B Interference of Light in the Double-Slit Experiment

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It is said that interference occurs when a peak (of the light wave) meets a trough and the wave cancels to zero, giving a dark band on the screen. However, if light waves are bands or "shells" of high densities of photons interspersed with bands of zero photons, then how can this be? When a peak meets a peak then yes, we get constructive interference (light bands). When a trough meets a trough there are zero photons (dark bands), but when a peak meets a trough then surely this is the mid point between light and dark with a "half" illumination. In other words, I do not see that destructive interference can occur with light since light is quantised. Can anyone confirm or refute?
 

PeroK

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It is said that interference occurs when a peak (of the light wave) meets a trough and the wave cancels to zero, giving a dark band on the screen. However, if light waves are bands or "shells" of high densities of photons interspersed with bands of zero photons, then how can this be? When a peak meets a peak then yes, we get constructive interference (light bands). When a trough meets a trough there are zero photons (dark bands), but when a peak meets a trough then surely this is the mid point between light and dark with a "half" illumination. In other words, I do not see that destructive interference can occur with light since light is quantised. Can anyone confirm or refute?
You are mixing your metaphors here. Either you treat light as a classical electromagnetic wave, in which case interference can be explained by peaks and troughs - or, more accurately, by sinusoidal oscillations in the electromagnetic fields. Or, you treat light as a quantised phenomenon, in which case the interference is caused by the oscillating phase of the light.

In fact, all of quantum interference boils down to the concept of quantum (probability) amplitudes being complex and able to cancel each other out.
 

vanhees71

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I don't understand your problem. The only what's quantum here is that you assume to build up an interference pattern with single-photon states. What you get is the same interference as within classical electrodynamics. The only difference is the interpretation that what's the intensity (energy density) of the electric field in the classical theory is a probability distribution for the detection of a photon on a screen as function of position.

An interference pattern is not simply "dark" or "light" but it's a continuous distribution. That's true for the energ density in classical as much as for the probability distribution in quantum electrodynamics.

Of course, if you really deal with single photons then each single photon leaves just one spot on the screen and not a continuous distribution. That's how quantum theory came into existence to begin with: Planck has realized in his request to find a theoretical explanation for his previously empirically found black-body-radiation spectrum (using measurements by Rubens and Kurlbaum) that he had to assume that electromagnetic radiation energy of an em. wave with frequency ##\omega## can be exchanged with matter only in "quanta" of size ##\hbar \omega$, and that's what a photon really is! It's not a little bullet like a classical one but it's a field quantum of a massless spin-1 field and because it's massless and of spin 1 it cannot be localized. So a classical point-particle picture makes no sense for it. Nevertheless it makes sense to localize a detection event, in this case by a screen (in former days a photoplate, today a CCD cam), and all you can now, if you deal with single photons is the probability to detect a photon at some "place" (of finite size and with finite resolution!) on the screen. So all that's known about the photon is the probability distribution to be detected. If you repeat the experiment very often with very many photons you get a pattern according to this probability distribution, and it's (almost always) the same as you'd expect from classical electrodynamics, using the energy density of the em. field as a measure for the light intensity at the screen.
 
I am suggesting we treat light slightly different to the two limited options you present. I know these are the usual explanations, but it is accepted that light comes in "lumps" or quanta. This was proven by Einstein. We seem to treat photons as having variable energy, but surely, the maximum energy of the EM wave is due to the maximum number of photons, not any difference in energy of any particular photon?
 
Vanhees71 - I understand what you say. However, if you treat photons the way I suggest, then yes, there is more probability of a photon hitting the screen where the wave has more photons. Your explanation and mine are not mutually exclusive, they are quite compatible. I am still not convinced that the standard explanation is the most accurate.
 

PeroK

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I am suggesting we treat light slightly different to the two limited options you present. I know these are the usual explanations, but it is accepted that light comes in "lumps" or quanta. This was proven by Einstein. We seem to treat photons as having variable energy, but surely, the maximum energy of the EM wave is due to the maximum number of photons, not any difference in energy of any particular photon?
You've posted this as an "A" level thread, I notice, which means at postgraduate level. Have you studied QED or QFT formally at university/graduate level? Or, have you been reading popular science books?

[Mentors' note: The thread level has been set to 'B']
 
Is the question advanced level or not?
 

PeroK

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Is the question advanced level or not?
I assumed it was a "B" in terms of the references and terminology; and that possibly your understanding of a photon appears to be at a popular science level.
 
