I Wave-particle duality: nature of wave-particle as it travels

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Hi,

I'm trying to conceptualize the life of a particle as it travels through free space. I wish to start simple and then build from there.

Speaking about the wave-particle duality that we observe in fundamental particles.

Let's start with electromagnetic radiation (then move on to particles with mass from there).

So a photon is emitted from a source (perhaps an electron moving from a higher state to a lower state), it then travels in all directions (spherically?) as a wave, then it encounters some form of matter that can absorb it and it gets absorbed as a photon.

So an electromagnetic emission starts life as a photon, travels as a wave through free space, then ends life as a photon.

1) Would this be a satisfactory conceptual explanation for what appears to happen?

2) If so, how is the wave propagating? I mean, I can visualize how gravity waves propagate. I can visualize how, say, ocean waves propagate, or shock waves propagate through a material. But I have trouble visualizing how the energy of a photon is propagating through free space as a wave. I understand that EM radiation is an oscillating electromagnetic field and that a photon does indeed have momentum, but how does it move?

3) Also, if the wave travels out spherically from the source, then is the energy evenly distributed throughout the sphere of travel?

4) If so, then when it encounters something that can absorb it, wouldn't the energy, that is evenly distributed throughout the sphere of travel, have to basically instantaneously move to the point at where the photon is being absorbed?

Thanks for the help and insight,
Peter

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A. Neumaier

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So an electromagnetic emission starts life as a photon, travels as a wave through free space, then ends life as a photon.
The photon starts like as a wave, travels as a wave (an excitation of the electromagnetic field - which permeates what you call ''free space''), and ends like as a wave. Its particle nature is only visible when and as long this wave is strongly localized as a wavelet. The form of the wave is spherical if the source is open in all directions, but more usually (e.g. for a laser source), the form of the wave is paraxial, focussed in a beam.

If you can visualize how gravity waves propagate - electromagnetic waves are very similar in most respect, except that gravity has twice as much spin.

When electromagnetic radiation (aka photons) hits an absorber, it is absorbed in whole pieces or not at all, not in arbitrarily dilute amounts. This discreteness is due to the quantum nature of the absorbing matter, which can attain an excited local state only when it gets a minimum amount of energy.
 

A. Neumaier

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how does it move?
The photon wavelet wiggles forward with the speed of light, pulled by its momentum, always growing at its head and shrinking at its tail. And it becomes a little fatter with time, since its energy tends to spread.
 
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The photon wavelet wiggles forward with the speed of light
I don't think "wiggle" is a good word here, it leads to common misconceptions of things flying in curves.

Let's start with electromagnetic radiation (then move on to particles with mass from there).
Start with massive particles. Photons are way more complicated.

3) Also, if the wave travels out spherically from the source, then is the energy evenly distributed throughout the sphere of travel?
In most interpretations of quantum mechanics, yes.

4) If so, then when it encounters something that can absorb it, wouldn't the energy, that is evenly distributed throughout the sphere of travel, have to basically instantaneously move to the point at where the photon is being absorbed?
In some interpretations of quantum mechanics, yes. In others, no.
 

A. Neumaier

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I don't think "wiggle" is a good word here, it leads to common misconceptions of things flying in curves.
A wiggling tail dosn't fly in curves. It wiggles even in its rest frame. (Allowing the photon to be massive, as you suggested).

Peter99 said he can imagine how water waves and gravity waves propagate. So I tried to help him within his imagery.

In my magination, water waves wiggle up and down and at the same time forward. But it is difficult to get them in transversal wavelet format. So I think of photons as little fish made of wiggles that travel like a wave travels but at the same time keep their fish form. This is as good as one can make an intuitive picture of a single photon, and far better as the traditional one of a little cannon ball.

Of course the picture only works for single photons, as was asked. It starts to fail miserably if one want to use it to model entangled photon pairs traveling in opposite directions. You would have to imagine invisible, arbitrarily stretchable strings of love joining the pair of wavelets that keeps them one body and soul while they separate farther and farther. These strings would weaken and disappear only with enough decoherence, though this is the usual fate of love at a distance that gets too long.
 
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In my magination, water waves wiggle up and down and at the same time forward.
Sure, but photons do not wiggle up and down. And I lost track how often I encountered and tried to correct that misconception, as wiggly photon lines appear everywhere in images.
 

