Insights Some sins in physics didactics - comments

[vanhees71]

Wave particle duality: Still true in QM where the Hilbert space is particles, and the Schroedinger equation is waves. Also true in non-rigourous QFT where there are Fock space particles and waves via the Heisenberg picture equations of motion for the operators.
de Broglie relations: Still true for the relativistic free quantum fields

This is exactly, why I consider the teaching of old quantum theory in the beginning of quantum physics courses as a sin. First of all in quantum theory there is no wave-paticle duality. In my opinion it's the greatest overall achievement of modern quantum theory to have get rid of such contradictory pictures about nature. Formally you are right, and the Schrödinger equation has some features of a classical (wave) field, but that's only a mathematical analogy. That any partial differential equation in a space-time with the symmetries and admitting a causality principle (orientation of time) we usually assume (Galilei or Poincare symmetry for Newtonian and special relativistic physics, respectively) has similar forms than any other is very natural, because these symmetries are restrictive enough to determine at least a large part of the form such equations should take. Nevertheless, the Schrödinger-wave function is not a classical field and thus does not describe any kind of classical waves. You don't observe waves, when you consider a single particle but a single particle being detected somewhere in space, and these particles are not "smeared" out in a continuum like way, as a superficial interpretation of the Schrödinger wave function as a classical field would suggest. The right interpretation was given by Born: It describes the probability amplitudes to find a particle at a place, i.e., its modulus squared is the position-probability distribution for particles.

Also I don't see, why you say the Hilbert-space formalism describes particles. The abstract Hilbert-space formalism consists of abstract mathematical objects, which have the advantage that you cannot mix them up with the hand-waving associations of the old quantum theory. That's why I think, the ideal way to teach quantum theory is to start right away with the basis-free formulation in (rigged) Hilbert space. Sakurai's textbook shows a clever way, how to do this without getting into all mathematical subtleties of unbound operators. The aim in teaching quantum theory must be to introduce the students to the fact that the micro-world is "unintuitive", and that's so, because our senses and brains are not made primarily to comprehend or describe the microcosm but to survive in a macroscopic world, which behaves quite "classically", although the underlying "mechanism" is of course quantum.

To teach this, you don't need old-fashioned precursor models, of which the worst is the Bohr-Sommerfeld model of the atom, because that's not even right in any sense of the modern theory. I never figured out, why the model gets the hydrogen energy levels right. The reason must ly in the very high symmetry of the hydrogen-atom hamiltonian (an SO(4) for the bound energy eigenstates, a Galilei symmetry for the zero-modes, and a SO(1,3) for the other scattering states). The same holds, of course true, for the N-dimensional harmonic oscillator which always has a SU(N) symmetry. For the harmonic oscillator it's clear, why it looks so classical also in quantum theory: The equations of motion of the operators representing observables in the Heisenberg picture are linear and thus the expectation values obey exactly the classical equations of motion.

 

[Dadface]

Nice article but I would like to point out a practical difficulty in presenting the photoelectric effect as described here.

In the UK photoelectricity is first introduced to AS level students who are 16 to 17 years old. The AS specification is such that there will be about 16 hours of teaching time available to teach the whole of the quantum theory unit photoelectricity being just one of four topics studied. Subtract the time taken for lab sessions, class discussions settling in time and so on and the teacher will be left with a maximum of about two hours to cover the subject.

In addition to timing problems, students (and probably most teachers whose maths is rusty) would not have the necessary maths expertise to follow this more detailed approach to the subject. I would suggest carry on teaching it as it is and inform the students that there are more sophisticated approaches to the subject but these are beyond the scope of AS.

I would be grateful if someone could clarify the following:
It seems to be suggested that there is a better alternative to the equation E = hf . Have I been reading this correctly? If so I can't see that there is a better way of calculating, for example, the frequency of the photons produced in electron positron annihilation.

 

[atyy]

This is exactly, why I consider the teaching of old quantum theory in the beginning of quantum physics courses as a sin. First of all in quantum theory there is no wave-paticle duality. In my opinion it's the greatest overall achievement of modern quantum theory to have get rid of such contradictory pictures about nature. Formally you are right, and the Schrödinger equation has some features of a classical (wave) field, but that's only a mathematical analogy. That any partial differential equation in a space-time with the symmetries and admitting a causality principle (orientation of time) we usually assume (Galilei or Poincare symmetry for Newtonian and special relativistic physics, respectively) has similar forms than any other is very natural, because these symmetries are restrictive enough to determine at least a large part of the form such equations should take. Nevertheless, the Schrödinger-wave function is not a classical field and thus does not describe any kind of classical waves. You don't observe waves, when you consider a single particle but a single particle being detected somewhere in space, and these particles are not "smeared" out in a continuum like way, as a superficial interpretation of the Schrödinger wave function as a classical field would suggest. The right interpretation was given by Born: It describes the probability amplitudes to find a particle at a place, i.e., its modulus squared is the position-probability distribution for particles.