I am questioning the mainstream explanation of the interference pattern in the DS exp. I believe that is "A"? So far, I have not been given a satisfactory explanation in view of my points.
 

PeroK

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I am questioning the mainstream explanation of the interference pattern in the DS exp. I believe that is "A"? So far, I have not been given a satisfactory explanation in view of my points.
Which one?

The classical electromagnetism explanation? Or, the QFT explanation?
 
If you read my original question, I'm sure it will become clear.
 

PeroK

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If you read my original question, I'm sure it will become clear.
Your original post, as I already pointed out, is a mixture of the two.
 
This is a genuine question to which I seek a genuine answer. Fundamentally, light is quantised (however we explain the overall wave effect). So, being quantised, a single photon will hit the screen at a point where the probability of this event is at its maximum. The wave must be made up of photons. This is imperative if light itself is made up of photons. The only way we can get a wave (of varying energy levels) is if the number of photons varies in a wavelike manner (sinusoidally) over time, over the path of the wave. To me, that must mean that there is more probability of a photons hitting the screen during the "peak" of the wave where there are many more photons than are at the trough. This seems a more complete explanation than just some "probability wave" existing in some ethereal way. Everything is physical, including light surely?
 

Nugatory

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However, if light waves are bands or "shells" of high densities of photons interspersed with bands of zero photons, then ......
They aren't - the relationship between photons and the intensity of the light at any given point is nothing at all like that.

The interference patterns produced by light (the subject of this thread) are a classical phenomenon demonstrated by Thomas Young at the start of the 19th century and explained by calculating the electromagnetic field at each point on the screen - the waves that are interfering are electromagnetic waves, no photons involved.

The dot-at-a-time interference pattern that builds up when a single-photon source is used is a quantum-mechanical phenomenon, but it is best understood as photons appearing at different points on the screen with different probabilities. The areas of low intensity are areas where negative probabilities overlap with positive probabilities and sum to near-zero.

Unfortunately there's no really good intuitive picture of what photon is; there's no substitute for a graduate-level course in quantum electrodynamics. However, there are some starting points:

Feynman's "QED: The strange theory of light and matter" is as close as you can get with a B-level treatment.

http://www.physics.usu.edu/torre/3700_Spring_2015/What_is_a_photon.pdf is an I-level starting point.

For an A-level treatment, you'd have to be familiar with something like https://web.physics.ucsb.edu/~mark/qft.html (mentioning this one because it has the great advantage of having a free preprint online).
 
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Thank you. But you did not answer my question, you simply rebutted it. I am convinced it is possible to explain or answer in one or two short paragraphs if someone really understands the physical nature of light?
 

PeroK

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The wave must be made up of photons. This is imperative if light itself is made up of photons. The only way we can get a wave (of varying energy levels) is if the number of photons varies in a wavelike manner (sinusoidally) over time, over the path of the wave. To me, that must mean that there is more probability of a photons hitting the screen during the "peak" of the wave where there are many more photons than are at the trough. ability wave" existing in some ethereal way.
Nothing like that. Electromagnetic radiation is not "made up of photons". A photon is a unit of electromagnetic energy. For reasons not explained by classical electromagnetism light, when it interacts with matter, can only transfer energy in quantised units.

To explain this quantisation you need QED, which is very different from classical electromagnetism.

You cannot, as you are doing, mix the two theories. In fact, your objection is really to your own interpretation of the theory of light, which tries to combine elements from both theories in a way that is, if nothing else, not the mainstream theory or explanation of the phenomena.
 
In the end, everything must be explicable by physical entities or events. QED is a way of working with the behaviour and characteristics of fields and particles. It does not explain the physical nature of light. I have suggested a physical explanation which I do not believe contradicts QED. I expected a more helpful approach here.
 

Nugatory

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Thank you. But you did not answer my question, you simply rebutted it. I am convinced it is possible to explain or answer in one or two short paragraphs if someone really understands the physical nature of light?
"One or two paragraphs" is a tall order when you consider that our understanding is the result of some of the smartest people who ever lived working on the problem for more than 200 years (roughly Newton to the middle of the 20th century). So you will understand what I say below is cutting some corners just a bit.....

Light is electromagnetic waves, as discovered by Maxwell in the 1860s.
When these waves interact with matter they transfer energy and momentum Because the electromagnetic field is quantized, these exchanges always involve discrete amounts of energy delivered at a single point. These quantities of energy are called "photons".

