Mathematicians' contributions to physics

[malawi_glenn]

Yes, once we physicsists know for sure that the Navier-Stokes equation has solutions, we can finally start using it to calculate stuff like wind and water flows :) Oh wait...

 

[apostolosdt]

I checked the book "Neoclassical Theory of Electromagnetic Interactions" by Babin & Figotin. I'm not opening a discussion of the book itself, but of two mathematicians' viewpoints on a well-established physical theory. After all, that's how both threads started.

The authors claim that it is feasible to use the classical interpretation of the EM phenomena down to atomic scales. No problem so far if we, open-minded, are willing to read about a new approach to EM. But it looks as if some "Kuhnian losses" are necessary in order to found the new theory; from the book's preface:

[..] Our theory, though similar to QM in some respects, is markedly different from it. In particular, (i) there is no need, in our theory, for the correspondence principle and consequent quantization procedure to obtain the wave equation; (ii) the Heisenberg uncertainty principle, though quite often applicable, is not a universal principle; (iii) there is no configuration space; (iv) there is no probabilistic interpretation of the wave function. [..]

I thought that adds to the present discussion constructively.

 

[coquelicot]

I checked the book "Neoclassical Theory of Electromagnetic Interactions" by Babin & Figotin. I'm not opening a discussion of the book itself, but of two mathematicians' viewpoints on a well-established physical theory. After all, that's how both threads started.

The authors claim that it is feasible to use the classical interpretation of the EM phenomena down to atomic scales. No problem so far if we, open-minded, are willing to read about a new approach to EM. But it looks as if some "Kuhnian losses" are necessary in order to found the new theory; from the book's preface:

[..] Our theory, though similar to QM in some respects, is markedly different from it. In particular, (i) there is no need, in our theory, for the correspondence principle and consequent quantization procedure to obtain the wave equation; (ii) the Heisenberg uncertainty principle, though quite often applicable, is not a universal principle; (iii) there is no configuration space; (iv) there is no probabilistic interpretation of the wave function. [..]

I thought that adds to the present discussion constructively.

Thank you for addressing the thread I opened previously.

Regarding your comment on the book, I think their authors does not claim to offer an alternative theory to quantum mechanics (e.g. if my understanding is OK, they do not pretend to be able to explain the double slits experiments), but their aim is to offer a theory which bridges the gap between microscopic and macroscopic phenomenons, at a point where it is even able to explain some microscopic phenomenons usually dealt with quantum mechanics. I may have not sufficiently understood though.

Could you explain in what sense you think the fragment you quoted adds to the present discussion constructively.

 

[coquelicot]

How about a simpler problem looking to be solved.

EXISTENCE AND SMOOTHNESS OF THE NAVIER–STOKES EQUATION
https://www.claymath.org/sites/default/files/navierstokes.pdf

from
https://www.claymath.org/millennium-problems/navier–stokes-equation

It's not so simply give that turbulence is a bit chaotic.

A lot has been written about the challenge problem. Yet - not much progress in a solution.

https://www.quantamagazine.org/mathematicians-find-wrinkle-in-famed-fluid-equations-20171221/

I think the original question of Malawi-Glenn was not a listing of the problems in physics that everybody knows about them, but rather what I meant when I wrote in another forum that "physicists are often unaware of the real problems in physics", in parentheses, as an answer to someone that presented physics books by mathematicians as (probably) bad.

 

[Astronuc]

I think the original question of Malawi-Glenn was not a listing of the problems in physics that everybody know about them, but rather what I meant when I wrote in another forum that "physicists are often unaware of the real problems in physics",

The title of the thread is "Mathematicians' contributions to physics." Malawi-Glenn also asked "What are the real problems?" to which one alluded in the statement that most many "physicists are often unaware of the real problems in physics". That seems a rather gross generalization, and as of yet, unsubstantiated. I'm curious as to "what real problems in physics that some, many or most physicists are unaware."

I provided the example of the PENELOPE and EGS5 codes, since they, or at least the PENELOPE author discusses some of the theory and mathematics involved, and how those equations are transformed into numerical methods.

At university, I took courses in mathematics, physics, mathematical physics, numerical analysis/methods, as well as a variety of engineering courses. We were tackling complex physics problems, and for some, looking for the best mathematical models to solve efficiently. I don't recall anyone being 'unaware', but rather many times, we knew there were approximations and simplifications, because some problems are highly non-linear, or highly coupled, for which there are no simple, nice solutions.

