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]

  • Post #114

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]

  • Post #115

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).

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."

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]

  • Post #116

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

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

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    • Post #118

    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

    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

    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

    Tejinder Singh promised to read my essay and comment on it. I would like to encourage all those who also might perhaps have trouble with my essay: Please do not hesitate uttering criticism.

    Eckard

    • [deleted]

    • Post #123

    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

    • [deleted]

    • Post #124

    Dear Eckard,

    I wish I knew German as well as you know English. If I did, I would gladly try to write in your language. By using the word "vice," I intended the meaning "defect," and by using the word "virtue," I intended the meaning "value." The algebra of the reals has both traits.

    You are right in regards to the Lagrangian, but let's keep things as simple as possible. To my mind, you have put your finger on the major problem with the foundation of math and physics. Euclid's definition of point must hold, in my opinion. However, what he understood in terms of ratios of measures also must hold. Ratios work in three ways, which we can call positive, negative and neither.

    On this basis, if a ratio is neither positive nor negative, it must be a unit ratio, n/n, n = 0 --> infinity in R. Hence, -n/n or n/-n or -n/-n are illegal ratios. No such ratios can exist. However, because, as Grassmann, Clifford and Hestenes understood, there are two interpretations of numbers possible, R- is a reality as well.

    The first interpretation of number is R. The quantity of things, the answer to the question "How much, or how many?" On the other hand, there is another interpretation of R, which results from a relation between two quantities in R, such as the ratio of n and m. Let's say both n and m

    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

    Dear Doug,

    I highly appreciate your readiness for unbiased dealing with my admittedly rather uncommon arguments.

    You wrote:

    "Ratios work in three ways, which we can call positive, negative and neither.

    On this basis, if a ratio is neither positive nor negative, it must be a unit ratio, n/n, n = 0 --> infinity in R. Hence, -n/n or n/-n or -n/-n are illegal ratios. No such ratios can exist. However, because, as Grassmann, Clifford and Hestenes understood, there are two interpretations of numbers possible, R- is a reality as well.

    The first interpretation of number is R. The quantity of things, the answer to the question "How much, or how many?" On the other hand, there is another interpretation of R, which results from a relation between two quantities in R, such as the ratio of n and m. Let's say both n and m"

    Well, in case of a ratio trichotmy holds. However what about irrational numbers?

    I learned from Fraenkel's 1923 book there are not three but four logical possibilities. Fraenkel himself was not unbiased. Following G. Cantor's insane intention, he did not accept the fourth possibility.

    I am arguing: Real numbers must be understood homogeneous, i.e. without distinction between rational and irrational ones. Only then they are truly essentially different from the rational ones. This requires to admit that numbers of infinite precision within a continuum of such truly "real" numbers cannot be subject to trichotomy. In other words: I consider Dedekind's extension from rational to real numbers reasonable on condition we do not try to enforce trichotomy for the real numbers too. This paradise is elusive.

    Best regards,

    Eckard

    • [deleted]

    • Post #127

    I have some further comments to make on this subject, but I will forebear in order to point you to the John Baez article that I referred to earlier. I finally found it, but I don't know if "clarifies" is the word that I should have chosen. Maybe the word "discusses" would have been a better choice.

    At any rate, take a look at it and see if it is helpful at all.

    It is here.

    Doug

    • [deleted]

    • Post #128

    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]

    • Post #129

    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]

    • Post #130

    Dear Eckard

    Sorry for my late reply. I was not aware of this post.

    Please do not get me wrong. I did not mean that Euclid's definition is a prejudice or yours. I just wanted to say that it is prejudice to think that a line is made up of points. That is all. Since a point is adimensional (with zero length), something finite (like a line) can only be constituted of things of finite lengths, therefore lines are not constituted of points. However one can find infinite many points in a line (and one can associate a real number to each point). This appears to me a dychotomy difficult to swallow. I agree with you that there is no other reasonable alternative to Euclid's definition.I will analyze Peirce's proposal.

    You: Aren't they just a fabrication that is based on Cantor's questionable naivety?

    Well Cantor just showed by induction that there are infinites sets "bigger" than others, but he did say anything about the idea of the infinite. The surreal numbers allow us in principle to deal with operations like infinite-1, sqrt{infinite}, etc. But to my knowledge, no one knows the physical meaning of that.

    You: What about division by zero, engineers like me do not shy back from equating anything/zero with infinity and anything/infinity with zero. I do not see progress in these questions since Bernoulli.

    Zero represents nothingness. The operation of division is a question. A question that ask for a number "a" such that "a" times "b"= "c". If c is different from zero and b=0 the question makes no sense, it cannot be asked. Why? because b=nothingness, and being b nothingness, nothing can be say about it.The same occurs if b=0 and c=0 but Weierstrass call this, an indeterminate form. Why? because the number "a" could take on any value. But if the nothingness does not exist these operations become fictitious.

    What do you think?

    Israel

    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

    Eckard

    Sorry it wasn't the essay of Robert (Spoljaric) though equally excellent, I was referring to in the above (25th) post, it was Rafael Castel. See; http://fqxi.org/community/forum/topic/835

    Two typo's crept in, in the 2ns line read 'was' for 'what', and there should be a 'to' somewhere further down.

    Do let me know how you get on. Best wishes

    Peter