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As a mathematician, I disagree, but this is probably because I already understand the math pretty well. I'd much rather have a clear picture of the most useful mathematical models for the various areas of physics (and where they fail) than slog through the centuries of failed experiments and feuds. Every time I ask a physicist for a clear picture of what light is (mathematically, what the model says it is), I get a mix of "it's a wave but also a particle" and random things that dead physicists have said about light.

I honestly don't care if Einstein thought God doesn't play dice, or if someone way back when thought an atom was like plum pudding. I do want physical intuition, but I want it through clear and well-explained mathematics.

That is, when I'm in the mindset to actually learn physics. Hearing about the history is fine and dandy if I want entertaining stories.

There is not such a thing. In case we'd been handled a manual of the physical world, it would make sense to tell people to RTFM, but there is no FM, and the whole point of Physics is that we can't just make it up.

There are two kinds of people that fight actual Physics from within, those that say Math is not important: physical intuition "has to" be enough, and those that say that it's just Math, so they are equally happy with perfectly reasonable correct models and completely absurd correct models. They churn out both, usually more of the latter. Both schools of opinionated thought miss that wherever you go you have to learn the trade and be humble.

They should have told you that we don't know what things are, we just deal with how they do their thing.

It's a wave, it's a particle... it's a state, a linear combination of the eigenstates of the EM Hamiltonian, which span a Hilbert space. That's what we got and every physicist knows it, they are just being polite. If they told you that, your next question would be: why on Earth would you think that? why not just [random brainstorming here]? I don't think you're really interested in the really long answer, but it has to do with the boring fact that Physics is, above all, an experimental science.

> There is not such a thing. In case we'd been handled a manual of the physical world...

I never asked for this, but rather for a clear overview of the models that exist, and where they fail. I understand it's experimental, and what interests me personally is (a) how can I use the existing models to do other fun things like write simulations and (b) where do the models break down so I can be more informed about the open directions in physics, which are almost always mathematical (what mathematical model describes the observations we see? how can we design an experiment that confirms or refutes a given mathematical model? etc.).

I honestly think a sort of guide or text your asking for would be interesting. Absent that, next time you find yourself in the "learning physics mood" around your physics friends it might be beneficial to restrict your question to particular regimes, or even better, just ask about very specific physical phenomena. I'm guessing the reason you get these big picture, nebulous responses is the questions you might be asking are a little too general...I'm basing off the one data point I have from your post, "what is light?"

"What is light?" garners a very nebulous answer because there is a wide range of phenomena called "light" and work done in understanding what light is. "What is light in a fiber optic cable?" is more specified because it specifies a length (and thus wavelength) scale, an energy scale (not high intensity that makes you have to worry about plasma generation), and a time scale (steady state physics which allow talking about modes (ie., fourier analysis), unless you care about transients). The length scale and time scale rule out quantum mechanics, and probably will lead you to essentially to solving Helmholtz, which will be much more your speed. See, you might not know to specify all those scales, but by asking for a specific example, your physicist friend will restrict their universe of discourse down instinctively to a model you could use.

So light may be a bad example. The same could be said if you ask, "what is gravity" or "what are magnets?". Better questions are like, "how do we understand orbits in the solar system?" or "why do magnets stick to refrigerators?"

>'Better questions are like, "how do we understand orbits in the solar system?" or "why do magnets stick to refrigerators?"'

What about how exactly do people predict how likely it is the orbit of an asteroid/comet will intersect that of the earth? That is a very interesting problem. It is not at all solved as well as it could be.

First homework, reproduce the JPL HORIZONS ephemerides in your own way: http://ssd.jpl.nasa.gov/horizons.cgi

Second homework, improve upon this either in accuracy or efficiency.

You can divide physics into roughly these core subjects: classical mechanics, classical field theory, special relativity, quantum mechanics, quantum field theory, general relativity, thermodynamics. What you are asking for is basically what is already taught in a physics curriculum, so you could read physics textbooks on the subject that you are interested in.

I believe you want to start with the Michelson-Morley experiment, and the reasons why it failed.

Modern physics, so far as anyone has explained it to me, seems to be two partial responses to the results of that experiment (and the behavior of their test device, the interferometer) that we're in the process of synthesizing in to one result.

Wikipedia reasonably outlines the main features that modern physics has to account for, and links out to the two main bodies of work.

