JRC,

Further to your points ... You write, "Where I don't follow your arguments is where the sensor determines discretion, as depicted on the saw-tooth graph. While I agree that that a continuous, and non-varying, input of energy would accumulate in exponential fashion as a function of time, isn't that time period present in the frequency term of your equation? How does the sensor know...

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JRC,

Further to your points ... You write, "Where I don't follow your arguments is where the sensor determines discretion, as depicted on the saw-tooth graph. While I agree that that a continuous, and non-varying, input of energy would accumulate in exponential fashion as a function of time, isn't that time period present in the frequency term of your equation? How does the sensor know it has finished receiving one wavelength of a one dimensional wave? Am I misunderstanding something, or completely? "

Yes! Three important points to consider here.

1) Associating a wavelength with time of absorption is incorrect! That may be how the current paradigm of Physics may view it. But I am presenting a different view. And worse than mixing metaphors is mixing paradigms! When does the sensor know when to absorb the "gulp" of energy that has accumulated? Simple. When "local equilibrium" at the interaction site is reached. When does the sensor know when to stop absorbing more "gulps" of energy? Easy. When global equilibrium is reached between the sensor and the source.

2) We have the exponential rate of "accumulation" of energy at the sensor, r, and the "frequency of radiation" , nu, (thought as the wave frequency). These are related but not identical concepts. The "wave" idea is physically imposed by us describing what we say happens. In contrast, I find the exponential rate of energy accumulation more sensible here. While physically nu can only be thought as a positive integer, r can be any real number positive or negative (describing both absorption or emission). This makes more sense. Don't you think?

3) Further, the interval of time for an amount of accumulated energy h to be absorbed by the sensor is h/kT (see my Chapter for a discussion of this). If anything this should be taken as the frequency of absorption! And not the exponential rate r (or nu). From this we clearly see the relationship between temperature T and "absorption frequency": the higher the temperature, the higher the frequency, and visa versa.

Do ask if any of this is still not clear.

Constantinos

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Constantinos,

In your reply to Jose you state, "The issue here is not whether we can derive Planck's Law 'with or with-out quanta',"

I see your point. While substituting eta in your equation for h in the derivation you use of Planck's Theorem, does have the exact form, it is not the same mathematical identity. Which I think is your major argument.

I have not found the...

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Constantinos,

In your reply to Jose you state, "The issue here is not whether we can derive Planck's Law 'with or with-out quanta',"

I see your point. While substituting eta in your equation for h in the derivation you use of Planck's Theorem, does have the exact form, it is not the same mathematical identity. Which I think is your major argument.

I have not found the derivation you employ in several references I briefly looked into but accept it as it is quite apparent you are very familiar with the vast body of work which has developed from his original formulations. Let me start there because I'm quite content with the simple reductions and think the derivation is good as it simplifies to an energy term on the left side. (And I really don't have the desire for a lot of math)

In essence, and I think this is important in how you introduce others to your work, what your identity does is to make global what is expressed locally to the incident waves from a source by the Planck identity. And more. It is scale independent, by averaging the energy term it can show the local value of h as the absolute value of a single wave event to be a time dependent action, while also extending relativistically to infinity. It was the limit at infinity that had me worried.

So in real terms and applications your equation is complimentary to Planck and does not displace Planck's (theorem) Law. And it can't without also refuting the basis of itself. Nor would many accept doing away with its reduction to e=hv.

Another aspect of the global feature is that it might be applicable to a 'flat flow' measurement. If you are familiar with mechanical maintenance and how an AC Induction Motor operates, the characteristic of 'slippage' gives a good illustration. Without digression in how its done, the magnetic field in the stator electromagnets rotates while inducing magnetic field regions in the rotor. But the rotor's physical rotation continually lags behind the stator field rotation, its 'slipping'. Now consider the slippage cylindrical plane as a flat wave. Similar to the shear plane of laminar flow in hydro-dynamics. Its not that the slippage doesn't give a perturbative reactance in producing an electromagnetic field, it does and its scale independent, you can hear it because to rotor's speed produces oscillation in the audible range.

In your paradigm of interaction of measurement as mathematical identities, that slippage illustration could possibly apply to a continuous flow through the medium of an emitter source. Interactively, evanescent waves which are those that reflect back into the interior of a medium, decay exponentially in intensity. That could be related to your 'if the speed of light is constant, light is a wave', and the interface at emitter and absorber.

So I think you can say that whether I recognize it or not, I'm responding in accord with your hypothesis that it is mathematical identity by which we do physics. Don't expect to purge physics anytime soon of it being used to discover 'what it is', that's why most people go into physics instead of math.

