Is Wave-Particle Duality Really Real? An Analysis of the Double Slit Experiment

[mintparasol]

Thanks to all who've replied here. I think it's kind of cool that a question from someone like myself who has very little understanding of the technical aspects of QM can get such a lively debate going!
I've been reading and re-reading the thread and some of the links posted here and I think I have a slightly better understanding of what's going on here than I had at the beginning.
Thanks again
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[Frame Dragger]

Thanks to all who've replied here. I think it's kind of cool that a question from someone like myself who has very little understanding of the technical aspects of QM can get such a lively debate going!
I've been reading and re-reading the thread and some of the links posted here and I think I have a slightly better understanding of what's going on here than I had at the beginning.
Thanks again
ad

Well, your question is at the heart of one of the major unsolved questions in modern physics. It was an interesting question, and bound to lead to some complex ruminations on the subject. And fireworks... musn't forget the fireworks lol.

 

[Mentz114]

FrameDragger:

The belief the the pattern is simply a function of many particles acting without wave-like behaviour flies in the face of experimental evidence, but is compatible with non SQM or dBB theories. Even dBB postulates a pilot wave to explain experimental evidence.

But SQM is saying that the pattern is determined by the wave-function otherwise there would be no interference pattern. SQM does not say that the particles behave like classical particles.

I still think it's wrong and somewhart contrived, but to relegate it [dBB] to an interpreation of the theory it rejects is probably unfair.

Saying that dBB is 'wrong' is somewhat wild and unconsidered. The same wave-function is used to calculate the trajectories and the same predictions are made. I don't think you know enough about dBB to say these things.

If you reject all this - do you think a Rubidium atom can somehow pass through both slits at the same time ?

 

[Frame Dragger]

FrameDragger:

But SQM is saying that the pattern is determined by the wave-function otherwise there would be no interference pattern. SQM does not say that the particles behave like classical particles.


Saying that dBB is 'wrong' is somewhat wild and unconsidered. The same wave-function is used to calculate the trajectories and the same predictions are made. I don't think you know enough about dBB to say these things.

If you reject all this - do you think a Rubidium atom can somehow pass through both slits at the same time ?

I realize (and have stated a couple of times) that wave-particle duality in SQM isn't simply classical waves and particles, but something else combining properties of both. I realize that the distribution on the screen is a result of the wave function of each non-classical particle. That said, depending on which theory and interpretation you subscribe to, yes... the rubidium atom, C60, or photon has wave-like properties that interefere with itself unless you place a detector in the path of the aperture.

It may be that an individual particle or atom interferes with itself, but that's impossible to confirm or refute right now as far as I know. The emergence of the pattern is the result of properties that you find in a single photon, and in some interpretations that would seem to indicate that a single particle in QM behaves like a wave at that point.

From what I've been reading of dBB (and a lot of it in the last few days after a rightous and right chastisement from Zenith) doesn't change my view of the theory. It still strikes me as last gasp of Classicism, but I've said all of this before. That said, it's the only respectable theory to survive as far as SQM re: Bell's Theorem. Personally, I don't believe the inverse of the inequalities is the case, and I think that experimental evidence found and analyzed over the next decade will eliminate it. If not, as I've stated before, and SQM fails to deliver then people will be open to different theories of the microscopic.

AS for the question about the rubidium atom, no, I don't believe one atom passes through two slits simultaneously, but it's certainly possible. What I believe has little impact on reality, and yes, I realize how ironic that statement is. I DO believe that a counterintuitive reality shouldn't be terribly shocking, and entanglement is surely as counterintuitive as it gets. Alas, there it is, with one simple, but unpalatable explanation, and dBB with a far more palatable image, but now depends on non-local hidden variables. I'm sorry, but I see that as retreat in the face of new thinking, not just academic pressures or the lack of popularity of a given theory.

 

[Mentz114]

Frame Dragger,

Fair enough. Quantum phenomena are certainly weird and trying to find intuitive meaning behind the equations is probably futile.

 

[wofsy]

I am just learning physics. Correct me please but it seems like the whole thing makes sense when you look at the quantum amplitudes as evolving according to a particular stochastic process that is similar to a Markov process.The amplitude for finding a particle in a state is the sum of the conditional amplitudes that it will land it that state given that it is in the possible previous states. If these amplitudes were real numbers rather than complex this would be a Markov process.

From this point of view, interference is not really a wave interference but rather a linear combination of conditional amplitudes. this is similar to a Markov process where the probability of finding a particle in a particular state is a sum of conditional probabilities.

