- #1
- 22,829
- 13,745
vanhees71 submitted a new PF Insights post
Some Sins in Physics Didactics
Continue reading the Original PF Insights Post.
Some Sins in Physics Didactics
Continue reading the Original PF Insights Post.
Last edited:
Exactly! Planck didn't like Einstein's "light quanta hypothesis". In contradistinction to that he was an immediate follower of Einstein's special relativity resolution of the puzzle concerning the lack of Galilei invariance of Maxwell electrodynamics, and he wanted to get Einstein to Berlin very much. Together with von Laue and other Berlin physicist he made Einstein an irresistable job offer, including the post of a director of the Kaiser-Wilhelm-Institut für Theoretische Physik, which consisted only of Einstein himself at the time, which meant minimal effort of time for him. In addition, and this was the most attractive feature of the offer for Einstein, he was free from any teaching duties but still being a professor at the University. For this, of course, Planck needed the agreement of the faculty, and in his letter of recommendation, he stated that Einstein was a genius, and one should not take it against him that he sometimes got over the line into speculation, particularly concerning his "light-quanta hypothesis".Fascinating, so the photoelectric effect did not really demonstrate light was a particle, it merely showed that the electron cannot resonate with the radiation field unless there are frequency components present that can lift the electron past the work function. IIRC, Planck derived his famous function using similar thinking, he didn't imagine the high frequencies were underoccupied because of light quanta, only because electrons could only give energy to the field in quantized bits.
I don't know what deliberations they had, I just mean that giving him the Nobel for the interpretation of the photoelectric effect could have proved disastrous if it had not turned out that light was quantized, merely the process of adding energy to the electromagnetic field inherited the required resonances from quantum mechanics. Then they might have felt they had made a mistake-- only to be vindicated later by quantum field theory! I was commenting that something quite similar to that might have happened had they given him the Nobel for GR with a cosmological constant in it, since then Hubble's observations would have made it look like they had been premature-- only to be vindicated later by dark energy. It just shows our many ups and downs with all of Einstein's great ideas.Interesting, where have you heard that the Nobel committee first wanted to give it for GR? I've never heard this, but only that they hesitated to give the prize for relativity at all. So there's no Nobel for the discovery of GR at all!
Yes, she tops the list of Nobel snubs: http://www.scientificamerican.com/slideshow/10-nobel-snubs/It's pretty funny with Nobel prizes anyway. A said case of negligence is Lise Meitner, who for sure should have gotten the prize together with Otto Hahn since she was the one who gave the correct interpretation of Hahn's results in terms of fission of Uranium nuclei. Hahn didn't have a clue! The reason seems to be that Siegbahn's influence in the Nobel-prize decisions prevented the Nobel prize for Meitner, whom he didn't like due to his antisemitic attitude.
Have you studied the quantum optics textbook of Mandel & Wolf? They perform careful calculations along these lines, both for the semi-classical case, and also the full quantum case.[...] So I think someone should actually do some calculations using the semi-classical theory of the photoelectric effect [...]
Oh...So I guess the amount of agreement is satisfactory!Have you studied the quantum optics textbook of Mandel & Wolf? They perform careful calculations along these lines, both for the semi-classical case, and also the full quantum case.
I remember @ZapperZ once said that multiphoton photoemission and angle-resolved photoemission can only be explained in terms of photons.All I can say is, after reading this, I will from now on say that the photoelectric effect was incorrectly interpreted as evidence that the radiation field comes in quanta, when in fact it was merely evidence that getting an energy E into an electron often requires resonant coupling to some electromagnetic power at frequency E/h. A radiation field that doesn't oscillate at that frequency is therefore not good at doing it. However, it turns out that radiation is regarded as quantized anyway.
Incidentally, I'm not even sure you need to quantize the radiation field to get spontaneous emission. It seems to me a classical treatment of the radiation field can work for that as well, if you simply let the Fourier mode that perturbs the electron be the electromagnetic field that the electron itself creates, in the spirit of the bootstrap effect sometimes used to analyze the radiative reaction force. Which leaves us with the question-- what is the best observational evidence that the radiation field needs to be quantized? The Compton effect? Even photon shot noise could conceivably be modeled as stochastic amplitude variations in a classical field, I would think. Maybe there's even some way to get the Compton effect with a classical field, if such stochastic amplitude variations are included?
