Continuation Causes Superior but Unrealistic Ambiguity by Eckard Blumschein

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

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

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

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

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

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

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

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

Eckard,

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

Constantinos

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

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

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

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