Continuation Causes Superior but Unrealistic Ambiguity by Eckard Blumschein

Eckard Blumschein

Dear Ben,

I apologize for not yet having read your essay. Thank you very much for already responding to mine.

1. Let me give a primitive example first. Imagine a cube with sides of length a. Volume V grows with a^3. Surface S grows with a^2: S/V=a^2/3.

Many decades ago, in order to easily investigate the eddy currents within a small metallic disc rotating through a magnetic field of a power meter, an enlarged analog model was build. Each dimension was enlarged by the same factor. The results were horribly wrong.

2. Yes. An similar example is to be seen in the ripples shown in my Fig.1. Notice: Those who were only familiar with the traditional FT-based spectrogram could not believe that this obviously causal and also with respect to other features more realistic figure was correct because it seemingly violated the uncertainty relation, which is to be seen valid just for discrete lines on the ridges of the continuous ripples.

3. With "completely digital structure" I meant quantization also of space and time. Because this is hard to imagine, I asked Lawrence Crowell for his fractal picture, and he showed it. Not just for Charles S. Peirce but also for Schroedinger, space and time were continua. Hopefully you got aware that and why I consider not just point charges, line currents, singularities and the like very useful but strictly speaking unrealistic ideals, but I consider continuous functions like sin(omega t), when thought to extend from minus infinity to plus infinity, also just unrealistic fictions.

4. I referred to what Minkowski himself wrote. By the time I will carefully read what you have to say concerning Lorentz tranformation.

5. My emphasis was on "only on condition", meaning in principle perhaps not. Acoustical cavities and coaxial electric cables admit longitudinal waves with very low frequency, too.

Best regards,

Eckard

Eckard Blumschein

Dear Doug,

Andy Akhmeteli pointed me to a different "clarification" by John Baez: "Division Algebras and Quantum Theory" arXiv 1101.56904v:

"Abstract: Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the "three-fold way". It is perhaps easiest to see it in the study of irreducible unitary representations of groups on complex Hilbert spaces. These representations come in three kinds: those that are not isomorphic to their own dual (the truly "complex" representations), those that are self-dual thanks to a symmetric bilinear pairing (which are "real", in that they are the complexifications of representations on real Hilbert spaces), and those that are self-dual thanks to an antisymmetric bilinear pairing (which are "quaternionic", in that they are the underlying complex representations of representations on quaternionic Hilbert spaces). This three-fold classification sheds light on the physics of time reversal symmetry, and it already plays an important role in particle physics. More generally, Hilbert spaces of any one of the three kinds - real, complex and quaternionic - can be seen as Hilbert spaces of the other kinds, equipped with extra structure."

This does of course not answer my original question, which was already answered by your hint with the "point in the middle left over". Nonetheless it shows to me that mathematicians like John Baez do not devote the due attention to what I consider important: the question of redundancy and ambiguity.

Regards,

Eckard

[deleted]

Dear Eckard,

While there is no negative distance in reality, there definitely is a left and right, an up and down and a backward and forward, relative to a selected position, and since space is usually defined as a set of positions satisfying the postulates of geometry, I think it important to not throw the baby out with the bathwater.

Sir W. R. Hamilton was an English astronomer and mathematician who coined the term "vector," first explained complex numbers as coordinates on a graph (or rotation made possible by an imaginary number), and is credited with the invention of quaternions (even though a Frenchman beat him to it and understood the true nature of quaternions better).

It was based on his ideas that Pait, arguing for Hamilton's quaternions, took on Heaviside and Gibbs, and lost the battle with their vector algebra, which has dominated ever since.

However, quaternions found a new life in computer calculations, since it greatly simplifies the manipulations of 3D rotations and avoids gymbal lock. They were mostly revived by David Hestenes, who first recognized the value of the ideas of Grassmann and Clifford and popularized them through his modification of Grassmann's geometric algebra (GA) (see here).

GA is slowly gaining acceptance, since it greatly simplifies vector algebra through the use of new concepts and definitions that combine scalars and vectors in something called the geometric product. It has to do with rotation and an inner and outer product.

As I mentioned, it was Hestenes' work on GA that drew attention to the work of Hamilton, Grassmann and Clifford, and it was mostly centered on the set of Clifford algebras upon which his work sheds so much light.

This lead me to a little known essay by Hamilton that is called "Algebra as the Science of Pure Time." Most people think that it was based on Kant's ideas of time. I don't think it has anything to do with the Greek concept of the continuum as a moving point.

It focuses on the comparison of moments of time, where we can say that two moments may be coincident, or else one is later or earlier than the other. Of course, his development was confined to the observer's frame of reference in the abstract.

Eckard Blumschein

Dear Doug,

The paper "THEORY OF CONJUGATE FUNCTIONS,OR ALGEBRAIC COUPLES; WITH A PRELIMINARY AND ELEMENTARY ESSAY ON ALGEBRA AS THE SCIENCE OF PURE TIME" by the Irishman Hamilton does indeed play a role in the history of complex and hypercomplex numbers. Nahin deals with the certainly more important former.

Steve Dufourny (I hope our Wallonic friend will forgive me if I misspelled his name), blamed me repeatedly for vanity. Is it really bad if I am convinced that so many so famous experts including Hamilton, John Baez, and Ken Wharton neglected a trifle? I consider essential what Claude Shannon formulated roughly as follows: While, in principle, the past is known to us but we cannot change it, the future is, in principle, unknown to us but can be influenced.

No matter how we interpret free will, I do not see any justification for the belief in a fatalistic block universe. Is it vanity to say that tense-less mathematical physics does not yet obey what is well considered in ordinary language?