One could find plenty of examples on particle transport theory, whether it be neutrons (and photons, electrons) in a nuclear reactor, or charged particles (protons, deuterons, tritons, alphas, nuclei) in fusion plasmas, stars or large clouds.

So

What are the REAL problems in physics?

 

[apostolosdt]

[...] a theory which bridges the gap between microscopic and macroscopic phenomenons, at a point where it is even able to explain some microscopic phenomenons usually dealt with quantum mechanics. I may have not sufficiently understood though.

Could you explain in what sense you think the fragment you quoted adds to the present discussion constructively.

I'm afraid, in the modern physical approach, there is no gap between microscopic and macroscopic phenomena, for quantum mechanics along with relativistic invariance principles are equipped well enough to describe both phenomena. The so-called classical approach is a bunch of approximations which, one, saves us a tremendous amount of mathematical analysis and numerical work, and, two, eventually offers similar results from the point of view of experimental verification. That's a point again raised and, once again, clearly answered recently in another thread.

My own belief is this. The poorly mathematically supported, far from complete, Standard Model must be correct because no other concept in human history enjoys that verification of one part in a hundred million. So, why don't we leave physics to do its thing and mathematics to do its thing?

Regarding your last question, I meant my post, not the quoted passage---sorry for not having been clearer.

 

[coquelicot]

I'm afraid, in the modern physical approach, there is no gap between microscopic and macroscopic phenomena, for quantum mechanics along with relativistic invariance principles are equipped well enough to describe both phenomena. The so-called classical approach is a bunch of approximations which, one, saves us a tremendous amount of mathematical analysis and numerical work, and, two, eventually offers similar results from the point of view of experimental verification. That's a point again raised and, once again, clearly answered recently in another thread.

My own belief is this. The poorly mathematically supported, far from complete, Standard Model must be correct because no other concept in human history enjoys that verification of one part in a hundred million. So, why don't we leave physics to do its thing and mathematics to do its thing?

Regarding your last question, I meant my post, not the quoted passage---sorry for not having been clearer.

Thank you.
I would like to ask you a practical question, as you seem to know the matter very well. I already know EM theory at the level of most graduate students (I believe). Nevertheless, my mathematician intuition tells me that the way the properties in dielectrics are justified in most classical books (e.g. Jackson, Griffith, Landau and Lifshitz) is hardly a diagrammatic persuasion, or a superposition of equations with some context but at the least insufficiently convincing. So, I am currently trying to understand the macroscopic Maxwell equations deduced from the so called microscopic one, in books by authors that dedicated a part of their life to this task, namely the books of De Groot and that of Robinson. To put flesh on bones, I would like, at the very least, a convincing explanation of the following facts: when a dielectric is inserted inside a uniform field (say), surface charges appear. If on the other hand there is a div field, then volume charges appear inside the dielectric (in addition to the charges that caused the field). This may seem elementary to most students, but it is not. The book of De Groot is somewhat hard to follow, and it will take me a while to read it. The book of Robinson is easier, but I dislike some aspects of his theory (I also like some other aspects like his idea that the macroscopic smoothing comes from the high pass filtering of the high frequencies in space). Actually, Robinson criticizes the book of De Groot, after having noted that he is more or less the only person that has dealt extensively with this topic since Lorenz. I also had a look at more recent articles etc.

Now I come to my point: what is boiling down is that there is no clear "main stream" in this domain, a theory about which most physicists would agree (I may be wrong and hope you will correct me).
Of course, I expect some persons will post unintelligent and anoying answers like "QM is the theory", without addressing the real and practical question I've just raised: The problem does not consist in invoking a theory that is supposed to solve every microscopic and macroscopic problem, but to actually provide the solution of the questions with the theory.
This is why the idea of a "Bourbaki" like group has popped up in this thread.
And again, I see a lot of theories, but I don't see a main stream theory for the question I raised above.

You seem to say that the Standard Model provides the deal. So, are you aware of a widely accepted work, which provides the solution to the questions above?

 

[dextercioby]

@coquelicot Which chapters in de Groot's book do you refer to? Which de Groot book, actually? What about Robinson?

 

[coquelicot]

@coquelicot Which chapters in de Groot's book do you refer to? Which de Groot book, actually? What about Robinson?

