Quantum theory for high-school students

[Demystifier]

I believe this could be interesting to many people here who are interested in quantum theory but are not (yet) professional physicists:
http://lanl.arxiv.org/abs/1803.07098

 

[Drakkith]

Nice link, Demystifier. I have a question though. I see that linear algebra is fundamental to understanding this lecture. Is understanding linear algebra an absolute requirement for understanding QM, or can QM be put into another mathematical form that doesn't involve linear algebra? Just curious.

 

[Demystifier]

Some problems in QM can be solved without linear algebra, but the general framework of quantum theory cannot be understood without linear algebra.

 

[PeterDonis]

One thing the lectures do not seem to explain is complex numbers; they start out by assuming the students already know about those. Is that a valid assumption for high school students?

 

[microsansfil]

There is also this course taught by Leonard Susskind : http://theoreticalminimum.com/courses/quantum-mechanics/2012/winter

http://theoreticalminimum.com/home

A number of years ago I became aware of the large number of physics enthusiasts out there who have no venue to learn modern physics and cosmology. Fat advanced textbooks are not suitable to people who have no teacher to ask questions of, and the popular literature does not go deeply enough to satisfy these curious people. So I started a series of courses on modern physics at Stanford University where I am a professor of physics. The courses are specifically aimed at people who know, or once knew, a bit of algebra and calculus, but are more or less beginners.

Best regards
Patrick

 

[microsansfil]

in the "Advanced Topics" paragraph it would have been nice to have a section about density operator. to study the behavior of a statistical mixture of states. In pratice, the state of a quantum system is often not perfectly determined. isn't it ?

Best regards
Patrick

 

[Demystifier]

One thing the lectures do not seem to explain is complex numbers; they start out by assuming the students already know about those. Is that a valid assumption for high school students?

Maybe it's not a valid assumption for an average high school student. But I don't think that average high school students would be interested in those lectures in the first place.

See also https://matheducators.stackexchange.com/questions/11436/why-do-we-teach-complex-numbers

 

[atyy]

I think it is weak on interpretation.

"There are many interpretations of quantum mechanics. These interpretations are not scientifically testable, since there is no way to distinguish one from the other, and thus they are in the realm of philosophy, not science"

That is only true in the sense that string theory is not science, a position I do not agree with. Even Messiah, who was quite a bit more careful. He considered a hidden variables and Copenhagen, and said that at that moment, they could not be distinguished.

Also, the statement of Bell's theorem is not correct.

• Locality: Both Alice and Bob measure their qubits at the same time in different places, so that their measurements cannot possibly disturb or influence each other without sending information faster than light.
• Realism: The values of the physical properties Q, R, S, T exist independently of observation, that is, they have certain definite values q, r, s, t which are already determined before any measurements took place (like in the envelope scenario).

 

[haushofer]

I think it is weak on interpretation.

"There are many interpretations of quantum mechanics. These interpretations are not scientifically testable, since there is no way to distinguish one from the other, and thus they are in the realm of philosophy, not science"

To me, that's one thing which I think is wrong with modern physics. I never understood how people can make such a sharp distinction between what's "phsyics" and what's "philosophy". It degrades physics into bookkeeping.

If I would write something about QM for high school students, I would use high school algebra to highlight the physical concepts. For instance, you can explain interference even without complex numbers: just say that the wave functions add due to linearity, not the probability, and that Borns rule then gives an interference term.

Notes like these turn students more into calculators. It gives a nice overview of the calculational aspects, but physics is imo more than that.

 

[haushofer]

One thing the lectures do not seem to explain is complex numbers; they start out by assuming the students already know about those. Is that a valid assumption for high school students?

In Holland it sure isn't, as far as I can tell :D

 

[vanhees71]

I think it is weak on interpretation.

"There are many interpretations of quantum mechanics. These interpretations are not scientifically testable, since there is no way to distinguish one from the other, and thus they are in the realm of philosophy, not science"

No, that's pretty strong, because it's true. Don't destract beginners with philosophy from the physics, is a good advice always!