Any stochastic process depends upon its initial conditions. The single and double slit are two different initial conditions.

The double slit has two initial states that generate the possible future states
according to this Markov like process of amplitudes.The single slit has only one. A triple slit would have three initial states and give a even different amplitude combinations.

When one measures which slit the particle has come out of you actually reduce the problem to a one slit case so there is no amplitude contribution any longer from the other slit. The stochastic process of amplitudes has a new initial condition that is one slit rather than two. Thus there is no interference.

This point of view explains why you see interference even when you send one particle at a time through the slits. A single particle evolves according to this Markov process of amplitudes. Measuring where the particle hits a detecting screen is much like measuring where a dust particle in a fluid will hit a barrier. Measuring many particles will produce a distribution of positions just as with dust particles. Different initial conditions will produce different distributions.

From what I can gather from reading, it seems that the Shroedinger wave equation should be called the Shroedinger diffusion equation. In fact, formally the Shroedinger equation for a free particle is a complex heat equation and just as the heat equation can be derived from a continuous Brownian motion, the Shroedinger equation can be derived form a continuous stochastic process of complex amplitudes.

The incredible thing about all of this to me is that there really is nothing else to say. That is the way it is. The classical picture of the dynamics of a particle is just inapplicable here. This quantum particle is not a particle at all but something different and ordinary usual concepts are not appropriate for it.

I would add that in Brownian motion we actually imagine a dust particle bouncing around randomly. In QM it seems that there there is no physical object bouncing around but merely a mathematical formalism that gives the right answer - every time. I think this is why Einstein disliked Quantum Mechanics whereas the theory of Brownian motion was his idea.

 

[Frame Dragger]

Frame Dragger,

Fair enough. Quantum phenomena are certainly weird and trying to find intuitive meaning behind the equations is probably futile.

I agree with literally every word in that quote. Maybe whatever supplants SQM/dBB/etc and GR will be more elucidating.

 

[Mentz114]

The amplitude for finding a particle in a state is the sum of the conditional amplitudes that it will land it that state given that it is in the possible previous states. If these amplitudes were real numbers rather than complex this would be a Markov process.

From this point of view, interference is not really a wave interference but rather a linear combination of conditional amplitudes. this is similar to a Markov process where the probability of finding a particle in a particular state is a sum of conditional probabilities.

OK, but if the amplitudes are governed by a wave function, then there is path dependent phase, and so interference will take place when you sum the amplitudes from the different paths. This can only happen with waves, so a wave phenomenon is happening. You've just rephrased it in path integral terms.

 

[wofsy]

OK, but if the amplitudes are governed by a wave function, then there is path dependent phase, and so interference will take place when you sum the amplitudes from the different paths. This can only happen with waves, so a wave phenomenon is happening. You've just rephrased it in path integral terms.

I was trying to point out that this is really a diffusion process. Waves that satisfy the wave equation are not diffusion processes.

The wave function does not satisfy the wave equation but rather a complex heat equation. I guess you do get waves when you look at stationary solutions in the presence of potentials.

 

[Mentz114]

I was trying to point out that this is really a diffusion process. Waves that satisfy the wave equation are not diffusion processes.

The wave function does not satisfy the wave equation but rather a complex heat equation. I guess you do get waves when you look at stationary solutions in the presence of potentials.

I don't know if we're talking about the same thing here. Solutions to the Schroedinger equation for realistic situations are always of the form

$$\psi(x,t)=Ae^{\frac{i}{\hbar}(Et+px)$$

where E and p are the energy and momentum. This is a wave even for a free particle.

 

[wofsy]

I don't know if we're talking about the same thing here. Solutions to the Schroedinger equation for realistic situations are always of the form

$$\psi(x,t)=Ae^{\frac{i}{\hbar}(Et+px)$$

where E and p are the energy and momentum. This is a wave even for a free particle.

To me, the broglie wave is a trivial case. The general Fourier transform is a super position of formal de Broglie waves and can no longer be looked at as a wave - for instance a de broglie wave has a definite momentum whereas a general Fourier transform does not -unless you want to take the mathematical view that any function that can be written as a Fourier transform is really a superposition of waves. There are some simple cases where you get a finite number of de Broglie wave glued together along their boundaries. But this picture is not right for complicated wave functions.


My point still stands that the wave equation is not satisfied here but rather a different kind of equation altogether.

