A World Without Quanta? by Constantinos Ragazas

Hello Constantinos,

As promised, I'm posting my comments on your essay. I'm not sure, if you will like it, but I've tried to do my best.

The main result is a claim that the well-known Planck radiation law could be derived mathematically, as " an exact mathematical identity (a tautology) that describes the interaction of energy". The presented derivation is based on the "Mathematical Identity" Eq.(1), where the r.h.s. depends on the average value Eav. Notice that the demanded integrability of E(t) is generally not sufficient for the existence of Eav, E(t) have to be at least continuous on the respective closed intervals. If Eav exists, then Eq.(1) becomes a trivial identity [math] \eta = \eta [/math] In my opinion, Eq.(1) and the whole "mathematical machinery" developed in the associated papers is rather superfluous for the task of "reverse engineering" the Planck formula. Instead, a direct calculation of Eav gives immediately

[math] E_{av} = \frac{1}{\tau}\int_{0}^{\tau}E_{0}e^{rt}dt = \frac{E_{0}}{r\tau}\left[e^{r\tau} - 1 \right] [/math]

and hence

[math] E_{0} = \frac{E_{av}r\tau}{e^{r\tau}-1} [/math]

which takes a Planck-like form. Assuming that the exponentiated expressions are equal

[math] r\tau = \frac{h\nu}{kT} [/math]

we get

[math] E_{av} = kT, \; \tau = \frac{h}{kT} [/math]

exactly as stated in your presentation. The assumption that

[math] \eta = h [/math]

is not needed here, notice also that the limit in Eq.(3) enforces that

[math] \eta = 0 [/math]

in contradiction to the previous statement (!)

The next problematic thing is the assumption that E(t) applies to the "sensor' rather than to the "source", because it seems to imply that the "source" radiates only when the radiation could be absorbed by an appropriate "sensor", tuned to the proper frequency. Notice that such a behavior would be rather awkward and, to my knowledge, was never observed.

The postulated "undefined and undefinable prime physis" fundamental quantity is another highly problematic thing. Several contradictory statements about the mysterious \eta quantity are scattered over the essay and the associated papers. According to the energy, momentum and force definitions given on page 4 of the essay it have to be a sufficiently smooth function of position and momentum variables. Later, on page 6, according to the discussion of the Schroedinger equation, it should be rather a complex-valued function to accommodate for the in general complex-valued wave function. Finally, while discussing the Planck constant h, there is a statement that "\eta can be any value". To my knowledge, a quantity which is compliant with all this statements cannot exist.

Well, maybe it means that a world without quanta cannot exist either ?

Best regards,

-Joachim.

Dear Joachim,

Thank you for taking the time to not only read my essay and referenced papers, but even to critique these on paper. I will try to answer you as clearly as I understand your points. Some of the mathematical notation did not clearly come through in the text and I'll try to piece together what you may have meant from the text itself.

1) "Notice that the demanded integrability of E(t) is generally not sufficient for the existence of Eav,"

I am not sure what you are saying here. If E(t) is an integrable function, then the integral of E(t) over an interval [0,t] must exist. And if such an integral of E(t) over an interval [0,t] exists, then certainly the 'average E' over that interval [0,t] must exist since this by definition is nothing but the ratio of the value of the integral over the interval. But this is just too simple to have escaped you! So you must have something else in mind! Whatever that may be, however, it is NOT what I have in mind. The math is clear and simple.

2) You write, "If Eav exists, then Eq.(1) becomes a trivial identity ".

Well YEA! That is a simple identity! But 'trivial' is a subjective assessment. That this simple mathematical identity leads to Planck's Law makes it not trivial at all, in my thinking!

3) You write, "Instead, a direct calculation of Eav gives immediately ... "

[sorry I can't cut/paste your equations here!].

Joachim, if you feel that calculating Eav is simpler, go for it! I don't see your point. Notice the clumsy backtracking that you are forced to do at the end of that series of derivations.

4) You write, "The assumption that η = h is not needed here"

That's because you made even bigger assumptions comparing Planck's Law with what you derived and setting exponential expression equal. I purposely wanted to avoid just that! But if you are comfortable with what you've done then I have no problem with this. Either way you are showing (as I am showing) that Planck's Law can be derived without using energy quanta. And that raises the possibility for "A World Without Quanta" existing!

5) You write, "notice also that the limit in Eq.(3) enforces that η = 0 in contradiction to the previous statement (!)"

Perhaps the mathematical limit enforces that η= 0. But since we cannot measure in physics below the threshold h, we have for all experimental purposes the mathematical limit produces once again Planck's Law. But as a best possible approximation rather than exact identity. And with lesser restrictions on E(t) - namely that E(t) be just any integrable function and not an exponential.