Nevertheless I had a shocking experience recently. Since from the next semester on, I have to teach theoretical physics to high-school-teacher students. I borrowed a school physics book for the "Oberstufe" (i.e., for the last 2-3 years before the final exams (Abitur in Germany)), and I was indeed shocked to see that this book hasn't changed much from the book I still have at home from my own high school studies 28 years ago (only that the one I have was a bit better in explaining things). The only thing what was new was that some more recent experimental findings in particle physics (like discovery of the Higgs boson). Everything else is more or less unchanged. The worst was indeed the QM section: Photons as little bullets, photo-electric and Compton effects as proof for photons, the Bohr model of the hydrogen atom; in relativity still the velocity-dependent mass etc. etc. All the years of didactics research (which I'm very skeptical about anyway) seems to have not lead to better and modern expositions of the state of the art in such topics. Sometimes it even went worse from my 28 yr old book: Instead of giving a quantitative result for the single- and double-slit as well as the gratings in the section on diffraction, using the nice geometrical way to add phase factors as was invented by Feynman in his famous popular-science lecture and book on QED, they just give some pretty confusing qualitative and very superficial treatment of this method. It's really frustrating :-((.

I think, it's of utmost importance to develop better ideas on how to catch high-school students with the beauty of the natural sciences since not only because the interest in STEM subjects is necessary from an economic point of view (unfortunately nearly the only point of view that is nowadays advocated by science and education politicians) but also to have an educated society that understands at least on a qualitative level how modern technology works and what are its advantages and what may be causing problems, etc. etc.

 

[atyy]

The worst was indeed the QM section: Photons as little bullets, photo-electric and Compton effects as proof for photons, the Bohr model of the hydrogen atom; in relativity still the velocity-dependent mass etc. etc.

Photons as bullets are ok, as long as one is also taught the limitations of the model. The textbook by Grynberg and colleagues does say that some single photon states "might be referred to as quasi-particle states, because they are the quantum states whose properties most closely resemble those of an isolated particle propagating at the speed of light, just as the classical state is the quantum state closest to a classical electromagnetic wave." https://books.google.com.sg/books?id=l-l0L8YInA0C&source=gbs_navlinks_s (p375)

Velocity-dependent mass is not wrong, so it is wrong to teach that the velocity-dependent mass is wrong. Purcell and Feynman were among those who used the velocity-dependent mass.

Use of the photo-electric effects etc as proof for photons is wrong, since alternative models exist. Aspect still uses it in his public lectures, but he is careful to say that it does not prove photons, only that all existing models require quantization of either matter or light.

I think, it's of utmost importance to develop better ideas on how to catch high-school students with the beauty of the natural sciences since not only because the interest in STEM subjects is necessary from an economic point of view (unfortunately nearly the only point of view that is nowadays advocated by science and education politicians) but also to have an educated society that understands at least on a qualitative level how modern technology works and what are its advantages and what may be causing problems, etc. etc.

That is laudable but a losing battle, when even Hawking hypes AI http://www.bbc.com/news/technology-30290540.

But to be a bit more serious and to tie in quantum mechanics and thermodynamics like Hawking did, what's your view on teaching "old quantum physics" like Planck's quantization and blackbody radiation? It is of course notable that Planck knew that it did not imply the quantization of light.

 

[bhobba]

One thing the lectures do not seem to explain is complex numbers; they start out by assuming the students already know about those. Is that a valid assumption for high school students?

In Australia - yes. It would be taught is grade 10 in the advanced math stream. Even if not in that stream early on in grade 11 as part of Math C or IB Math HL. For those taking an accelerated course that complete normal math grade 11 and do uni subjects grade 12 probably done in grade 9. I think such accelerated students is what this paper is aimed at.

The paper is a good intro IMHO. Only thing is I would also like to see Susskinds book mentioned:
https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20

Of greater concern to me is it uses calculus. That's not usually encountered here in Aus, unless again you are in an accelerated program, until grade 11. Complex numbers are covered before calculus.

Thanks
Bill

 

[weirdoguy]

Purcell and Feynman were among those who used the velocity-dependent mass.

Yeah, 50 years ago... It's 2018, time to move on with what's really used amongst scientists.