The problem is once you get away from those broad properties the model has to satisfy, there's several competing inplementations with somewhat different features/explanatory power.

I partly agree with you, but at the same time it seems that when teaching physics (intro level) they spend a bit too much time first teaching incorrect theories and even worse trying to pass it off as correct when there clearly is a better one.

Not saying they shouldn't teach past methods.

I doubt that they teach incorrect theories today. A thing to understand here is that all theories are considered correct, the only difference between them being the area which they describe the best (or more efficiently). They are all approximations and thus can be thought of as all being correct and incorrect at the same time. From the philosophical standpoint, however, you are correct - modern theories do replace the older ones; unfortunately, to apply the quantization procedure you need to be able to understand what it is that you are applying this procedure to - and that is something that is described by the old, "incorrect" theory.

I think context/scale/application is important. Classical Newtonian physics takes us pretty far pretty accurately until we get to more micro or macro scales. For example, if wanting to model a physics engine in software and the Newtonian models are considerably more performant, then could make sense to sacrifice the accuracy.

Well, it has to be said: a mathematician's outlook on physics is completely different from a physicist's. For a mathematician, physics is not much more than a bunch of more or less fixed mathematical models, each describing, approximately, some aspect of the physical world. For a physicist, on the other hand, not only are these models in a perpetual state of flux, but the physical world itself is seen as an indivisible whole, so that these "aspects" - the ones that are being modeled mathematically - are themselves just narrow views into the real physical world in which we live...

My brother was a physicist at Sandia. He said bluntly that mathematicians are not scientists. My point is not snark. It's that you may want to study physics from a physics/science POV rather than a mathematician's POV.

Also, I'd recommend Stewart over Thomas. I'd recommend Halliday Resnick and I'd recommend against Giordano.

I learned just enough vector calculus in college to know I didn't know enough to actually understand Maxwell's equations & electromagnetic fields, or most of the other fun mathematical techniques introduced in mid-level physics and engineering classes for modeling interesting "real-world" systems.

Later, when I realized what I was missing out on, I tried to teach myself the missing concepts. I failed, until I found H.M. Schey's "Div, Grad, Curl, and All That: An Informal Text on Vector Calculus." It's a pragmatic, friendly, slim little math book that reads more like lecture notes than a classic textbook, and I can fairly say it's taught me everything I know about those operators (which isn't much).

So if you are like me, and got to calc III, vector math, and/or liner algebra without learning div, grad, curl and partial differential equations... check out the book. it's great: https://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161

Also: can we get three cheers for HYPERPHYSICS?? http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html

Math is about given the definition and understand the results through consistency. For example, given the set of Maxwell's equation and a set of boundary condition, figuring out or understanding the solution -- that is mathematics. So as a mathematician, you would like to have the definition (assumption) and equation, which provides the clear (mathematical) picture.

But physics is different. Physics is about the question whether those assumption (including many hidden assumption) can be wrong and how to interpret the mathematical equation even when the equation gives confirmed results. So Maxwell's equations is not a clear picture on what the light is. Maxwell's equation just describes one aspect of how light behave under one set of assumptions. There are other aspects of light and there are different set of maths that physicists tried to describe them. There are physics intuition on what light is, but that is subjectively dependent on which physicist you are asking. In physics, there is simply no mathematically equivalent of "clear picture" where you simply just accept what is given and go from there. In physics, it is "what is given" in question.

It depends on which subset of physics you restrict to. Often times. Math is often "bent" to match physical intuition and people drop some mathematical models over others because they match intuition and experiment better. As a result, there is no consistent narrative across the whole field and even across subfields in some cases.

Often times, there are no "failed theoretical frameworks", it's not like special relativity is "right" and newtonian mechanics is "wrong", they are right in different physical regimes. If they are down right wrong, then they wouldn't be known to us anyway.

If you stick to parts where theoretical physicists live, it's easier to find mathematical consistency and coherence, like QFT. Outside of that region, what things are and what approximations you use really come down to "what matches experiment best" at best and "what people will allow me to publish with" at worst.

> it's not like special relativity is "right" and newtonian mechanics is "wrong", they are right in different physical regimes

Hence I said, "where they fail" not "whether they fail." Is there even a single mathematical model of the physical world that does not fail in some way?

I was specifically referring to the part of that sentence regarding "centuries of failed experiments and feuds." Yes, you don't need to go through all the models, but many of what people with a lay knowledge of physics call failed models aren't really failed, they just apply in regimes that they could probe at the time in terms of theory and experiment. You might not have been referring to that.