Well, it's a wave in Hilbert space, which is "particle space" (I'll explain that below).

Also I don't see, why you say the Hilbert-space formalism describes particles. The abstract Hilbert-space formalism consists of abstract mathematical objects, which have the advantage that you cannot mix them up with the hand-waving associations of the old quantum theory.

In QM, the Hilbert space is a particle space because if we have one particle, then we write ψ(x). If we have two particles then we write basis functions that are ψ_m(x₁)ψ_n(x₂). So we still have particles, it just so happens they don't have definite position and momentum at all times.

That's why I think, the ideal way to teach quantum theory is to start right away with the basis-free formulation in (rigged) Hilbert space. Sakurai's textbook shows a clever way, how to do this without getting into all mathematical subtleties of unbound operators. The aim in teaching quantum theory must be to introduce the students to the fact that the micro-world is "unintuitive", and that's so, because our senses and brains are not made primarily to comprehend or describe the microcosm but to survive in a macroscopic world, which behaves quite "classically", although the underlying "mechanism" is of course quantum.

The way I was taught had the quantum mechanical axioms quite early, but we still got the old quantum theory. Lecture 1 was dimensional analysis to motivate the introduction of Planck's constant. Lecture 2 was old quantum theory, including all the wonderful thermodynamics. Lecture 3 was the quantum mechanical axioms (state is a ray, etc).

To teach this, you don't need old-fashioned precursor models, of which the worst is the Bohr-Sommerfeld model of the atom, because that's not even right in any sense of the modern theory. I never figured out, why the model gets the hydrogen energy levels right. The reason must ly in the very high symmetry of the hydrogen-atom hamiltonian (an SO(4) for the bound energy eigenstates, a Galilei symmetry for the zero-modes, and a SO(1,3) for the other scattering states). The same holds, of course true, for the N-dimensional harmonic oscillator which always has a SU(N) symmetry. For the harmonic oscillator it's clear, why it looks so classical also in quantum theory: The equations of motion of the operators representing observables in the Heisenberg picture are linear and thus the expectation values obey exactly the classical equations of motion.

I'm not sure either, I too think it has to do with the symmetry. The Bohr-Sommerfeld quantization somehow has a notion of integrability in it, and the hydrogen atom is integrable in some sense. (Actually, I never know exactly what a quantum integrable system is, since integrability is really a classical concept). Anyway, the semiclassical quantization is still useful, for example, to explain phenomena like "scars" http://www.ericjhellergallery.com/index.pl?page=image;iid=22 .

So I would still like to know if the QM calculation you used has a simple "old quantum theory" interpretation without Einstein's photons, closer to Planck's view. Could we say that somehow the wave has to be of a certain frequency because of a resonance effect?

 

[vanhees71]

Nice article but I would like to point out a practical difficulty in presenting the photoelectric effect as described here.

In the UK photoelectricity is first introduced to AS level students who are 16 to 17 years old. The AS specification is such that there will be about 16 hours of teaching time available to teach the whole of the quantum theory unit photoelectricity being just one of four topics studied. Subtract the time taken for lab sessions, class discussions settling in time and so on and the teacher will be left with a maximum of about two hours to cover the subject.

In addition to timing problems, students (and probably most teachers whose maths is rusty) would not have the necessary maths expertise to follow this more detailed approach to the subject. I would suggest carry on teaching it as it is and inform the students that there are more sophisticated approaches to the subject but these are beyond the scope of AS.

I would be grateful if someone could clarify the following:
It seems to be suggested that there is a better alternative to the equation E = hf . Have I been reading this correctly? If so I can't see that there is a better way of calculating, for example, the frequency of the photons produced in electron positron annihilation.

NO, this I don't buy! You must not teach high school students misleading stuff (in fact, we were told "old quantum theory" also before the modern theory was taught in high school, and our (btw. really brillant) teacher said, before starting with the modern part that we should forget the quantum theory taught before, and she was right so.

Of course, in high school, you cannot teach the abstract Dirac/Hilbert-space notation and also not time-dependent perturbation theory, but you can completely omit misleading statements referring to the "old quantum theory". At high school we learned modern quantum theory in terms of wave mechanics. I don't know, how the schedule looks in the UK, but in Germany, usually one has a modul about classical waves before entering the discussion of quantum theory, and thus you can easily argue in the usual heuristic way to introduce first free-particle non-relativistic "Schrödinger waves", but telling right away the correct Born interpretation. This gains you time to teach the true stuff and not waste it for outdated misleading precursor theories that are important for the science historian only (although history of science makes a fascinating subject in itself, and to a certain extent it should also be covered in high school).

