Physics Suffers from Unwarranted Interpretations by Eckard Blumschein

Hi William Amos,

I noticed that you followed the instructions given by fqxi and the formulation of the topic almost as closely as did Noson Yanofsky with perhaps more success in the contest. I don't agree with those like Yanofsky who consider symmetry a mystic basic principle behind physics. My essays intend to reveal the reasons, not just the historical but also the logical ones, that led to such unwarranted belief.

What about reality vs. interpretation, as an old engineer, I consider the conjecture of reproducibly confirmed and logically consistent reality in contrast to mere imagination a reasonable distinction.

Best of luck in your life,

Eckard

My reply to Matt Visser tries to once again explain my suspicion that theoretical physics might use complex calculus not as proper as required.

Dear Matt,

You got me and perhaps may essay repeatedly wrong. I am not David Garfinkle, and I hope you will not go on getting me wrong concerning complex calculus. While complex calculus is an application of complex numbers, theorists like you tend to be not aware of a few trivial trifles:

You are guessing that what you called an algebraic field extends the real numbers in the sense it offers additional freedom. Actually, the description of a physical quantity in complex domain is subject to Hermitean symmetry which means, it doesn't convey more essential information as compared with the unilateral and real-valued original function; let's say of either elapsed or future time. Future processes cannot be measured, past processes cannot be prepared.

Certainly you preferred what I consider the risky habit of introducing a physical quantity within complex domain.

In other words, when writing exp(i theta) instead of cos(theta) you are omitting i sin(theta).

A simple objection against this habit is that it implies an arbitrary and therefore unwarranted and often ambiguous choice of the sign of rotation.

When someone like Schrödinger applied complex calculus on a real-valued function of elapsed time (extending from -oo to 0), he applied as do I Heaviside's trick in order to prepare it for the integration (from -oo to +oo) required by Fourier transformation. In a first step, zeros are attributed to the not yet existing future. The now zero-valued future part is then split into a positive and a negative mirror picture of the originally unilateral function. This creates multiple but necessary redundancies: an even and an odd component, both extending from -oo to +oo. The third step, Fourier transformation into complex domain leads to the mentioned symmetries of real part and imaginary part. An original function of time mutates into complex functions of positive and negative frequency (from -oo to +oo). A function of frequency in original domain gets the so called analytic signal, i.e. two complex symmetrical functions of past and future. So far nothing is wrong. We may benefit from complex calculus in either complex frequency or complex time domain. If no seemingly redundant component was omitted and not just the inverse Fourier transformation but also the inversion of preparing operations were properly performed, we safely arrive back in the original unilateral domain.

Schrödinger's original communications, in particular his 4th reveal the way he speculatively introduced the complex wave function as a trick to reduce the degree of equation from four to two.

Perhaps not just Dirac ignored that elapsed as well as future time are always positive too when he argued that frequency (and the Hamiltonian) must always be positive. Weyl confessed: So far there is no explanation in sight for the [mirror] symmetry of time in quantum physics. The envisioned symmetry of almost all fundamental particles with their antiparticles was not found.

There was something that puzzled me for a while when I compared cosine transformation in IR+ with Fourier transformation in IR and questioned the unavoidability of ih. Heisenberg's matrices seem to confirm the necessity of complex calculus in Schrödinger's picture. Meanwhile I understand that Heisenberg's square matrices also correspond to Hermitean symmetry in IR. A real-valued alternative corresponds to (triangular) half-matrices with elements only above or only below the diagonal which may reflect the border between past and future.

Accordingly I felt not just forced to criticize Einstein's imprecise wording "past, present, and future" but also to reintroduce Euclid's notion number as a measure, not a pebble.

Concerning ict, cf. the essay by Phipps.

Matt, I agree with your statement: "If a well-developed branch of pure mathematics turns out to have some use in the natural sciences, then the natural scientists will quickly appropriate that strain of pure mathematics and turn it into applied mathematics..." Yes, G. Cantor's well-developed cardinalities in excess of aleph_1 didn't turn out to have some use in the natural sciences.

Regards, Eckard Blumschein

P.S.: Michael Studencki, I apologize for hurting you. Read my essay(s), and you will find why I reinstate Euclid's notion of number based on the measure one, not on a pebble a la Hausdorff. So far, I did not yet read your bio and also not your essay. I consider Relativity and the belonging held for real spacetime in contrast to reasonable relativity not as harmless as you seems to describe it.

In Germany we have a proverb "sitting between the chairs". Maybe, the truth concerning Relativity/relativity sits likewise between academic pros and cons.

Let's benefit from comparisons; this is Robert McEachern's comment on my essay:

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Quote/ Eckard, I think the title of your essay hits the nail on the head. It is indeed the unwarranted interpretations, slapped onto the equations of mathematical physics, that cause all the problems in understanding the nature of reality.