The Feynman book I mentioned above is more than a few paragraphs, but is an easy hour-or-so sort of read, and there is no simpler math-free treatment of the subject.
 

DrChinese

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In the end, everything must be explicable by physical entities or events. QED is a way of working with the behaviour and characteristics of fields and particles. It does not explain the physical nature of light. I have suggested a physical explanation which I do not believe contradicts QED. I expected a more helpful approach here.
One way of thinking of your problem is in terms of Feynman's path integral approach (Nugatory references that in #14). Each photon may takes many paths to the screen. Where the paths are out of phase with each other, there is cancellation. Where they are in phase, there is a probability of the photon being detected. The interference pattern is the result.

This is a reasonably satisfactory explanation to most scientists, but it may not be to you. Because you are demanding a "physical" entity or event, you may reject explanations which do not fit your particular definition (which are not a restriction to others). However, you must admit that an accurate description/prediction is going to be hard to reject, even if it does not satisfy your particular requirements.

One of the reasons that quantum principles are often described as "strange" (again see reference in #14) is precisely because there are a few assumptions which must be made that often appear "un-physical". You must ultimately work through that yourself. No one will be able to convince you that something that accurately describes the physical, is indeed physical.
 

vanhees71

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This is a genuine question to which I seek a genuine answer. Fundamentally, light is quantised (however we explain the overall wave effect). So, being quantised, a single photon will hit the screen at a point where the probability of this event is at its maximum. The wave must be made up of photons. This is imperative if light itself is made up of photons. The only way we can get a wave (of varying energy levels) is if the number of photons varies in a wavelike manner (sinusoidally) over time, over the path of the wave. To me, that must mean that there is more probability of a photons hitting the screen during the "peak" of the wave where there are many more photons than are at the trough. This seems a more complete explanation than just some "probability wave" existing in some ethereal way. Everything is physical, including light surely?
I'm still puzzled about the level you expect me to answer your question. Although you labeled the thread A, I've not the impression that you have understood enough QT to get satisfied by an answer at A level.

To really understand what a photon is, I'd advice you to follow #14. I'd however suggest another book, because you won't find the answer in a high-energy-particle QFT book but rather in a book about quantum optics. Of course both use the same theory, namely QED, but the physics phenomena treated by the different communities (high-energy physicists vs. quantum opticians) are quite different. I find the book

J. C. Garrison, R. Y. Chiao, Quantum Optics, Oxford University Press

very nice. There are for sure also tons of good manuscripts online.

I already tried to boil it down to a non-mathematical answer, which of course always bears the danger to be misunderstood, because it's impossible to talk about physics, particularly quantum physics, without mathematics. But let me try again:

The meaning of the sentence "light is quantized" is that electromagnetic-field energy is absorbed and emitted by matter consisting of charged particles in "quanta" of energy ##\hbar \omega##, where ##\omega## is the frequency of an em.-field mode you can always decompose the (free) em. field to.

To describe this you do not need to quantize the em. field yet, but semiclassical descriptions are adequate, i.e., you quantize the matter particles (in this case most importantly electrons) and keep the em. field as classical. That said, you see that it's not so simple to give the sentence "light is quantized" a proper meaning. Particularly it doesn't imply that you can say that "light consists of photons" when thinking of a "photon" as a little bullet-like object. This "particle picture" is to a a certain degree possible for massive particles, but not for massless quanta as the photon. Nevertheless the semiclassical approximation is completely adequate to understand why (a) there is an interference pattern (just use classical electrodynamics with adequate boundary conditions for the double-slit) and (b) if you dim down your light source enough there appear only single dots on the screen building up the interference pattern after some time when enough dots have appeared: The dots appear from the absoption of the light quanta by the material of the screen. In this picture, however we have not made use of the full quantum picture of the em. field.

We are forced to use the full theory (a) to understand the phenomenon of spontaneous emission which you necessarily need to get the correct black-body formula by Planck when analyzing it's derivation from the point of view of kinetic theory (as was done by Einstein already in 1917, i.e., before modern QT and quantization of the em. field has been discovered, which happened in 1925 by Born and Jordan, using the groundbreaking idea by Heisenberg) and (b) in our context if instead of dimmed light one uses a true single-photon source (which is not so easy; that's why reliable true single-photon source have become available only in the mid 1980ies and in full glory even later with the use of parametric down conversion exploiting non-linear optics using strong lasers).

