Maxwell's Equations and Black Body radiation

[Alan Grayson]

When one solves ME's, one gets continuous wave solutions. But somehow they give the wrong prediction for BB radiation. The correct solution requires quantizing the energy packets into discrete packets of energy. But prior to the advent of QED, in 1900, how did Planck incorporate this discreteness into a continuous theory to yield the correction solution of the BB problem? TIA, AG

[Alan Grayson]

On Wednesday, May 27, 2020 at 3:16:47 AM UTC-6, Alan Grayson wrote:

When one solves ME's, one gets continuous wave solutions. But somehow they give the wrong prediction for BB radiation. The correct solution requires quantizing the energy packets into discrete packets of energy. But prior to the advent of QED, in 1900, how did Planck incorporate this discreteness into a continuous theory to yield the correction solution of the BB problem? TIA, AG

The BB radiation distribution is what it is, and can be measured. But how does the postulate of discrete energy packets, aka photons, yield a theory, presumably using a continuous theory such as ME's, to predict it? TIA, AG 

[Lawrence Crowell]

These are questions that can be looked up in something such as Wikipedia. 

LC

[Alan Grayson]

On Thursday, May 28, 2020 at 2:45:42 PM UTC-6, Lawrence Crowell wrote:

These are questions that can be looked up in something such as Wikipedia. 

LC

Wiki has a good article on this. Oddly, when I took E&M courses, undergraduate and graduate, I don't recall this issue ever being discussed, at least not in detail. I don't recall any detailed discussion of Planck's radiation law; that is, how it's derived. AG 

[John Clark]

On Thu, May 28, 2020 at 6:28 PM Alan Grayson <agrays...@gmail.com> wrote:

> Wiki has a good article on this. Oddly, when I took E&M courses, undergraduate and graduate, I don't recall this issue ever being discussed, at least not in detail. I don't recall any detailed discussion of Planck's radiation law; that is, how it's derived. AG 

Wow, you must have had some pretty crappy physics courses!

John K Clark

[Alan Grayson]

In E&M, Yes, but surely not in QM. When we got to Maxwell's displacement current, the professor did some hand-waving related to delta functions, which was very unsatisfying. A good course in E&M would, IMO, include a rigorous discussion of Planck's BB formula, since it is where quantum physics begins, and including a rigorous treatment Maxwell's displacement current and wave solutions of the Maxwell's equation. I doubt you have had a good course in QM, and in physics in general, since you deny that theories of physics start with postulates, when they  obviously do. AG 

[Alan Grayson]

If you doubt my position on postulates when it comes to physical theories, let me give you a simple example, namely the invariance of the measured SoL (independent of motion of source and recipient). This postulate is highly un-intuitive, but it was used by Einstein in his 1905 paper on SR to derive the Lorentz transformation. In QM, Schroedinger's equation is one of the postulates, as well as Born's Rule, and so forth.  AG

[Alan Grayson]

Clark, since you claim implicitly to having a serious understanding of E&M, can you give a proof of Planck's BB radiation law? AG 

[John Clark]

On Fri, May 29, 2020 at 10:46 AM Alan Grayson <agrays...@gmail.com> wrote:

> Clark, since you claim implicitly to having a serious understanding of E&M, can you give a proof of Planck's BB radiation law? AG 

Of course I can't! Mathematicians prove things, physicists don't. Physicists propose theories and if it turns out the theory is compatible with empirically derived results then it is generally accepted by the scientific community, at least within a certain range of applicability. No physicist gives a hoot in hell for a theory that is contradicted by experimental results regardless of how closely it follows somebody's "postulates".