To some extent I agree with the essay by Hadjidakis "Has the time ...".

You wrote:

"While there is no negative distance in reality, there definitely is a left and right, an up and down and a backward and forward, relative to a selected position, and since space is usually defined as a set of positions satisfying the postulates of geometry, I think it important to not throw the baby out with the bathwater."

Well, we are almost free to choose the origin of our coordinate systems. Almost means: The domain of certainty ends and the domain of possibilities begins in reality at the point NOW. You certainly know the famous sentence: Give me a fix point, and I will turn the world upside down. Notions like left and right, up and down, forward and backward refer, as you correctly wrote, to a selected position. In other words, they are relative ones.

Are there logical, natural limits? I think so. Any distance cannot be negative. Likewise, elapsed time is always positive. The sliding relative to our ordinary time scale point NOW is a fix point that allows us to turn theories upside down that are obviously leading from one paradox into the next one. Blame me for vanity. I apologize for hurting so many. I do not consider myself a PC potato watching the anticipated movie of my past and future life. Please accepts this as to grasp in what sense redundancy grows from R to R to C and so on.

Regards,

Eckard

Regards,

Eckard

[deleted]

Dear Eckard,

When we consider the approach of the pendulum to the plumb line, the plumb line is definitely in its future. If the plumb line and the arc of the pendulum's swing are divided into n and m parts, respectively, then we can describe the projected position of the pendulum on the plumb line in terms of x/n, as x --> n, and the actual position of the pendulum in terms of y/m, as y --> m.

I think that we can all agree that a "now" moment arrives when x = n and y = m. However, the plumb line is still in the future of the pendulum at this point, since both n and m cannot be points of no spatial extent, but only magnitudes of some extent, ad infinitum. Clearly, we cannot say that the two are coincident, until both 1/n and 1/m --> 0.

Yet, if we are to measure the diminishment of these two remaining units, we have to further sub-divide them into n and m parts, and the process starts over, ad infinitum. Hence, we see that Zeno's paradox is in full force, in this case, even though we know that x --> 0 and y --> 0, eventually.

How do we resolve this paradox? I submit that one way is to transform the remaining y unit into its inverse. Since x is wholly dependent on y, it can serve as a measure of y's transformation into its inverse. When y's transformation is complete, x = 0.

But what is the inverse of y, if not -y? and doesn't x --> 1, in the other "direction," as y --> -y? How, then, does x --> 0 and x --> 1, simultaneously? The only way to resolve this new paradox, as far as I can tell, is to admit that x too has an inverse, namely -x. Consequently, as y --> 0, -y --> 1, simultaneously, and as x --> 0, then -x --> 1, simultaneously.

Such a transformation, in both cases, involves an instant change in "direction," at all "points" along the length of the units. It is only at this boundary between the two, opposite, "directions" that we can consistently define a point of no spatial extent and an instant of no temporal duration.

The physicists describe just such a constant transformation, as the potential energy of position is transformed into its inverse, the kinetic energy of motion and vice-versa. Therefore, this approach not only seems reasonable to me, but exhibits a hint of that unreasonable effectiveness of math in the natural sciences, that Wigner points out.

Warm regards,

Doug

[deleted]

Dear Doug,

You intended to demonstrate that negative quantities are necessary. Well, this is true for mathematical physics with emphasis on mathematical in a derogative sense. I see so called harmonic oscillator as well as your pendulum as examples for strictly speaking unrealistic models. In reality, no oscillator oscillates for good.

You might argue that for instance sound pressure is the alternating components of atmospheric pressure. Maybe you heard of mammals blooding out of their ears because they were exposed to 210 dB re 20 microPa. Yes, I refer to whales in water. Air cannot convey symmetrical waves of such SPL because there the negative half wave is limited to the atmospheric pressure.

In your example, neither kinetic not potential energy is negative. If I recall correctly, energy typically corresponds to distance from origin in phase plane, and realistic trajectories of stable systems are strictly speaking inward directed spirals. What about your definitions of x and y, aren't they arbitrary?

You wrote:"Such a transformation, in both cases, involves an instant change in "direction," at all "points" along the length of the units. It is only at this boundary between the two, opposite, "directions" that we can consistently define a point of no spatial extent and an instant of no temporal duration."

Really? Isn't this at odds with Euclid's definitions of a point as having no extension in general and of a number as always denoting a measure, not a point?

While quantities like distance and elapsed time do not have an inverse, differences between distances or between elapsed times can of course be negative. Consequently, the logarithm of e.g. a relation between two distances can also be negative.

As long as physicists always prefer the "more general" R instead of the tailor-made R, people may continue mocking: mathematical physics is if three out of two men left a room and therefore one man has to come in as to make the room empty.

Warm regards,

Eckard

[deleted]

Dear Eckard,

You wrote:

"In your example, neither kinetic not potential energy is negative. If I recall correctly, energy typically corresponds to distance from origin in phase plane, and realistic trajectories of stable systems are strictly speaking inward directed spirals. What about your definitions of x and y, aren't they arbitrary?"

Well, of course, but we need labels. No one is arguing the ontology of negative cabbages. However, if the point of the plumb line, which the location of the pendulum crosses, is designated '0' then, according to normal convention, we can label the top of its swing to the right as positive 1, and the top of its swing to the left as negative 1.