I don't understand the 2nd question. Of course, the energy eigenvalue $E$ and the frequency of the corresponding eigenmode of the Schrödinger field are related by $E=\hbar \omega=h f$, where $\omega=2 \pi f$ and $\hbar=h/(2 \pi)$. Usually nowadays one doesn't use the original Planck constant $h$ but $\hbar$, because you don't need to write some factors of $2 \pi$ when using $\omega$ instead of $f$.

 

[vanhees71]

Well, it's a wave in Hilbert space, which is "particle space" (I'll explain that below).
In QM, the Hilbert space is a particle space because if we have one particle, then we write ψ(x). If we have two particles then we write basis functions that are ψ_m(x₁)ψ_n(x₂). So we still have particles, it just so happens they don't have definite position and momentum at all times.
The way I was taught had the quantum mechanical axioms quite early, but we still got the old quantum theory. Lecture 1 was dimensional analysis to motivate the introduction of Planck's constant. Lecture 2 was old quantum theory, including all the wonderful thermodynamics. Lecture 3 was the quantum mechanical axioms (state is a ray, etc).
I'm not sure either, I too think it has to do with the symmetry. The Bohr-Sommerfeld quantization somehow has a notion of integrability in it, and the hydrogen atom is integrable in some sense. (Actually, I never know exactly what a quantum integrable system is, since integrability is really a classical concept). Anyway, the semiclassical quantization is still useful, for example, to explain phenomena like "scars" http://www.ericjhellergallery.com/index.pl?page=image;iid=22 .

So I would still like to know if the QM calculation you used as a simple "old quantum theory" interpretation without Einstein's photons, closer to Planck's view. Could we say that sonehow the wave has to be of a certain frequency because of a resonance effect?

It's a bit strange to me to say the Schrödinger waves are in Hilbert space. It's simply a scalar complex valued field which describes waves, but just in the mathematical sense. It's not like the waves of a measurable field quantity like, e.g., the density of air or water (sound waves) or the electromagnetic field, but its physical meaning is given by the Born rule.

What the quantum mechanics is supposed to describe is, of course, given by the choice of the problem. If you have a single particle, you start by defining observables by assuming some operator algebra, heuristically taken from some classical analgous situation. Of course, you cannot derive this in a mathematical sense from anything, but you have to more or less guess it. What helps you, are symmetries and (Lie-)group theory to guess the right operator algebra. The self-adjoint operators live on a Hilbert space, and the rays in this Hilbert space represent the (pure) states. Then, if $|\psi \rangle$ is a normalized representant of such a ray, a wave function is given wrt. a complete basis, related to the determination of a complete set of compatible observables, $|o_1,\ldots,o_n \rangle$, i.e.,
$$\psi(o_1,\ldots,o_n)=\langle o_1,\ldots o_n|\psi \rangle.$$
That's it. In my opinion there's no simpler way to express quantum theory than this. Admittedly it's very abstract und unintuitive, but that's the only way we have found so far to adequately describe (pretty comprehensively) the phenomena in terms of a pretty self-consistent mathematical scheme.

 

[atyy]

It's a bit strange to me to say the Schrödinger waves are in Hilbert space. It's simply a scalar complex valued field which describes waves, but just in the mathematical sense. It's not like the waves of a measurable field quantity like, e.g., the density of air or water (sound waves) or the electromagnetic field, but its physical meaning is given by the Born rule.

What the quantum mechanics is supposed to describe is, of course, given by the choice of the problem. If you have a single particle, you start by defining observables by assuming some operator algebra, heuristically taken from some classical analgous situation. Of course, you cannot derive this in a mathematical sense from anything, but you have to more or less guess it. What helps you, are symmetries and (Lie-)group theory to guess the right operator algebra. The self-adjoint operators live on a Hilbert space, and the rays in this Hilbert space represent the (pure) states. Then, if $|\psi \rangle$ is a normalized representant of such a ray, a wave function is given wrt. a complete basis, related to the determination of a complete set of compatible observables, $|o_1,\ldots,o_n \rangle$, i.e.,
$$\psi(o_1,\ldots,o_n)=\langle o_1,\ldots o_n|\psi \rangle.$$
That's it. In my opinion there's no simpler way to express quantum theory than this. Admittedly it's very abstract und unintuitive, but that's the only way we have found so far to adequately describe (pretty comprehensively) the phenomena in terms of a pretty self-consistent mathematical scheme.

Yes, it's a bit strange, but that it's not wrong shows that there is nothing wrong with wave-particle duality. Again in non-rigourous QFT, the Fock space is still a particle space. Then if we take the Wilsonian viewpoint and accept a lattice regularization, the lattice is again QM, which is a particle space.

 

[atyy]

What if the photoelectric effect could be shown with single photons? Would that vindicate Einstein's analysis?