A. Neumaier

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Sure, but photons do not wiggle up and down. And I lost track how often I encountered and tried to correct that misconception, as wiggly photon lines appear everywhere in images.
Well, it is the standard picture for photon lines in Feynman diagrams. This cannot be altered.

But it is only imagery for the intuition, not reality. There is no good imagery for the more appropriate transversal wiggling, so one has to allow for a few more grains of salt. How would you paint the motion? Or do you simply suggest that one should not use any imagery at all?
 
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But it is only imagery for the intuition, not reality.
Yes, we know that. Others do not.
And while I was not thinking about Feynman diagrams: explaining that virtual particles are not real is another windmill-fight.
How would you paint the motion?
What would be wrong with a straight line? Not in Feynman diagrams, but at least in other diagrams (e.g. light bulb + light).
 

A. Neumaier

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Yes, we know that. Others do not.
So this must be emphasized over and over again.
explaining that virtual particles are not real is another windmill-fight.
I know. Feynman opened a Pandora box with which we now have to live....
What would be wrong with a straight line?
The problem here is that it immediately creates another puzzle: One then has to explain how waves can move along strainght lines. Geometric optics and all that. It is not intuitive enough to catch on and replace the common simpler but less appropriate imagery.
 

vanhees71

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Sure, but photons do not wiggle up and down. And I lost track how often I encountered and tried to correct that misconception, as wiggly photon lines appear everywhere in images.
Well, it's said that Schwinger never used Feynman diagrams. So it's possible to do QFT without Feynman diagrams, but it's even more complicated than with them and, I'm pretty sure, much less fun ;-).

Then you asked, what's wrong with a straight line. Very simple, it usually depicts fermions (dashed lines depict (pseudo-)scalar bosons, dotted lines Faddeev-Popov ghosts, double straight lines ##\Delta## resonances, and pigtail lines non-abelian gauge bosons as gluons in QCD). So there's nearly no line style left to depict photons, and they where wiggly lines already in Feynman's original papers ;-)).
 
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Then you asked, what's wrong with a straight line. Very simple, it usually depicts fermions (dashed lines depict (pseudo-)scalar bosons, dotted lines Faddeev-Popov ghosts, double straight lines ##\Delta## resonances, and pigtail lines non-abelian gauge bosons as gluons in QCD). So there's nearly no line style left to depict photons, and they where wiggly lines already in Feynman's original papers ;-)).
Sure, but all those things are purely convention. We could use dotted lines for photons, and wavy lines for Faddeev-Popov ghosts.
Anyway, I was not talking about Feynman diagrams with the complaint above.
 

vanhees71

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Sure, the trouble is that sometimes Feynman diagrams are sold as something depicting the real "mechanism" behind interactions between particles, but what they are in fact depicting when applied to relativistic quantum field theory "in vacuo" (i.e., to scattering processes of a few particles) are just formulae used to calculate transition matrix elements to describe scattering processes in perturbation theory. It's just an ingenious short-hand notation for these formulae invented by Feynman in a very intuitive way. At the famous Shelter Island conference in 1948 he and Schwinger, who used quantum-field theoretical formalism rather than any kind of pictures, to calculate such matrix elements, both coming to the same result. Also Tomonaga already during the war used techniques quite similar to Schwinger's. It was finally Dyson who used QFT to derive Feynman's diagrammatic fules. Unfortunately in the popular-science culture only the intuitive picture of Feynman diagrams are presented as if this intuition is the real thing, and then all kinds of weird ideas come up like "vacuum fluctuations" or "virtual particles", which have a definite meaning of course in the sense of QFT, but that's often completely deformed by the pop-sci writers :-(.
 
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Hi,

OK, well I had four questions, and now I have 20. But I guess that's the way of things. I appreciate the input!

That's OK about the wiggly fish imagery A. Neumaier put forth. I understood. It's interesting that you all are (casually) talking about a photon traveling and not a wave.

By "free space" I meant just space without matter present. Again, just trying to keep things simple as it all can get very complicated very quick. Would there be a better term or is there a conventional term to describe free space as I have defined it here?

When electromagnetic radiation (aka photons) hits an absorber, it is absorbed in whole pieces or not at all, not in arbitrarily dilute amounts. This discreteness is due to the quantum nature of the absorbing matter, which can attain an excited local state only when it gets a minimum amount of energy.
Yes, but thanks for the clarification.