Even though both of these poles are positive, in the sense that the rise of their swings is in opposition to gravity, the location of the pendulum at either pole is the result of motion in two, opposed, "directions." If we plot the motion, and correlate it with potential and kinetic energy, we can see how the two types of energy are inverses:

Position of Pendulum: -1, 0, +1

Energy of Position: -1, 0, +1

Energy of Momentum: 0, 1, 0

Thus, the fact that kinetic energy is the inverse of potential energy does not require negative reality, only negative labels to describe the reality.

Wouldn't you agree?

Regards,

Doug

[deleted]

Dear Eckard,

You wrote:

"This does of course not answer my original question, which was already answered by your hint with the "point in the middle left over". Nonetheless it shows to me that mathematicians like John Baez do not devote the due attention to what I consider important: the question of redundancy and ambiguity."

The reason this is so, I believe, is due to the fact that they have had to construct the 1D, 2D and 3D inverses by inventing real numbers and imaginary numbers. They invented real numbers via logic and symbols, and imaginary numbers via rotations.

In a sense, by combining these ad hoc inventions, they have been able to increase the algebra of 20 (the reals, R), to 21 (the complexes, C), to 22 (the quaternions, H), and to 23 (the octonions, O), but the O algebra is non-associative. Hence, they run into problems with trying to use it in physical theory.

Since the algebra of C only lacks the distributive property, they mostly use it, but evidently they can use the R and the H algebras, as well (the latter probably as H+H).

But what they would really like is an R3 algebra that has all three division algebra properties intact. The fact that R- is redundant to R+ and that the arrow of time has to be added to remove ambiguity in physical interactions modeled with DEQs, is not immediately relevant to their challenge of pathological algebras that they are having to cope with, though it might still be after a solution is found.

Regards,

Doug

[deleted]

Sorry, "1D, 2D and 3D inverses" should read "1D, 2D and 3D algebras."

Eckard Blumschein

Dear Doug,

You wrote: "... we need labels."

I agree that use of labels is superior. However, I maintain: Redundancy and arbitrariness can be avoided in principle by choosing an appropriate point of reference.

You are quite right: "if the point of the plumb line, which the location of the pendulum crosses, is designated '0' then, according to normal convention, we can label the top of its swing to the right as positive 1, and the top of its swing to the left as negative 1."

However, the normal convention is arbitrary.

Just add what you wrote:

"Energy of Position: -1, 0, +1

+Energy of Momentum: 0, 1, 0"

The sum is strange: -1, 1, +1

You wrote: "Thus, the fact that kinetic energy is the inverse of potential energy does not require negative reality, only negative labels to describe the reality."

I consider the sum of kinetic and potential energy in a closed system constant:

sin^2(x)+cos^2(x)=1.

"Wouldn't you agree?" I would like to do so because I need supporters in this contest, and I hope it is for you just a little step to accept what I consider a key.

Isn't there still growing confusion not just among students who have to swallow an abundance of allegedly counter-intuitive theories from Cantor's transfinite alephs up to white holes? I observed even here in the contest a widespread readiness among laymen to spontaneously welcome new suggestions ranging from a variable Planck's constant by Constantinos Ragazas to Peter Jackson's exciting ideas and the tendency among experts to favor overly formalized "serious" speculations. Not even Georgina Parry did consequently challenge idolized theories. I consider my arguments in Appendix C strong ones. I just avoided to open one more frontal attack.

Best regards,

Eckard

pjackson

Hi Eckard.

I will clarify;

"The LT is not required as the light signal from the centre of the stream only does c"

The LT was essentially used by Einstein to prove the limit 'c' for all (co-moving) observers. That is what I refer to it as being "REQUIRED" for. . - BUT, if an observer only receives light at 'c', and the light 'pulse' he observes is only MOVING at 'c', the LT is simply superfluous! It was a mistake not to understand the point, which Georgina has taken up and proved well, that 'apparent' velocity from another reference frame is not the same as actual velocity. The light signals from the pulse to the observer are new, 'scattered' (and polarised) signals, in sequence one after the other, giving only the 'impression' of something moving at c

pjackson

Eckard

My clarification /answer in the above thread missed this;

"we must now resort to the big gun with a curved trajectory to falsify our model; GR."

It was a bit of a play on words, a 'big gun' as the ruling paradigm of General Relativity, as both big guns and GR have curved trajectories! but also to give it the sternest test; How would the DFM stand up under the test of GR and gravity!

It's opened up an astonishingly simple solution, and I've since gone further; Have you ever wondered how a passing asteroid can exert more gravity on us if it moves faster? That's what inertial/gravitational mass equivalence says. Stupid? Perhaps not, as the DFM shows how it works. Add up all the plasma ions (photo-electrons) with inertial mass but zero rest mass (they evaporate at rest), that grow around matter accelerated in a void (i.e. the LHC pipe) proportionally to speed, and we find it perfectly equivalent!

It was also found that the (quantum particle) plasma coma/tail of a comet did have that gravity as it 'bent' and dilated space time (diffracted through the plasma halo) by 2 arc secs, exactly as predicted.

Of course this may look, waddle, swim and quack like a duck but not be one. So do we all ignore it? I anyway decided that while everyone else was away hungrily searching for quantumish relatives of my similitudinal 'ducky' thing I'd try roasting it with some orange. It tasted perfect! I offer everyone as much as they wish, (including as sandwiches while off looking for those mysterious ducks if they wish).

I hope you might try a taste?

Peter

Eckard Blumschein

Dear Peter,

I blame my age for feeling not in position to immediately understand your many metaphors and claims.

My dictionary gave stern, sterner, sternest for something very serious and strict, OK.

DFM seems to be your private abbreviation, and if D stands for digital, I did not yet understand how this is meant.