 

[Mentz114]

wofsy,
you've probably got an interesting case to argue but this thread is not the place, so maybe you could start a new one about diffusion.

 

[Frame Dragger]

I don't know if we're talking about the same thing here. Solutions to the Schroedinger equation for realistic situations are always of the form

$$\psi(x,t)=Ae^{\frac{i}{\hbar}(Et+px)$$

where E and p are the energy and momentum. This is a wave even for a free particle.

@wofsy: ...And not to put to fine a point on it, but that is a central tenant of SQM. If you're (Wofsy, not Mentz114) advocating a different theory that's one thing, but if you believe your description is in line with QM... it simply isn't. In fact, if you want an example of just such a momentum distribution graph, the link I provided earlier for Mentz about C60 is a visual of just this equation in action.

 

[Mentz114]

To be more precise, the plane-wave solution I quoted above won't be enough for most cases, but a linear combination of plane waves makes a nice wave-packet.

Just nit-picking ...

 

[wofsy]

I agree that this is no place to argue about QM formalism. I was just trying to explain the double slit experiment in terms of the dynamics of QM laws. The stochastic process view helped me a lot.

All I was saying is that the Shroedinger equation is not the wave equation. The wave equation involves the second derivative in time as well as space. The Shroedinger equation only uses the first derivative of time. This is a huge difference. When one uses only the first derivative you get entirely different dynamics. Instead of wave propogation you get stochastic processes. For instance, the heat equation only uses the first derivative in time.

It was revealing for me to read in Feynmann's Lectures On Physics that the Shroedinger equation falls simply out of the Markov like process of amplitude evolution. The hidden reality here was the stochastic process of complex amplitudes just as the hidden reality in heat flow is Brownian motion. This hidden reality generalizes to all QM situations such as spin or chemical bonds. In these cases,wave-particle duality does not apply.

For me, thinking about what is really meant by a wave here has been key for trying to understand the theory. It seems that simple wave packets - a finite number of superposed de Broglie waves - can be thought of as waves formally since they look like waves with localized amplitudes - but for the life of me I do not know what it means to think of de Broglie waves as particles and then superpose these particles to get another particle. That just isn't right. However with standard linear waves such superposition makes total sense.

 

[Frame Dragger]

To be more precise, the plane-wave solution I quoted above won't be enough for most cases, but a linear combination of plane waves makes a nice wave-packet.

Just nit-picking ...

"...just this equation" as in, "This very equation" not, "This equation alone". ;)

 

[mintparasol]

Well, your question is at the heart of one of the major unsolved questions in modern physics. It was an interesting question, and bound to lead to some complex ruminations on the subject. And fireworks... musn't forget the fireworks lol.

The lack of consensus is illuminating (pardon the pun!)

I had been under the impression that QM models were as immutable as, say, special relativity or the laws of thermodynamics

 

[Frame Dragger]

The lack of consensus is illuminating (pardon the pun!)

I had been under the impression that QM models were as immutable as, say, special relativity or the laws of thermodynamics

That definitely depends on who you ask, but I doubt that anyone here is filled with a deep and abiding certainty about QM,dBB,etc... etc... and when you get into the realm of interpretations, well... the only concesus is probably forced. I think everyone here has done a fine job of advocating a viewpoint, but that is all that most people can claim. QM and GR both cry out for either unification, or a new theory to replace them (crazy unlikely in the case of GR at least ;) ). The question of what will emerge from an understanding of how the world of the very small is 1.) unlike the world we observe, but from which that world emerges 2.) Like the world we observe, but for various reasons appears to be unlike 3.) OTHER... is unsolved and open for debate.

That's a pretty gross simplification on my part, but that's the kicker... without the math none of these theories make much sense using Classical analogues past the introductory period. The fact that terms such as "Observer" and "Information" take on new meanings as they become terms of art in the field, doesn't help for some people either. That's a work in progress for you though!

 

[DrChinese]

I had been under the impression that QM models were as immutable as, say, special relativity or the laws of thermodynamics

The mathematical formalism itself is essentially immutable (of course that could change) and has remained in place for over 80 years. What changes is the mapping of the formalism to underlying mechanical processes, something which is not strictly required for any theory. This "mapping" is the source of the debate and confusion, just in case that point was not clear from the above.

And by the way, there is a similar debate raging about relativity and its interpretations. Although the one about QM is more well known and tends to have more *robust* debate.

