the photon, and the religious stories of things that don't exist until you look at them, let's look carefully with logic and reason instead.

What happens in a double slit diffraction experiment? It IS known.

You fire a single photon at the slits. It goes through one of them. It's straight path is deflected at the slit in some unknown manner. It lands on the detector and you count it as a "flash" at a certain position. Well and good.

But it doesn't start to get interesting until you do this over and over a great many times. Much to your wonder and amazement a pattern starts to emerge on the screen which is not a simple mechanical scattering of hard particles. It is easily recognized as an interference pattern such as that produced by a wave going through two slits. But note carefully that this is NOT a wave interference pattern! It is a statistical function of the counting of photon landing sites which for some odd reason TAKES THE FORM of a double slit diffraction pattern!

This is the mystery! Block one of the slits and even though each photon particle clearly does not have the "reach" to interact with the second slit, it clearly "knows" it's no longer there! And that is proved because the statistical landing pattern changes!

The Standard Model "explains" this by saying that photon particles are actual dual entities that are both waves and particles at the same time and switch back and forth depending on what you are doing to them etc. Well that has to be nonsense. Since there are two things happening apparently, then let's just MAKE them two separate things! We might say therefore that there are photon-particles as well as some kind of waves that seem to interact with them and matter by changing their trajectories. This could be true and is the basis of some theorizing, but we should remember that we have little proof that the statistical landing patterns that are observed to be similar to diffraction functions are actually DUE to any kind of waves. There remains the possibility that somehow the mathematical functions produced are identical with those observed with waves for some other unknown action having nothing to do with waves. The assumption that mathematical wave solutions are always produced ONLY by waves is, in a phrase, a leap of faith.

So if one assumes that photons are logically traditional particles, it is clear that any "splitting apart" explanation is nonsense. The photon clearly must go through only one slit. The fact that it's deflection statistics produce wave function solutions is the mystery. Clearly it must be that SOMETHING ELSE is "associated" with each photon that does the "measuring and deflecting". What that is seems to be pretty much open for speculation at this time. There are theories that in addition to a photon there are actual waves of some type that may actually be the "probability waves" of QM traveling from the source to the target or in the other direction that somehow "deflect" photons as they traverse the experiments. But it should be clear from the wild illogical "explanations" of QM that there is MUCH that is little understood here.

 

[Cthugha]

You fire a single photon at the slits. It goes through one of them. It's straight path is deflected at the slit in some unknown manner. It lands on the detector and you count it as a "flash" at a certain position. Well and good.

First of all: In almost all experiments you do not fire single photons at the slits. In most cases you do not even fire a well defined number of photons at the slits. Coherent light as well as thermal light does not have a fixed photon number, but some intrinsic photon number uncertainty.

The Standard Model "explains" this by saying that photon particles are actual dual entities that are both waves and particles at the same time and switch back and forth depending on what you are doing to them etc. Well that has to be nonsense.
[...]
So if one assumes that photons are logically traditional particles, it is clear that any "splitting apart" explanation is nonsense. The photon clearly must go through only one slit.

The idea, that photons are logically traditional particles is wrong. The idea that photons are traditional particles going through just one of the slits is simply not compatible with experiments. However, contrary to what you say, qm does not predict photon particles to be dual entities switching back and forth between wave and particle behaviour. Probability amplitudes have wave character. This is true for any probability amplitude, whether it is about electrons, photons or buckyballs. Photons are quantized excitations of the em-field. If you think of photons as traditional (classical) particles, you deny the role of the underlying fields, which must go wrong as any basic text on QFT or quantum optics will show you.