6) You write, "The next problematic thing is the assumption that E(t) applies to the "sensor' rather than to the "source", because it seems to imply that the "source" radiates only when the radiation could be absorbed by an appropriate "sensor", tuned to the proper frequency. Notice that such a behavior would be rather awkward and, to my knowledge, was never observed."

The 'sensor' is where measurement takes place or energy is absorbed. The 'interaction of measurement' is a functional relationship between the intensity of energy, the energy absorbed by the sensor, and the average energy. I simply wanted to contrast this with the traditional way Planck's Law was derived. You can choose to make something else of this, or not. If you do seek to make something else out of this distinction beyond what I was intending, then I am afraid you'll be missing the real point of my derivation - which is and remains as showing that Planck's Law is a mathematical identity that describes the interaction of measurement. It is a mathematical identity no less than the Pythagorean Theorem -- with application to Physics.

7) You write, "The postulated "undefined and undefinable prime physis" fundamental quantity is another highly problematic thing."

What I wanted to highlight with this is that starting with the quantity η it is possible to define and to mathematically derive Basic Law of Physics. I only gave a thumbnail sketch of this. Much is left out and needs to be filled in by others as well. I purposely avoided any discussion about any specific properties. But you are absolutely correct in that the definitions of energy, momentum, and force do require that η be smooth. I only alluded to Schrodinger's equation as having the same underlying form as the definition of energy I give. I simply overlooked all constants and i in making such very broad comparison. But that's all. It is meant only as an interesting suggestion for others to consider.

Hope I adequately addressed your points.

Best wishes,

Constantinos

Hello again Constantinos,

Let me clarify my points:

1) If E(t) is not continuous in [0,t], but only integrable, then Eav may be "out of range", i.e. not allowed as a value of E(t). Certainly, exponential real functions used in your derivations are extremely regular and not affected by such problems. Indeed, "the math is clear and simple" in such cases, but nevertheless the general statements are flaved when seeen as rigorous mathematics.

2) Well, I guess that starting from Eq.(1) it is possible to promote many known relations or "laws" to "mathematical identities (tautologies)" in a similar way, the key is here to find the right, sufficiently regular functions (like exponentials in your essay) and a justification to fix appropriately some "free parameters" (like Eav=kT)

3) Indeed, it is a "clumsy backtracking" :-) Or a "fit" if your permit, which sounds more "scientific" :-) But your approach is, in my humble opinion, in the same league, only done in a different, rather excrutiating way.

4) Well, a "fit" is always only a "fit", even if done in different steps. I do not think, that it may be regarded as a "mathematical derivation of the Planck Law".

5) In a mathematical approach to physical problems we cannot change the rules because of some physical limitations or constraints, otherwise we may get at best some heuristics, if not plainly wrong results. We may of course change the employed mathematics and, e.g., use nonstandard analysis instead, but always in consistent way!.

6) From the physical point of view, a blackbody radiates because it is a blackbody, and the Planck formula describes that radiation sufficiently well when compared with experimental data. There are several known derivatons of the Planck formula, the Einstein derivation [Phys.Z.18, 121 (1917)] based on a two-level model involves also an exponential form for E(t) at the "source". But it is not only a"fit" or Ansatz there, as it reflects the statistics of the radiating atoms at thermal equilibrium, i.e. it tells us something about the possible radiation mechanism.

The measurement of the blackbody radiation is another story, and if we want to measure the radiation itself, we have to eliminate somehow the detector influence, usually through proper setup and calibration. The detector radiates too !

The model presented in your essay tries to describe the interaction between the radiating blackbody and a detector working in a very specific way and it is at the same time claimed that it reflects exactly the radiating blackbody. This is a wrong approach in my opinion, although it may lead nevertheless to a correct formula. The Ansatz for E(t) (I mean here the formula itself) does not allow for a differentiation between the "source" and the "sensor".

7) The statements about the "prime physis" quantity that may be found at various places in the essay and the papers are really confusing. Particularily, the identity \eta=\eta, remainded me at some point the famous verse "I am that I am" from the Torah.

Going down to earth, "prime physis" have to be rather an action functional, maybe something in the spirit of the Hamilton-Jacobi or Hamilton-Jacobi-Bellman approaches. In principle, it should allow to derive most of your statements about energy, momentum, etc., without sacrifying mathematical rigor. On the other hand, I'm afraid that it would be hard to get some new physics out of it, or even some new results in that way, unless the system under consideration will be sufficiently complicated (as, e.g., in Ref.18 or Ref.20).