 

[Frame Dragger]

The mathematical formalism itself is essentially immutable (of course that could change) and has remained in place for over 80 years. What changes is the mapping of the formalism to underlying mechanical processes, something which is not strictly required for any theory. This "mapping" is the source of the debate and confusion, just in case that point was not clear from the above.

And by the way, there is a similar debate raging about relativity and its interpretations. Although the one about QM is more well known and tends to have more *robust* debate.

To be fair to those scientists who stake their careers and reputations on various theories... it's easy to see politics stifling science in hindsight, but when your *** is on the line... not so easy. So, in some cases the debate is spirited for the sake of retaining one's viewpoint or standing, and sometimes it's spirited because the math says very strange things about the universe that we as humans do not see in our everyday lives (and recognize as such at least).

GR and SR have plenty of debate, including ideas such as treating time as separate from space. Einstein's theories however, have had the benefit of experiments which refute some counterclaims and support it. Time dilation, gravitational lensing, and more have been directly observed. By its very nature, QM defies that same degree of precision in the absence of new thinking, math, and technology.

Want to test GR? Make some really great telescopes and wait for the right time (or make some really good gyros and lasers in the extreme). Want to test SQM? Build the Large Hadron Collider and cross your fingers. You see the problem... ;)

 

[eaglelake]

No... you missed my point entirely. The experiment involving Rubidium showed a single atom having a unique wavefront just as a single photon does. The fact that it takes multiple passes (as you say, a buildup) to make the pattern visible is a limitation of our detection methods. If one could image a photon more exactly there would be a wavefront causing an interference pattern, visible or not. The dual nature of the quanta seems pretty clear. That's a limitation of the experimental apparaturs, but it's clear from the distribution... built over time as you say... that each individual photon, atom, etc, while observed at any given time to be particle or wave -like... has both properties at all times.

I repeat, no experiment has ever “showed a single atom having a unique wavefront just as a single photon does.” ( A single photon doesn’t either). The detection of a single particle is seen as a single dot on the screen and no wave properties can be discerned from it! The quantum experiment does not reveal any wavefront for a single particle. I assume that the wave you refer to is the state function, which is a probability amplitude. It is defined in a linear vector space and no one has ever observed it in 3-space. The results of an experiment are always visible to us. Your interpretation sounds like deBroglie-Bohm, and that’s OK, but it is speculation about “what is really happening”. Both the quantum theory and experiment are silent on such things.

Further, Bohr’s complementarity principle is widely accepted and considered as a fundamental tenet of quantum mechanics; we never observe both particle and wave properties at the same time. The experiment does not reveal “both properties at all times.”

All we know for certain is that the double slit experiment yields an angular distribution of scattered particles that has maxima and minima, which we identify as constructive and destructive interference. Quantum mechanics was invented, in part, to explain such interference effects in particle scattering.

Best wishes.

 

[Galap]

To be fair to those scientists who stake their careers and reputations on various theories... it's easy to see politics stifling science in hindsight, but when your *** is on the line... not so easy. So, in some cases the debate is spirited for the sake of retaining one's viewpoint or standing, and sometimes it's spirited because the math says very strange things about the universe that we as humans do not see in our everyday lives (and recognize as such at least).

GR and SR have plenty of debate, including ideas such as treating time as separate from space. Einstein's theories however, have had the benefit of experiments which refute some counterclaims and support it. Time dilation, gravitational lensing, and more have been directly observed. By its very nature, QM defies that same degree of precision in the absence of new thinking, math, and technology.

Want to test GR? Make some really great telescopes and wait for the right time (or make some really good gyros and lasers in the extreme). Want to test SQM? Build the Large Hadron Collider and cross your fingers. You see the problem... ;)

There do exist alternative theories to GR, for example the Brans Dicke theory (http://en.wikipedia.org/wiki/Brans–Dicke_theory), which is also consistent with observations. The only reason it doesn't get much attention is that GR to most people just simply makes sense in and of itself and doesn't have 'disturbing' or 'wierd' elements like QM does.

Now because GR makes sense does it mean that Brans Dicke theory is unneccesary? No. Any theory is acceptable until experimental evidence shows it to be untrue. That's why we still use QM and GR: because of any two theories out there, they have probably given us the best predictions of anything. The only problems are that QM 'doesn't make sense' and that the two don't mesh very well.

 

[mintparasol]

Ok, I've read some of the links posted here and have gleaned a little more understanding of what's going on here by some of your replies. I won't pretend to understand the math but think I have a better understanding of what's going on here in layman's terms.