Simply ban the word "proved" from your lexicon whenever you are talking about science. However when teaching something you want to present your subject as solid as possible so there is sort of conflict with inconclusive statements that science can make.I see his argument as correct, so much so in fact that I am smacking my head and saying "doh" for ever repeating the everyday argument that the photoelectric effect proved that light had to come in quanta.
In science cause for rejecting some model is falsification of it's predictions. You could rather say that:It was basically a coincidence stemming from the existence of a time period in which we did not understand the quantum mechanics of the electron, that we ever thought that way, so we don't need to re-enter a mistaken mindset every time we bring up the photoelectric effect! vanhees71 is saying that once we understood the quantum mechanics of the electron, we had cause to reject Einstein's explanation of the photoelectric effect, but since quantum electrodynamics came along in short order, that rejection never actually happened.
I agree with all of your more careful restatements, yet you are saying the same thing. We have taken vanhees71's points here.Simply ban the word "proved" from your lexicon whenever you are talking about science. However when teaching something you want to present your subject as solid as possible so there is sort of conflict with inconclusive statements that science can make.
In science cause for rejecting some model is falsification of it's predictions. You could rather say that:
Once we understood the quantum mechanics of the electron, we had no cause to reject (pathced) wave model because of the photoelectric effect.
And if you assert a different historical sequence, in which the quantum mechanics of an electron is discovered prior to the photoelectric effect, there is no Nobel prize there-- it's more like "ho hum, yes quantum mechanics works in other situations than just atoms." No one even imagines the radiation is quantized, there's just no need for it from that experiment. Einstein was right about the cosmological constant too, it seems, but we don't teach students "scientists concluded there is a cosmological constant because it is needed to make the universe static, and modern observations of dark energy confirm that there is indeed a cosmological constant." Instead we call it Einstein's greatest blunder-- even though he was right!
It's pretty funny with Nobel prizes anyway. A said case of negligence is Lise Meitner, who for sure should have gotten the prize together with Otto Hahn since she was the one who gave the correct interpretation of Hahn's results in terms of fission of Uranium nuclei. Hahn didn't have a clue! The reason seems to be that Siegbahn's influence in the Nobel-prize decisions prevented the Nobel prize for Meitner, whom he didn't like due to his antisemitic attitude.
I'd say no, although you can doubt this in some sense: Of course, the photoeffect must also be describable in terms of QED. The setup, most similar to the semiclassical one in my article, is to use a free atom and a coherent state of the em. field as "initial state" and a free electron of momentum ##\vec{p}##, another coherent state of the em. field, and a free proton in the final (asymptotic) state. You should get the same, or a very similar, result as in the semiclassical treatment. In some sense you can indeed say, Einstein's picture is not that wrong, because the corresponding transition-matrix element describes the processes as absorption of one photon out of the coherent field (and even more, because it includes the change of the state of the em. field due to the interaction with the atom in 1st-order perturbation theory).
Nevertheless, at this level of accuracy of the description and just making a measurement to demonstrate the validity of Eq. (1) from Einstein's paper, does not "prove" the necessity of a quantization of the em. field, because there is this semiclassical calculation, leading to this formula (1).
This is again a somewhat more philosophical than physical question. Strictly speaking both Einstein and Planck where wrong, but Einstein got the black-body law right around 1917. Concerning the photoeffect at the level of sophistication discussed in his 1905 paper you cannot distinguish between the light-quantum picture, i.e., that light consists of light particles in Einstein's sense and knock out electrons in collision-like events, and Planck's view that there's a classical electromagnetic wave, but the absorption of em. field energy can only be in energy quanta of size ##\hbar \omega##.
It's also true that Einstein was well aware that the "old quantum theory" was far from satisfactory, and his long struggle with the "radiation problem" finally lead to the development of modern quantum theory. So one should not diminish Einstein's and Planck's achievements in "old quantum theory", but I still consider it a sin to start quantum physics lectures with this old quantum theory, which introduces wrong pictures already on the qualitative level, which then you have to "unlearn" again. It's unnecessary and confusing for the students. On the other hand, it's also very important to have some insight into the historical developments to fully appreciate the modern picture of contemporary physics. I guess that 100 years later also this status of science may be seen as just a historical step to a better understanding of nature. That's just the way science (hopefully!) works.
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.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.
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.
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}(x_{1})ψ_{n}(x_{2}). 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 [Broken].
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?