De Groot S.R. Suttorp - Foundations of Electrodynamics (all the chapters are relevant).
Robinson F.N.H. - Macroscopic Electromagnetism

 

[dextercioby]

How can Robinson comment on de Groot, since Robinson's book appeared in 1972, while de Groot's in 1973? Unless it was a 2nd edition published more recently.

 

[coquelicot]

How can Robinson comment on de Groot, since Robinson's book appeared in 1972, while de Groot's in 1973? Unless it was a 2nd edition published more recently.

Sorry, you are probably right. If my memory is exact, Robinson criticizes the whole work of de Groot from 1950 (you can imagine that the book of de Groot has not pop up from nowhere).

 

[Astronuc]

How can Robinson comment on de Groot, since Robinson's book appeared in 1972, while de Groot's in 1973? Unless it was a 2nd edition published more recently.

Sorry, you are probably right. If my memory is exact, Robinson criticizes the whole work of de Groot from 1950 (you can imagine that the book of de Groot has not pop up from nowhere).

There is a chapter entitled "Statistical Foundations of Electrodynamic Theory in the book
Physics in the Making by AA. Sarlemijn and M.J. Sparnaay, 1989

The author of the chapter is L.G. Suttorp, who cites two books by S.R. de Groot, one coauthored with Suttorp
Groot, S.R. de, 1969, The Maxwell Equations (North-Holland, Amsterdam)
Groot, S.R. de and L.G. Suttorp, 1972, Foundations of Electrodynamics (North-Holland, Amsterdam)

Perhaps Robinson reviewed the draft/proof, or he received a pre-print.

Suttorp also cites three book by F.N.H. Robinson,
Robinson, F.N.H, 1971, Physics
Robinson, F.N.H, 1973, Macroscopic Electromagnetism (Pergamon Press, Oxford)
Robinson, F.N.H, 1975, Phys. Rep.

Ref: https://staff.science.uva.nl/l.g.suttorp/articles/making89.pdf

There is this article - "V Foundations of the Macroscopic Electromagnetic Theory of Dielectric Media,"
J Van Kranendonk, JE Sipe, Progress in Optics, Volume 15, 1977, Pages 245-350
"This chapter is concerned with the derivation of the macroscopic Maxwell equations and associated constitutive relations from the underlying microscopic equations describing the dynamics of the constituent particles and the electromagnetic fields created by these particles."
Ref: https://www.sciencedirect.com/science/article/abs/pii/S0079663808704803

 

[coquelicot]

There is this article - "V Foundations of the Macroscopic Electromagnetic Theory of Dielectric Media,"
J Van Kranendonk, JE Sipe, Progress in Optics, Volume 15, 1977, Pages 245-350
"This chapter is concerned with the derivation of the macroscopic Maxwell equations and associated constitutive relations from the underlying microscopic equations describing the dynamics of the constituent particles and the electromagnetic fields created by these particles."

Actually, there are many other articles, and the book of Babin and Figotin cited in this thread and elsewhere is another view. But what is the main stream?

And you have another book that processes the subject in a very particular and (probably) interesting manner:
F.W Hehl, Y.L. Obukhov, fundations of classical electrodynamics.

But what is the main stream ?

 

[apostolosdt]

De Groot S.R. Suttorp - Foundations of Electrodynamics (all the chapters are relevant).
Robinson F.N.H. - Macroscopic Electromagnetism

OK, coquelicot, I've got access to both books, but I can't promise I will read them front-to-end. To be honest, I had never heard of Robinson or de Groot. Is de Groot the senior author of the "Non-Equilibrium Thermodynamics" book as well? He is referred to as a theoretical physicist; I take it to be him, although I came across a number of mathematicians with that name.

[...] as you seem to know the matter very well. I already know EM theory at the level of most graduate students [...] You seem to say that the Standard Model provides the deal. So, are you aware of a widely accepted work, which provides the solution to the questions above?

Now, thanks for your kind words, but that's hardly the case; there are more proficient members in these forums than me. But, I'll bite and see what I can do with your question, although, having read about EM thru the standard texts years ago, your question sounds more like a puzzle than a physical one.

 

[malawi_glenn]

I am very glad that the discussion is still going on! However, the book thread is re-opened https://www.physicsforums.com/threa...ic-interactions-by-babin-and-figotin.1050807/ ;)

 

[coquelicot]

I am very glad that the discussion is still going on! However, the book thread is re-opened https://www.physicsforums.com/threa...ic-interactions-by-babin-and-figotin.1050807/ ;)

Actually, that's not the same book(s), and my question is much wider. You can see it as an example of what real problems a real mathematician can somewhat worry about, if you wish.