Basically, as I see it, we see no evidence of the wave property of light from the firing of a single photon. We fire it thru the slits and it hits the detector screen and is detected at a point. We have no way of determining in advance where it will hit the detector screen. It is only after firing a whole lot of photons, either all at once, or one at a time, that the wave nature of light is revealed to us by means of an interference pattern at the detector.
This means to me at least, that we get a more meaningful view of the properties of light by considering the properties of many photons rather than the properties of a single photon.
It's interesting that the time factor (i.e. whether you fire the photons all at once or one at a time) makes no difference to the result of the experiment.

 

[Frame Dragger]

Ok, I've read some of the links posted here and have gleaned a little more understanding of what's going on here by some of your replies. I won't pretend to understand the math but think I have a better understanding of what's going on here in layman's terms.

Basically, as I see it, we see no evidence of the wave property of light from the firing of a single photon. We fire it thru the slits and it hits the detector screen and is detected at a point. We have no way of determining in advance where it will hit the detector screen. It is only after firing a whole lot of photons, either all at once, or one at a time, that the wave nature of light is revealed to us by means of an interference pattern at the detector.
This means to me at least, that we get a more meaningful view of the properties of light by considering the properties of many photons rather than the properties of a single photon.
It's interesting that the time factor (i.e. whether you fire the photons all at once or one at a time) makes no difference to the result of the experiment.

You now understand the SQM interpreation of the experiment. I'd call the thread a rousing success! Differences in whether the experiment reveals the wave nature of light, or if it is the result of an ensemble, or pilot wave... you have the actual details of the mechanics down pat.

Finally, remember that if you CAN add an additional measuring device, it doesn't matter if you use the data or not. The fact that you COULD have by deploying more observation means that you can't see evidence of duality.

 

[mintparasol]

You now understand the SQM interpreation of the experiment. I'd call the thread a rousing success! Differences in whether the experiment reveals the wave nature of light, or if it is the result of an ensemble, or pilot wave... you have the actual details of the mechanics down pat.

Finally, remember that if you CAN add an additional measuring device, it doesn't matter if you use the data or not. The fact that you COULD have by deploying more observation means that you can't see evidence of duality.

Hmmm, is it right to say then that we observe individual photons as particles and we find wave properties only when we measure the properties of many photons emanating from the same source. To me, this clears up the 'mystery' of duality completely

 

[Mentz114]

This means to me at least, that we get a more meaningful view of the properties of light by considering the properties of many photons rather than the properties of a single photon.

Yes, Maxwell's equations are the classical way. Light is waves.

It's interesting that the time factor (i.e. whether you fire the photons all at once or one at a time) makes no difference to the result of the experiment..

Agreed. This is what led Feynman to say that the photon interferes with itself.

In the deB-B pilot wave model, the trajectory depends only on the initial conditions and there's no randomness except there.

[Edit : I posted simultaneously with the post above ...]

 

[Frame Dragger]

Hmmm, is it right to say then that we observe individual photons as particles and we find wave properties only when we measure the properties of many photons emanating from the same source. To me, this clears up the 'mystery' of duality completely

It leads you to an Interpretation probably. Mentz is offering the De-Broglie Bohm Pilot Wave Interpretation, I'm for SQM. They are on equal empirical footing, if not political footing (not their fault).

The more I learn about dBB, the more I find myself on the fence. I'm no convert, but it strikes me as a guess on par with SQM.

 

[DrChinese]

Basically, as I see it, we see no evidence of the wave property of light from the firing of a single photon.

I would say that is true with the double slit setup itself. However, there are other setups that show the wave nature of light on a single particle basis. I am thinking of certain special interferometer setups, for example (assuming that you accept that an interferometer shows wave effects). Not sure if that is relevant to your thinking, but thought I would mention it, see Figure 2 of this:

Non-local generation of entanglement of photons which do not meet each other

 

[mintparasol]

Thanks again to everyone, this thread has really helped my understanding.

I have some more questions, I hope you don't mind!

:- If I conduct the double slit experiment by firing one photon at a time, do I find that every now and again, a photon is 'blocked' by the dark part of the slitted screen or do all the photons always find a way thru the slits to the detector screen?

:- Is there any relationship between the frequency/wavelength of light emitted by a particular atom and the physical size/circumference of said atom?

:- I'd be grateful if someone could spend the time explaining exactly how the protons are generated and focussed down the tube in the double slit experiment. Also, to help refresh my memory of how photons are emitted from atoms in the first place. I understand it's to do with the excitement of atom-bound electrons and that the electron emits a photon as it 'jumps' from one state to another but could do with a refresher course!