Cordially, jrc

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Constantinos,

I'm not sure if we got off on a mis-step or if my lack of formal math education leaves me perplexed in how you state things that would be self evident in pure mathematics. But I have long recognized that our empirical measure is based on wholey arbitrary units evolving from earth bound metaphor, and that it is by mathematical axiomatic operations that we define physical...

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Constantinos,

I'm not sure if we got off on a mis-step or if my lack of formal math education leaves me perplexed in how you state things that would be self evident in pure mathematics. But I have long recognized that our empirical measure is based on wholey arbitrary units evolving from earth bound metaphor, and that it is by mathematical axiomatic operations that we define physical relationships. The exponential function giving 'e' is an exponential identity, and so is the harmonic series that we find in radioactive decay. But a proportional constant is an equality, so I don't understand why you said that Planck's Law could not be an identity because he introduced a physical constant. It has become quite common for the quantum to be taken only as a finite, specific quantity of energy rather than as a time dependent empirical unit only applicable to a single waveform of any frequency, per 1/f. And the size of the unit is dependent on the assigned size of the unit in Boltzman. But taken only as a constant unit value does not identify any kind of operation.

Yes, the plot lines of COBE and blackbody radiation are identical and should be a great corroboration of Wien's intuitive reasoning that repetitive absorption and emission would thermalize radiation towards a mean distribution.

Yes, the photoelectric effect as commonly interpreted as per Einstein is in contradiction to the postulate of constant speed of light, and many before have said that it only behaves like a particle hitting the spot when its absorbed. I could ( and have ) shear off a high tensile bolt with a half-inch drive air impact wrench with a lower supply pressure if I have the beats set too high. The supply can be regulated in a continuous manner at the compressor reservoir, and the cyclic rate is set by bleeding off the exhaust on the gun. Its a continuous function but still translates to batta-batta-batta.

I am sorry not to follow your mathematical construct, especially in that there is a observational experimental limit that leaves us with 'the Photon'. And it is not at all clear to me how your methodology determines the cyclical rate of accumulation along the one-dimensional wave. Those whom have commented have limited themselves to general agreement on a philosophical level but haven't offered mathematic discussion, and I think I'd need to watch & learn from that sort of learned discussion to get a handle on what is a mathematical paradigm. Cordially, jrc

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JRC,

You write, "... me perplexed in how you state things that would be self evident in pure mathematics. "

I am not sure what you are saying here. The only "self-evident" idea I have ever said in any discussion is "we can only know what we think we know". As corollary to this, we cannot know "what is" physical reality. But can only know our measurements, observations and...

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JRC,

You write, "... me perplexed in how you state things that would be self evident in pure mathematics. "

I am not sure what you are saying here. The only "self-evident" idea I have ever said in any discussion is "we can only know what we think we know". As corollary to this, we cannot know "what is" physical reality. But can only know our measurements, observations and understanding of our experience of physical reality.

It seems to me a core misunderstanding is what is a mathematical identity. And why Planck's Law as was and is is not a mathematical identity. But I am demonstrating and arguing it IS! So let me focus on this and forego your other points of agreement/disagreement for another time.

Simply, a mathematical identity does not depend on any physical suppositions in its derivation. Like, for example, the physical existence of "energy quanta" having energy given by hv used by Planck, Einstein etc. to derive Planck's Law. My derivation of Planck's Law does not make any physical assumptions. It is a pure math derivation. Thus, a mathematical truth.

As such, it describes the functional relationship between the "incremental change" of a quantity, its "average over that interval", and its "instantaneous value" at the start of that interval. Notice! Nothing here about physics, energy, frequency, etc. I show Planck's Law in its mathematical essence is just that!

You write, "... I don't understand why you said that Planck's Law could not be an identity because he introduced a physical constant". It's more than that. The derivation depended on the assumption of the physical existence of "energy quanta" having energy given by hv. Thus, it is not a mathematical derivation that does not depend on physical assumptions having a "physical view". Math does not claim any "physical view".

Certainly we can substitute in any mathematical identity quantities and equivalences consistent with the mathematical meaning of those parts in the mathematical identity. Thus, if we know or assume the "change of energy" is given as hv, and the corresponding "average energy" for this is given by kT we can substitute these values in my mathematical identity to get Planck's Law in the form familiar in Physics.

This is no different than making appropriate substitutions in the Pythagorean Theorem. But this does not make the Pythagorean Theorem any less a mathematical identity. Again, the issue here is the physical assumptions used in the derivation. A mathematical identity makes no such assumptions!