 

[Zafa Pi]

There is also this course taught by Leonard Susskind : http://theoreticalminimum.com/courses/quantum-mechanics/2012/winter
http://theoreticalminimum.com/home
Best regards
Patrick

I was shocked that Susskind as unaware that "The Law of Large Numbers" is a theorem, especially the weak law.

 

[vanhees71]

Photons as bullets are ok, as long as one is also taught the limitations of the model. The textbook by Grynberg and colleagues does say that some single photon states "might be referred to as quasi-particle states, because they are the quantum states whose properties most closely resemble those of an isolated particle propagating at the speed of light, just as the classical state is the quantum state closest to a classical electromagnetic wave." https://books.google.com.sg/books?id=l-l0L8YInA0C&source=gbs_navlinks_s (p375)

Velocity-dependent mass is not wrong, so it is wrong to teach that the velocity-dependent mass is wrong. Purcell and Feynman were among those who used the velocity-dependent mass.

Use of the photo-electric effects etc as proof for photons is wrong, since alternative models exist. Aspect still uses it in his public lectures, but he is careful to say that it does not prove photons, only that all existing models require quantization of either matter or light.

We obviously disagree about this. One should not teach outdated concepts like velocity-dependent mass, even when Feynman (with the greatest didactics in physics after Sommerfeld) uses this concept. Purcell's textbook in the Berkeley physics course series is the only textbook I explicitly discourage students to read, because it's more confusing than helpful. The best book with the same aims, i.e., to teach electrodynamics at the undergrad level relativistically from the very beginning is, Melville Schwartz's book Principles of Electrodynamics (he's a Nobel laureate as Purcell by the way).

That is laudable but a losing battle, when even Hawking hypes AI http://www.bbc.com/news/technology-30290540.

I've no clue, what this has to do with physics didactics. I'm sure it's worth thinking carefully about possible problems of any new technology, but this has nothing to do with physics didactics. It's of course true that to enable people to think about dangers of technology it's mandatory to offer them a good education in the natural sciences and math.

But to be a bit more serious and to tie in quantum mechanics and thermodynamics like Hawking did, what's your view on teaching "old quantum physics" like Planck's quantization and blackbody radiation? It is of course notable that Planck knew that it did not imply the quantization of light.

I think "old quantum physics" shouldn't be taught in a physics course at all. One must not teach outdated models but the modern ones to avoid to build up unnecessarily wrong intuitions like photons as little bullets (sorry, I don't see any sense in which the modern concept of photons is compatible with particle-like paradigms at all) or orbits of electrons around a nucleus as a model of atoms. Rightfully, nobody ever discusses to teach Aristotelian physics before teaching Newtonian mechanics. I cannot understand, why one should teach the Bohr model of atoms or why one needs wrong ideas on photons to introduce QT.

On the other hand, it's also important to teach some history of science and how modern science has been developed, and this should include also the history of quantum theory (in fact, it's hard to motivate the quite abstract formulation of modern quantum theory without arguing with the historical development of the subject) and thus "old quantum mechanics", but it should be taught as the way how modern quantum theory has been finally discoved in 1925/26 and that the physicists at the time were forced to give up the classical-physics intuitions by observations and experiments. It's also good to know that the great physicists involved with it, among them Bohr and Einstein, knew very well that "old quantum mechanics" is not satisfactory. Einstein even didn't think that modern quantum theory is satisfactory at all, and until the end of his live he tried to get a more satisfactory picture about "photons" and of course to formulate all of physics in a unified classical field theory with no success, and today the best theory we have is quantum theory. That it is not the final theory is also pretty probable. However, we have no clue, how a better theory might look. The irony is that so far the standard model of particle physics is too successful in describing all outcomes of experiments at the available energies (including the LHC) to get a handle on physics beyond the standard model.

 

[haushofer]

Photons as bullets are ok, as long as one is also taught the limitations of the model...

...or if you're a Bohmian adherent :P Guided bullets, that is ;)

 

[vanhees71]

I've not yet seen any convincing application of the Bohmian interpretation of QT to relativistic QFT, particularly not one with photons, i.e., massless spin-1 fields.