The photon wavelet wiggles forward with the speed of light, pulled by its momentum, always growing at its head and shrinking at its tail. And it becomes a little fatter with time, since its energy tends to spread.
"Pulled by it's momentum"? Really? I always envisioned momentum to have more of an inertial quality to it... more pushed then pulled... or maybe not even pushed but not pulled either. But then we are talking about a massless particle. Is pulled the better way to envision this? If so, why?

Start with massive particles. Photons are way more complicated.
This surprised me. I mean, a photon I think of as elementary and doesn't go through an actual energy-mass transfer from wave form to particle form. Could you elaborate on this?

So in question 3 and 4 you answered respectively:

In most interpretations of quantum mechanics, yes.

In some interpretations of quantum mechanics, yes. In others, no.
So do the same people who say No to #3 also say No to #4?

How do they interpret collecting a photon, that has traveled billions of light years, as happening effectively in zero time? Are they saying that it does not take zero time but just an extremely small amount of time? Because then, conceivably, the energy is spread out over a HUGE area and the back end is (twice) billions of light years away. Say a ten billion light year diameter, so the energy at the back end would have to travel approximately 9.46E25 meters if it took a straight line to the detector. How quickly do modern detectors detect a photon in that what is the delta t for the transducer to make the detection? The actual gathering of the energy, not the instrumental overhead. I guess they can't gather the energy in less then 5E-44s (Planck Time) can they? However one looks at this, the energy has to travel hugely past the speed of light.

OK, a new question but related directly to the above, is there any evidence (empirical not theory) that electron tunneling happens with a time lag?

I remember my ex-wife, who was in graduate school studying particle physics (She did a lot of work a SLAC and a bit at CERN while I was doing the undergrad thing), bringing home a group of friends (all grad students) and we would all sit there and talk about this kind of stuff. I loved it then and I still love it!

Thanks for the input and insight,
Peter

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Oh ya, and just to comment on this whole Feynman diagram thing. Obviously he just used the wiggly line symbolically. It's the same as on electrical schematics, they use the same wiggly line symbol to indicate light transmission (for photo-detectors and such) . I tutored for years and don't remember having any trouble with this in that students didn't seem confused. At least I don't remember anyone being confused about this. But I can see how perhaps one could be confused and obviously some of you have have run into trouble with students (?) getting the wrong idea about it. As A. Neumaier said, "A photon wavelet...(travels) always growing at its head and shrinking at its tail" and if one looks at the transverse wave of EMR then it invokes a wiggly feeling. I see no trouble with it, in fact, I think it's appropriate.

Peter
 

Nugatory

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This surprised me. I mean, a photon I think of as elementary and doesn't go through an actual energy-mass transfer from wave form to particle form. Could you elaborate on this?
Massive particles like electrons are way easier to work with because with them we can ignore the effects of relativity. Non-relativistic quantum mechanics works when the speeds are small compared with the speed of light and the energies are small compared with the amount of energy needed to create additional particles - and neither of these conditions applies to photons. Thus, for photons we need all the relativistic machinery of quantum electrodynamics where the concept of wave-particle duality never even appears.

However, even when working with massive particles and non-relativistic quantum mechanics, the notion of wave-particle duality often confuses more than it clarifies - and I submit this thread as empirical evidence in support of that proposition. Come to think of it.... That's another ongoing thread right now: https://www.physicsforums.com/threads/legitimacy-of-particle-wave-duality.863688/ and my opinion is down at #6.

I find it best to think of quantum objects as things that have some wave-like properties and some particle-like properties, but are neither. It is an unfortunate historical accident that physicists use the word "particle" to describe these quantum objects even though they do not behave much like the little tiny billiard balls that are implied by the colloquial English sense of the word.
 

A. Neumaier

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maybe not even pushed but not pulled either
There are three possibilities - pulled, pushed, or self-propelled. A photon cannot help moving with the speed of light; so I picture it as being pulled. Or pushed; it is perhaps a little better, but it doesn't really matter. Pictures are just that - little mental illustrations drastically simplifying the real thing. One can do it in any way one feels comfortable with, as long as one remembers that each mental picture has its (sometimes severe) limitations.
How do they interpret collecting a photon, that has traveled billions of light years, as happening effectively in zero time?
The traveling time doesn't matter. The detector responds with a firing rate proportional to the impinging intensity, no matter how low or irregular it is - and whenever it fires one says ''a photon arrived''. This is figurative talk, too, since in models where the electromagnetic field is not quantized (so that there are no photons in the model), the detector still behaves in the same way. All imagery and language used must be viewed in this light: It simplifies in order to allow being put into words and intuition, and the simplification is valid only to the extent it sensibly matches what can actually be observed.
electron tunneling happens with a time lag?
Yes, though it is somewhat controversial. See, e.g., http://arxiv.org/abs/1301.2766. By the way, I think that tunneling is another one of these misguided imageries: Since it is impossible to tunnel through an infinitely high potential barrier, height matters, unlike in true tunnels, where only the distance to the next valley matters. This suggests that the tunneling electron was in fact climbing the barrier.
 