Constantinos

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JRC, you write further ...

"Yes, the plot lines of COBE and blackbody radiation are identical and should be a great corroboration of Wien's intuitive reasoning that repetitive absorption and emission would thermalize radiation towards a mean distribution."

I don't follow you here. Typically for any physical law based on some mathematical model of "what is", the experimental...

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JRC, you write further ...

"Yes, the plot lines of COBE and blackbody radiation are identical and should be a great corroboration of Wien's intuitive reasoning that repetitive absorption and emission would thermalize radiation towards a mean distribution."

I don't follow you here. Typically for any physical law based on some mathematical model of "what is", the experimental data hopefully fits the theory -- but never identically! And the closer we look into the physical experimental measurements, the rougher and more divergent our theoretical fit is. Such identical fit between experimental data and theory can only happen for mathematical identities.

For example, if we had very precise measurements of points of a very precise circle drawn by very fine instruments, the experimental coordinates of points on such circle will fit very identically with the Pythagorean Theorem. That would be so BECAUSE the Pythagorean Theorem is a mathematical identity. Something similar to this is happening between the COBE spectrum and the theoretical blackbody radiation curve based on Planck's Law. And THIS is explained by my purely mathematical derivation of Planck's Law, proving this Law is a mathematical identity. There is just no other explanation for this!

I can summarize my argument on this as follows. "If the physical law is a mathematical identity, then the experimental data fits very identically to the theoretical curve."

The reverse is not valid, however. Nor can we properly argue, as physicists often do, because experiments and theory fit very identically our physical law is absolutely true. Or our physical law is a mathematical identity. A mathematical identity must be mathematically derived and proven to be true absolutely.

You write,

"Yes, the photoelectric effect as commonly interpreted as per Einstein is in contradiction to the postulate of constant speed of light, and many before have said that it only behaves like a particle hitting the spot when its absorbed."

That's news to me. Who and how and when it was shown that the CSL Hypothesis contradicts the Quantum Hypothesis? I have a short need and elegant proof of this! And it all ties together with all of my other results and derivations.

Constantinos

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Constantinos,

I grew up in a small family publishing business, I started having income tax with-held when I was 11 years old and worked in the business in a production capacity through high school. My grades suffered but I got one hell of an education. I'll give you some free editorial advice. In the popular press you just have to tease people so they will read on. But in scientific...

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Constantinos,

I grew up in a small family publishing business, I started having income tax with-held when I was 11 years old and worked in the business in a production capacity through high school. My grades suffered but I got one hell of an education. I'll give you some free editorial advice. In the popular press you just have to tease people so they will read on. But in scientific writing, which is more art than science, don't waste people's time. You will gain a wider audience, by physicists whom might cite your work in support of their own if you present your work concisely in clarity of no uncertain terms. But they will not pay attention to an interminable argument that they must support if they cite your work,

Case in point: you stated in your last paragraph of 4/4/15 @ 01:40 GMT -------- "--- Who and how and when it was shown that the CSL Hypothesis contradicts the Quantum Hypothesis?"

That is a politician's stump trick. I didn't suggest that and you know it. I had stated the contradiction in '...the photoelectric effect as commonly interpreted as per Einstein..' which is as a particle. That's what won him the Noble. That's in contradiction of Einstein's SR.

You want, and need, a wider audience than me. I spent a month trying to figure out what you were driving at and you finally summed it up (fairly nicely - ed) in the clarification you posted 3/3/15 @ 20:27 GMT. That is kind of what you should lead with in commenting on other's essays. Say; HEY - LOOK! I provide PROOF of Planck's Hypothesis! Then you can briefly give the argument that it is necessary in light of the strictly empirical origin of the quantum, and that while true to form the formulations themselves lack a basis of mathematical truth, which You can provide. And then you can say that it leads to some surprising results. Because that gives physicists a new toy. Let them play with it. And with there being a classical revival, a continuous rationale of the quantum that is mathematically complete would be welcome. Too much work is based on calibrating measures to that value to attempt to dethrone it without another finite benchmark. And the way you present your arguments sounds like an intent to vanquish the quantum entirely.

And, no, I don't think you do follow what I said about Wien. He was taking a chance. Because physics uses math, but like the color purple it is a figment of human imagination, and physics is about what it is that is physical.

I'll end with an old editorial device that tells the writer and the typositor that its time to pull a galley proof.

- 30 -

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Constantinos,

The standard interpretation of the photoelectric effect is that light is a particle (photon) in a multiple of n integers of h (the quantum), the detection of which is dependent on the 'work function' necessary to eject an electron from the target metal. That particle can only be 'massless' if its a particle, or it will violate the infinite mass prohibition in SR. What you are...