And yes, there is no single mathematical model of the physical world that I am aware of. None.

One last thing that I should say that I probably didn't say clearly enough: from physics comes the mathematical models, not the other way around. Relativity didn't come out of newtonian mechanics, it came out of a change of the underlying physical model which then yield relativistic models that reduce to newtonian mechanics.

As someone who as a student was good at math and bad at physics, I'd rather disagree. Take for example the gravity formula F_{A->B} = G * M_A * M_B/d(A,B)^3. It's very easy to interpret that, but where does that come from? I can see why the gravity gets lower when the distance between A and B is higher, but why does it depend of the inverse of the cube of the distance? The formula is very easy to read, but since I didn't know where it came from, I would forget easily.

On the other hand, it would have been intellectually pleasing(at least for me) to know how Physicists came with it, what's the motivation behind 1/d(A,B)^3, how did people come up with G, how it was measured, etc.

> F_{A->B} = G * M_A * M_B/d(A,B)^3

Your formula is wrong. It's either:

    F_{a} = F_{b} = G * m_a * m_b/r^2

    \vec{F} = G * m_a * m_b/|r|^3 * {\vec{r}}
> but where does that come from?

You find that by studying physics, not history of physics.

> it would have been intellectually pleasing(at least for me) to know how Physicists came with it, what's the motivation behind 1/d(A,B)^3, how did people come up with G, how it was measured, etc.

Yes, understanding a specific change in the state of physics at time T is most certainly helped by understanding it at time T-1. But make no mistake here, this is still physics and not history of physics (whatever that means).

Thanks for correcting me. The fact that I remembered the formula wrong proves that I didn't understand that formula well enough to remember it. It was been about 13 years since I didn't do any physics, and I forgot most of it, however, I remember well the math I learnt because I understood them much better.

it's r^2 in the denominator. one idea is to think of the geometry: the surface area of a sphere is proportional to r^2. therefore if you think of a constant "influence" at a given distance, you might divide it by the surface area (to get r^2 in the denominator)

Yes, it's trivial to deduce Newton's law of universal gravitation from the divergence theorem. But to deduce that the divergence theorem applies, you need the lagrangian and the least action principle.

Conceptually the least action principle is the fundamental concept in classical mechanics, everything is derived from it, plus symmetry.

Historically this has all been done backwards. Once you have Newton's law of universal gravitation, it's trivial to prove that the gravitational flux must be constant for every enclosing surface. It's easy, in terms of mathematics required, to come up with a least action principle from that (albeit not as easy as the inverse deduction). However, if you think of Newton's laws as fundamental, it is not a very natural thing to do. Why would you do it? Lagrange was a very deep thinker to see why the least action principle is the truly fundamental thing. He was doing this way before Noether's theorem. He was doing this before the concept of energy was formalized! They knew that a quantity with what we now know as units of energy was conserved, and they knew momentum was conserved, but they didn't know what these things were, especially as no other form of energy except kinetic and potential energy was known back then. Truly a visionary thinker.

It's probably a matter of taste.

Once you understand the maths clearly, it becomes much easier to understand the failures of the past. For example, reading Newton and Leibniz on calculus makes it clear that it was epsilon/delta waiting to get out.

I guess my point is that, since most people find the math hard, writers put history in as what appears to be filler, which I find as mostly an obstacle.

Ha, this immediately calls to mind Scott Aaronson's approach to teaching Quantum Mechanics in one of his lectures:

> There are two ways to teach quantum mechanics. The first way -- which for most physicists today is still the only way -- follows the historical order in which the ideas were discovered. So, you start with classical mechanics and electrodynamics, solving lots of grueling differential equations at every step. Then you learn about the "blackbody paradox" and various strange experimental results, and the great crisis these things posed for physics. Next you learn a complicated patchwork of ideas that physicists invented between 1900 and 1926 to try to make the crisis go away. Then, if you're lucky, after years of study you finally get around to the central conceptual point: that nature is described not by probabilities (which are always nonnegative), but by numbers called amplitudes that can be positive, negative, or even complex.

> Today, in the quantum information age, the fact that all the physicists had to learn quantum this way seems increasingly humorous. For example, I've had experts in quantum field theory -- people who've spent years calculating path integrals of mind-boggling complexity -- ask me to explain the Bell inequality to them. That's like Andrew Wiles asking me to explain the Pythagorean Theorem.