 

[DrChinese]

The Standard Model "explains" this by saying that photon particles are actual dual entities that are both waves and particles at the same time and switch back and forth depending on what you are doing to them etc. Well that has to be nonsense. Since there are two things happening apparently, then let's just MAKE them two separate things! We might say therefore that there are photon-particles as well as some kind of waves that seem to interact with them and matter by changing their trajectories. This could be true and is the basis of some theorizing, but we should remember that we have little proof that the statistical landing patterns that are observed to be similar to diffraction functions are actually DUE to any kind of waves. There remains the possibility that somehow the mathematical functions produced are identical with those observed with waves for some other unknown action having nothing to do with waves. The assumption that mathematical wave solutions are always produced ONLY by waves is, in a phrase, a leap of faith.

So if one assumes that photons are logically traditional particles, it is clear that any "splitting apart" explanation is nonsense. The photon clearly must go through only one slit. The fact that it's deflection statistics produce wave function solutions is the mystery. Clearly it must be that SOMETHING ELSE is "associated" with each photon that does the "measuring and deflecting". What that is seems to be pretty much open for speculation at this time. There are theories that in addition to a photon there are actual waves of some type that may actually be the "probability waves" of QM traveling from the source to the target or in the other direction that somehow "deflect" photons as they traverse the experiments. But it should be clear from the wild illogical "explanations" of QM that there is MUCH that is little understood here.

QM is a formalism, and it is a lot better than you give it credit for. For example, where is it wrong?

The issue is when people try to give explanations beyond the scope of the formalism. Whether it is a wave or a particle matters not to the formalism. The Heisenberg Uncertainty Principle alone can explain double slit interference, see for example: http://arxiv.org/abs/quant-ph/0703126

So if you have an issue with the QM explanation, it seems to me to be with the semantics and not the formalism or its application (of which you have provided no specific criticism).

If you are not aware of it, the Bohmian model operates more closely to your description of particles/waves. It is equivalent to QM. It states that a photon goes through a specific slit (the closer one to where detected) while a related pilot wave goes through both slits.

 

[bjacoby]

QM is a formalism, and it is a lot better than you give it credit for. For example, where is it wrong?

So if you have an issue with the QM explanation, it seems to me to be with the semantics and not the formalism or its application (of which you have provided no specific criticism).

The problem is not with a formalism which has obviously been tweaked to a high degree, but with the concept of "wrong". You say I take issue with mere "symantics". I say that words actually have meanings. I say logic and definitions have a role in science and elastic versions of these "explain" nothing.

No question that the formalism "works" to a degree, meaning that mathematical predictions can be obtained that approximate what is observed. But the fundamental questions of philosophy remain. What is a "photon"? If a particle has a certain meaning then one must reconcile that meaning with the particle nature of photons. A particle does not have a wave nature. And to say so is nonsense. A wave has a wave nature and to call that wave a particle is likewise nonsense. Words really do have meanings.

So the question here is not to disprove the results of the formalism, but to establish a logical philosophy that does not require magic, does not violate causality, or has a lot of mysterious undefined operations and terms. Obviously when one attempts to describe the formalism in words it doesn't work. There is a great wandering in the wilderness. The formalism works. The description of it does not!

Why is that? Well one reason in my opinion is that everyone wants to pretend that there are no mysteries here. Nobody is willing to say "We really don't know why this works as it does." And the end result is a myriad of "explanations" that include bogus ideas like "action at a distance", things that don't exist until you look at them, and "particles" that split and go through two holes at once and magically recombine in some fashion to give correct answers.

No. The problem is not in our stars or our semantics, but in your philosophy!

 

[bjacoby]

First of all: In almost all experiments you do not fire single photons at the slits. In most cases you do not even fire a well defined number of photons at the slits. Coherent light as well as thermal light does not have a fixed photon number, but some intrinsic photon number uncertainty.

The idea, that photons are logically traditional particles is wrong. The idea that photons are traditional particles going through just one of the slits is simply not compatible with experiments. However, contrary to what you say, qm does not predict photon particles to be dual entities switching back and forth between wave and particle behaviour. Probability amplitudes have wave character. This is true for any probability amplitude, whether it is about electrons, photons or buckyballs. Photons are quantized excitations of the em-field. If you think of photons as traditional (classical) particles, you deny the role of the underlying fields, which must go wrong as any basic text on QFT or quantum optics will show you.