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Constantinos,

The standard interpretation of the photoelectric effect is that light is a particle (photon) in a multiple of n integers of h (the quantum), the detection of which is dependent on the 'work function' necessary to eject an electron from the target metal. That particle can only be 'massless' if its a particle, or it will violate the infinite mass prohibition in SR. What you are saying that all the energy necessary to eject the electron is carried in one wave at or above the threshold frequency and absorbed by the metal as a culmulative exponential rate in the duration of 1/f. I think 'massless particle' is a contradiction, and that the 1/f rationale is viable as an action dependent on the target.

However, if a wave of a given frequency can carry any amount of energy per 1/f then wouldn't that match the same distribution of frequencies expected by Wien and colleagues, and researchers of the blackbody experiments?

May I remind you that my post to Steve did not in anyway presume upon you, nor what you had said in yours would have been construed by anyone that I had. I would not have defended his rating in that manner if I'd expected response from him, and if you have read a number of essayists you would have recognized that unlike yourself, there have been a number for whom its 'my way or the highway' and have issued derogatory and derisive condemnations of others commenting on their work if in disagreement of a strictly QM or Relativistic approach. One individual even stated he deliberately gave ratings of 1 to those whom he considered unqualified in QM! I haven't bothered to look to see if anyone has member status or not, but did want to point out the obvious distasteful prejudice while simply giving Steve high marks for a cross-disciplinary approach and acknowledgement of some originality. And then bow out and engage elsewhere. You have been challenging me.

The holy grail in physics today, is to find where symmetry is broken. What Wien et.al. expected to find was a smooth curve of distribution in which the change in slope was in the same direction, limiting at a one to one correspondence of intensity and frequency. What they found was a smooth curve that changed direction of slope near the maximum and rolled over to top off. That means a break in physical symmetry that causes thermal energy to seek a path of least resistance. If your methodology can independently find that break in physical symmetry while maintaining a continuous function that does not break mathematical symmetry, by which I properly mean fully reversable, your book would fly off the shelves. If you have shown that, I simply haven't seen it. May I be excused, please. john

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Constantinos,

Well...its started to rain on me, so I've had a little time to let things gel without trying to push it. Strictly from the standpoint of a continuous flow of energy at uniform light velocity, I see your point that given an exponential rate of absorption by which we measure frequency and energy value, Planck's quanta must be taken as empirical experimental derivation of the...

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Constantinos,

Well...its started to rain on me, so I've had a little time to let things gel without trying to push it. Strictly from the standpoint of a continuous flow of energy at uniform light velocity, I see your point that given an exponential rate of absorption by which we measure frequency and energy value, Planck's quanta must be taken as empirical experimental derivation of the least observable average.

Your conclusions are as disruptive of conventional thinking in Classical mechanics as they are in QM! And I must say just intuitively that the geometric relationships look fascinating. Eta, the accumulation of energy as a waveform of energy of a given frequency is absorbed, effectively slows the energy from light velocity to relative rest at the exponential rate. That rate can be plotted along a straight line, just as I could mark out ten equal intervals on a board and show the additive factoral of 1+1/1! +1/2! +1/3! +1/4!... +1/10! and then also take the full length of board as a light second with a frequency of 10, and each of those intervals subject to the same factoral scheme. That is the natural exponential function: e = (1+1/n)^n. And that graphs as a hyperbolic function. But then, the shape of wave must be addressed which adds a second hyperbolic function which relates the rapidity of change of the cosine of the angle of a hyperbola as a natural log, and in browsing for references I found that rapidity is used in research such as CERN in factoring the Lorentz Term 'gamma' in the time parameter of v/c. So for the absorption of a continuous flow of energy following a sinusoidal path to be an accumulation at the natural exponential rate, means the event is a coincidence of two hyperbolic functions, one along a proper timeline, and the other which Minkowski identified with Lorentz in SR. So the deceleration of the energy @ c to mass @ ~0 makes the convergence of the two hyperbolic functions 'go ballistic!', that is to rotate into a parabolic plane on which we find the acceleration of gravity.

I didn't dig into it, but I also found what appears to be such a convergence of hyperbolic function in what is called Cubical Parabolic Hyperbola, at mathworld; http://mathworld.wolfram.com/CubicalParabolicHyperbola.html

P
lease forgive my intuitive liscence, its been more then a quarter century since I had my old T-I 30 ,rigged with a clip for a 9V plug-in adapter, in any kind of serious use. And that pretty rudimentary. But from as well as I can follow, you make very strong argument that a given frequency can translate a continuous range of energy content per 1/f. That it is the cyclic rate of accumulation that is reacted to by any relative rest mass entity that gets in the way of an electromagnetic wave.

