Approaches for teaching Modern Physics in Grade School and University

[paralleltransport]

I think @vanhees71 hits on the point. The physics education has 2 parts, one is general knowledge (cultural) one would say where knowing what topics are "out there" enriches you culturally. Teaching that people think about black holes, Schrödinger cats etc... in that context to inspire young students is fine. The other part is to teach problem solving skills students can use later in life (most people don't end up professional physicists).

Personally, it's the latter that attracted me to physics as a student. I was taught to think about the world in a precise quantitative way. The best way to do so was through classical physics, which at the high school level is just an exercise of crystallizing day to day intuition into equations. Trying to do so with modern physics seems out of order since there's not intuitive crutch and the students haven't built enough math technology to use that for problem solving (which is the key goal here).

 

[robphy]

Trying to do so with modern physics seems out of order since there's not intuitive crutch and the students haven't built enough math technology to use that for problem solving (which is the key goal here).

Some thoughts about modern physics:

• Does each generation have to endure 17th, 18th, 19th, 20th century physics before 21st century physics?
• "Therefore, I apologise, if apology is necessary, for departing from certain traditional approaches which seemed to me unclear, and for insisting that the time has come in relativity to abandon an historical order and to present the subject as a completed whole, completed, that is, in its essentials. In this age of specialisation, history is best left to the historians."- J.L. Synge in Relativity: The Special Theory (1956), p. vii
• There may be new intuitions.. new ways of looking at old topics (and new topics) that can be developed. The next generation doesn't have to learn things the way the previous generation did, possibly stumbling over the same the roadbumps and conceptual barriers.
  
  [For example, I think relativity should be taught with Minkowski spacetime diagrams, which have been traditionally considered too mathematical... But, instead many books reason with moving boxcars... the way Einstein did... the physicist's way... not that mathematical way. Geometric intuition from high school could be modified and developed for relativity... but no... we're stuck in boxcars with cryptic transformation equations... and can't see the geometry of spacetime.
  
  Along these lines, I often wonder about electromagnetism... When in the history of introductory textbooks did we start drawing field vectors? They haven't always been there. At some point in the future, could we have drawings of differential forms or tensors... or is the vector field the last word in teaching electrodynamics? I wonder if someone told the first textbook author using vector field diagrams... that's too mathematical.
  
  Sadly, that's what Edwin Taylor told me about rapidity in relativity... why it was omitted from the 2nd edition of Spacetime Physics... some felt it was too mathematical.
  ]
• There may be someone out there who catches onto something important about some modern physics topic without having the traditional prerequisites or isn't tied down to a classical viewpoint ... someone who thinks differently from the crowd. Sure, it could be argued as unlikely. Maybe folks should just stay in their [classical] lanes.

My $0.03.

 

[andresB]

Some thoughts about modern physics:

• Does each generation have to endure 17th, 18th, 19th, 20th century physics before 21st century physics?

I don't remember studying living forces, caloric theory, or aether theory. Things like mechanics, thermodynamics, and classical electrodynamics are 21st century physics, explaining phenomena that each generation encounters when seeing nature, and with innumerable applications to current technology.

 

[vanhees71]

Some thoughts about modern physics:

• Does each generation have to endure 17th, 18th, 19th, 20th century physics before 21st century physics?

Yes and no. There is no way to learn physics without first learning Newtonian mechanics and with it starting to build up a "tool box" of mathematical methods. Of course, nobody would teach Newtonian mechanics using the Principia as a "textbook" but rather will use modern vector analysis and (in my opinion as soon as possible) the action principle and the geometrical point of view in the sense of Klein's Erlanger program (groups, symmetries, Noether). That's what proved useful for "modern physics". E.g., I don't think that one can really understand quantum theory without a good knowledge in the group-theoretical methods to explain why the specific algebra of observables look the way they look for either non-relativistic QM or special-relativistic QFT or to understand the step from special to general relativity (making global symmetries local and the "gauge principle" helps a great deal).

• "Therefore, I apologise, if apology is necessary, for departing from certain traditional approaches which seemed to me unclear, and for insisting that the time has come in relativity to abandon an historical order and to present the subject as a completed whole, completed, that is, in its essentials. In this age of specialisation, history is best left to the historians."- J.L. Synge in Relativity: The Special Theory (1956), p. vii

Sure, the historical approach is never a good one to present the logical order of a subject. It should be talk with the view on the most successful methods to be used to understand contemporary physics. On the other hand a good knowledge of the historical development of those methods is of great use to understand the subject too, but it should be separated. The best way for me is how Weinberg used to write his textbooks, starting with a historical overview, which is independent of the development of the subject itself, which then is explained in a logical order.

• There may be new intuitions.. new ways of looking at old topics (and new topics) that can be developed. The next generation doesn't have to learn things the way the previous generation did, possibly stumbling over the same the roadbumps and conceptual barriers.
  
  [For example, I think relativity should be taught with Minkowski spacetime diagrams, which have been traditionally considered too mathematical... But, instead many books reason with moving boxcars... the way Einstein did... the physicist's way... not that mathematical way. Geometric intuition from high school could be modified and developed for relativity... but no... we're stuck in boxcars with cryptic transformation equations... and can't see the geometry of spacetime.

I see Minkowski diagrams as ambivalent. They are harder to read than one might think. Particularly you have to switch off your Euclidean thinking you are used to from hammering in this subject starting from elementary school. On the other hand they can help to visualize the algebraic (or rather analytical-geometry) treatment of special-relativistic spacetime.