First of all, I don't care about all experiments, only the one I'm talking about. Shine a laser at a dual slit. Put up a channel plate viewer to see single photons. Insert ND filters until photons are coming one at a time. How long do you want me to wait between photons?

Obviously you can't say the idea that photons are traditional particles is "wrong" since you really can't tell us what photons are, can you? It is clear, however, that photon propagation involves much more that simple traditional particles. What exactly do the words "quantized excitations of the EM-field" actually mean? Can you explain that for us in detail?

So what is wrong with the idea of saying that LIGHT is a combination of particles and waves of some type? Why is there a requirement that both must be somehow merged into a mythical wave-article?

We DO know that light is NOT waves. Energy transfer is too fast. And energy transfers are limited to certain values. Plus we know that the physical dimensions of these light "particles" are too small to in any way sense the presence of the other slit. The bottom line is exactly as I have stated it. Particles in the classical sense appear to be shooting along but have their trajectories modified by matter in some way so as to produce trajectory statistics that are wave solutions. (please note, however that these are NOT actual wave solutions which are mathematically continuous and differentiable, while our "diffraction" results are statistical distributions of points which are NOT continuous nor differentiable)

Maxwell noted long ago that energy (information) can only be transferred in two mechanisms: by particles or by waves. There are no other mechanisms. Light energy has long ago been determined not to be transmitted by waves for the reasons I stated.

So as you say, the logical assumption is that SOMEHOW a "wave" must also be involved in this operation. Of course you can't possibly tell me what exactly a "probability wave" is. But we all know that such formalism actually does give more or less correct predictions even if we can't explain why.

So why won't you admit you can't explain why? Then perhaps we can begin to speculate as what might be involved...

 

[Cthugha]

First of all, I don't care about all experiments, only the one I'm talking about. Shine a laser at a dual slit. Put up a channel plate viewer to see single photons. Insert ND filters until photons are coming one at a time. How long do you want me to wait between photons?

I am sorry to hear that. There are lots of other experiments, which tell us a lot more about the properties of light, but I will see how far I can get without citing them. However I would like to stress that using a ND filter in laser beam path does not give you single photons. You just damp the amplitude of the coherent state. The photon number uncertainty of a single photon (or other Fock) state is 0, while the photon number uncertainty of a coherent state is always on the order of the mean photon number. If you really use single photons, for example one out of two photons of an entangled beam you will not see the double slit pattern because the light you use is too incoherent. However, this is not central to your concern, I suppose, but one should keep in mind that having single detector clicks does not assure that you have single photons. By the way, if you are really just interested in the double slit, you might find this paper interesting:
http://arxiv.org/abs/quant-ph/0703126
It is a preprint of T.V. Marcella Eur. J. Phys. v.23, p.615 (2002) and

Obviously you can't say the idea that photons are traditional particles is "wrong" since you really can't tell us what photons are, can you? It is clear, however, that photon propagation involves much more that simple traditional particles. What exactly do the words "quantized excitations of the EM-field" actually mean? Can you explain that for us in detail?

Well, how deep is your understanding of QM? I could tell you stuff about QM formulations of harmonic oscillators and stuff, but that would not help much, if you do not have some basic knowledge in QM, QFT and quantum optics. If you are a layman, let me boil down all of that to a simple "a photon is the sum of its properties". Besides that, this forum has a great FAQ article (in the general physics subforum) on wave-particle-duality and why there is not really one in QM. You might want to read it.

So what is wrong with the idea of saying that LIGHT is a combination of particles and waves of some type? Why is there a requirement that both must be somehow merged into a mythical wave-article?