The sentence "How would ... !" does not end with a question mark.

In all, your overly emphatic style will perhaps not be appreciated by peers.

I got the impression you evaded the question whether or not you consider the Lorentz transformation appropriate and correctly interpreted. Am I wrong in that?

Regards,

Eckard

pjackson

Eckard

Sorry, I'd referred to the Discrete Field Model (DFM) previously and in my essay, I too easily forget it does need repeating. The question mark what missing by convoluted English convention due to its rhetorical nature, as it wasn't a quote or a 'fresh' question but an explanation of the question I had asked.

I must also remember metaphors can be lost in translation, and respect and thank you for your view on what I also recognise as apparent over assertiveness. I've been previously criticised for 'understatement', and wished to be more 'direct' but seem have over compensated.

Lorentz Transformation (LT) Sorry, It seems I wasn't 'direct' enough there! In the DFM the LT as currently applied is shown as completely redundant. I think it was Robert S's essay (I must write down the spelling of his name! - see my thread) that demonstrates the real 'motion' transformation mathematically.

However, there is a clear place for the LT exponential curve in the power input requirement for acceleration i.e. in the LHC, where infinite power is needed at over 99.9999etc % 'c'.

(would I be wasting my time with a metaphor about 'sideways promotion' in business?)

But what I'd really like you to do Eckard is to understand 'why'. Not just mathematically but in real local reality terms.

Light changes speed when it goes through a zone with a refractive index 'n', (i.e. glass or a plasma) which, if the 'zone' is a boundary zone surrounding an inertial frame, (i.e. co-moving), maintains 'c' for an observer within the new frame.

To any 'stationary' or moving observers outside that frame it will move at c/n plus the relative v. i.e. c v. But that doesn't matter as nothing really breaches 'c', not even the 2nd order signal telling all the other observers of its APPARRENT speed from their frame. Georgina shows that beautifully.

So few have seen the beautifully simple consequences of that I'm quite distraught. I hope you'll try again as it does prove the LT redundant.

A While ago I promised you a simple video. I did post it but you may have missed it; http://fqxi.org/data/forum-attachments/1_YouTube__Dilation.htm

Please do practice picturing a light pulses entering a moving glass (n = 1.55) box in your mind, then again from the different inertial frames one by one. I have found that in that glass box lie the solutions to ...most things.

best wishes

Peter

pjackson

PS.

Arthur Eddington was leading the duck hunting party so they're in safe hands. But you'll be pleased to know the LT was plucked out with all the other feathers, down and entrails.

I'm trying to find the comet Ref. but here are 2 of dozens to be going on with in case you wish to check out the scientific basis. Just ask for any more.

http://sci.esa.int/jump.cfm?oid=48440

Anderes E Knox L, van Engelen A. Lense mapping

against CMBR ion scattering. Phys.Rev.D (Accepted

Mon Jan 31 2011). (no hyperlink yet)

Xing-Hao Y, Quiang L. Gravitational lensing analysed by the

graded refractive index of a vacuum J. Opt. A: Pure Appl. Opt. 10

075001. http://dx.doi.org/10.1088/1464-4258/10/7/075001

Best wishes

Peter

[deleted]

Dear Eckard,

You wrote (for some reason, this doggone editor eliminates all plus signs for me!!!):

"Just add what you wrote:

Energy of Position: -1, 0, +1 plus Energy of Momentum: 0, 1, 0

The sum is strange: -1, 1, +1

I consider the sum of kinetic and potential energy in a closed system constant: sin^2(x) plus cos^2(x) = 1."

As you point out, the sum of the kinetic and potential energy remains a constant value, as their relative values change inversely, but when the same relationship is expressed in terms of sine squared and cosine squared, using the Pythagorean theorem, the algebra eliminates the negative sign, because it has two square roots for -1: -12 = +12 = 1.

Thus, the sum is strange, but only because of the limitation of the algebra. In this case, it appears that what might normally be considered a vice in the algebra of R, is now regarded as a virtue!

Regards,

Doug

[deleted]

Dear Doug,

At first I would like to again express my gratitude for giving me the correct hint to Baez's "point in the middle left over".

I wrote: Nonetheless it shows to me that mathematicians like John Baez do not devote the due attention to what I consider important: the question of redundancy and ambiguity."

You explained:"The reason this is so, I believe, is due to the fact that they have had to construct the 1D, 2D and 3D inverses by inventing real numbers and imaginary numbers. They invented real numbers via logic and symbols, and imaginary numbers via rotations."

I guess, they simply took the real line R between minus infinity and plus infinity for granted. Descartes reportedly hesitated to adopt R, and you are familiar with Hamilton: On one hand, he "felt his notation [of a couple (a,b)] somehow better since it avoids the absurd" [a+ib]. On the other hand he meant "... these definitions are really not arbitrarily chosen" (cf. Nahin p. 81 who commented "indeed not").

Really not? I do not share Nahin's opinion. Let's begin with a real function f(x)=cos(x) that describes a measured quantity and with Euler's identity F(x)=exp(ix)=cos(x)+i sin(x). In order to relate f(x) to the anti-clockwise rotating phasor in complex plane we may either arbitrarily add +i sin(x) or split cos(x) into exp(x) + exp(-x) and arbitrarily omit exp(-x). In both cases f(x) and F(x) are related to each other not via an identity but an arbitrary transformation. We may benefit from the chosen complex plane, no matter whether we gave preference to the positive or negative sign. If we intend to interpret a result we got in complex plane, then we are well advised to perform the due inverse transformation.