 

[vanhees71]

I don't understand what you mean by "particle space". Quantum theory is about quanta, not particles nor classical fields, no matter in which of the many equivalent ways you express it. Of course, you can treat the photoeffect also with single photons. For that you have to quantize the electromagnetic field. The only difference at this order is that for the excited bound states there's a transition probability from an excited (bound) state to a lower state under emission of (one or more) photons, spontaneous emission, and that's why Planck's Law shows the necessity for the quantization of the em. field, as Einstein has figured out in 1917 from another semiclassical argument within old quantum theory. To get the correct radiation law, he had to assume spontaneous emission, and that was later explained by Dirac when introducing the formalism for non-conserved "particle numbers" in terms of creation and annihilation operators.

 

[Ken G]

To me, the crucial insight of any "wave theory" is simply the importance of interference. So the problem with "wave/particle duality" is only in how we came to understand waves, historically, in terms of the interference in actual observables (displacements, pressures, etc.). But when Huygens realized that wave propagation was an interference among many different processes going on at the same time, and Feynman discovered how to think about it as a superposition of path integrals, it seems to me we should have generalized what we mean by "waves" to include complex fields that show the same behavior, from which real (observable) fields can just be obtained by matching real initial conditions by use of the complex conjugate (which is how real waves are often analyzed anyway). Take away those real initial conditions, and you have a complex wave theory. Could not such a thing be formalized in terms very similar to "new" quantum field theory? In other words, maybe the problem was not old quantum mechanics, but old wave theory.

Also, I think the main problem with "wave/particle duality" is that it is often explained like "sometimes it acts like a wave, sometimes like a particle." That makes it sound confusing and downright schizophrenic. But there's no need to describe it like that, the wave aspects are consistent, the particle aspects are consistent. What works for me is to say that particles are "told what to do" by wave mechanics. Even trajectories are things that short-wavelength waves do just fine, so there never was anything "different" about what particles do, it was always wave mechanics we just had no reason to see it that way. So to me, the photoelectric effect looks simply like the requirement that if you will get a big response out of an electron (like knocking it out of a metal or forcing a transition in an atom) with a very weak field, you need to find a way to repeat over and over that tiny energy coupling between the field and the electron, in a resonant way, until you accumulate the big response. Like if your house was on springs, and you wanted to raise it an inch, you'd just very gradually bounce it at the resonant frequency until the amplitude was an inch. So that kind of process picks out power from the driving field at the necessary resonant frequency. Behind all that lovely formal mathematics, there is still something quite simple that is physically going on-- the particle is picking out a particular mode from the field, because that is the mode that produces constructive interference in all the possible ways the necessary energy transfer can occur, none of which would independently have sufficient amplitude to be of any consequence, a la Huygens.

So it seems that would have been the greater insight from the photoelectric effect and all types of stimulated emission, and possibly spontaneous emission too (in a kind of radiation reaction force sense). That's what I take from vanhees71's argument-- Einstein thought he was discovering the photon, but that discovery would have to wait-- he was really discovering the quantum mechanics of the electron and he didn't know it! No wonder he never liked quantum mechanics so much...

 

[ZapperZ]

I find the discussion in this thread very confusing and difficult to follow. This is because in some cases, one appeals to the historical context of the derivation, but then one switches to present-day knowledge and criticize the former. I don't get it.

Still, let's get a few things out of the way:

1. Very much like the use of "relativistic mass", is it still news that the basic, simple, historical photoelectric effect is not a "proof" of the existence of photons or quantized electromagnetic field? The paper by J.J. Thorn et al. has been cited many times in this forum (do a check if you don't believe me). In it, the status of the photoelectric effect has been clearly stated as far as the idea of photons is concerned. This paper was published in 2004, and this idea has existed even way before that (see the citation). Are we all just slow to catch on?

2. Is there such a thing as a "proof" in physics? So is the problem here the photoelectric effect description, or overzealous teachers or writers who somehow stated such a word without realizing the fallacy of it?

3. Note that the classical derivation, using modern quantum theory, arrived at the same mathematical expression for the photoelectric effect that Einstein described. So Einstein's insight on the phenomenon gave the same mathematical formalism without any knowledge of the quantum phenomenon of solids and before the existence of modern QM. This leads to his interpretation that this is due to a quantized light based on what was known back then. How is this not any different than our current situation with quantum mechanics itself where we all agree on the formalism, but many of us differ in its interpretation?

4. Because of #3, it is a valid reason to award Einstein with the Nobel Prize, because the mathematical description is still valid (and note that this is coming from someone who had previously written about https://www.physicsforums.com/threads/violating-einsteins-photoelectric-effect-model.765714/ based on newer experiments). Note that the Nobel citation for Einstein's prize read:

.. for his services to theoretical physics, and for his discovery of the law of the photoelectric effect.

i.e. the mathematical description of the photoelectric effect. It says nothing about the quantized light. As far as I can tell, nothing that has been uncovered here contradicts that.