Well, QM usually does not really do that. QM has one single description from which both particle and wave behaviour can be explained. QM always deals with probability amplitudes. This is where the wavelike aspect comes from. However it does not only apply to electrons, photons and such stuff, but theoretically also to cars, trees and such stuff. The reason why you do not see tree interference in double slit experiments is a matter of decoherence. This is also where the intuitive classical description goes wrong. The classical particle point of view is usually what you have after decoherence: Some discrete and definite position. However in QM the particle aspect boils down to discrete and quantized photon numbers. This is not the traditional meaning of a particle.

We DO know that light is NOT waves. Energy transfer is too fast. And energy transfers are limited to certain values. Plus we know that the physical dimensions of these light "particles" are too small to in any way sense the presence of the other slit. The bottom line is exactly as I have stated it. Particles in the classical sense appear to be shooting along but have their trajectories modified by matter in some way so as to produce trajectory statistics that are wave solutions. (please note, however that these are NOT actual wave solutions which are mathematically continuous and differentiable, while our "diffraction" results are statistical distributions of points which are NOT continuous nor differentiable)

Energy transfer is too fast? This is nonsense. That the energy transfer is limited to quantized values is of course true. This is what constitutes particles in QM. Your statement about the physical extents is however wrong. If you wanted to define some spatial extent for light, the closest thing you get is the coherence volume, which is the volume inside which photons are indistinguishable. By the way this is also the quantity, which defines whether there is a double slit pattern. If both slits are inside of one coherence volume, you will see interference. Otherwise you will not.
By the way, note that I never said that photons are waves. You just do not get around seeing wavelike behaviour because everything shows wavelike behaviour in QM.

Maxwell noted long ago that energy (information) can only be transferred in two mechanisms: by particles or by waves. There are no other mechanisms. Light energy has long ago been determined not to be transmitted by waves for the reasons I stated.

Well, you should start with the very basics of QM. As I said before, the wavelike aspect, which is often mentioned is a consequence of QM itself, not of the photons.

So why won't you admit you can't explain why? Then perhaps we can begin to speculate as what might be involved...

Going back to the deepest reasons of course I do not know why. However, this is not physics and just not interesting. I also do not know, why gravity works as it works on the deepest level, why there is electromagnetic force and why there is magnetism. You can always ask "why" on a deeper level and get to the final speculative answers

a) because god made it that way.

b) because the natural constants accidentally have exactly such values that our world turns out to be the way it is.

c) because the flying spaghetti monster arranged it.

So - to me - a photon is the sum of its properties. And to me the simplest model explaining all of its properties is the model I adopt. So to me it is a quantized excitation of the em field.

 

[bjacoby]

1. I just knew I was going to get into trouble for using the words ND filter! Let's just say or equivalent. While I'm using the double slit (or single slit for that matter!) as an example there are a lot of interesting subjects here having to do with coherence, self-confined beams and the like. I am purposely trying to not turn this into a discussion of the details of high-powered mathematics so that lurkers are not lost. On the other hand, I am trying to keep such fundamentals in mind so that I am not saying things that are demonstrably wrong.

2. You are obviously dying to tell me to go read a freshman textbook. However, suffice it to say that I studied graduate level QM under R. Mills (yes THAT Mills) and Yang. I know you find it difficult to understand how someone so properly indoctrinated would go bad and start questioning the gospel, but it happens. The only difference between then and now is that a few more practical problems have been calculated using QM. Back then the hydrogen atom was about it. Harmonic oscillators and energy wells are just mathematical exercises. They are not practical problems, even though everyone pretends that they are. I guess my problem is I need to upgrade to the latest version of QM...

3. I can see we actually ARE having problems with semantics here. I am assuming that the "on" in photon implies it's a particle. You are saying that the word "photon" is just a word like "turtle" that implies all the properties of the object. Thus your word is a name for the entire object and mine implies certain properties of an object which while associated with additional properties may or may not have those additional properties be part of it's own.

4. So I say there is no requirement that a "light particle" be a merger of both particle and wave properties and you say, yes it does because QM derives both these properties from some vague probabilistic formalism. But the fact is that QM is NOTHING but formalism. It does not and probably cannot describe what a light particle "is". It only predicts how it is likely to behave to some degree.