You wrote: "... the O [octonions] algebra is non-associative. Hence, they run into problems with trying to use it in physical theory. Since the algebra of C only lacks the distributive property, they mostly use it, but evidently they can use the R and the H algebras, as well (the latter probably as H+H).

I do not deny additional problems with algebras of further extended numbers. My focus is on the peculiarity of all elapsed or as elapsed anticipated time as well as of all distance: They are always real, and they always have a natural point zero. In other words: They are real and one-sided. So far I see there aspects persistently ignored in mathematics. As a consequence, many experts did not believe that the results of my real-valued calculations of a spectral analysis can be correct. They even ignored compelling arguments: Their own ears are not synchronized to our agreed time scale, and they cannot perform complex calculus. The moving pictures expert group gave preference to MP3, which turned out to excellently work with cosine transform instead of Fourier transform.

Restriction to one-sided real functions is partially quite accepted. Nobody is using a negative radius, and negative temporal distance is also rather abstruse. Some theorists seem to enjoy worrying people with negative probability, negative energy, or the like. Electrical engineers remain calm. They are familiar with negative (differential) resistance. I blame most physicists for still sticking on not just Pauli's belief in a mystery.

Best regards,

Eckard

[deleted]

Eckard,

You also wrote:

"Isn't there still growing confusion not just among students who have to swallow an abundance of allegedly counter-intuitive theories from Cantor's transfinite alephs up to white holes? I observed even here in the contest a widespread readiness among laymen to spontaneously welcome new suggestions ranging from a variable Planck's constant by Constantinos Ragazas to Peter Jackson's exciting ideas and the tendency among experts to favor overly formalized "serious" speculations. Not even Georgina Parry did consequently challenge idolized theories. I consider my arguments in Appendix C strong ones. I just avoided to open one more frontal attack."

I concur with your line of thought on this. You may may be interested in this quote from David Hestenes:

"...there is a great proliferation of different mathematical systems designed to express geometrical ideas - tensor algebra, matrix algebra, spinor algebra - to name just a few of the most common. It might be thought that this profusion of systems reveals the richness of mathematics. On the contrary, it reveals a wide-spread confusion - confusion about the aims and principles of geometric algebra."

Doug

Constantinos Ragazas

Dear Eckard,

I almost missed your reference to me in your post below! It would be helpful if there were automatic 'alerts' send to those affected by such comments!

Clearly, from your quote on my thinking, or more accurately your understanding of this,

"... a widespread readiness among laymen to spontaneously welcome new suggestions ranging from a variable Planck's constant by Constantinos Ragazas to ..."

it is clear to me that you don't understand my thinking! Not that this should be a surprise - that being the nature of new ideas. But you could have addressed your misgivings about my ideas directly with me! I would have clarified!

Simply, dear Eckard, it is NOT my position that Planck's constant (and all that is associated with this in Physics) can be considered as a variable! Rather, the quantity that Planck's constant is a value of ( the time-integral of energy) CAN be considered as a variable! Consider integrating energy at a point over a time interval from 0 to t. Wont that quantity (that integral) be a 'variable'?

There is nothing inconsistent (mathematically or physically) in everything that I demonstrate in my essay. In fact, most all of these will appear in a chapter in a book on Thermodynamics this July. The coauthor that has invited me to this project is Hayrani Oz, a Professor of Aerospace Engineering at Ohio State University. He finds my work (including the 'quantity eta', same type as Planck's constant) commendable and in total agreement with methods and ideas he has been using in his own work and teaching for many years. Whereas I use 'eta' for the time-integral of energy, he uses what he calls 'enerxaction'.

In my essay I do, however, present an argument as to why Planck's constant exists, and what it really means! Read my essay more carefully, and if you have questions PLEASE address these to me instead!

I have greatly valued your past support and contributions in these FQXi blogs, Eckard, and I continue to do so. But that comment took me by completely surprise!

Best regards,

Constantinos

Eckard Blumschein

Dear Constantinos,

Please accept my sincere apology for not addressing my comments directly to you and to Peter. I consider myself still as one out of your supporters. You might recall our discussion concerning dS/dt=L=T-V while H=T+V. See my current discussion with Doug. Do you see any difference between the action S and what you are calling eta?

Here at 833, I am in position to refer to what I wrote on h:

"Planck's constant h is just required as to get a dimensionsless argument pq/h of non-linear functions like also cos(omega t). It may be called quantum of action, but it has the meaning of the smallest quantum of energy only on condition there is a lower limit to the circular frequency omega. Wave guides have such a cut-off frequency for transversal waves."

In other words: I consider h a natural constant similar to c. Is c a quantum? The Latin word quantum asks how large or how much. Cantor was insisting that infinity is not uncertain but a quite clearly defined quantum. What did the title of your essay "World without Quanta?" suggest if not continuity? You wrote: "Planck's constant h is customarily thought of as 'action'." Isn't it rather called quantum of action? I do not see you answering the question whether there is a world without quanta of what you called eta.

I tried an admittedly uncommon mathematical interpretation of the quanta as ripples to be seen in my Fig. 1. You are a mathematician. I wonder why you are preferring instead a physical interpretation that seem not to hurt anybody.

The only utterance of you I am taking amiss is that you are denying the possibility of flaws affecting the fundamentals of mathematics and of wrong interpretations.

I do not yet see how the renaming of action into eta alias enerxaction may have any consequence for physics and technology.

Best regards,

Eckard

Constantinos Ragazas

Eckard,

...I ask all those wishing to verify my true thinking on Planck's constant to read my essay,"A World Without Quanta?"