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This surprised me. I mean, a photon I think of as elementary and doesn't go through an actual energy-mass transfer from wave form to particle form. Could you elaborate on this?
There is no transfer. Particles are quantum objects. They are neither classical waves nor classical particles. Some properties of quantum objects are not so different from classical waves or classical particles, but those are always just similarities. The classical concepts never capture the properties of quantum objects properly.
So do the same people who say No to #3 also say No to #4?
The options:
- the energy spreads out evenly, and it does not get redistributed (e.g. many worlds)
- the energy spreads out evenly, and it gets instantly redistributed (some collapse interpretations)
- the energy goes in a specific direction but we cannot know which, it does not get instantly redistributed (e. g. de-Broglie-Bohm)
- we cannot make proper statements about the energy distribution before we measure it, so the questions are meaningless (ensemble interpretation and some others)
- probably some I forgot
How do they interpret collecting a photon, that has traveled billions of light years, as happening effectively in zero time?
Yes, some interpretations are nonlocal (they have effects that act faster than the speed of light).
OK, a new question but related directly to the above, is there any evidence (empirical not theory) that electron tunneling happens with a time lag?
Time lag between what and what? That is a highly non-trivial question.
 

vanhees71

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Yes, some interpretations are nonlocal (they have effects that act faster than the speed of light). Time lag between what and what? That is a highly non-trivial question.
Quantum theory predicts indeed long-ranged correlations that are stronger than possible in local hidden-variable theories (Bell's inequality being violated) for subsystems of entangled systems, and this has been indeed confirmed to high accuracy. This, however, has nothing to do with "effects that act faster than the speed of light". By construction, local relativistic quantum field theory does not admit such "spooky actions at a distance" (micro-causality).
 
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I said "some interpretations", not "quantum theory". Quantum theory is local - and you'll find countless threads where I highlight this. Some interpretations are nonlocal.
 

vanhees71

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Well, then these interpretations go beyond quantum theory and thus are new theories rather than interpretations!
 

A. Neumaier

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Here are some examples related to the question towards the end of post #13: superluminal tunneling time But please don't hold me responsible for the content of the links on that (automatically created) page!
 
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Hi,

OK, first of all just WOW! I thank you all for your knowledge and insights into this highly abstract subject. I enjoy this so much and I didn't realize how much I have missed this. My ex-wife attended UC Berkeley (USA) during her undergrad and I was around many amazing people. I immersed myself in the knowledge base that existed there and I learned a huge amount just by listening to them talk. At UCSC, where I did undergrad and my ex-wife did her graduate work, again, many amazing people. The knowledge base here at this website is also very impressive.. I am glad I found it.

I realize that all of you are working hard to "come down" to my level and I can tell that when answering these questions you are thinking about the math and then "converting" that into conceptual ideas. This can be very difficult when dealing with ideas that are so abstract that they pretty much defy the human brain being able to visualize it. I appreciate all the effort and please excuse my ignorance as I'm sure it shows!

Obviously, in order to discuss this at a more rigorous level with all of you, I need to get back into the math and so I have some work to do. I am working from text books that are about 20 years old but I'll continue with this as I am sure I can rebuild a working knowledge base quicker with familiar text books.


Massive particles like electrons are way easier to work with because with them we can ignore the effects of relativity. Non-relativistic quantum mechanics works when the speeds are small compared with the speed of light and the energies are small compared with the amount of energy needed to create additional particles - and neither of these conditions applies to photons. Thus, for photons we need all the relativistic machinery of quantum electrodynamics where the concept of wave-particle duality never even appears.