5. So where we stand is you are defending a vast and complex formalism of epicycles because it nicely explains the motion of the planets. And I am suggesting that perhaps one needs a new way to look at things that simplifies everything by a change of point of view.

6. But while you note that wave-like behavior is a property of QM, light is nevertheless a fooler because in the classical macroscopic sense it looks all the world like a high-frequency version of Maxwellian EM radiation. And in fact "electromagnetic spectrum charts" have always portrayed it as such. But if one looks close enough it's obvious that this idea is wrong. As I said before, energy transfers are too fast for light to be merely high frequency waves in the luminiferous aether. And there are other problems as well as we both note. But wave characteristics do persist. And they transfer to statistics. And we find they take the form of 'probability waves" whatever that might be. Just what is the medium that "imaginary probability waves" propagate in? Obviously the standard answer is that these waves need no medium just as no EM wave needs a medium. All these waves propagate quite nicely in "nothing at all". But that is a philosophical paradox like talking about the properties of "nothing at all". One cannot logically separate properties from the object that possesses those properties. It's nonsense. Particles on the other hand transmit energy and information from one place to another with no philosophical conundrums. Which is why I suggest the need for a higher point of view.

7. Let me say I am not asking "why" as you suggest. I'm asking "what logical model?". You on the other hand are suggesting that QM formalism is some kind of model. In spite of it's ability to predict to a degree, I suggest that there are too many unexplained definitions (such as probability waves) and illogical constructs (waves without media) to qualify as a model. You can accept it as useful, but don't call it a model.

As for the original question if photons travel in straight lines, I suggest that they do unless they interact with matter or fields and are deflected. Which oddly enough is a property of classic particles.

As for "why" I kind of like your spaghetti monster theory!

 

[DrChinese]

4. So I say there is no requirement that a "light particle" be a merger of both particle and wave properties and you say, yes it does because QM derives both these properties from some vague probabilistic formalism. But the fact is that QM is NOTHING but formalism. It does not and probably cannot describe what a light particle "is". It only predicts how it is likely to behave to some degree.

5. So where we stand is you are defending a vast and complex formalism of epicycles because it nicely explains the motion of the planets. And I am suggesting that perhaps one needs a new way to look at things that simplifies everything by a change of point of view.

So where is the criticism? How is QM a "vast and complex" formalism? If simplification can give us something, where is the simpler model? You imply that everyone else is in the "Earth is the center of the Solar System" camp and you are in the "Sun is the center" camp. Great. As far as I know, everyone here is open to a better theory and everybody here is interested in seeing scientific progress. But it takes a lot more than words, and a lot more than desire. And certainly a lot more than empty assertions of "logic".

The only person trying to play games with the definition of a photon seems to be you. Your criticism basically is: it must be either a particle or a wave and not both. A strange assertion indeed for someone with your background.

 

[Cthugha]

1. I just knew I was going to get into trouble for using the words ND filter! Let's just say or equivalent. While I'm using the double slit (or single slit for that matter!) as an example there are a lot of interesting subjects here having to do with coherence, self-confined beams and the like. I am purposely trying to not turn this into a discussion of the details of high-powered mathematics so that lurkers are not lost. On the other hand, I am trying to keep such fundamentals in mind so that I am not saying things that are demonstrably wrong.

Ok, I work in a field, where the small difference between a damped coherent beam and a real single photon might matter, so I always put special emphasis on this point. However, as you know, what you are doing, let's move on.

2. You are obviously dying to tell me to go read a freshman textbook. However, suffice it to say that I studied graduate level QM under R. Mills (yes THAT Mills) and Yang. I know you find it difficult to understand how someone so properly indoctrinated would go bad and start questioning the gospel, but it happens.

No, I just wanted to know, on which level we can discuss.