Best regards,

-Joachim.

Hello Joachim,

Let me clarify your points:

1) You write, "... Eav may be "out of range", i.e. not allowed as a value of E(t)". Nowhere in any of my results is Eav associated with a particular time, say E(t) = Eav. So this objection is mute and inconsequential.

2) You write, "... I guess that starting from Eq.(1) it is possible to promote many known relations or "laws" to "mathematical identities (tautologies)" in a similar way".

Certainly mathematical identities can be applied to physics whenever appropriate. I am using this 'trivial' mathematical identity Eq.(1) to derive Planck's Law. But if you know of other such applications of this 'trivial' identity to physics, I'd be very happy to know about them? But what's your point? Say there were 100 more such applications (like there are probably for the Pythagorean Theorem), does that take away anything from this application to Planck's Law? Please ...

3) You write, "...I do not think, that it may be regarded as a "mathematical derivation of the Planck Law"."

Actually, I am showing Planck's Law is only a reflection in Physics of a larger mathematical truth! Planck's Law I show is not a 'Law of Physics' but rather a Mathematical Identity applied to Physics. In much the same way that we can apply the Pythagorean theorem to measure distance. Here, we are measuring 'intensity of energy', knowing the amount of energy that is absorbed at a given temperature. Of course, this happens when measurement is made! And that is exactly why the experimental blackbody spectrum is indistinguishable from that obtained using Planck's Law!!!

4) You write, "In a mathematical approach to physical problems we cannot change the rules because of some physical limitations or constraints,..."

What rules am I changing? Or do you mean our 'views' which in fact do constraint us and mentally limit us? Physics has failed to provide us with a 'physical view' that 'makes sense'. It's time we change the rules! We can start with a proper understanding of Planck's Law as a mathematical identity that describes the interaction of measurement!

5) You write, "From the physical point of view, a blackbody radiates because it is a blackbody,"

Oh! And I thought it was because of some oscillators that clink on to the wall of a furnace! Now I know better! It is really because "a blackbody radiates because it is a blackbody". That makes perfect physical sense. Thank you!

6) You write, "... the identity \eta=\eta, remainded me at some point the famous verse "I am that I am" from the Torah"

That's the nature of IDENTITY! You should read the Torah more faithfully. It contains much truth!

7) You write, "..."prime physis" have to be rather an action functional..."

I left eta as an undefined quantity in my essay. Thus, all the results I have listed are purely mathematical and very general. Of course, these mathematical results are Basic Law in Physics - such as Newton's Second law of Motion, Conservation of Energy and Momentum, Kinetic Energy, Boltzman's Entropy Equation, etc. Planck's constant is such a quantity eta! Eta can be thought as being both 'action' as well as 'accumulation of energy'. All these results are obtained without prescribing any structure or properties to eta. If we were to give eta more specific structure, we will be able to obtain more results! I can only do so much! Perhaps you can do more ...

Best,

Constantinos

Constantinos,

let me try once again, hopefully this time with more success:

1) It seems that either "integrable" is synonymous to "continuous on closed intervals" in your essay/papers, or you questioning some well known mathematical results. As I wrote, only the general statements involving "any integrable function" are problematic. If still in doubt, then consult a reasonable calculus handbook or ask a friendly mathematician.

2) Well, just try the same with the Fermi-Dirac distribution, with the Ansatz E(t)=E0e-rt and apropriate "fit", this time fitting for -rt, and voila, you have it!

But it is only "the art of fitting", nothing more.

You skipped my point 3), does it mean that you agree with me here ?

In the following 3) below refers to my point 4), and so on.

3) "Mathematical truth" refers to formal constructions, developed in an axiomatical/deductive way, while "physical truth" reflects the knowledge gained from experiments. In theoretical physics, mathematical methods are used to model the "physical truth", maybe with predictive results, but nothing more. Even the most elegant results have to be rejected if not confirmed experimentally. Sure, Pythagorean theorem may be used to measure distances, but this theorem does not impose that the physical space is Euclidean!

4) You wrote "What rules am I changing ?" Let me cite your answer on the pointed out contradiction:"Perhaps the mathematical limit enforces that \eta= 0. But since we cannot measure in physics below the threshold h, we have for all experimental purposes the mathematical limit produces once again Planck's Law"

It seems that you simply ignore the results that are inconvenient.

5) The blackbody radiation is a property of the blackbody, therefore in a sense "blackbody radiates because it is a blackbody" as I wrote in my previous posting in a somewhat strange-looking wording.

If you determine the radiation spectrum of some object, and it can be identified as blackbody spectrum corresponding to a definite temperature T, then this object is identified as a blackbody heated to the temperature T.