Constantinos

[deleted]

Dear Eckard,

Happy to have this discussion with you. I know there is room for misunderstanding what I show in my essay, "A World Without Quanta?". Many of my results, (all mathematically argued!) go against the current thinking of Physics. The most startling of these is to mathematically demonstrate that Planck's Law is in fact a mathematical truism (and not a Law of Physics) that describes the interaction of energy (energy exchanges). This derivation of Planck's Law does NOT use energy quanta, yet it is possible to show how energy quanta manifest in physics.

Planck's Law marks the very beginnings of Quantum Physics and a 'classical' derivation of Planck's Law has been sought for more than 100 years. Surprisingly, the derivation in my essay is a very simple and ellegant proof that uses continuous processes only. Most likely, the very simplicity of this proof is the reason it was missed by physicists for more than a century. So, just from this alone, I can confidently argue for "a world without quanta".

But I show much more! The mathematical derivation of Planck's Law in my essay acts like a Rosetta Stone to translate known physics into a consistent and sensible formulation. This I try to do in a limited but very suggestive way in my essay. It allows for a 'physical view' that 'makes sense'. I will not argue all the results in my essay and in my papers here. But I want to hilight also a significant connection between entropy and time that is a mathematical consequence of Planck's Law. This leads to a rewording of The Second Law of Thermodynamics to assert that 'all physical processes (events) take some positive duration of time to manifest'.

You write: "Do you see any difference between the action S and what you are calling eta?"

In my essay the quantity eta is 'prime physis' and is undefined and undefinable. However, energy can be defined as the time-derivative of eta and momentum can be defined as the space-derivative of eta, as well as other physical quantities. Basic Law of physics can then be mathematically derived from these. So, eta can be thought of BOTH as 'accumulation of energy' as well as 'action'. Planck's constant is commonly thought as a 'quantum of action'. There is no contradiction to this with anything in my essay. But in addition, Planck's constant can ALSO be thought as a 'minimal accumulation of energy' that can be measured. It turns out that thinking of h as 'accumulation of energy' has advantages in that it gives deeper and greater meaning to Planck's Law. Furthermore, using eta (aka enerxaction by Oz) combines Hamiltonian and Lagrangian mechanics. Hayrani Oz has much to say on this. I dare not step into his shoes!

You write: " I consider h a natural constant similar to c"

Interestingly dear Eckard, one of the 'Rosetta Stone' consequences of my derivation of Planck's Law is to show that though this Law can be written with any value 'eta' instead of h, the Law can be shown to ALWAYS REDUCE to its usual familiar form!!! Moreover, it becomes clear that Planck's constant h is really not a natural universal constant, but rather h is the 'fixed eta' used as a 'standard of measurement' for Kelvin temperature. So the existence and value of h has more to do with our theoretical regime and our system of measurement. In a sense, the physical theory we use to 'see' Nature has a 'conceptual focal point' beyond which we cannot 'see'. That 'focal point' is h.

You write: "The only utterance of you I am taking amiss is that you are denying the possibility of flaws affecting the fundamentals of mathematics and of wrong interpretations. "

Dear Eckard, I know how you feel about all the mathematical abstractions. I don't care for much of that either. But this becomes a problem in Physics only if Physics becomes too enamoured with the beauty of pure math and does not proved a 'physical view' that makes sense. Math is just a language. We cannot fault good math for bad physics. From my perspective, the 'business of physics' is to provide us 'physical explanations' and a 'physical view' that makes sense. Physics has failed us in that!

You write: "I do not yet see how the renaming of action into eta alias enerxaction may have any consequence for physics and technology."

It is much more than renaming Physics, Eckard! It is a serious matter of reformulating Physics! The thumbnail sketch I sought to present in my essay shows that physics can be about 'a world without quanta'. Hayrani Oz, my coauthor, has much to say how this approach has great use in simplifying engineering problems. He's been doing this with his students successfully for many years.

Best,

Constantinos

Eckard Blumschein

Dear Constantinos,

If I compare your essay with the essay "Quantum Theory without Quantization" by Ken Wharton, I clearly prefer yours although Ken's already was rewarded with a FQXi membership proposal. The main reason for me to reject Ken is his readiness to accept the fatalistic idea of an a priori given block universe. Admittedly, I agree with his BIQ while I do not see that you even understood how fundamental and hard to decide the question "discrete or continuous" is.

Best regards,

Eckard

[deleted]

Hello Eckard,

The question "discrete or continuous" has as many meanings as minds to ponder on these. Your favorite math villains, Cantor, Dedekind and others, had their own understanding of these. As also modern physicists do, and in as many varied ways. I like the view that 'discrete' means 'countable' while 'continuous' means 'measureable' (I think John Merriman may have expressed this in such simple terms). And Reality is both. I view the ocean as continuous while the bucketfuls of water we draw from the ocean as discrete. I also state that energy propagates continuously while interacts discretely. And in my essay I show how all this is perfectly self consistent. No duality dilemmas here!

Eckard, I know that you like to look for structural cracks in the joints of the conceptual beams of a theory. You bring an engineer's mind to the problems with modern physics. Your vast technical knowledge makes you especially effective in raising such issues. I admire that thoughtfulness. But that thoughtfulness is not me. My approach is different. But we both join in calling for a return to 'physical realism'. To me, much of modern physics involves more 'Ptolemaic epicycles' seeking to describe the dizzying orbits of ideas removed from physical experience. But do we need to know how epicycles work in order to understand ellipses?