In terms of the quantized em. field light emitted from a laser is a quantum state of the electromagnetic field called "coherent state". If the intensity of the coherent state is high, you can neglect the quantum fluctuations at all and you are back at a situation where classical electrodynamics is a very good approximation. If you dim down the laser enough, the coherent state is a superposition, where the vacuum state dominates and it's a good approximation to only take the next term, which is a single-photon state. That means only rarely per unit time (which you can resolve with your detector) you absorb a photon on the plate and thus see "particle-like behavior of light", but it's not really a particle hitting the screen.

Finally, as said already above, nowadays you can also prepare true single-photon states, but for the double-slit setup that again doesn't make any difference compared to the dimmed laser! You still see the single point-like detection events on the screen, because one photon is absorbed each time there's such a detection event. All QED does and can do in this situation is to describe the probability distribution of the location of these detection events, and that's also all we can observe.

Now you write

In the end, everything must be explicable by physical entities or events. QED is a way of working with the behaviour and characteristics of fields and particles. It does not explain the physical nature of light. I have suggested a physical explanation which I do not believe contradicts QED. I expected a more helpful approach here.
I hope, I'll not disappoint you, but physics is a natural science, and all physics does is to try to systematically observe nature and try to figure out how to systemize the observed patterns of how nature behaves, i.e., in shorter words it uses the observation that there are such regular patterns and that they can be expressed in terms of mathematical models and theories. As it turns out, it's even impossible to adequately talk in "natural language" about realms of our experience which is not directly related to our daily experience, directly with our senses, like the microscopic phenomena related to the atomistic structure of matter (leading to the fundamental building blocks, called elementary particles and radiation, and the description of their interactions in terms of quantum (field) theory) or the very big realm of astronomy and cosmology (where general relativity has to be applied).

In this sense what we have tried to give as an answer already refers to the "physical nature of light". I don't know, what else you expect, i.e., what would be a "more helpful approach here".
 
Perok/Vanhees71/Nugatory/Dr.Chinese/Mentz114 - Thank you all very much for your answers which I believe are as far as you can practically go without referring to a source of education material. I understand and accept what you say. I do respect the current state of knowledge on these topics but do not admit to my being as closed minded as Dr.Chinese has perhaps suggested.
I simply seek a physical interpretation of the interference pattern in the DS exp, which can also be viewed as a probability distribution as well as being a physical manifestation. I do not think the two interpretations (a QM or a classical wave description) are separate alternative views. I believe they must meet somehow at an interpretation that satisfies both and my thoughts on photons were aimed at doing that. I expect you are finding me naïve but despite what QFT says, I find it difficult to accept that any entity, (photons, electrons, etc) do not exist along a path until they hit the screen, whereupon they suddenly spring into existence for some reason, in the pattern described.
I think physicists should have an open mind on attempts to fully explain this, especially when it is admitted that no one intuitively understands the DS exp'.
Thank you.
 

vanhees71

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Yes, physicists must have an open mind, but you cannot deny established scientific facts, among which is that the best description of light ever achieved is QED, and according to QED a photon cannot be localized in principle. There's not even a position observable in the usual sense!
 
vanhees71,
But I have said, I understand and respect the current state of knowledge on this field and I am not denying any established facts. However, just because we have reached a certain level of understanding and that level is "the best description of light ever achieved", that should not stop us from trying to improve our knowledge, which I am sure you will agree, is incomplete.
A photon is certainly localised when it hits the screen? I agree that anything travelling at the speed of light does not experience distance or length, since it will get anywhere ahead in no time at all and that means distance has become irrelevant to it. In this sense, it is true that a photon cannot be localised, except when you intercept it (at the screen). Special Relativity explains this quite intuitively.
We agree, it seems.
 

vanhees71

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No, the photon is not localized when it hits the screen. What's localized is the "pixel" (e.g., in a modern CCD camera some molecule in the semiconductor material) which interacts with the electromagnetic field. It's simply impossible to localize a photon since you cannot even define a complete position operator. That's why it doesn't make sense to say "it [the photon] will get anywhere ahead in no time". The signal velocity of electromagnetic waves in free space is still the speed of light in vacuum, ##c##, as in classical electrodynamics. Indeed, special relativity (i.e., the representation theory of the proper orthochronous Poincare group is the key starting point to understand relativistic QFT, particularly massless fields and their quanta).
 
vanhees71,

Thank you for your comments.
 

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