John K Clark

 

[Alan Grayson]

You're just displaying your ignorance, shamelessly as suggested by your emotional insistence. Physics starts with postulates about how nature behaves. It's basically guesswork as Feynman asserts. I gave you some examples. And one can prove specific results from postulates, as Einstein did in his 1905 paper on SR in DERIVING the LT. Postulates are accepted if they give good predictions. No one doubts that, so you're affirming something no one disputes. Similarly, Planck didn't pull his BB radiation formula out of his hat. He must have started with some postulates, from which he derived his formula, and we accept the formula as "true" since it accurately predicts what is measured. If you can't say anything about Planck's formula, except obvious superficial comments such as the fact that he quantizes of the frequency modes, you know nothing more about this subject compared to someone like me who admits his courses in E&M were "crappy". AG

[smitra]

On 29-05-2020 16:11, Alan Grayson wrote:
> On Friday, May 29, 2020 at 6:26:20 AM UTC-6, John Clark wrote:
>
>> On Thu, May 28, 2020 at 6:28 PM Alan Grayson <agrays...@gmail.com>
>> wrote:
>>

>>> _> Wiki has a good article on this. Oddly, when I took E&M

>>> courses, undergraduate and graduate, I don't recall this issue
>>> ever being discussed, at least not in detail. I don't recall any
>>> detailed discussion of Planck's radiation law; that is, how it's

>>> derived. AG _

>>
>> Wow, you must have had some pretty crappy physics courses!
>>
>> John K Clark
>
> In E&M, Yes, but surely not in QM. When we got to Maxwell's
> displacement current, the professor did some hand-waving related to
> delta functions, which was very unsatisfying. A good course in E&M
> would, IMO, include a rigorous discussion of Planck's BB formula,
> since it is where quantum physics begins, and including a rigorous
> treatment Maxwell's displacement current and wave solutions of the
> Maxwell's equation. I doubt you have had a good course in QM, and in
> physics in general, since you deny that theories of physics start with
> postulates, when they obviously do. AG
>

http://insti.physics.sunysb.edu/~siegel/history.html

Saibal

[Brent Meeker]

Seems to be a rant from the 1950's.

One thing that's interesting about the way physics is taught is that it
tends to repeat the historical sequence from Newton on.  Partly this is
because Newtonian mechanics is still very useful, even for physicists
and especially for engineers.  It's also teaches how the scientific
method has been applied to get where we are.  I notice that this is
quite different from the way engineering is taught...engineers seldom
know much about the history of their subject .

Brent

[Alan Grayson]

Clark; take the noble path. Acknowledge that what I wrote above is correct. TY, AG 

[Alan Grayson]

Some other examples: using Newton's law of gravitation, one can mathematically DERIVE the result that planet trajectories are conic sections; using mathematics one can show that Newton's equations of motion, Hamilton's equations of motions, and Lagrange's equations of motion are equivalent; using mathematics one can show that the HUP is implied by the principles or postulates of QM (although the principle was established by Heisenberg independent of the postulates of QM). Are you ready to take the noble path and acknowledge that I am correct about the relationship of mathematics to the principles or postulates of physics? AG

 

[Alan Grayson]

On Thursday, May 28, 2020 at 2:45:42 PM UTC-6, Lawrence Crowell wrote:

These are questions that can be looked up in something such as Wikipedia. 

LC

Here, presumably, is the derivation of Planck's blackbody radiation formula.  https://en.wikipedia.org/wiki/Planck%27s_law#Derivation . Near the beginning is a reference to, and dependence on quantum theory. But in 1900, quantum theory didn't exist. AG

[Alan Grayson]

On Wednesday, June 3, 2020 at 11:03:17 PM UTC-6, Alan Grayson wrote:

On Thursday, May 28, 2020 at 2:45:42 PM UTC-6, Lawrence Crowell wrote:

These are questions that can be looked up in something such as Wikipedia. 

LC

Here, presumably, is the derivation of Planck's black-body radiation formula.  https://en.wikipedia.org/wiki/Planck%27s_law#Derivation . Near the beginning is a reference to, and dependence on quantum theory. But in 1900, quantum theory didn't exist. AG

I think we have to assume that Planck started his proof of the black-body radiation formula with an assumption that now is a result of quantum theory. AG

[John Clark]

On Sun, May 31, 2020 at 6:58 PM Alan Grayson <agrays...@gmail.com> wrote:

> Some other examples: using Newton's law of gravitation, one can mathematically DERIVE the result that planet trajectories are conic sections; using mathematics one can show that Newton's equations of motion, Hamilton's equations of motions, and Lagrange's equations of motion are equivalent;

Yes, you can prove MATHEMATICALLY that Newton and Lagrange's equations are exactly equivalent, but more than a century ago it was proven EXPERIMENTALLY that both those equations are equally WRONG, or at least less correct than Einstein's equations of motion.  Perhaps someday somebody will find equations that make predictions even better than Einstein's, but they could not be proven to be better mathematically, they'd have to be proven to be better experimentally.  