However, even when working with massive particles and non-relativistic quantum mechanics, the notion of wave-particle duality often confuses more than it clarifies - and I submit this thread as empirical evidence in support of that proposition. Come to think of it.... That's another ongoing thread right now: https://www.physicsforums.com/threads/legitimacy-of-particle-wave-duality.863688/ and my opinion is down at #6.

I find it best to think of quantum objects as things that have some wave-like properties and some particle-like properties, but are neither. It is an unfortunate historical accident that physicists use the word "particle" to describe these quantum objects even though they do not behave much like the little tiny billiard balls that are implied by the colloquial English sense of the word.
Very nice explanation!! Thank you.

The traveling time doesn't matter. The detector responds with a firing rate proportional to the impinging intensity, no matter how low or irregular it is - and whenever it fires one says ''a photon arrived''.
Ahhh! I see. So the energy of the EM wave must first "become" a photon and then the detector detects it?

Since it is impossible to tunnel through an infinitely high potential barrier, height matters, unlike in true tunnels, where only the distance to the next valley matters. This suggests that the tunneling electron was in fact climbing the barrier.
I didn't know this!! I thought tunneling could occur even through an infinitely high potential barrier. I guess I have forgotten some of my basic physics here. So if it is climbing the barrier, would this be a consequence that could be described or explained by the uncertainty principal?

There is no transfer. Particles are quantum objects.
I must admit I hesitated to use the word "transfer". I would have rather used he word "convert." Although you may object to this as well. Read my next post down on this thread. It basically describes my overall thinking about this entire subject. But I readily concede that I have much studying to do in order to gain a better grasp on Quantum Mechanics. The next post down is just some thoughts but it is driving me right now to better understand Quantum Mechanics so I can determine if the thoughts have any validity or not.

The options:
- the energy spreads out evenly, and it does not get redistributed (e.g. many worlds)
- the energy spreads out evenly, and it gets instantly redistributed (some collapse interpretations)
- the energy goes in a specific direction but we cannot know which, it does not get instantly redistributed (e. g. de-Broglie-Bohm)
- we cannot make proper statements about the energy distribution before we measure it, so the questions are meaningless (ensemble interpretation and some others)
OK, so would this suggest that we really just don't know yet? Per option #4, we need to figure out a way to actually measure the behavior, gain THAT knowledge, and go from there?

Time lag between what and what? That is a highly non-trivial question.
Yes, I wasn't specific. What I meant was from the moment that the electron is incident upon a potential barrier and starts to tunnel, to the moment it "appears" on the other side of the barrier. Is that time interval equal to zero, or does it have some finite value? A. Neumaier suggested that it was non-zero but that it was controversial.

Quantum theory predicts indeed long-ranged correlations that are stronger than possible in local hidden-variable theories (Bell's inequality being violated) for subsystems of entangled systems, and this has been indeed confirmed to high accuracy. This, however, has nothing to do with "effects that act faster than the speed of light". By construction, local relativistic quantum field theory does not admit such "spooky actions at a distance" (micro-causality).
Three sentences that will keep me studying for a long time just to truly understand. But I ask, confirmed how? Empirically?


Thanks again for all of your insights and efforts!
Peter

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Hi,

Some further thoughts:

I guess this is what is driving me right now. Why I came here looking for input and people who understand all this better then I do. Please excuse any ignorance of innocence or lack of deeper knowledge that I may display here. I wrote this early on in this discussion but never posted it. These are just conceptual ideas but maybe there is a grain of truth or reality in them. Actually, this is what I am trying to determine right now.

It reads:
=========

Wave-Particle duality: reformulation of questions

Perhaps I didn't ask the right questions but thanks to MFB and A. Neumaier I have been able clarify my thoughts and reformulate my questions. I appreciate the input and the insight.

I think what I was asking was WHY do electric, magnetic, gravitational, and other (space-time?) fields as well as mass-less particles propagate/travel at the speed of light? I was looking for a more fundamental understanding of this. I've been "out of the mix" for a couple of decades now and I was curious (for a reason and a specific end which I get into further down) if this was better understood now. I remember asking my university professors this question years back and I believe this could not be answered.

The best answers I got was that "they just do" and that "it seems to be an intrinsic aspect of this universe that they do."

What I was wondering is was the mechanism for this better understood now?

For instance, we could ask why do ocean waves travel at the speeds that they do and behave the way that they do? And one answer could be "they just do." But of course, with a deeper understanding of the fluid dynamics and materials, we can do better then that and explain that water is composed of molecules that interact in this way and that way and we can formulate mathematical models that describe, predict, and allow us to model their behavior. Thus, giving us a better and deeper fundamental understanding of the mechanisms involved.