Sometimes, dear Eckard, we need to step back and ignore the details in order to see the 'big picture'. Do we have a better understanding of the architecture of a cathedral were we to know how each brick is positioned in the structure? I have been accussed of having a 'simple and naive' view of physics. Considering where the 'complex theories' of modern physics have taken us, I take this accussation as a complement! In my essay I give a simple thunbnail sketch of 'a world without quanta'. Were this view help bring us closer to 'physical realism', I would be deeply greatified.

Best,

Constantinos

[deleted]

Dear Conatantinos,

In science, unambiguous and understandable languages tend to indicate trustworthy work.

Already "!!!! is suspicious.

I did not find in my dictionary the word physis. Don't 'prime physis' and 'undefined and undefinable' sound mystical?

You uttered:"I know how you feel about all the mathematical abstractions". How can you know my feelings?

You are repeatedly claiming:"... a 'classical' derivation of Planck's Law has been sought for more than 100 years." Sought by whom an how? Why didn't you give belonging references?

I presume that the seeming discrepancy between L=T-V and H=T+V is due to different coordinate systems. Has Hayrani Oz more to say on this?

I have to justify myself for using the word touchstone nearly synonymous to criterion of correctness. And I am a bit shocked by the unexpected result that Lorentz metric might possibly be ill-founded.

How do you justify your metaphor Rosetta stone with respect to the many notorious paradoxes of quantum physics?

Regards,

Eckard

[deleted]

Dear Eckard,

I do enjoy your 'voice' and style of your comments. It's at the same time refreshing and challenging. I can only hope to be as good in my answers as you are in your questions.

You will not find 'physis' in your German-English dictionary since this is a Greek word. Physics derives from it! Simply, 'prime physis' referes to 'first nature'. I find appropriate to use this term to describe the quantity eta in my essay . As 'first nature' it is undefined and undefinable. Other physical quantities like energy and momentum can be defined in terms of it. In my essay , 'prime physis eta' is the only quantity that connects mathematical results to physical nature.

You write, "How can you know my feelings? ". O.K. I don't know your "feelings". This was a statement of 'empathy' (agreement?) with previous statements you've made.

The 'classical' derivation of Planck's Law has been sought by physicists at the time (and some decades later) when Planck derived his formula using 'energy quanta'. This marks the beginnings of Quantum Physics. If you like, just disregard that statement all together. It does not change the substance and validity of my results.

As to the Rosetta Stone metaphore, all I meant by it is that the formulation of Planck's Law in my essay leads to many other connections to known Physics. For example, Planck's Law and Boltzmann's entropy equation can be shown to be mathematically equivalent.

You write, "... I am a bit shocked by the unexpected..." . We are all shocked by the unexpected! It's in the nature of the unexpected. But the shock is neither confirming nor denying what may shock us. Just like there are problems with 'point masses', we should suspect also 'events' happening instantly at t=s. As I show in my essay , Thermodynamics requires 'more time' than 'no time'.

I'll let Hayrani Oz speak for himself! But he is too busy right now to engage in this forum. I can only direct you to a pdf file of his response to Ken Wharton. You can find this attached under my post under Ken's essay.

Constantinos

Eckard Blumschein

Dear Constantinos,

Sorry for my typo. I learned to ask myself: Is there possible a dispensable word in a paper I intend to publish. The word physis needs an explanation while primordial is common. A single link to your essay might be helpful. I asked for at least one reference that confirms your statement "The 'classical' derivation of Planck's Law has been sought by physicists ...". Maybe you are right?

Let's compare your idea of threshold with my and perhaps also Schroedinger's picture of more than just a single mode. I am not familiar with the details. I just vaguely recall that Schroedinger managed to calculate the spectrum of the Hydrogen atom non-relativistically. What can you add?

Regards,

Eckard

[deleted]

Dear Eckard,

One think you should know about me. I don't make comparison references. Just like I don't pass judgements on others. I am not a scholar. But I am a free and independent thinker.

You write,

"...Schroedinger managed to calculate the spectrum of the Hydrogen atom non-relativistically. What can you add?"

Not much on that at this time. There are many things I don't know. Most everything! But do I need to know the 'whole truth' to know the truth I know? I am always ready to argue and defend my ideas. I am constantly surprised with the unexpected 'gold nuggets' I find in this 'gold mind' I call the Rosetta Stone. Those with better skills and better tools will find even bigger ones. But they'll need to follow the Light into the Mind.

Constantinos

Eckard Blumschein

Dear Constantinos,

I would like to once again confirm my support for your attitude. Hopefully you will benefit from this support and from my criticism.

All the best,

Eckard

[deleted]

Dear Eckard,

Thanks for confirming! I do value your support of my attitude. Do you equally confirm my many mathematical derivations in my essay resulting from this attitude? If not, which one specifically you have questions about? My Planck's Law derivation? The equivalence of Boltzmann's entropy equation to Planck's Law? The mathematically argued connection between entropy and time? My interpretation of The Second Law to say that 'all physical processes (events) need a positive duration of time to occur'? My existence argument of Planck's constant and what it really means? Or something else of the many results in my essay too numerous to list in this post?

I take all your advice seriously and reflect on it. Reflect on the results I have in earnest put forth. All are mathematically argued. Some may surprise you.

All the best,

Constantinos

Eckard Blumschein

Dear Constantinos,

Perhaps I understand your unhappiness. I am sorry, I feel not in position to judge your mathematical work. Even if I did endorse it, we both together would certainly not manage to convince editors of refereed journals that it is not just correct but even a Physis and a Rosetta stone.