John K Clark

[Alan Grayson]

Obviously, my comment about those equations was in the context of non-relativistic physics. Moreover, I gave you other examples to falsify your claims. No point in arguing with a dishonest person. AG 

[John Clark]

On Fri, Jun 5, 2020 at 10:33 AM Alan Grayson <agrays...@gmail.com> wrote:

> No point in arguing with a dishonest person. AG 

I agree, Mr.Carl Sagan co-author.

 John K Clark

[Alan Grayson]

the

 John K Clark

There's a simple choice in this matter. Someone who denies that QM has postulates from which the HUP is implied, either knows little or nothing about QM, or won't acknowledge it due to dishonesty. AG 

[John Clark]

On Sat, Jun 6, 2020 at 8:44 AM Alan Grayson <agrays...@gmail.com> wrote:

> There's a simple choice in this matter. Someone who denies that QM has postulates from which the HUP is implied, either knows little or nothing about QM, or won't acknowledge it due to dishonesty. AG 

Mr.Carl Sagan co-author, you can prove that one mathematical statement can be derived from another, but if they deal with physics then the only way to know if EITHER statement is even approximately true is to test them experimentally. And if the new physical statement can't be derived from the physical "postulates" but it nevertheless makes better predictions then it's time to find new improved physical "postulates". Oh and you forgot IHA.

John K Clark

[Alan Grayson]

You have command of the obvious, but fail to understand how theories of physics are structured.  IHA =? AG

[John Clark]

On Sat, Jun 6, 2020 at 9:21 AM Alan Grayson <agrays...@gmail.com> wrote:

 

>> Oh and you forgot IHA.

 

> IHA =? AG

 Mr.Carl Sagan co-author, it means I Hate Acronyms.

John K Clark

[Alan Grayson]

Is "HUP" beyond your pay grade? Further, you apparently prefer Kepler to Newton. Kepler deduced from measurements that Mars has an elliptical orbit, whereas Newton's law of gravitation implies much more; namely, that they can move in conic sections. But that requires applying mathematics to a postulate about gravity. Too deep for your bias to accept? AG

[John Clark]

On Sat, Jun 6, 2020 at 9:43 AM Alan Grayson <agrays...@gmail.com> wrote:

>  Kepler deduced from measurements that Mars has an elliptical orbit, whereas Newton's law of gravitation implies much more; namely, that they can move in conic sections.

If gravity is an inverse square law that follows Newton's rules and if there are only 2 massive objects in the universe then you can prove mathematically their orbit will follow a path that is a conic section. But even if you lived in a universe where Newton was 100% right and Einstein was wrong, Mars would not have an elliptical orbit or that of any conic section because there are more than 2 massive objects in the universe. And of course we know now that gravity does not follow Newton's rules.

John K Clark

[Alan Grayson]

I was expecting this cop-out.  No point in arguing with bias and stupidity. You're the Trumper of physics. AG

[John Clark]

On Sat, Jun 6, 2020 at 1:08 PM Alan Grayson <agrays...@gmail.com> wrote:

>No point in arguing with bias and stupidity.

You're right again Mr.Carl Sagan co-author.

John K Clark

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[Alan Grayson]

On Saturday, June 6, 2020 at 11:15:12 AM UTC-6, John Clark wrote:

On Sat, Jun 6, 2020 at 1:08 PM Alan Grayson <agrays...@gmail.com> wrote:

>No point in arguing with bias and stupidity.

You're right again Mr.Carl Sagan co-author.