5. I also find it unfair that we apply modern quantum theory to reexamined the naive photoelectric effect, and yet we ignore modern EXPERIMENTS that have expanded the photoelectric effect as a more generalized photoemission phenomenon. If Einstein had access to high-powered laser, the quantum effect of light will be even more apparent via the multiphoton photoemission. I am aware that this is not within the scope of the thread's derivation, but this point should be mentioned.

Zz.

 

[Dadface]

NO, this I don't buy! You must not teach high school students misleading stuff (in fact, we were told "old quantum theory" also before the modern theory was taught in high school, and our (btw. really brillant) teacher said, before starting with the modern part that we should forget the quantum theory taught before, and she was right so.

Of course, in high school, you cannot teach the abstract Dirac/Hilbert-space notation and also not time-dependent perturbation theory, but you can completely omit misleading statements referring to the "old quantum theory". At high school we learned modern quantum theory in terms of wave mechanics. I don't know, how the schedule looks in the UK, but in Germany, usually one has a modul about classical waves before entering the discussion of quantum theory, and thus you can easily argue in the usual heuristic way to introduce first free-particle non-relativistic "Schrödinger waves", but telling right away the correct Born interpretation. This gains you time to teach the true stuff and not waste it for outdated misleading precursor theories that are important for the science historian only (although history of science makes a fascinating subject in itself, and to a certain extent it should also be covered in high school).

I don't understand the 2nd question. Of course, the energy eigenvalue $E$ and the frequency of the corresponding eigenmode of the Schrödinger field are related by $E=\hbar \omega=h f$, where $\omega=2 \pi f$ and $\hbar=h/(2 \pi)$. Usually nowadays one doesn't use the original Planck constant $h$ but $\hbar$, because you don't need to write some factors of $2 \pi$ when using $\omega$ instead of $f$.

Vanhees there really are practical difficulties for any high school teacher in presenting the subject as you suggested. Just look at the relevant section of the Cambridge International AS/A level syllabus. Quantum theory is 25 out of 26 different topics. In addition to covering all of the topics teachers need to teach experimental and practical skills and do numerous other things such as incorporating social, environmental, economic and other aspects into their lesson plans. And, of course, there is the continuing amount of meetings and paperwork to contend with. Taking everything into account, the time teachers have to cover photoelectricity is very limited. Quantum theory is just one small part of a very large syllabus.
Have a look at the syllabus requirements and you will see exactly what it is teachers have to teach. To do otherwise would jeopardise the chances of their students. I don't see anything wrong in teaching a subject as the syllabus demands and then informing the students that the subject is far more developed than what has been taught so far. Most of them know that anyway.

 

[atyy]

I don't understand what you mean by "particle space". Quantum theory is about quanta, not particles nor classical fields, no matter in which of the many equivalent ways you express it.

Well, these things are called "particles" by convention, because in the classical limit the classical particle is recovered.

NO, this I don't buy! You must not teach high school students misleading stuff (in fact, we were told "old quantum theory" also before the modern theory was taught in high school, and our (btw. really brillant) teacher said, before starting with the modern part that we should forget the quantum theory taught before, and she was right so.

OK, but this doesn't mean one should not teach old quantum theory first. It just means we don't say that the photoelectric effect with large numbers of coherent photons cannot be explained without quantization of the EM field.

If we only teach absolutely correct things, then we also cannot teach QM (first quantized language), because it is not relativistic.

But if we teach QFT (second quantized language), we will also find there is only a low energy effective theory. So there has to be some non-perturbatively defined regularization, eg. the lattice, which basically means we go back to QM

But if we start from lattice theory instead, we run into problems with chiral fermions.

So at present we have a theory that is only perturbatively defined by some presumably asymptotic expansion, but we have nothing to which it is asymptotic to, so we have no theory. So we have no laws of physics. Which basically proves Many-Worlds is correct. Because in Many-Worlds, all possibilities happen, so what we observe must happen in at least one world. So we should basically teach MWI and the anthropic principle, since that is the only interpretation that is proven to capture all observations with perfect consistency.

 

[atyy]

5. I also find it unfair that we apply modern quantum theory to reexamined the naive photoelectric effect, and yet we ignore modern EXPERIMENTS that have expanded the photoelectric effect as a more generalized photoemission phenomenon. If Einstein had access to high-powered laser, the quantum effect of light will be even more apparent via the multiphoton photoemission. I am aware that this is not within the scope of the thread's derivation, but this point should be mentioned.

I agree with your general point that old quantum theory should be taught, but aren't multiphoton effects also explained without quantizaton of the electromagnetic field? I think the formalism is similar to that in vanhees71's blog post, except that one has to go to higher orders in the perturbation expansion, eg. http://cua.mit.edu/8.421_S06/Chapter9.pdf.

