B QM concept of photon.... still a bit of a mystery today?

[CPW]

TL;DR Summary

Deeper understanding needed... QM concept of the photon, still "poorly understood"?

Hi PF.

I desire deeper understanding of fundamental physics, and quantum mechanics can be a challenge for me (compared to other topics in physics).

I read in the intro of the physics textbook chapter that QM explains many phenomena, e.g. why copper conducts electricity and glass does not. In same chapter the authors explain the concept of a photon for light, but also state that the concept of the photon is still "poorly understood."

Is that still true today? The concept of a photon still a bit of a mystery?

 

[PeroK]

Is that still true today? The concept of a photon still a bit of a mystery?

A photon is the particle associated with the quantized electromagnetic field. From that perspective it is well understood.

@vanhees71 will no doubt fill in the requisite mathematical description.

 

[malawi_glenn]

Considering that quantum electrodynamics (QED) is possibly the most accurate scientific theory humankind has ever invented/discovered, and that photons are a huge part in that theory, I'd say photons are very well understood

 

[dextercioby]

Perhaps you can tell us the name & author of the book, so we know (and everyone reading here) to avoid it.

 

[Vanadium 50]

The year of publication might be valuable too. If it's a century old...

 

[Nugatory]

Is that still true today? The concept of a photon still a bit of a mystery?

It’s not so much that it a mystery as that it is unlike the classical objects that we are intuitively familiar with. That makes it difficult to come up with any layman-friendly English-language description. The math is clear and not notably mysterious, but it is also not even slightly accessible in a B-level thread.

(You could take a look at this writeup…. )

 

[CPW]

Perhaps you can tell us the name & author of the book, so we know (and everyone reading here) to avoid it.

"The concept of a light quantum, or a photon, turns out to be far more subtle and mysterious than Einstien imagined. Indeed, it is still very poorly understood." - Halliday/Resnick/Walker Chapter 39 of 6th edition "Fundamentals of Physics". Published in 2001.

That reading sparked by post to PF today.

 

[dextercioby]

@CPW , You can drop that wrong statement from reading. This is a general level physics textbook. It should not contain such absurd exaggerations.

 

[vanhees71]

Argh, one more book I thought useful, which you can't recommend anymore. The irony is that the work Einstein got his Nobel prize for is the only one which is completely obsolete today, known as "the old quantum theory" with all the mysterious properties like wave-particle dualism etc. His works on relativity (classical part) and statistical physics are, of course, valid today. It's amusing that Einstein's Nobel certificate explicitly says that the prize was not (!) given for relativity, which was due to some philosophical dispute dominated by a then famous philosopher Bergson, who thought that the relativsitic notion of time was flawed ;-)).

Today we exclusively use "modern quantum theory", which has been discovered almost at the same time (1925-1926) in three formulations: "matrix mechanics" (suggested by Heisenberg, worked out by Born, Jordan, and Heisenberg in 1925), "wave mechanics" (Schrödinger 1926), and "transformation theory" (Dirac 1926). Born and Jordan had already in 1926 also the idea of field quantization, applied to the electromagnetic field, but this was overlooked for some time and had to be rediscovered by Dirac in 1927.

Unfortunately the introductory chapters of textbooks still use the old wave-particle dualism and the wrong picture of photons as "light particles" of the old quantum theory, which regularly leads to confusion. The problem with that approach is that you have unlearn these claims again when going on to study the now established modern quantum theory.

Photons are the least particle-like entities of the entire business. The reason is that they have to be described as massless fields with spin 1 within relativistic quantum field theory. This implies that that they do not even admit the definition of a proper position operator, i.e., it doesn't make sense to talk about "point particles" in the context of photons from very basic principles. Thus photons are not only not localizable but you cannot even really define what "localizable" in a strict sense should mean.

A much better intuitive picture is to think of photons in terms of electromagnetic waves, known from classical electrodynamics since Maxwell's and Hertz's works in the 19th century. The only "particle-like aspect" is that a single-photon must be understood as a specific state of the quantized electromagnetic field, where strictly only one quantum of this field is present. This implies that you can detect only the "entire photon" or "nothing" at a certain place and time, where the place is determined by the location of the photon detector (e.g., a CCD camera or a photo plate). From the fundamental theory of the interaction of the em. field with charged particles you find out that the detection probability at a certain place and time is proportional to the energy density of the electromagnetic field, and that's all you can know about the photon (plus the probability for a given polarization state, if this is also measured).

 

[gentzen]

Argh, one more book I thought useful, which you can't recommend anymore.

Don't be ridiculous. Either it is a good book for its target audience, which is consistent in its own ways. Or it is suboptimal for its target audience, for whatever reasons. One or two wrong statements, or even an entirely wrong chapter will not fundamentally change this. And students have to develop some mechanisms for dealing with wrong or inaccurate statements in textbooks anyway.

 

[Vanadium 50]

If we woeren't allowed to use books with any mistakes in them, libraries would become dumpsters.