Cordially, jrc

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Constantinos,

I'm glad we got to a point of some mutual understanding, too. The concept underlying your hypothesis is one that was abandoned long ago for lack of a mathematically consistent rationale that fit the experimental interpretations of the era, and is still difficult to grasp. What I found most difficult was in confronting the numerous iterations of the quanta in arguing against...

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Constantinos,

I'm glad we got to a point of some mutual understanding, too. The concept underlying your hypothesis is one that was abandoned long ago for lack of a mathematically consistent rationale that fit the experimental interpretations of the era, and is still difficult to grasp. What I found most difficult was in confronting the numerous iterations of the quanta in arguing against doing so. It just reinforced the conventional approach. A lawyer I know, whose father was also a lawyer (funny how that goes), is fond of a saying of his Dad's; "A barrel sits on its own bottom". Meaning, don't remind the court that your adversary has a case (!).

But don't feel yourself so all alone in trying to figure out what the heck physicists think they are talking about. Your message is the same that is always being sought, and in one sense goes to what Tom Ray points out - that we might not find answers until we find better mathematics to define measurement of space, time, action. Everything in front of me is in the anterior hemisphere of my observation, everything behind me is in the posterior hemisphere. Similarly, everything above is in the upper hemisphere and all below, the lower. Same with the right or left, so we can measure from one octant to another. But not as if a line from my upper left octant goes to a point in my lower right like a beam of light through a lens of barium glass. There is nothing upside-down and backwards to the physical relationship between what's in front and what's behind me. So we have to develop the math of bijective complex planes with the rules of IFF. Non-commutative algebras. There has GOT to be a simpler way! In human daily experience we don't even think about it! We just move without confusing where things are around us, and without knocking over our neighbor's beer.

Incidentally, without sorting out the whole rationale of your conditional criteria of 'if and only if', it did make me wonder if there would be an operational correspondence to the 'if and only if' criteria of complex analysis. (That, I'll leave to those who like to play with math!)Topology is a math of continuous simple connectivity.

I have often thought what physics needs is a writer in mathematics of the sort Isaac Asimov was in physics. And I still occasionally refer to my $4.49 used copy of the 1988 printing, three volumes in one, 1966 copyright, 'Understanding Physics'. It presents in conversational prose with the simplest math, how the ideas in physics developed, and what the thinking at the times were. And in hindsight, that gives a perspective of "what hadn't been known, or considered then?" The argument between the corpuscular (particle) form of light that held sway in the 18th century and the wave form that was ascendant in the 19th, was never completely resolved, and morphed into the strange world of todays physics. Today's physicists have no more difficulty accepting non-locality and superposition than did earlier physicists accepting that to be a wave and move through a solid crystal, light had to be a transverse wave similar to that on the surface of water. While if it also moved through the ether as a longitudinal wave like the compression and rarification of sound through the same water, the ether would have to be both orders of magnitude more rare than the thinnest gas yet more rigid than steel. Today the 'massless particle' would be expedient even without Lorentz, because if the 'light particle' had any mass at all the sheer numbers of them that would have struck the earth would have added up to enough to make the orb heavy enough that we would have spiraled into our star long before we climbed out of the sea.

Perhaps what makes the limiting conditions of what amount of energy materializes as a periodic waveform, is how massive gravitationally, a source is in relation to its physical size volumetrically, compared to the amplitude of the wave. Perhaps frequency is a consequence of how fast the energy of any quantity might potentially seek to stream away from the source but runs into the limit of light velocity. Like a dog getting excited by a sound on the porch, and trying to stop just as it hits the limp rug on a freshly waxed hallway floor. And... so how is it physically(?), that the probability for energy to spread across frequencies is observed as the curve of intensity of frequencies in blackbody radiation, when the domain of probability for any frequency would be f^2? If we accept the continuous paradigm, perhaps it is simply that a too feeble a quantity, will not escape the gravitational integrity of the source mass. And mass is only a 'mass of energy' until a unit quantity specific to a unit volume is determined which exhibits the characteristics we associate with matter, not least of which is longevity.

Much to chew on. It would be nice to hear what people with well developed math would have to say. I honestly get to a point, where I exceed my own limitations in trying to gather new knowledge in a way I can assimilate, and find myself as I have recently, on the threshold of not knowing a damned thing. It's time for me to step back and focus on other things that don't require much focus. Cordially, jrc

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