Thanks again,
ad

 

[huffypuffy]

J12345 - are you attributing consciousness to particles? Bohr would just say that the measurement is the collapsing of the wave function, and that's the easy way out that physicists have followed for decades. You miss the subtle questions that we need to start asking again.

No man. Cause the device is used a day prior to the decision. which means for the statement "The measurement collapses the wave function" to be true, As soon as the device measured the gate, the wave function would collapse at the instant the device measured and the result would be set in stone. But that's not the case. our (human) measurement breaks down the wave function. Devices have been seemingly seen to collapse the function in sophisticated experiments. But we don't know if it is due to our influence now do we? We can think we had nothing to do with it. But A human built it.

Like global warming programs were no good cause the guy writing the program must agree with the hypothesis or the program won't give the results they created it to give.

Now if someone can set up an experiment that could show a human is not needed, you still can't ignore the fact that human observation breaks down the wave function as proven in the original experiment.

Does anyone know where the results are from the original delayed decision portion of the experiment? Before wheeler expanded on it years later. I really do smell a rat.

 

[Dmitry67]

This is yet another good example while CI (and other collapse interpetations) do more harm then good.

I understand that there are no experimental data that can favor say BM over MWI or vice versa, but after the discovery of Quanrtum Decoherence the 'wavefunction collapse' should follow the 'either', 'Phlogiston' et catera

 

[mintparasol]

Thanks again to everyone, this thread has really helped my understanding.

I have some more questions, I hope you don't mind!

:- If I conduct the double slit experiment by firing one photon at a time, do I find that every now and again, a photon is 'blocked' by the dark part of the slitted screen or do all the photons always find a way thru the slits to the detector screen?

:- Is there any relationship between the frequency/wavelength of light emitted by a particular atom and the physical size/circumference of said atom?

:- I'd be grateful if someone could spend the time explaining exactly how the protons are generated and focussed down the tube in the double slit experiment. Also, to help refresh my memory of how photons are emitted from atoms in the first place. I understand it's to do with the excitement of atom-bound electrons and that the electron emits a photon as it 'jumps' from one state to another but could do with a refresher course!

Thanks again,
ad

Anyone?

 

[DrChinese]

Thanks again to everyone, this thread has really helped my understanding.

I have some more questions, I hope you don't mind!

:- 1. If I conduct the double slit experiment by firing one photon at a time, do I find that every now and again, a photon is 'blocked' by the dark part of the slitted screen or do all the photons always find a way thru the slits to the detector screen?

:- 2. Is there any relationship between the frequency/wavelength of light emitted by a particular atom and the physical size/circumference of said atom?

:- 3. I'd be grateful if someone could spend the time explaining exactly how the photons are generated and focussed down the tube in the double slit experiment. Also, to help refresh my memory of how photons are emitted from atoms in the first place. I understand it's to do with the excitement of atom-bound electrons and that the electron emits a photon as it 'jumps' from one state to another but could do with a refresher course!

Thanks again,
ad

1. Yes, that happens frequently.

2. "Size" of an atom has nothing to do with it. When a electron drops from one shell to another, a photon of a specific frequency is emitted and that frequency is a function of the energy difference between the shells.

3. You can use a variety of sources to get the double slit effect. The usual requirement is that the light be coherent, and a laser produces such light. Coherent light is light in which the waves are - in basic terms - lined up so that there is constructive interference but no destructive interference between photons. (So the peaks are at the same points...)

 

[mintparasol]

1. Yes, that happens frequently.

2. "Size" of an atom has nothing to do with it. When a electron drops from one shell to another, a photon of a specific frequency is emitted and that frequency is a function of the energy difference between the shells.

3. You can use a variety of sources to get the double slit effect. The usual requirement is that the light be coherent, and a laser produces such light. Coherent light is light in which the waves are - in basic terms - lined up so that there is constructive interference but no destructive interference between photons. (So the peaks are at the same points...)

Thanks,
I had a strong 'vision' of what's going on with duality the night before last, hence the questions.

I've no doubt that this vision is flawed due to incomplete understanding of the processes so I'll keep my mouth shut for fear of ridicule but will ask another question:-

Is the energy difference between the shells a function of the radial distance of the shells from the nucleus of the atom?

 

[mintparasol]

Is the energy difference between the shells a function of the radial distance of the shells from the nucleus of the atom?

Anyone?