Where we differ, seems to be that you believe that avoiding the usage of particular mathematical techniques, will solve the problem, whereas I believe that the problem is that mathematical identities have no unique one-to-one physical identity. For example, the statement:a(b+c) = ab+ac, is a mathematical identity, but not a physical identity. The left-hand-side requires one multiplier to construct it physically. But the other side requires two. Another example, pertaining to hearing, is: sin(a)+sin(b)=2sin(0.5[a+b])cos(0.5[a-b])

From this math identity, one might suppose that one could CHOSE to perceptually hear EITHER a superposition (sum) of two tones, or an amplitude modulated single tone (beats). But one CANNOT do that; depending on the frequency separation of the tones, one always perceives one form of the identity, but never the other. The math identity is not a physical identity. Thus, different physical identities, different physical realities, cannot be entirely described by mathematical identities. This is the ultimate reason why entirely different physical "interpretations", can be slapped onto mathematically identical equations. The same thing happens with the Fourier Transforms (and hence superpositions and wave-functions), at the heart of Quantum Mechanics. Physicists remain blissfully ignorant of the fact that Fourier Transforms are mathematically identical to filter banks, not just superpositions of wave-functions. The filter-bank "interpretation" completely eliminates the very existence of wave-functions, and consequently, all the nonsense about wave-function collapse and mysterious superpositions etc.

In both the hearing and QM cases, the cause of the difference between the math and the physical, is the "amplitude detection" of the filter-bank signals being described by the math. /Unquote

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I rather see various unwarranted interpretations. I begun with the interpretation of the notion number, and I omitted e.g. what I consider the misinterpretation of Michelson's 1881/87 null results, see Phipps.

No, I don't focus on a single problem. I collected a treasure of paradoxes from set theory to Special Relativity and beyond on the one hand and sound hints to ways out on the other hand. I never agreed with those who suggested a bijection between reality and abstraction and even ascribed singular points to reality.

What about mathematical identity, could it be you got me wrong? When I revealed time symmetry just an artifact due to careless use of complex calculus, I criticized the confusion between mathematical identities and the TRANSFORMATION into an arbitrarily chosen fictitious complex domain; translation from there back to the adequate immediate picture in real domain is a must.

As you know, I claimed elsewhere to understand hearing not just as formally as do you in terms of Fourier transformation and filter banks but from a more natural physiological perspective with restriction only to already existing data (IR+). If you will read my essay carefully, you will not just find your excellent previous essay quoted; you might also stumble about my seriously meant characterization of functions as unrealistic if they are thought to extend in time from -oo to +oo.

Best,

Eckard

Dear Giovanni,

Let me first try and answer your question. Mister moon was imagined male, lady Luna female; this more or less ideal model of a pretty old point mass in space is not the only one that was repeatedly changed, corrected, explored, and even exploited.

What about rational vs. real numbers, I largely agree with G. Cantor on that rational numbers are discrete, i.e. numerically distinguishable. Real numbers are not altogether numerically distinguishable. Stiefel spoke of a fog, Weyl of a the sauce of continuum. While I would with pleasure call this continuum of real numbers the mathematical one, set theory occupied and mystified the notion mathematical continuum. Therefore I am calling the continuum of the liquid of measures the Peirce continuum or the logical one, something every part of which has parts.

Are there spacial and temporal continua? The attribution of continuity to space or time is reasonable guesswork. I see a more serious problem in the persistently denied fact that elapsed and future times denote essentially different scales. That's why I see spacetime belonging to speculation and Phipps providing light at the end of the tunnel.

With right line you did perhaps mean straight line?

Thank you very much for your good wishes,

Eckard

Dear Joe Fisher,

My essay does neither address gravity nor Hawking. What about spacetime, I prefer attributing it to Poincaré 1904 and Minkowski, and I see its root in a unwarranted guess by Maxwell, Michelson, Lorentz, and others, cf. Phipps. I don't guess that we need dealing e.g. with the GZK paradox in order to question SR.

I agree with you on that reality "is not mathematical". In particular modern mathematics lost connection to common sense.

I am arguing that there is an ignored paradox: Mathematics putatively demands using complex Fourier transformation for frequency analysis, i.e. integration over time from -oo to +oo. Perhaps one must be self-taught like you, just a user of MP3, or a physiologist in order to admit that a real-valued cosine transformation, i.e. integration only over elapsed time, yields the same result except for an unnecessary arbitrarily chosen reference.

I enjoy Leifer's cut between useful and in principle aviodable mathematics.

Eckard Blumschein

Dear Michel,

Thank you in particular for pointing me to pink noise and disagreeing with ubiquitous causality.