In so far as this relates to quantum mechanics, it would seem that Shrodingers equation is saying something about the structure of the universe (which might yield a solution to the question of the nature of the speed of light) that we have yet to understand. The solutions to Shrodingers equation necessarily contain i (the square root of -1, just to be explicit) and this is quite hard for us to understand in a physical way (and indeed, i is mathematically undefined). We must CONVERT this into physical meaning by performing a mathematical operation on the solutions, namely by taking the square of the absolute value which yields a probability density function. Only then can we begin to understand the solutions to Schrodingers equation.

I remember one of my professors saying that "we cannot derive Schrodingers equation from more basic principals, it IS the basic principal." Doesn't then the equation itself say something about the structure of the universe? Almost as if there is another "layer" to the structure of the universe that Schrodingers equation is revealing to us. A "subspace" (for lack of a better term - a different type of space-time) if you like. Something that can only be described using i.

So the equation and the use of i is not just a mathematical construct that we simply use as a tool, but that it actually represents an unknown structure of the universe that actually exists.

This is why I asked the questions that I asked. I was attempting to understand whether we better understood any of this.

I find certain things quite interesting, like quantum foam, which seems as if free space (just 3D space, no matter around) itself is alive and interacting with "something else" all the time.

Also, instantaneous information exchange at a distance or instantaneous action at a distance. Which is why I asked about the energy of a spreading EM wave having to instantaneously move to the point where it then "becomes" a photon upon interacting with matter. Almost as if there exists a spacial dimension with no time constraints. A directional vector could well be established and "things" could move from point A to point B in zero time.

When we convert the solutions of Schrodingers equation into a probability function, isn't this somewhat like the energy of an EM wave converting to a photon? So the solutions to Schrodingers equation describe the wave like nature and describe some kind of "subspace" that this wave lives in, and the probability function describes the particle and it's behavior in the physical space that we know and experience.

[Mentor's note: Speculation inconsistent with the PhysicsForums rules has been removed from this post]
 
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Nugatory

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OK, so would this suggest that we really just don't know yet? Per option #4, we need to figure out a way to actually measure the behavior, gain THAT knowledge, and go from there?
That's pretty much the challenge that Einstein and his collaborators laid down in the 1935 EPR paper: http://www.drchinese.com/David/EPR.pdf

Subsequent developments have shown that it's not going to be that easy. Bell's theorem shows that no theory that would have satisfied the EPR authors can match all the predictions of quantum mechanics; and observation confirms that the QM predictions are correct. Thus, we have to take seriously the disconcerting possibility that there is no underlying behavior there to measure and #4 really is the way the world works - it's not a call to action but a "road closed ahead" sign.
 

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I think what I was asking was WHY do electric, magnetic, gravitational, and other (space-time?) fields as well as mass-less particles propagate/travel at the speed of light? I was looking for a more fundamental understanding of this.
....
For instance, we could ask why do ocean waves travel at the speeds that they do and behave the way that they do? And one answer could be "they just do." But of course, with a deeper understanding of the fluid dynamics and materials, we can do better then that and explain that water is composed of molecules that interact in this way and that way and we can formulate mathematical models that describe, predict, and allow us to model their behavior. Thus, giving us a better and deeper fundamental understanding of the mechanisms involved.
There are a bunch of threads on this question over in the relativity subforum. The answer that is most in the spirit of your question is that the speed of light follows from the properties of electricity and magnetism - you can calculate it from Maxwell's equations in a manner analogous to the way that you calculate the speed of ocean waves from the known fluid dynamics of water. Indeed, Maxwell did exactly that in 1861
(I will caution you that this formulation is not consistent with the best modern approach to deriving the behavior of light, but that's a digression here. You can read through the threads in the relativity forum if you want more).

I remember one of my professors saying that "we cannot derive Schrodinger's equation from more basic principles, it IS the basic principle."
He wasn't exactly wrong, but that does fall in the category of "Lies to children undergraduates" (https://en.wikipedia.org/wiki/Lie-to-children). There's a fascinating chapter in Ballentine where he identifies the basic principles which lead to Schrodinger's equation. Ballentine is not an undergraduate text, but it is indispensable if you want to understand QM at a level beyond what your professor was giving you.
 

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