I admit a suspicion of mine: You certainly know that Einstein was influenced by Boltzmann when he agreed with Ritz to not agree. Ritz meant: Future cannot influence past. Even the late Einstein denied the separation between "past, present and future". I consider Ritz correct in this case, and I am arguing that the idea of a spacetime that includes the past and likewise the future is anticipatory and reflects a fatalistic attitude.

If I recall correctly, Georgina Parry shared Einstein's presentist view while she nonetheless denies the reality of spacetime. I did not yet take the time to thoroughly analyze her essay and the belonging discussion.

Anyway, I suspect that there might be hidden mistakes around the use of probabilities and distributions. Did you read the essay by Joel H. Meyer, a Medical Doctor? In a previous contest I mentioned an obviously unrealistic result by Gompf et al. as a reason for me to distrust single electron counting.

Let's ahow that we are not yet too old as to find out mistakes.

Good luck to us both,

Eckard

[deleted]

Dear Eckard,

Your criticism is always well intended, wise and helpful. I consider you a friend and a supporter. We share, along with many others in this forum, many misgivings on the current 'state of physics'. And we seek earnestly to 'find meaning where meaning is not found'. Whereas you look for such by deeply examining the math used in physics, I tend to question the 'physical view' of physics.

But I have come around more to your view that there may be something amiss in the way math is used in physics. Math abstracts too much from physics. Unwittingly, we may be drawing wrong conclusions. Certainly, 'point masses' may be a problem. But also spacetime, as many have argued in this forum. My misgivings about a spacetime continuum is that it appears to me that this viollates basic laws of thermodynamics. In my humble opinion, it may be incorrect to 'instantiate' physical events by (x,y,z,t). I believe thermodynamics requires that physical events have 'extention' in space and 'duration' of time.

This necessity of thermodynamics takes many forms. In my explanation of the double-slit experiment I argue that 'there is an accumulation of energy over some duration of time before manifestation of energy'. This view also appears in my mathematical derivation of Planck's Law. I also demonstrate this in my essay with the mathematical relationship I derive between thermodynamic entropy and time. And you have argued in the past that this idea may also explain the Gompf et al. false measurements.

Eckard, it is my belief that the only mathematics we should apply to physics is that which describes the 'interaction of measurement'. My derivation of Planck's Law is such. No wonder it is so remarkably accurate. Mathematical models of the Universe may contain abstractions that are unrealistic.

Constantinos

Eckard Blumschein

Dear Constantinos,

Does "math abstract too much from physics"? No. I rather see all those morons or charlatans who confuse an abstract model with the object from which it was abstracted. Having experiences an even worse rating now, I pretend ensuring all fans of the Greatest that he is of course an exception. I am here still waiting for a miracle, the promised comments by Tejinder Singh.

I appreciate your partial agreement with my criticism, and I also agree with your thermodynamic argument against spacetime. Did you read the excellent book by Zeh?

What about my aversion against what Bourbaki declared foundational to mathematics, a clueless and somewhat sad professor of mathematics pointed me not to Cantor who was obviously let's say exotic but to Weierstrass who got respected after many poor years when he shocked the community with a monster function. Meanwhile I understood the trick. He used the two mutually excluding aspects of infinity simultaneously. In these decades of the 19th century, the good old notion number was redefined with serious consequences from naive set theory to Hausdorff continuum and category theory, affecting physics too.

I agree on that experiments are touchstones for theories. However, the correct design of experiments and the correct interpretation of the results are crucial.

Best regards,

Eckard

[deleted]

Gentlemen:

I came across this dialogue 21 months after it has taken place!

I will not discuss enerxaction publicly in all of its details until I choose to do so. Because of this, I do not expect one to understand and appreciate its (and Ragazas' allied concepts via eta) scientific and technological significance until I do so. At this point, the only comment I have is about Blumschein's question above in this chain:"I presume that the seeming discrepancy between L=T-V and H=T+V is due to different coordinate systems. Has Hayrani Oz more to say on this?

Here is what I have to say for now: There is not a matter of discrepancy and or a coordinate system difference between the Lagrangian function L and the Hamiltonian function H; both are due to fundamentally different mechanics views of two individuals well-respected in the literature. Operations on the time integrals of these functions when broadened under the concepts of enerxaction dynamics yield for one of them an incorrect and for the other one a correct description of equilibrium phenomena. The difference between these two functions is not a matter of a simple sign mistake either. I will kindly leave you pondering on which one is the correct one and which one is the incorrect one, and why?

The Foundations of classical mechanics we use today are built on shaky grounds and unsolidified concepts. Not only the answers but the questions we ask must also be right!

Best regards, Hayrani OZ

[deleted]

Dear Doug,

My dictionary tells me: A vice is a moral fault in someone's character or behavior. I would blame contradictory arrows of positive directions rather than a limitation of the algebra.

I only very vaguely recall, in connection with the notion of action, that the Lagrangian is not the sum of but the difference between kinetic and potential energy. Maybe I am wrong here. Nonetheless I expect confusion if, e.g., the positive incrementation dx of x remains unchanged while the direction of force changes its sign at zero. I also recall oddities with modal analysis in cylindrical coordinates.

Just for fun I will quote from Nahin, p. 14, how already John Wallis confused himself:

Since a/0, with a larger than 0, is positive infinity, and since a/b, with b smaller than 0 is a negative number, then this negative number must be greater than positive infinity because the denominator in the second case is less than the the denominator in the first case. This left Wallis to the astounding conclusion that a negative number is simultaneously both less than zero and greater than positive infinity ...".

Best regards,

Eckard

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