Let's benefit from special mathematics for elapsed time by Eckard Blumschein

Already, just from your abstract, I concur! Misinterpretation or in some cases, seemingly blind acceptance, have hidden the complete harmonic balance provided by the complex exponential. Since the days of Euler and Fourier, imaginary or "irreal" numbers, as you aptly say, have not been fully appreciated. They exist for a mathematical reason, and it has been left to Kramers and Kronig, and we scientists, to figure out the physical interpretation. Perhaps we have arrived. I look forward to reading your essay.

By the way, when I was in high school, I built an arc welder from 8 old microwave oven transformers and an IGBT from International Rectifier- I can fully appreciate your hands-on approach... welding "by ear" is an interesting study indeed!

Hello Ryan,

First of all I have to apologize for giving rise to a mistake.

When I am suggesting "irreal numbers" I do not include imaginary ones. Charles Francis is a moderator of sci.physics.fundamentals. He denies real numbers. We largely agree on some consequences. However, I prefer to quasi redefine the real numbers because I consider time not a Hausdorff continuum but a Peirce continuum each part of which has parts. My point is: Uncertainty might not primarily be a physical but rather a mathematical phenomenon.

By the way, read my essay and be not too much disappointed because I see forward and backward directed time mathematical artifacts, too.

If you are interested in the role of the restriction of perceivable signals to the past, you might find some stuff at http://home.arcor.de/eckard.blumschein/M283.html and other messages ranging up to M285. Currently there is a discussion on cochlear amplifier managed by Matt Flax.

Hi, Eckard,

I've now read your essay, because of your comment on Dirk Vertigan's comment stream. Some of your essay is interesting, but I guess I'm unable to see clearly how I would use your methods in my mathematical context.

Peter.

Hi Peter,

I envision physics and to some extend also mathematics to benefit from a painful but fertile loss of several illusions - provided I am at least largely correct.

While I'll study in detail the mathematical context of your essay 281 before going into the nitty-gritty, I would already like to claim that everybody may take advantage of my point of view - provided I am at least largely correct.

Let me joke:

Even those who are denying time and frequency are not aware of using within their ears log frequency scales.

Moreover, ears built on the basis of common theory would not work well.

In such sense we are doomed to benefit from a correct natural "notion" of time underlying to the process of evolution.

Technology has been coming closer and closer to natural solutions. Cosine transform has already proven beneficial in

coding of real-time data, too.

Werner Heisenberg speculated: I believe that the existence of the classical "path" can be formulated as follows: The path comes into existence only if we observe it.

He obviously refers to path in an abstract sense. While notions like "elapsed time" and "reality" can also be transferred into abstraction, they primarily denote something tangible.

Somewhere here, I met the old idea, we need experiments with higher and higher energy as to better understand time.

I am not sure. Will the LHC really find the Higgs boson and confirm standard theory?

Given my doubts are justified, maybe quantum computing will also never work as promised. Those who invested a lot in it will certainly not welcome their disillusion while physics as a whole should benefit.

Regards,

Eckard

Once again I feel mistaken, this time in a discussion concerning T H Ray's essay where Ray and Westafer repeatedly refer to my essay. I never wrote that I don't assign physical meaning to complex analysis.

I wrote that complex representations must not be used without the necessary care. Do not expect from an old EE like me lacking appreciation of for instance complex impedance.

In this case real and imaginary part are used to denote two related quantities. R is considered real, L accordingly belongs to the imaginary part. Engineers learned how to enter and leave the complex domain, step by step. In case of permeability, L relates to a real part, while R belongs to the imaginary part.

Likewise, experts of signal processing like their so called analytic signal while they are usually working not with complex functions of time and of real positive frequency but with functions of real and positive time and accordingly complex functions of positive as well as negative time.

Unfortunately, Carlo Rovelli so far ignored my ask to explain step by step how physics introduces imaginary quantities. I do not blame him personally for being apparently unable to do so.