> As a direct result of this "QWERTY" approach to explaining quantum mechanics - which you can see reflected in almost every popular book and article, down to the present -- the subject acquired an undeserved reputation for being hard. Educated people memorized the slogans -- "light is both a wave and a particle," "the cat is neither dead nor alive until you look," "you can ask about the position or the momentum, but not both," "one particle instantly learns the spin of the other through spooky action-at-a-distance," etc. -- and also learned that they shouldn't even try to understand such things without years of painstaking work.

> The second way to teach quantum mechanics leaves a blow-by-blow account of its discovery to the historians, and instead starts directly from the conceptual core -- namely, a certain generalization of probability theory to allow minus signs. Once you know what the theory is actually about, you can then sprinkle in physics to taste, and calculate the spectrum of whatever atom you want. This second approach is the one I'll be following here.

Here's the full lecture.[0] The approach was interesting enough that I bought his full book[1], but unfortunately it was a little over my head.

[0] http://www.scottaaronson.com/democritus/lec9.html [1] https://www.amazon.com/Quantum-Computing-since-Democritus-Aa...

> it was a little over my head

Well, I guess, there may be something wrong with his approach after all.

I think you can start either at a complex simulation paper and read up on the theory backwards from there (if you wish to simulate something) or then from basics and move up from there.

Or, you can start from the bottom. For the latter this should be a good place to start:https://www.staff.science.uu.nl/~gadda001/goodtheorist/

Physics is like exploring properties of a set where you are given a relation between individual elements of the set. Physical intuition us the knowledge of general relations that can be expected to hold for all elements.

If you don't want the physical intuition, then you don't want the physics at all; You should stop claiming to want to learn physics and never stray further from the one true path than the applied mathematics building.

And as a physicist, I disagree with you. Not specifically about your view of history (which I still think is important), but the way you think about Nature in general.

Quoting Feynman www.feynmanlectures.caltech.edu/II_02.html

> The physicist needs a facility in looking at problems from several points of view. The exact analysis of real physical problems is usually quite complicated, and any particular physical situation may be too complicated to analyze directly by solving the differential equation. But one can still get a very good idea of the behavior of a system if one has some feel for the character of the solution in different circumstances. Ideas such as the field lines, capacitance, resistance, and inductance are, for such purposes, very useful. So we will spend much of our time analyzing them. In this way we will get a feel as to what should happen in different electromagnetic situations. On the other hand, none of the heuristic models, such as field lines, is really adequate and accurate for all situations. There is only one precise way of presenting the laws, and that is by means of differential equations. They have the advantage of being fundamental and, so far as we know, precise. If you have learned the differential equations you can always go back to them. There is nothing to unlearn.

> It will take you some time to understand what should happen in different circumstances. You will have to solve the equations. Each time you solve the equations, you will learn something about the character of the solutions. To keep these solutions in mind, it will be useful also to study their meaning in terms of field lines and of other concepts. This is the way you will really “understand” the equations. That is the difference between mathematics and physics. Mathematicians, or people who have very mathematical minds, are often led astray when “studying” physics because they lose sight of the physics. They say: “Look, these differential equations—the Maxwell equations—are all there is to electrodynamics; it is admitted by the physicists that there is nothing which is not contained in the equations. The equations are complicated, but after all they are only mathematical equations and if I understand them mathematically inside out, I will understand the physics inside out.” Only it doesn’t work that way. Mathematicians who study physics with that point of view—and there have been many of them—usually make little contribution to physics and, in fact, little to mathematics. They fail because the actual physical situations in the real world are so complicated that it is necessary to have a much broader understanding of the equations.

> What it means really to understand an equation—that is, in more than a strictly mathematical sense—was described by Dirac. He said: “I understand what an equation means if I have a way of figuring out the characteristics of its solution without actually solving it.” So if we have a way of knowing what should happen in given circumstances without actually solving the equations, then we “understand” the equations, as applied to these circumstances. A physical understanding is a completely unmathematical, imprecise, and inexact thing, but absolutely necessary for a physicist.

From personal experience, there are such mathematics-oriented people in physics too, not just mathematicans. And some of them push a lot of papers, typically by applying the same method over and over again in different subfields, resulting in infinitesimal incremental "advances".

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