 

[ZapperZ]

I agree with your general point that old quantum theory should be taught, but aren't multiphoton effects also explained without quantizaton of the electromagnetic field? I think the formalism is similar to that in vanhees71's blog post, except that one has to go to higher orders in the perturbation expansion, eg. http://cua.mit.edu/8.421_S06/Chapter9.pdf.

I don't know. It looks like it is employing the dipole transition matrix for each transition due to photon absorption. That smells very much like it already assumes the photon model.

BTW, here is a reference that I have on an example of multiphoton photoemission. Look at Eq. 1 and how it manifests itself as the slope of the charge with light intensity.

http://qmlab.ubc.ca/ARPES/PUBLICATIONS/Articles/multiphoton.pdf

Zz.

 

[Ken G]

I think a few key points are getting lost here. There are two things that vanhees71 never implied, and I never implied them either: 1) that the photoelectric effect was thought to "prove" light was quanta (we all know science doesn't prove, but we use the word loosely sometimes, that was never the issue), and 2) that Einstein was to be blamed for some incorrect interpretation of his experiment. The whole point, it seems to me, relates to how we teach the significance of the photoelectric effect. Because the Nobel was awarded for it, and because it was awarded because that experiment was initially thought to demonstrate the photon nature of light, that's the way it still gets taught. It seems to me vanhees71 is merely pointing out that we don't need to teach it that way, just because it was once thought about that way, and just because a Nobel committee saw it that way. This isn't about the history of discovery, it is about what are the actual ramifications of that experiment, given what we now know, and how history can follow some ironic turns that need to be ironed out in hindsight. I think that's a valid point, and the objections being raised are somewhat extraneous to that point.

 

[stevendaryl]

This article is suggesting that the photo-electric effect doesn't actually prove anything about the quantization of the electromagnetic field; the quantization of energy levels of matter is sufficient to explain it. So does ANYTHING prove the quantization of the E&M field? I guess not, because Feynman's "absorber theory" reformulates QED so that there are no additional degrees of freedom in the E&M field.

On the other hand, it seems strange to treat matter (fermions) completely different than gauge particles, when their physics is so similar.

 

[stevendaryl]

OK, but this doesn't mean one should not teach old quantum theory first. It just means we don't say that the photoelectric effect with large numbers of coherent photons cannot be explained without quantization of the EM field.

If we only teach absolutely correct things, then we also cannot teach QM (first quantized language), because it is not relativistic.

I agree. I think that it is important to separate empirical results from the theoretical models developed to explain those results. But I think it's okay to teach old models, as long as we make it clear that they are just models, which are at best approximations.

 

[ZapperZ]

This article is suggesting that the photo-electric effect doesn't actually prove anything about the quantization of the electromagnetic field; the quantization of energy levels of matter is sufficient to explain it. So does ANYTHING prove the quantization of the E&M field? I guess not, because Feynman's "absorber theory" reformulates QED so that there are no additional degrees of freedom in the E&M field.
.

But there is a problem here because for metals, the conduction bands are not "quantized" states, as if there are no discrete energy levels. The article cited photoemission from atoms and solids.

And yes, there are plenty of other experiments that show the photon's presence, including the Thorn's which-way experiment that I cited. Read the paper.

Zz.

 

[Demystifier]

I would also like to propose some sins in physics didactics:

- The Michelson-Morley experiment is taught to be a proof that aether does not exist. Nevertheless, this experiment by itself does not prove it. The experiment does not exclude the possibility that the aether is dragged by the Earth. (Of course, there are other experiments that exclude this possibility, but not the Michelson-Morley one.)

- The spinorial transformation of the Dirac wave function is often taught as being derived from the Dirac equation. However, the Dirac equation does not really imply the spinorial transformation. The Dirac equation allows also a (physically equivalent) alternative, according to which the wave function transforms as a scalar:
http://lanl.arxiv.org/abs/1309.7070 [Eur. J. Phys. 35, 035003 (2014)]

- In 1930 Einstein proposed the photon-in-the-box thought experiment, which was supposed to demonstrate an inconsistency of the time-energy uncertainty relations. The Bohr's resolution of the problem, based on adopting some principles of general relativity, is often taught to be the correct way to save consistency of the time-energy uncertainty relations. But it is not. The correct resolution of the photon-in-the-box paradox, similarly to the latter EPR paradox, is the non-local nature of quantum correlations:
http://lanl.arxiv.org/abs/1203.1139 [Eur. J. Phys. 33 (2012) 1089-1097]

 

[Ken G]

- The Michelson-Morley experiment is taught to be a proof that aether does not exist. Nevertheless, this experiment by itself does not prove it. The experiment does not exclude the possibility that the aether is dragged by the Earth.