• 
  
  Along these lines, I often wonder about electromagnetism... When in the history of introductory textbooks did we start drawing field vectors? They haven't always been there. At some point in the future, could we have drawings of differential forms or tensors... or is the vector field the last word in teaching electrodynamics? I wonder if someone told the first textbook author using vector field diagrams... that's too mathematical.
  
  Sadly, that's what Edwin Taylor told me about rapidity in relativity... why it was omitted from the 2nd edition of Spacetime Physics... some felt it was too mathematical.
  ]

Vectors have been introduced into physics by Gibbs and Heaviside, and we can be thankful for that great step forward. I find a picture with field lines pretty intuitive.

Of course in some sense it's good to teach classical electromagnetism with "relativity first", i.e., as a classical relativistic field theory. After all it's the paradigmatic example for exactly this, and many formal derivations are much easier in the four-tensor formalism than in the tradiational one (the retarded propagator/potentials/fields, the conservation laws of energy, momentum, angular momentum and the center-of-energy theorem, the homopolar generator, Faraday's Law, constitutive relations in moving media,...). Also here, however, you must make some compromise, because it's hardly a good approach for completely starting to learn the subject. You need to build some intuition about "traditional" 3D Euclidean vector calculus first ("div, grad, curl, and all that").

• There may be someone out there who catches onto something important about some modern physics topic without having the traditional prerequisites or isn't tied down to a classical viewpoint ... someone who thinks differently from the crowd. Sure, it could be argued as unlikely. Maybe folks should just stay in their [classical] lanes.

My $0.03

Feynman!

 

[vanhees71]

I don't remember studying living forces, caloric theory, or aether theory. Things like mechanics, thermodynamics, and classical electrodynamics are 21st century physics, explaining phenomena that each generation encounters when seeing nature, and with innumerable applications to current technology.

Imho one should put thermodynamics and statistical physics (or rather substitute thermodynamics entirely by statistical physics) at the very end, when quantum-many-body theory is available to the students. This avoids a lot of the immense problems of classical statistical physics, which then can of course be derived from quantum statistical physics as an appropriate approximation.

 

[andresB]

Imho one should put thermodynamics and statistical physics (or rather substitute thermodynamics entirely by statistical physics) at the very end, when quantum-many-body theory is available to the students. This avoids a lot of the immense problems of classical statistical physics, which then can of course be derived from quantum statistical physics as an appropriate approximation.

Isn't that more or less the usual thing? I saw thermodynamics at the same time as QM II, and stat mechanics after that.

However, I don't see how a deep knowledge of QM is required for classical thermodynamics.

 

[paralleltransport]

Some thoughts about modern physics:

• Does each generation have to endure 17th, 18th, 19th, 20th century physics before 21st century physics?
• "Therefore, I apologise, if apology is necessary, for departing from certain traditional approaches which seemed to me unclear, and for insisting that the time has come in relativity to abandon an historical order and to present the subject as a completed whole, completed, that is, in its essentials. In this age of specialisation, history is best left to the historians."- J.L. Synge in Relativity: The Special Theory (1956), p. vii
• There may be new intuitions.. new ways of looking at old topics (and new topics) that can be developed. The next generation doesn't have to learn things the way the previous generation did, possibly stumbling over the same the roadbumps and conceptual barriers.
  
  [For example, I think relativity should be taught with Minkowski spacetime diagrams, which have been traditionally considered too mathematical... But, instead many books reason with moving boxcars... the way Einstein did... the physicist's way... not that mathematical way. Geometric intuition from high school could be modified and developed for relativity... but no... we're stuck in boxcars with cryptic transformation equations... and can't see the geometry of spacetime.
  
  Along these lines, I often wonder about electromagnetism... When in the history of introductory textbooks did we start drawing field vectors? They haven't always been there. At some point in the future, could we have drawings of differential forms or tensors... or is the vector field the last word in teaching electrodynamics? I wonder if someone told the first textbook author using vector field diagrams... that's too mathematical.
  
  Sadly, that's what Edwin Taylor told me about rapidity in relativity... why it was omitted from the 2nd edition of Spacetime Physics... some felt it was too mathematical.
  ]
• There may be someone out there who catches onto something important about some modern physics topic without having the traditional prerequisites or isn't tied down to a classical viewpoint ... someone who thinks differently from the crowd. Sure, it could be argued as unlikely. Maybe folks should just stay in their [classical] lanes.

My $0.03.

The way I think about it, the way we teach physics is just tied to the way the math curriculum is taught. If the main goal is to teach problem solving skills, then one should pick the most elegant formulation of the theory using available math that is taught in that grade, to teach as a vehicle for solving problems. It really doesn't matter whether it's 19th, 20th century physics or older as long as students can problem solve with it.

So the order things are taught using vectors and F=ma (Newton style classical mechanics) is because that's the math that is taught in secondary school. If secondary school taught differential forms, exterior algebra, then sure, the physics curriculum will reflect that to make use of the deeper perspective.

Regarding relativity, spacetime diagram and rapidity is definitely fair game to teach in high school physics (needs only basic algebra and coordinate geometry). So if relativity is taught, then using that tool is fair.

The more ambitious goal is to say, who cares what math they are being taught concurrently, let's teach both the math and the physics at the same time. That's very difficult to do.

The final consideration is practicality. The number of people who need to use classical physics, thermo in their daily job vastly outnumber the number of people who need to use quantum physics, stat mech. Therefore the school curriculum prioritizes accordingly. Basically the physics curriculum in secondary school is designed to train future physicists, the same way the math curriculum is not designed to train future mathematicians.

 

[jedishrfu]

Thats a good insight that physics must necessarily follow the math rollout. Math has similar issue of building on prior math. Other science fields aren't constrained in the same way.