 

[malawi_glenn]

Actually, that's not the same book(s), and my question is much wider. You can see it as an example of what real problems a real mathematician can somewhat worry about, if you wish.

I know, it was just a heads-up ;)

 

[Frabjous]

To put flesh on bones, I would like, at the very least, a convincing explanation of the following facts: when a dielectric is inserted inside a uniform field (say), surface charges appear. If on the other hand there is a div field, then volume charges appear inside the dielectric (in addition to the charges that caused the field). This may seem elementary to most students, but it is not.

This discusses it a little.



Smith-White (1949). I found the reference in the Herring Archive which is an interesting collection of old references. http://large.stanford.edu/herring/a/a1/a12/

You might also like this arXiv article by Griffiths.
https://arxiv.org/abs/1506.02590

 

[coquelicot]

This discusses it a little.

View attachment 323877View attachment 323878View attachment 323879

Smith-White (1949). I found the reference in the Herring Archive which is an interesting collection of old references. http://large.stanford.edu/herring/a/a1/a12/

You might also like this arXiv article by Griffiths.
https://arxiv.org/abs/1506.02590

I've read the article of Griffiths. Thank you so many, very interesting (it also provides all the relevant derivation of the formulae in one place.

 

[Vanadium 50]

Of course, I expect some persons will post unintelligent and anoying answer

I would not go there.

I have had and continue to have a successful career in physics. Almost 1700 papers, almost a quarter-million cites, and an h-index over 200.

Do some of the theories I use have inconsistencies. Yup. Even QED has a Landau pole. Do I care? Nope.
Do some of the empirical laws I use have unphysical regions? Yup. Do I care? Nope. Don't use them there.
Are some of the calculation tools I use less than rigorous? Yup. Do I care? Nope.

I realize that this gets some mathematicians' goat, Not my problem. If I can measure x and compare it to theory, I'm good.

Could I stop measuring things and wait for the mathematical rigor to catch up? I could - but that would stop progress. So I don't.

Physicists use mathematics. Doesn't make them mathematicians.

 

[apostolosdt]

I would not go there.

I have had and continue to have a successful career in physics. Almost 1700 papers, almost a quarter-million cites, and an h-index over 200.

Do some of the theories I use have inconsistencies. Yup. Even QED has a Landau pole. Do I care? Nope.
Do some of the empirical laws I use have unphysical regions? Yup. Do I care? Nope. Don't use them there.
Are some of the calculation tools I use less than rigorous? Yup. Do I care? Nope.

I realize that this gets some mathematicians' goat, Not my problem. If I can measure x and compare it to theory, I'm good.

Could I stop measuring things and wait for the mathematical rigor to catch up? I could - but that would stop progress. So I don't.

Physicists use mathematics. Doesn't make them mathematicians.

Can be read as today’s physics manifesto.

 

[coquelicot]

Do some of the theories I use have inconsistencies. Yup. Even QED has a Landau pole. Do I care? Nope.
Do some of the empirical laws I use have unphysical regions? Yup. Do I care? Nope. Don't use them there.
Are some of the calculation tools I use less than rigorous? Yup. Do I care? Nope.

I realize that this gets some mathematicians' goat, Not my problem. If I can measure x and compare it to theory, I'm good.

Could I stop measuring things and wait for the mathematical rigor to catch up? I could - but that would stop progress. So I don't.

Physicists use mathematics. Doesn't make them mathematicians.

Thank you for agreeing with me that mathematicians tend to write books in physics more rigorously than physicists, and tend to reject mathematically incoherent theories.

In mathematics, we call this "q.e.d." (quod erat demonstrandum).

 

[apostolosdt]

Thank you for agreeing with me that mathematicians tend to write books in physics more rigorously than physicists, and tend to reject mathematically incoherent theories.

In mathematics, we call this "q.e.d." (quod erat demonstrandum).

ln physics, we call it “q.e.d.” (quantum era demonstrandum).

 

[fresh_42]

In mathematics, we call this "q.e.d." (quod erat demonstrandum).

ln physics, we call it “q.e.d” (quantum era demonstrandum).

On PF, we call it "q.e.e." (quod erat expectandum).