I'd take that a step farther. One might hold that it would be odd for the Earth to drag aether, so in that sense the Michelson-Morley experiment could be viewed as good evidence there is no aether. But isn't the deeper point that it's actually not evidence of that at all, rather, it is evidence that the aether concept is simply not helping us understand the situation? After all, both Poincare and Lorentz himself interpreted that experiment as simply saying that the aether has some physical action on clocks and rulers that covers its tracks. Einstein said, who needs that, just make c a law. So it was a classic example of Occam's Razor, but it was certainly not a no-go theorem, and it is indeed sometimes taught that way. We must all recognize that if some experiment tomorrow shows that we need an aether after all, then no past experiments would need to come out any different, we'd just need to dust off Poincare and Lorentz.

 

[Greg Bernhardt]

I would also like to propose some sins in physics didactics:

- The Michelson-Morley experiment is taught to be a proof that aether does not exist. Nevertheless, this experiment by itself does not prove it. The experiment does not exclude the possibility that the aether is dragged by the Earth. (Of course, there are other experiments that exclude this possibility, but not the Michelson-Morley one.)

- The spinorial transformation of the Dirac wave function is often taught as being derived from the Dirac equation. However, the Dirac equation does not really imply the spinorial transformation. The Dirac equation allows also a (physically equivalent) alternative, according to which the wave function transforms as a scalar:
http://lanl.arxiv.org/abs/1309.7070 [Eur. J. Phys. 35, 035003 (2014)]

- In 1930 Einstein proposed the photon-in-the-box thought experiment, which was supposed to demonstrate an inconsistency of the time-energy uncertainty relations. The Bohr's resolution of the problem, based on adopting some principles of general relativity, is often taught to be the correct way to save consistency of the time-energy uncertainty relations. But it is not. The correct resolution of the photon-in-the-box paradox, similarly to the latter EPR paradox, is the non-local nature of quantum correlations:
http://lanl.arxiv.org/abs/1203.1139 [Eur. J. Phys. 33 (2012) 1089-1097]

Maybe a follow up entry? :)

 

[ZapperZ]

I would also like to propose some sins in physics didactics:

- The Michelson-Morley experiment is taught to be a proof that aether does not exist. Nevertheless, this experiment by itself does not prove it. The experiment does not exclude the possibility that the aether is dragged by the Earth. (Of course, there are other experiments that exclude this possibility, but not the Michelson-Morley one.)

I disagree. That's like saying "OK, so you found that there's no unicorn. But that was because you were looking for 4-legged unicorns. What if there are 2-legged unicorns?"

The MM-experiment was specifically testing a particular characteristic of light, and based on what was described at that time, it tested it perfectly well. Besides, if you bring the same setup to the ISS, the MM-experiment is equally up to the challenge to even test the ether drag. So the experiment in itself is adequate.

Zz.

 

[Ken G]

This article is suggesting that the photo-electric effect doesn't actually prove anything about the quantization of the electromagnetic field; the quantization of energy levels of matter is sufficient to explain it. So does ANYTHING prove the quantization of the E&M field? I guess not, because Feynman's "absorber theory" reformulates QED so that there are no additional degrees of freedom in the E&M field.

On the other hand, it seems strange to treat matter (fermions) completely different than gauge particles, when their physics is so similar.

I think a big issue is the question, what is the "quantum" in "quantum mechanics?" We might say it's first quantization, and then the quantum in "quantum field theory" is second quantization. But first quantization doesn't give us photons, it just gives us the analysis vanhees71 gave. So his remarks can be interpreted as suggesting that we separate what experiments support the theory of first quantization from the experiments that support second quantization, and not simply follow the historical path there. I think we must agree that had Bohr come up with his model of the atom before Einstein did the photoelectric effect experiment, then that experiment is just a way to generalize the concepts of first quantization to other regimes. There might not be any hint that second quantization is needed, so if we teach it the historical way, we are promoting misconceptions about the differences between these two brands of "quanta".

 

[rude man]

" ... the introduction of a velocity-dependent mass in special relativity, which is a relic from the very early years after Einstein’s ground-breaking paper of 1905. "

The statement is incorrect. See below.

I have never liked the elimination of rest mass as a separate parameter. It changes several formulae that were accurate before this change, not the least being E = mc^2 for a moving particle.

If it was good enough for Richard Feynman it's good enough for me. Reminder: the milennial edition of "The Feynman Lectures on Physics" was issued just a year or two ago. It includes significant revised material from earlier editions but the use of rest mass as a separate parameter was retained. And wisely so IMO.

 

[ZapperZ]

" ... the introduction of a velocity-dependent mass in special relativity, which is a relic from the very early years after Einstein’s ground-breaking paper of 1905. "

The statement is incorrect. See below.

I have never liked the elimination of rest mass as a separate parameter. It changes several formulae that were accurate before this change, not the least being E = mc^2 for a moving particle.

If it was good enough for Richard Feynman it's good enough for me. Reminder: the milennial edition of "The Feynman Lectures on Physics" was issued just a year or two ago. It includes significant revised material from earlier editions but the use of rest mass as a separate parameter was retained. And wisely so IMO.