 

[MRMMRM]

This is from the 10th edition and 2015 not the 6th and 2001, its still in that one. Light is a probability wave, made up of a discrete and quantifiable amount of particles, we call them photons. Like you can't have 1/2 or 1/4 of a human, but you still see it all the time in statistics, you can't have 1/2 or 1/4 of a photon. The concept of a photon is the easy part to understand, its the Schrodinger wave function(basic rule #2) and Heisenberg uncertainty principle (Von Neumann projection, basic rule #7) that expands or collapses the wave function that is the strange part. It is usually best to just look at the math, and Feynman diagrams.

 

[vanhees71]

Don't use this book. It's entirely misleading. There is no other way to understand photons than to learn relativistic QFT.

 

[PeroK]

Don't use this book. It's entirely misleading. There is no other way to understand photons than to learn relativistic QFT.

That's not practical for first-year undergraduates!

 

[vanhees71]

Since when do you cover relativistic QFT in the first year undergraduate curriculum?

 

[PeroK]

Since when do you cover relativistic QFT in the first year undergraduate curriculum?

Exactly. That's the target readership for Halliday and Resnick. So, they just say something basic about photons.

 

[MRMMRM]

I think its just more important to understand Einstein did not think quantum mechanics was correct, and that something better than statistical/ probablilistic descriptions of quantum mechanics would come along eventually.

 

[PeroK]

I think its just more important to understand Einstein did not think quantum mechanics was correct, and that something better than statistical/ probablilistic descriptions of quantum mechanics would come along eventually.

Not if you want to be a physicist in the 21st Century!

 

[vanhees71]

Exactly. That's the target readership for Halliday and Resnick. So, they just say something basic about photons.

Well, they say something wrong about photons. Why do you need this at all?

 

[MRMMRM]

Well, they say something wrong about photons. Why do you need this at all?

What did they say that's wrong?

 

[vanhees71]

I can only judge from what you quoted: "Light is a probability wave, made up of a discrete and quantifiable amount of particles, we call them photons."

This is an outdated qualitatively wrong picture for nearly 100 years!

 

[MRMMRM]

I can only judge from what you quoted: "Light is a probability wave, made up of a discrete and quantifiable amount of particles, we call them photons."

This is an outdated qualitatively wrong picture for nearly 100 years!

You are telling me basic rule #6 (Born's rule) in the sticky of this forum, correct?
It states that the probability density of finding a particle at a given point, when measured, is proportional to the square of the magnitude of the particle's wavefunction at that point. It was formulated by German physicist Max Born in 1926. Albert applied it to photons, when he should have been appling it to electrons as Max did.

 

[vanhees71]

Since photons cannot be described by a wave function since they don't even have a position operator, you cannot apply the 1st-quantization formalism to photons.

Even if you describe non-relativistic massive particles, which indeed can be described by a wave function, these wave functions do not "consist of particles" but its modulus squared is the probability distribution for its position.

 

[MRMMRM]

When you guys say you will need to unlearn the quantization of light into photons, it sounds like you are saying

is wrong, or atleast not an example of true quantization. You then make it sound as if subatomic particles do not follow any rules of energy quantization, and its just wave functions and probable positions.

 

[vanhees71]

No, that's not what I said. The one thing that stays right from the "old quantum theory" is the relation between the single-photon energy and momentum and the frequency and wave numbers of the plane-wave modes of the em. field, $E=\hbar \omega=hf$ and $\vec{p} = \hbar \vec{k}$.

What's wrong (already at a qualitative level of the description) and then leads to misunderstandings which have to be unlearned later is the idea that photons are somehow like "massless point particles". Also the claim that the photoelectric or Compton effects, treated at the level of such introductory chapters on QT, were a demonstration for the quantization of the em. field, is wrong. Both follows as well from semiclassical theory, i.e., by quantizing the charged particles (here the electrons bound in a metal or (quasi-)free electrons, respectively) and treating the em. field as classical field.

The most simple example for the necessity of field quantization is spontaneous emission, i.e., the fact that due to the presence of field fluctuations an atom prepared in an excited atomic energy state spontaneously emits a photon and the electron relaxes to a lower atomic energy state. Another example, which needs field quantization, is the HOM experiment with single photons. Last but not least also the Planck spectrum of thermal radiation demonstrates the necessity for field quantization (and both spontaneous and induced emission), as has been demonstrated by Einstein in an unfortunately much less known work in 1917 than the one of 1905.

 

[PeterDonis]

Light is a probability wave, made up of a discrete and quantifiable amount of particles, we call them photons.

The textbook you referenced does not say this. It does say what the OP quoted in post #7 (you highlighted that sentence), which is not accurate for the reasons that have been given. But when talking about what is inaccurate or incomplete in the textbook, we should be talking about what it actually says.