The only difference between then and now is that a few more practical problems have been calculated using QM. Back then the hydrogen atom was about it. Harmonic oscillators and energy wells are just mathematical exercises. They are not practical problems, even though everyone pretends that they are. I guess my problem is I need to upgrade to the latest version of QM...

Well, with the arrival of lowdimensional semiconductor structures like quantum wells, wires and dots, energy wells have indeed become practical problems.

3. I can see we actually ARE having problems with semantics here. I am assuming that the "on" in photon implies it's a particle. You are saying that the word "photon" is just a word like "turtle" that implies all the properties of the object. Thus your word is a name for the entire object and mine implies certain properties of an object which while associated with additional properties may or may not have those additional properties be part of it's own.

Ok, there are a lot of other "on"s out there and usually this indeed means that the things mentioned are particles or quasiparticles. No problem with the assumption that "on" means a particle. However we might not agree on what a particle is...

But the fact is that QM is NOTHING but formalism. It does not and probably cannot describe what a light particle "is". It only predicts how it is likely to behave to some degree.

Sure, that is what models do. But what "is" a photon to you besides all the properties one can measure? Any model can only predict behaviour and does not tell us more.

5. So where we stand is you are defending a vast and complex formalism of epicycles because it nicely explains the motion of the planets. And I am suggesting that perhaps one needs a new way to look at things that simplifies everything by a change of point of view.

Go ahead. If you find another model that predicts the outcomes of QM and is easier or needs less assumptions, you are very welcome to publish it.

As I said before, energy transfers are too fast for light to be merely high frequency waves in the luminiferous aether.

I don't get your point. The maximum energy transfer rate happens at c. I do not see, where this is too fast for waves traveling at c.

And there are other problems as well as we both note. But wave characteristics do persist. And they transfer to statistics. And we find they take the form of 'probability waves" whatever that might be. Just what is the medium that "imaginary probability waves" propagate in? Obviously the standard answer is that these waves need no medium just as no EM wave needs a medium. All these waves propagate quite nicely in "nothing at all".

Well, empty space is different from nothing at all from a philosophical and physical point of view. Why do you need another medium?

But that is a philosophical paradox like talking about the properties of "nothing at all". One cannot logically separate properties from the object that possesses those properties.

To quote Glauber's Nobel lecture again:
"It is worth recalling at this point that interference simply means that the probability amplitudes for alternative and indistinguishable histories must be added together
algebraically."

If you like to, you can consider this as a property of our empty space (and time).

As for "why" I kind of like your spaghetti monster theory!

Hehe, everybody does. ;)

7. Let me say I am not asking "why" as you suggest. I'm asking "what logical model?". You on the other hand are suggesting that QM formalism is some kind of model. In spite of it's ability to predict to a degree, I suggest that there are too many unexplained definitions (such as probability waves) and illogical constructs (waves without media) to qualify as a model. You can accept it as useful, but don't call it a model.

Well, I do not see the problem with probability amplitudes and do not see the logical fallacies you see. The more philosophical approach to which picture one should have on what probability amplitudes are, is a matter of the interpretation of QM, which I suppose is what you would consider as a model. However, there are plenty of interpretations, from Kopenhagen over Bohm to multiple worlds. Therefore to me, QM is definitely a model. Models explain and predict stuff you can measure. What you call logical model is in my eyes a question of the interpretation of QM. And there are indeed still plenty of people out there trying to make heads or tails out of the philosophical implications of the fundaments of QM. You will find plenty of discussions on the pros and cons of Kopenhagen/Decoherence/Bohm/MWI around here. However my favorite interpretation comes from N.D. Mermin. His "in a nutshell" version of his interpretation always makes me laugh:

"My complete answer to the late 19th century question "what is electrodynamics trying to tell us?" would simply be this: Fields in empty space have physical reality; the medium that supports them does not.

Having thus removed the mystery from electrodynamics, let me immediately do the same for quantum mechanics: Correlations have physical reality; that which they correlate, does not."