I don't what's "incorrect" about that. In fact, check out one of my earlier posting about this:

https://www.physicsforums.com/threads/relativistic-mass.642188/#post-4106101

Note that even Einstein later on stopped using it.

Zz.

 

[atyy]

I don't know. It looks like it is employing the dipole transition matrix for each transition due to photon absorption. That smells very much like it already assumes the photon model.

I think that although the dipole approximation is used, it is a treatment in which the EM field is not quantized. The Hamiltonian they use for the two-photon process is http://cua.mit.edu/8.421_S06/Chapter9.pdf (Eq 9.3), which looks to me of the same form as http://cua.mit.edu/8.421_S06/Chapter7.pdf (Eq 7.31), which has a classical EM field. In their notation if the EM field is quantized, I would expect to see an expression more like their Eq 7.46.

BTW, here is a reference that I have on an example of multiphoton photoemission. Look at Eq. 1 and how it manifests itself as the slope of the charge with light intensity.

http://qmlab.ubc.ca/ARPES/PUBLICATIONS/Articles/multiphoton.pdf

That is interesting. I had to look up the Fowler-Dubridge theory they mention, on which the BSB theory is based. It basically assumes the E=hf from old quantum theory like Planck and Einstein.

 

[atyy]

Of course, you can treat the photoeffect also with single photons. For that you have to quantize the electromagnetic field. The only difference at this order is that for the excited bound states there's a transition probability from an excited (bound) state to a lower state under emission of (one or more) photons, spontaneous emission, and that's why Planck's Law shows the necessity for the quantization of the em. field, as Einstein has figured out in 1917 from another semiclassical argument within old quantum theory. To get the correct radiation law, he had to assume spontaneous emission, and that was later explained by Dirac when introducing the formalism for non-conserved "particle numbers" in terms of creation and annihilation operators.

Probably the strongest argument for teaching the "old quantum theory" view of E = hf and the photoelectric effect using E = hf is that the photoelectric effect is still how we detect single photons!

 

[stevendaryl]

- The spinorial transformation of the Dirac wave function is often taught as being derived from the Dirac equation. However, the Dirac equation does not really imply the spinorial transformation. The Dirac equation allows also a (physically equivalent) alternative, according to which the wave function transforms as a scalar:
http://lanl.arxiv.org/abs/1309.7070 [Eur. J. Phys. 35, 035003 (2014)]

I seem to recall a somewhat heated discussion the last time this was brought up, but I don't remember what the objections were.

It seems that there are maybe three approaches to understanding the gamma-matrices in the Dirac equation:

1. They are just four constant matrices, and the index does not imply that they form a vector.
2. They are matrix-valued components of a 4-vector.
3. Each gamma matrix is a vector. The index \mu in \gamma_\mu indicates which vector, rather than which component.

I'm not 100% sure whether the third approach is well-worked-out, but it is the approach taken by Hestenes in his "geometric algebra", which is inspired by Clifford algebras. In a Clifford algebra, the anticommutation relation

e_\mu e_\nu + e_\nu e_\mu = 2 g_{\mu \nu}

is supposed to hold for basis vectors e_\mu; the \mu indicates which basis vector, rather than which component.

 

[carllooper]

Explanations in physics, (be they old or new explanations), are for many people themselves in need of an explanation.

Put an equation in front of many people and it won't explain anything.

There is a case for pointing out to students particular experiments (observations) which can act as inspiration for particular explanations, regardless of whether such explanations are deemed today as correct or otherwise.

Now we can not prove that any particular experiment has historically inspired any particular explanation or understanding. But nor is that the goal. The goal is to identify those experiments which could have inspired a theory, or could re-inspire that same theory ... re-inspire the very understanding we might be otherwise entertaining and expressing in an otherwise difficult equation.

We can explain an explanation in this way.

C

 

[rude man]

" ... the introduction of a velocity-dependent mass in special relativity, which is a relic from the very early years after Einstein’s ground-breaking paper of 1905. "

The statement is incorrect. See below.

I have never liked the elimination of rest mass as a separate parameter. It changes several formulae that were accurate before this change, not the least being E = mc^2 for a moving particle.

If it was good enough for Richard Feynman it's good enough for me. Reminder: the milennial edition of "The Feynman Lectures on Physics" was issued just a year or two ago. It includes significant revised material from earlier editions but the use of rest mass as a separate parameter was retained. And wisely so IMO.

I don't what's "incorrect" about that. In fact, check out one of my earlier posting about this:

https://www.physicsforums.com/threads/relativistic-mass.642188/#post-4106101

Note that even Einstein later on stopped using it.

Zz.

Well, you said it was a relic from the early years of 1905. Feynman taught the course in question at Caltech in the '60's.

I'm aware Einstein later changed his mind but Feynman certainly did not.