 

[PeterDonis]

When you guys say you will need to unlearn the quantization of light into photons

Nobody has said this. What has been said is that "the quantization of light into photons" does not work the way you have been describing; it can't be described mathematically in terms of ordinary wave functions. It needs to be described in terms of quantum fields.

 

[MRMMRM]

The textbook you referenced does not say this. It does say what the OP quoted in post #7 (you highlighted that sentence), which is not accurate for the reasons that have been given. But when talking about what is inaccurate or incomplete in the textbook, we should be talking about what it actually says.

No, it actually describes light as a probability wave, that's why I said it. Just 8 pages past the one with the quote from OP. Then describes experiments that explain this wave-particle view.

While describing all the different versions of experiments they do give the caveat:
"Bear in mind that the only thing we can know about photons is when light
interacts with matter—we have no way of detecting them without an interaction
with matter, such as with a detector or a screen."
Which is still true to this day. So quantum fields can describe matter particles, but it can't describe a photon.
I've described photons as a whole photon or no photon... to me that is also quantization and it doesn't really matter if you think of it as a field, particle, or wave. Mapping continuous infinite values to a smaller set of discrete finite values. Is this wrong, do I have to unlearn this?

 

[PeterDonis]

it actually describes light as a probability wave

In a different place than you quoted before, yes. In this particular case, though, the "wave" is simply the same wave that appears in the classical analysis, just reinterpreted as the probability of getting a click in the photon detector. There is no need to view the individual photons as following trajectories through spacetime--unless you want to take the Feynman "sum over histories" view and say that the "photon" follows all of the possible trajectories through spacetime from source to detector, with each trajectory contributing to the total amplitude. In which case you've discarded the original "particle" concept of a photon anyway.

the only thing we can know about photons is when light
interacts with matter—we have no way of detecting them without an interaction
with matter

This is true of any quantum "particle". It's just as true of electrons as of photons.

quantum fields can describe matter particles, but it can't describe a photon.

This is simply false. Quantum fields have no problem at all describing the behavior of light, including those behaviors that lead us to describe light as "photons". You are getting very close to a warning here.

I've described photons as a whole photon or no photon

This is fine if you're talking about photon detections. But it doesn't work at all when you look at the underlying quantum fields, except in the very rare cases where the quantum field is in an eigenstate of photon number. That is certainly not the case in almost all experiments involving light, including the double slit. The most common state of light in experiments is a coherent state, which has no definite photon number at all (in fact it has a nonzero amplitude for any number of photons, from zero to infinity).

 

[MRMMRM]

I'll take the warning, but I don't see the difference in these statements and feel like I'm mostly agreeing with you guys and you are saying I'm wrong. Both imply describing somethings behavior, is not describing properties of the thing its self.

"Photons cannot be described by a wave function, they don't even have a position operator, you cannot apply the 1st-quantization formalism to photons."

"Quantum fields can describe matter particles, but it can't describe a photon."

 

[PeterDonis]

I don't see the difference in these statements

Here it is:

"Photons cannot be described by a wave function, they don't even have a position operator, you cannot apply the 1st-quantization formalism to photons."

These are all true statements about the mathematical formulation of quantum theory for photons, which is a quantum field theory. None of the statements you referenced in the textbook contradict any of these statements.

"Quantum fields can describe matter particles, but it can't describe a photon."

This is a claim that there is no quantum field theory for photons, which is manifestly false; see above. None of the statements you referenced in the textbook are making this claim.

 

[PeterDonis]

I don't see the difference in these statements

"Photons cannot be described by a wave function, they don't even have a position operator, you cannot apply the 1st-quantization formalism to photons."

"Quantum fields can describe matter particles, but it can't describe a photon."

If you think a quantum field theory means that there would have to be a wave function or a position operator or a 1st quantization formalism for photons, you need to go spend some time learning quantum field theory. None of those things are required for a quantum field theory.

 

[vanhees71]

No, it actually describes light as a probability wave, that's why I said it. Just 8 pages past the one with the quote from OP. Then describes experiments that explain this wave-particle view.

While describing all the different versions of experiments they do give the caveat:
"Bear in mind that the only thing we can know about photons is when light
interacts with matter—we have no way of detecting them without an interaction
with matter, such as with a detector or a screen."

This is of course correct, and it's the modern view (by the way that was also Planck's view in contradistinction to Einstein, but of course before 1926 there was no idea of field quantization in the modern sense).

Which is still true to this day. So quantum fields can describe matter particles, but it can't describe a photon.
I've described photons as a whole photon or no photon... to me that is also quantization and it doesn't really matter if you think of it as a field, particle, or wave. Mapping continuous infinite values to a smaller set of discrete finite values. Is this wrong, do I have to unlearn this?

Quantum fields perfectly describe both "matter particles" and "photons". QED, together with the rest of the Standard Model, is among the best theories ever discovered. It makes predictions for some quantities (like the anomalous magnetic moment of electrons and most probably also muons or the Lamb shift of the hydrogen-atom energy levels, etc.), which are accurate to more than 12 significant digits.