I am distinguishing between ubiquitous causality and its only logical alternative of resorting in something supra-natural. This implies to also distinguish between conjectured causality and a naive determinism as exemplified in La Mettrie's "L'Homme machine". Well, there is perhaps no reason why nature shouldn't play dice, but this doesn't contradict to ubiquitous causality.

Having often used non-causal signal processing myself, I feel aware of this as pragmatic sinning against consequent logical correctness.

What about the corner frequency between pink and white noise, I did never deal with this question. So a suspicion of mine might be wrong: I just got aware that the white (higher frequency) part looks irregular as to be expected while the pink (LF) part looks smooth. Maybe, the latter is an artifact of windowing?

Having tried twice to understand your glittering essay, I felt being perhaps too old and also to less familiar with the details as to always get what you meant. When someone else used the expression "lighthearted" I asked him why he hided himself behind humor, and he frankly explained it to me. Why did you invoke moonshine?

Indeed, Schrödinger managed to explained the Hydrogen spectrum without Relativity, and non-Relativistic quantum theory is accepted as serious.

Accordingly I am capitalizing Relativity.

Best,

Eckard

Dear Michel Planat, dear Tim Maudlin,

I hope to manage making my essay a bit more understandable to experts:

What happened to mathematics? Part 1

Georg Cantor's naГЇve transfinite cardinalities have not by chance proved useless despite of evidence that was more or less accepted in 1873 and 1890.

Let's understand the ideal continuum as a directed measure every part of which has parts while a point has no parts, and any amount of points, no matter how "dense" can therefore not constitute a continuum. For the sake of simplicity we may restrict to one continuous dimension: Length means the distance from a point zero of reference to something that refers to a chosen basic measure called one. This agrees with Euclid's definition of number as a measure and with Salviati alias Galileo Galilei who already used the method of bijection when he arrived at the reasonable conclusion that the relations smaller than, equal to, and larger than don't apply for infinite quantities but only to finite quantities: There are not more natural numbers than squares of them. The converse is not true. With infinite quantities Galileo meant infinite series. The Latin word quantus asks for a measure: how large? The distinction between finite and infinite doesn't ask for a quantity but for a quality of a chosen model.

In point set theory the expression "subset of a set" is used instead of "part of continuum", and a pair of points could be interpreted as the measure, a piece of continuum. However, G. Cantor's point sets are thought to be set together of distinct, i.e. zero dimensional, points, not of pairs of points. Although Fraenkel admitted in 1923 that Cantor's naГЇve definition of an infinite point set is logically untenable [ ], there is still no corrected one. The naГЇve set theory has been replaced by bundles of axioms, e.g. ZFC. Nobody so far put the due attention to a seeming trifle: Not just Cantor but also Dedekind gave preference to the archaic pebble-like notion of number instead of Euclid's measure.

A yardstick may illustrate the fundamental difference between both notions of number, see Fig. 1. Modern mathematics follows those who attribute the notion number to pebble-like marked points on it instead of a sum of spaces between points. Imagine the yardstick chopped into single pieces being still immediately adjacent to each other. Then each cut alias point is located exactly in between two pieces.

In modern point set topology a point a is considered embedded into the surroundings a-пЃҐ and a+пЃҐ. This causes trouble in case of a=0 within IR+ and gave rise to tricks like (-1,0)U(0,1)=(-1,1)\{0}, a so called deleted neighborhood.

With the traditional Euclidean notion of number as a measure, a point is something that has no parts and accordingly no measure. Here one cannot perform the numerical distinction of a single point that is embedded within the continuum of real measures. Singular points can then only be addressed in the discontinuous rational measures. Likewise there is no chance to distinguish between open and closed REAL measures, and only non-zero measures can be numerically excluded or added.

Obviously, topology strongly depends on the choice of the notion number.

Best,

Eckard

James,

Thank you for pointing me to isodual mathematics. I will have a look at it.

If you are unbiased looking for more pearls you might find out what is behind the essay of Phipps, and how Renaissance, propagation of ideas, and the experimental method made Europe rapidly superior to Asia.

Eckard

Corrections to part 1:

? in a-? and a? should read epsilon

1873 and 1890 should read 1874 and 1891, respectively

[ ] should read Fraenkel, A: "Einleitung in die Mengenlehre" Springer, Berlin, 1923

Fig. 1 can be described as follows:

0----|----|----|----|----|----|----| yardstick

1 1 1 1 1 1 1 measures between subsequent points

0 1 2 3 4 5 6 7 numbers attributed to subsequent points

|...................6..................| number 6 attributed to six measures

|.........3.......||.......3........| twice three measures

There is no distance between ||

Eckard

Dear Edwin Eugene Klingman,

Thank you for your warm words. I added some corrections to part one of "What happened to mathematics? Part 1" and will add Part 2 soon.

Eckard