John K Clark

You mean no perfect conic sections as orbits? That's a no-brainer Mr. Trumper. AG 

On Saturday, June 6, 2020 at 8:09:14 AM UTC-6, John Clark wrote:

On Sat, Jun 6, 2020 at 9:43 AM Alan Grayson <agrays...@gmail.com> wrote:

>  Kepler deduced from measurements that Mars has an elliptical orbit, whereas Newton's law of gravitation implies much more; namely, that they can move in conic sections.

If gravity is an inverse square law that follows Newton's rules and if there are only 2 massive objects in the universe then you can prove mathematically their orbit will follow a path that is a conic section. But even if you lived in a universe where Newton was 100% right and Einstein was wrong, Mars would not have an elliptical orbit or that of any conic section because there are more than 2 massive objects in the universe. And of course we know now that gravity does not follow Newton's rules.

John K Clark

I was expecting this cop-out.  No point in arguing with bias and stupidity. You're the Trumper of physics. AG

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[Alan Grayson]

On Saturday, June 6, 2020 at 11:31:39 AM UTC-6, Alan Grayson wrote:

On Saturday, June 6, 2020 at 11:15:12 AM UTC-6, John Clark wrote:

On Sat, Jun 6, 2020 at 1:08 PM Alan Grayson <agrays...@gmail.com> wrote:

>No point in arguing with bias and stupidity.

You're right again Mr.Carl Sagan co-author.

John K Clark

You mean no perfect conic sections as orbits? That's a no-brainer Mr. Trumper. AG 

The Mr. Trumper of Physics, aka John Clark, refuses to admit that MATHEMATICS is often applied to the POSTULATES of physics, to give important new insights. For example, using Newton's Law of Gravitation, it was demonstrated, using MATHEMATICS, and starting with that POSTULATE, that planetary orbits are conic sections; a HUGE result! But for Mr. Trumper of Physics, this is not good enough because that result was superceded by GR. Clark reminds me of a Trumper who refuses to admit obvious facts about how physics progresses; and continues to hold the falsified view that physics doesn't use mathematics in the creative way just described. AG

[John Clark]

Alan Grayson aka Mr.Carl Sagan co-author wrote:

 

> John Clark refuses to admit that MATHEMATICS is often applied to the POSTULATES of physics, 

Postulates yields results that are exact and that's why physics doesn't have any, only mathematics does.

> to give important new insights.

In your original post you weren't talking about finding important new insights, you demanded a mathematical PROOF that Planck's Black Body formula was true. And that's ridiculous. Mathematics can never prove that any physical theory is true, but with experiment and observation we can show that one physical theory is less wrong than another.

> For example, using Newton's Law of Gravitation, it was demonstrated, using MATHEMATICS, and starting with that POSTULATE, that planetary orbits are conic sections; a HUGE result!

Sure it was important to learn that Newton's laws led to conic section orbits if there were only 2 massive objects in the universe, but the only way we could know if that was even approximately true for the planets in our solar system is through observation not through mathematics. And Einstein tells us that Newton's laws are NOT correct and thus even in a 2 object universe orbits would not be conic sections, in fact no orbit would be stable because all orbits involve accelerating mass and accelerating mass produces Gravitational Waves.Gravitational Waves radiate away the orbit's energy so the orbit would always be a slow inward spiral.  And a slow inward spiral is not a conic section.

 John K Clark

[Alan Grayson]

Insofar as you continue to practice Trump physics (in refusing to acknowledge simple facts), your comments are totally worthless. For you "postulate" is a dirty word when applied to physics. You can use "principle" if you ever choose to cease your dishonesty. The invariance of the SoL in SR is exactly that, a POSTULATE or PRINCIPLE, from which Einstein DERIVED the Lorentz Transformation. As for Planck's black-body radiation law, the MATHEMATICAL DERIVATION, the link for which I posted, is based on several assumptions. Of course, all physical theories must be validated by experiments, but you use that fact to ignore the process of evolution of physical theories. As for you comment on conic sections, you seem to deliberately ignore the fact that in physics we use idealized cases to reach important insights. The reasons for your foolishness is obvious. In physics, you are a despicable Trumper with an invariant agenda; to make up self-serving facts and interpretations which serve a simple minded purpose; make you feel good, which can be reasonably characterized as  stupidity.  AG

[John Clark]

Alan Grayson aka Mr.Carl Sagan co-author wrote:

> you seem to deliberately ignore the fact that in physics we use idealized cases to reach important insights.