 

[diPoleMoment]

Photons as bullets are ok, as long as one is also taught the limitations of the model. The textbook by Grynberg and colleagues does say that some single photon states "might be referred to as quasi-particle states, because they are the quantum states whose properties most closely resemble those of an isolated particle propagating at the speed of light, just as the classical state is the quantum state closest to a classical electromagnetic wave." https://books.google.com.sg/books?id=l-l0L8YInA0C&source=gbs_navlinks_s (p375)

Velocity-dependent mass is not wrong, so it is wrong to teach that the velocity-dependent mass is wrong. Purcell and Feynman were among those who used the velocity-dependent mass.

Use of the photo-electric effects etc as proof for photons is wrong, since alternative models exist. Aspect still uses it in his public lectures, but he is careful to say that it does not prove photons, only that all existing models require quantization of either matter or light.

I still do not understand how electromagnetic spectrum with different wavelengths of a photon particle can be explained as a particle with a wave function, separate but from the same particle. If both mechanical and quantum are both true. There has to be a resolution to those opposing ideas. If the mass of the photon is so infinitesimal to not have a relevant value in mathematical calculations, then is it the energy that the photon results from that causes the different wavelengths.

My reasoning for this explanation is that there is a mechanical experiment that has a laser hitting a piece of metal. If that laser light of a particular wavelength hits a piece of metal it will release electrons of a certain amount at a specific rate of time. Increase the amplitude the rate of electrons escapes but at the same amount per increased amount of time. Then if the laser light wavelength is increased at the same initial amplitude, more electrons escape for the same rate of time.

If this is true, then the quasi-particle state has a mechanical reference where the particle is electric energy (kinetic energy) in motion with a magnetic force (potential energy?). I realize I could be totally wrong, but there has to be a factor that is consistent no matter what the parameters are.

 

[atyy]

I think "old quantum physics" shouldn't be taught in a physics course at all. One must not teach outdated models but the modern ones to avoid to build up unnecessarily wrong intuitions like photons as little bullets (sorry, I don't see any sense in which the modern concept of photons is compatible with particle-like paradigms at all) or orbits of electrons around a nucleus as a model of atoms. Rightfully, nobody ever discusses to teach Aristotelian physics before teaching Newtonian mechanics. I cannot understand, why one should teach the Bohr model of atoms or why one needs wrong ideas on photons to introduce QT.

https://arxiv.org/abs/1312.4057
Aristotle's Physics: a Physicist's Look
Carlo Rovelli

On the other hand, it's also important to teach some history of science and how modern science has been developed, and this should include also the history of quantum theory (in fact, it's hard to motivate the quite abstract formulation of modern quantum theory without arguing with the historical development of the subject) and thus "old quantum mechanics", but it should be taught as the way how modern quantum theory has been finally discoved in 1925/26 and that the physicists at the time were forced to give up the classical-physics intuitions by observations and experiments. It's also good to know that the great physicists involved with it, among them Bohr and Einstein, knew very well that "old quantum mechanics" is not satisfactory. Einstein even didn't think that modern quantum theory is satisfactory at all, and until the end of his live he tried to get a more satisfactory picture about "photons" and of course to formulate all of physics in a unified classical field theory with no success, and today the best theory we have is quantum theory. That it is not the final theory is also pretty probable. However, we have no clue, how a better theory might look. The irony is that so far the standard model of particle physics is too successful in describing all outcomes of experiments at the available energies (including the LHC) to get a handle on physics beyond the standard model.

Yes, I agree, that's what I mean by teaching old quantum physics (and that's how I was taught it too).

 

[vanhees71]

https://arxiv.org/abs/1312.4057
Aristotle's Physics: a Physicist's Look
Carlo Rovelli

Interesting! I'll have a look. Concerning the didactics, I'd say there's some justification for not teaching Aristotelian physics but Newtonian physics in the abstract:
"Aristotelian physics is a correct and non-intuitive approximation of Newtonian physics". If it's non-intuitive, why should you teach it and not rather start with Newton from the beginning? Of course, you cannot start with the most modern theory (Q(F)T+GR), because you cannot understand it with the foundations laid by Galileo and Newton ;-)).