 

[malawi_glenn]

and tend to reject mathematically incoherent theories

Which is why mathematicians are not that important for the overall progress of physics? ;)

 

[coquelicot]

Which is why mathematicians are not that important for the overall progress of physics? ;)

So, let ban Galileo, Pascal, Descartes, Fermat, Euler, Lagrange, Legendre, Gauss, Jacobi, Cauchy, Riemann, Levy-civita, Lie, Von Neuman, Noether, and all the other useless crackpots from the physics.

Oh, I forgot to ban Newton, who was primarily a mathematician and a teacher of mathematics at the university. From Wikipedia:
Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at the University of Cambridge.

 

[coquelicot]

ln physics, we call it “q.e.d.” (quantum era demonstrandum).

(liked it).
You may be right after all, maybe I should consider Vanadium50 is not representative for the physics, a quantum jump in some sense. But that's your fault, you wrote above "Can be read as today’s physics manifesto". ;-)

 

[malawi_glenn]

Who said anything about banning and calling mathematicians crackpots?

Do you have any, more contemporary, mathematicians? Or are you just gonna use names which are ~100 years old? Are you mathematicians still content with writing books on classical physics? Because god forbid writing a book on qft or string theory.

 

[coquelicot]

Who said anything about banning and calling mathematicians crackpots?

Do you have any, more contemporary, mathematicians? Or are you just gonna use names which are ~100 years old? Are you mathematicians still content with writing books on classical physics? Because god forbid writing a book on qft or string theory.

I will not enter into the discussion of the type "who are the best, mathematicians of physicists". That's ridiculous for me. It is evident that professional physicists, who are often excellent mathematicians too, and who deal with physics full time, contribute more to physics than mathematicians who only occasionally deal with this matter. On the other hand, I'm afraid that when god sees posts like "the author of such or such book is a mathematician, hence the book is bad", he really wants to forget writing his book in physics.

 

[coquelicot]

I apology for not being able to answer to further posts. I have to travel and will probably be too busy during the next weeks. Hope this thread will continue though.

 

[malawi_glenn]

I apology for not being able to answer to further posts. I have to travel and will probably be too busy during the next weeks. Hope this thread will continue though.

Have a safe trip!

 

[malawi_glenn]

thoughts on Edward Witten?
Is he a physicist or a mathematician? Or both?

What are his "real" contributions to physics? I can think of topological qft which is (?) somewhat useful for condensed matter physics. Sure you will say "what about supersymmetry?" ... has supersymmetry been verified?

He was the first physicist to receive the fields medal.

 

[Vanadium 50]

maybe I should consider Vanadium50 is not representative for the physics,

Aye, No True Scotsman puts sugar on their porridge!

 

[pinball1970]

thoughts on Edward Witten?
Is he a physicist or a mathematician? Or both?

What are his "real" contributions to physics? I can think of topological qft which is (?) somewhat useful for condensed matter physics. Sure you will say "what about supersymmetry?" ... has supersymmetry been verified?

He was the first physicist to receive the fields medal.

Feynman too? He started out on maths then switched.

 

[pinball1970]

thoughts on Edward Witten?
Is he a physicist or a mathematician? Or both?

What are his "real" contributions to physics? I can think of topological qft which is (?) somewhat useful for condensed matter physics. Sure you will say "what about supersymmetry?" ... has supersymmetry been verified?

He was the first physicist to receive the fields medal.

I thought the rivalry was a bit more jokey till I read this thread! ; )

 

[berkeman]

Thread closed temporarily for Moderation...

 

[jedishrfu]

Rather than go off the rails here, I think its appropriate to end the thread with Feynman's Messenger lecture given at Cornell in 1963.

Thank you all for contributing here. And to those physicists and mathematicians turning in your graves, you rest easy knowing Prof Feynman resolved this issue long ago.

He has an interesting take on physics and math. Often physicists try to think outside the box bending math to work in their new theory. Ultimately though, they need to ground their theory in solid mathematics.

In Feynman's example, he talks about a physicist looking for math that works in 3D and the mathematician says I have this even better notation that works in N dimensions and the physicist says thanks but no thanks until they hit a roadblock and find they need more dimensions and sheepishly goes back to the mathematician for help. (this story stars around 44 minute mark)



As an aside, this is true in many professions like hardware engineers may have a disdain for programmers and vice versa but they need each other to make a successful project. In one such big company project, I ran into this mindset and where the hw engineers hated our "complicated" C programs. They preferred their simple BASIC programs until one day they ran out of RAM on a PC DOS machine and needed our help to get around it.