Far from ignoring it for years I've been trying to convince Bruno that mathematical approximations help us understand physical phenomena but simulations are always simpler than the real physical thing; therefore physics is not an approximation of mathematics but mathematics is an approximation of physics. So physics is more fundamental than mathematics. I mean... if a mathematical model of what the path of a hurricane will do does not conform to what it actually does we don't say the physical hurricane made an error, we say the computer model made an error.

John K Clark

[Alan Grayson]

The fact that our models are simplifications of reality, means that the principles of physics on which are models are derived, are also approximations. So, again, your argument about the relationship of mathematics to physics fails. Conic sections to model planetary orbits are hugely successful. The fact that they're not exactly perfect is obvious, and cannot honesty be appealed to, to claim that mathematics is "merely" approximate, whereas the principles of physics are somehow more perfect. We know this isn't generally true, since GR is superior to NM, but even GR will someday be supplanted by a better understanding of gravity. AG 

[Alan Grayson]

Correction; ... on which OUR models are derived ...  AG 

[Alan Grayson]

The bottom line is this; firstly, that physics DOES have POSTULATES or PRINCIPLES as starting points for its theories; and secondly, that mathematics is generally used to see the consequences of these postulates or principles.  What you claim is simply false, other than the obvious; that our models are imperfect. AG

[Alan Grayson]

Or take the case of classical EM theory. We have four postulates or principles, taken from experience, namely Maxwell's equations; and the results obtained by mathematics, namely the existence of wave solutions. Are the principles or postulates, or the consequences perfect? Of course not, but huge advances nevertheless. Now we have QED. Much superior to the old theory, but nevertheless likely to be subsumed in the future by a better theory. And so it goes. AG 

[Bruno Marchal]

On 8 Jun 2020, at 15:56, John Clark <johnk...@gmail.com> wrote:

Alan Grayson aka Mr.Carl Sagan co-author wrote:

> you seem to deliberately ignore the fact that in physics we use idealized cases to reach important insights.

Far from ignoring it for years I've been trying to convince Bruno that mathematical approximations help us understand physical phenomena but simulations are always simpler than the real physical thing; therefore physics is not an approximation of mathematics but mathematics is an approximation of physics.

That follows easily from Aristotle metaphysical postulate that there is some physical reality “out there”. That’s OK when doing physics, and that is OK when studying Aristotle Metaphysics, but you cannot equate physics and metaphysics without further explanation, when doing metaphysics with the scientific attitude and/or method.

Note that when just doing physics, you might need all sort of hypotheses, but you don’t need to do any special hypothesis in metaphysics. 

So physics is more fundamental than mathematics.

Assuming Aristotle metaphysics/theology. But there has never been evidences for this. Just 1500 years of banishing, the pagan philosophers, if not burning them as heretic.

I mean... if a mathematical model of what the path of a hurricane will do does not conform to what it actually does we don't say the physical hurricane made an error, we say the computer model made an error.

That’s reasonable. But when the question is “what is a hurricane?” is studied, the question is no more that simple, and the answer will depends on your metaphysical hypothesis. With mechanism, we have only “computer models”, and the physical is no more identifiable with any “computer model”, as it is an emerging first person plural experience arising from a non computable statistics on all computation, and nobody knows what that can give, except by pointing the finger to “that” (the realm of our experiences) when we assume mechanism.

One of the difficulty here is that we are programmed at the start to anticipate some reality, instinctively, and we have to anticipate that what we see is real, but we don’t have to anticipate that what we see is fundamentally real. That’s how science begun: by doubting in metaphysics (Plato).

Bruno

John K Clark

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