Yes, I agree, that's what I mean by teaching old quantum physics (and that's how I was taught it too).

Well, our high school teacher told us from the very beginning that she has to teach it, because it's part of the mandatory curriculum. She also let no doubt about what opinion she had concerning this curriculum ;-)). Of course, one must say, that she was a postdoc in atomic physics before she became a high school teacher, and that's why she also taught us the Schrödinger equation, including some of the most simple cases for energy-eigenvalue problems like the rigid box and the harmonic oscillator. She was the best teacher in high school I had, and I guess it's much because of her that I studied finally physics rather than electrical engineering, which I wanted to do first, because I liked tinkering with simple electronics ;-))).

 

[haushofer]

I've not yet seen any convincing application of the Bohmian interpretation of QT to relativistic QFT, particularly not one with photons, i.e., massless spin-1 fields.

I guess one runs into trouble concerning, among others, Newton-Wigner localisation, right?

I'm not familiar with Bohmian quantum field attempts, but I'll have a look.

 

[PeterDonis]

If both mechanical and quantum are both true

They aren't. The photon is not a "particle".

 

[Zafa Pi]

Photons as bullets are ok, ...

wrong intuitions like photons as little bullets

atyy I know how you feel. I was recently criticized by the NRA for saying bullets are like big phat photons. They have wave properties and disperse, interfering with innocent bystanders.

 

[dlgoff]

Melville Schwartz's book Principles of Electrodynamics

Do you mean Melvin Schwartz's Principles of Electrodynamics?

 

[bhobba]

I still do not understand how electromagnetic spectrum with different wavelengths of a photon particle can be explained as a particle with a wave function, separate but from the same particle

That's not what it is - see:
http://www.physics.usu.edu/torre/3700_Spring_2015/What_is_a_photon.pdf

What happens is the EM quantum field interacts with something and that interaction, in some cases can be explained as if its particle like eg when seeing a flash on a photo-multiplayer screen,

Sometimes it's like a wave as well as shown by the usual interpretation of the double slit - although IMHO that is not the best explanation:
https://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

Note the above, like the usual explanation is not quite right either - just better than the usual one IMHO:
https://arxiv.org/pdf/1009.2408.pdf

To make it even worse the above it not the full story either. Physics can be maddening lke that.

Either way best to forget this so called wave-particle duality - its one of the many myths about QM out there:
https://arxiv.org/abs/quant-ph/0609163

Thanks
Bill

 

[bhobba]

If this is true, then the quasi-particle state has a mechanical reference where the particle is electric energy (kinetic energy) in motion with a magnetic force (potential energy?). I realize I could be totally wrong, but there has to be a factor that is consistent no matter what the parameters are.

You should look into Noether - fields have energy as well because of that famous theorem, and laser light can be handled by classical EM (not its production of course - but what it is)
http://phys.columbia.edu/~nicolis/NewFiles/Noether_theorem.pdf

Oh - forgot to mention - of course EM can be written in Lagrangian form so Noether applies.

Thanks
Bill

 

[Zafa Pi]

They aren't. The photon is not a "particle".

Feynman as well as many other luminaries () call it a particle. But they all may be using a non-technical casual terminology, even in technical talks.
So I ask, what would you call it? Suppose a precocious 12 year old passes by (or even a famous biologist) and asks you, Mr. Donis, what's a photon? You wouldn't say a particle of light?
I certainly hope you don't tell her to read Ballentine. I also hope it is something short, she's in a hurry.

 

[vanhees71]

Do you mean Melvin Schwartz's Principles of Electrodynamics?
View attachment 222688

Yes, that's the book, I had in mind.

 

[vanhees71]

Feynman as well as many other luminaries () call it a particle. But they all may be using a non-technical casual terminology, even in technical talks.
So I ask, what would you call it? Suppose a precocious 12 year old passes by (or even a famous biologist) and asks you, Mr. Donis, what's a photon? You wouldn't say a particle of light?
I certainly hope you don't tell her to read Ballentine. I also hope it is something short, she's in a hurry.

How about calling it "Light Quantum" and try to tell the 12 year old first that light is described as an electromagnetic field?