It seems that you ignored the rest of my point 6) ? Because I think it is important, let me repeat it below:

--------

The measurement of the blackbody radiation is another story, and if we want to measure the radiation itself, we have to eliminate somehow the detector influence, usually through proper setup and calibration. The detector radiates too !

The model presented in your essay tries to describe the interaction between the radiating blackbody and a detector working in a very specific way and it is at the same time claimed that it reflects exactly the radiating blackbody. This is a wrong approach in my opinion, although it may lead to a correct formula. The Ansatz for E(t) (I mean here the formula itself) does not allow for a differentiation between the "source" and the "sensor".

--------

In other words, a blackbody radiates in approximately the same way when measured or not. Just imagine a device for remote temperature measurement, do you think that the temperature of the measured object is as indicated on the device only during the measurement ? And what when the device is broken ?

6) Although I agree with your statement about Torah, I'm still confused by the contradicting statements about \eta, see below

7) You wrote: "I left eta as an undefined quantity in my essay. Thus, all the results I have listed are purely mathematical and very general."

Pardon me, but it is simply impossible to derive _any_ results for an undefined quantity. Or I'm missing something important here ? Maybe you mean the physical interpretation of \eta, not the definition ?

Any mathematical construction needs a non-contradictory set of axioms, definitions, etc., otherwise it is _not_ mathematics for sure.

You wrote also: "Perhaps you can do more ..." Maybe, but I'll definitely start from checking the present status of such approaches, look for similarities, etc. One could waste a lot of time trying to crack open doors!

Best regards,

-Joachim.

Joachim,

I can see that you like to argue! Me too! This can go on for a very long time! Hope one of us gets tired of this soon!

You write: "...consult a reasonable calculus handbook or ask a friendly mathematician."

My background is mathematics! An 'integrable function' is by definition one whose integral EXISTS! And if the integral exists over [0,t] than the ratio of the integral over the interval also exists. By definition this ratio IS the AVERAGE! Please ...

You write: "You skipped my point 3), does it mean that you agree with me here ?".

No I do not agree with you! I just got tired of addressing irrelevant trivialities whose only aim is to divert the discussion from the more salient relevant points.

I think I will stop with that!

Constantinos

Dear Constantinos,

Indeed, our discussion seems to lead nowhere. I do not think that my points are only "irrelevant trivialities", just ask another competent persons about that.

I wrote my comments only because you asked for it, and because we are here at FQXi to discuss even the strangiest things.

All the best and good luck with your efforts,

-Joachim.

Constantinos,

Okay and thanks for the reply.

Kind regards,

Alan

I'm still rooting for you brother! :) May your heart be at peace, and your mind beautiful.

Yasu Constantinos

As I understand it your essay and addenum are mathematical elucidations of a physically realistic model of physics based on a unique new derivation of Planck's constant (h). That is great. You singled out Einstein's quantum assumption as the basis of the conceptual troubles that faced quantum mechanics later on. I fully agree with your approach and think that that the idea (that the photon is a point in space as well as a package of energy) is at the basis of half the trouble with the foundational understanding (and future development) of physics today. I have presented my reasons for that in my present fqxi paper and also in the earlier 2005 Beautiful Universe paper on which it is based.

You have presented the idea of energy absorption in "equal-sized sips" that is only manifested when 'delta E' energy is accumulated. As I understand this is somehow related to the so-called 'semi-classical theory' that has been debated following Einstein's 1905 paper and then abandoned when Schrodinger presented his equation. I liken the gradual absorption of energy in the sensor and its sudden release to that of water in the Japanese garden 'deer-chaser' mechanism .

The other half of the trouble with physics today that you do not deal with (gravity and quantum mechanics incompatibility) is also due to one of Einstein's assumptions - the constancy of the speed of light in SR (and GR) and again the sensible objections raised at the time were swept away by SR's success, albeit for the wrong reasons. I wish I had your skill to describe my physical intuitions in mathematical form! Incidentally your continuous derivation of planck's constant (h) solves a fundamental problem in my own theory: the spinning of the universal node I theorized is continuous yet the transfer of momentum is in units of (h). Your formulation can explain that little problem.

Best wishes from Vladimir

Hello Vladimir, and thank you for your good wishes.

I am pleased that we agree on many important points. Certainly what I have demonstrated in my papers and essay is that it is possible to have "A World Without Quanta" and demystify Physics of the many counter-intuitive and non-sensical results. 'Physical Realism' in Physics is not only possible but necessary!

Have you read my very short proof of the proposition that "if the speed of light is constant, then light is a wave"? This is a mathematical proof that shows Einstein's CSL postulate contradicts his 'photon hypothesis'!

What more need we say! Furthermore, as I argue in the essay, the Second law of Thermodynamics requires that every physical event takes some positive duration of time to occur. It cannot occur 'instantaneously' at t = s. Thus, the whole concept of 'spacetime continuum' where a 'physical event' is represented by (x,y,z,t) contradicts Thermodynamics.

Constantinos

Dear Constantinos,

More power to us to help demystify physics - I cannot imagine it will be easy to do that using our partial forays against this or that concept - it is all connected, and unless it is all re-written correctly from scratch it will not be a clear and simple theory.

I mention this because your starting point is accepting the c=constant hypothesis, then you cleverly show that assuming light velocity is constant implies wave motion, On the other hand you reject the concept of spacetime because of the thermodynamics argument. However the constancy of the speed of light is the basis and reason for flexible and continuous spacetime. This may constitute a contradiction?

In my theory I assume that light velocity in vacuum is not constant but is a maximum of c and slows down in gravitational fields - the concept of spacetime has to be trashed once and for all, and the Lorentz transformations applied in an 'absolute' universe as I have outlined.

Best wishes from Vladimir

Hello Vladimir,

You write, "...your starting point is accepting the c=constant hypothesis...".

Just to clarify this point, nothing in my essay or papers assume CSL. It is not needed, it is not necessary, it is not relevant to my work. To tell the truth, I really have not much considered SR or GR in my work, with the exception of the spacetime continuum. And this only in the context of my results concerning entropy, time, and the Second Law of Thermodynamics. For me it makes so much sense that there must be a positive duration of time for any physical event to occur. That it just is plainly false to talk about 'events' happening instantaneously at t = s.

I believe that CSL must be derived and not simply assumed. I have some ideas how that can be, which are in line with what you argue: that c is a maximum but the speed of light can vary in a 'vacuum'. One problem! I don't believe in 'vacuums'. Though we can think and consider 'empty space' as a mathematical abstraction, physically and philosophically it does not make sense. 'Physical space' by definition can't possibly be 'empty'.

All the best,

Constantinos

Hello Constantinos

Sorry if I misunderstood your ideas. I too do not believe in the vacuum (in my theory everything - matter space, radiation is made up of the lattice nodes, but I used the word vacuum to stress the fact that the speed of light can change in a gravitational potential in space...a different case than when it slows down while passing through a transparent medium such as glass or water (refraction). In fact the two effects are identical in my theory ...

It is interesting to think of things this way: Einstein proposed CSL = contracting space / dilating time. In other words observations are absolute (light) but spacetime are relative. This is so physically unrealistic and unnecessary. Rather, think of it this way: c = variable measured distance traveled / fixed (absolute) time interval. In fact as many have argued - a time interval can be thought of as a change of state of the entire universe and there is not time dimension. I wonder how the laws of thermodynamics can be stated in such a world?

Best wishes from Vladimir

Dear Vladimir,

I am entirely guided by 'physical realism' in all my reflections and reasoning in physics. I have as much trouble with 'lattice points' as I do with 'vacuums'! Does that mean that 'vacuums' and 'lattice points' cannot be considered? I don't go that far. Certainly these and other abstract mathematical formulations have been successfully used in physics.

But here is my problem with all this. We do not 'know' what all these results so obtained mean! These don't 'make sense' to us, though we believe these have 'mathematical certainty'. Physics, unlike mathematics, requires more of us. Having 'mathematical certainty' is not enough! We must also maintain the connection of our ideas with our 'senses'. Who do you trust to know the truth about time-travel. The 'man in the street' or the 'theoretical physicists'?

Simply put, all my efforts are to 'find meaning where meaning is not found'. I have done that successfully with Planck's Law; showing that the counter-intuitive concept of 'energy quanta' and 'bundles of energy' is not necessary. In my essay I prove that Planck's Law is a 'mathematical truism' and not a 'physical law' and can be derived continuously without statistics.

Have you discussed your ideas with Peter Jackson and Ray Munroe? They may be more in tune with this than I.

Best wishes,

Constantinos

Dear Constantinos,

You are more focused in your approach to physics than my rather swashbuckling forays into imagined worlds of nodes gyrating to create us and our universe!

Perhaps both our approaches are necessary, considering how mainstream physics seems to hover between the entrenched even ossified positions of many physicists, with the wild quantum-weirdness-many-universes infinite dimensions where 'anything goes' seems to be the slogan. Both Peter Jackson and Ray Munroe have already kindly encouraged me with their stimulating responses. I should spend more time on physics and hope to do so. More power to them and to you.

Vladumir