I read in a book by Atmanspacher "The Pauli-Jung-Dialog" the claim that quantum mechanics is the only discipline in physics where i is not dispensable, not even in principle. The given references did not persuade me. Instead I found out that the fathers of quantum mechanics were sometimes definitely not cautious enough. Maybe, I overlooked the missing careful foundation?

E. Blumschein

Eckard,

I'm sorry if I misrepresented your view. Real elapased time values also play a major role in my own mathematical model, though I do not see how we get a positive real time value without passing through the complex plane.

Tom

Tom,

I am an engineer. We learned and understood that complex plane is a tool, not something natural. My criticism might look like a triviality. Well, tri via relates to three ways. I am claiming that physics is not always on the right way. Something natural should not depend on an arbitrary decision. I wrote that the ear does not know when Christ was born and where Greenwich is. When the ear performs a frequency analysis, it can only refer to the actual moment. Consider for instance your current age. It is of course positive and increases steadily. Do not get me wrong:

It did not matter whether it was positive or negative if we hat always to assume positive as well as negative values.

If we do not need a changing sign, then we do not need a sign at all. Negative numbers are a possible, not a mandatory extension. If they are not necessary then they are are a redundant burden.

You cannot move within your age. It is rather a measure for the sum of all influences on you.

I will tell you what caused me to deal with quantum mechanics: A textbook on signal processing by Karrenberg, an edition of Springer (!). The author did not present mathematical formulas but exclusively simulated diagrams.

This is funny. However, he demonstrated what he called a symmetry principle in a very obviously nonsensical manner and justified it by referring to symmetries in quantum mechanics.

Nonetheless Karrenberg's pictures clearly demonstrate how the imaginary part of a given function of time changes if one shifts the arbitrarily chosen point of reference.

He also made simulations that, if correctly interpreted make obvious why Prof. Nimtz in Koeln came to the wrong measurement of signal propagation with superluminal velocity.

Some people are still believing in such seemingly evident results. PRL accepted and published in 1997 a paper by Gompf et al. with "single photon measurements" that were at odds with what experts could expect and what was actually to bee seen in direct streak observation. It is not my business to find out sophisticated mistakes. I merely can suggest a very simple touchstone: Avoid mistakes due to misinterpretation in connection with complex plane. Let's benefit from the unambiguity of real-valued calculation.

Best success,

Eckard

Well Eckard, I have nothing against engineers. :-) My father (who died before I was three)was a radio technician in the 40s when radio was still pretty young. I taught myself algebra from the circuit books he left behind and I built receivers from cast-off parts. I still remember my fascination and puzzlement over the resonant coils (these were the days of vacuum tubes and wound coil plug-ins were still often used by hams and "DXers" like me) that reverberated, like tuning forks, when introduced to invisible waves transmitted over hundreds and thousands of miles through no medium but empty space.

Later when I learned how electromagnetic waves propagate, hardware no longer fascinated me (and besides, transistor circuits lack that certain elegance and ease of assembly that I had grown accustomed to). I learned the wave had two parts, transverse to each other, keeping the same beat in harmony with opposing destinations.

When I learned about time and dimensions and fields, I understood how events are continuously connected. And when I learned that some events just happen discontinuously, I was--like you--scandalized. And then when I turned to higher abstraction, and encountered this wonderful field of universal complex numbers, I understood how complex analysis--by assigning point values to lines in a 2-dimensional plane--restored harmony between the wave function and the particle event in a positive real result with a conjugate counterpart. The mechanics were perfectly reconciled with reality in a unitary relation.

I don't find complex analysis unphysical or metaphysical or a mistake of misinterpretation of physical reality. I find it useful.

Best success to you as well.

Tom

Tom,

I consider my old-fashioned training in EE at TU Dresden from 1960 to 1966 excellent. Among my teachers was "Nabla Jot" Lehmann, an early pioneer of small computers. During my whole carriere as a teacher myself, I used complex calculus and designed a lot of problems for students.

Why do you assume I was scandalized by something quite normal?

If a function of time is continuous, then the corresponding complex function of frequency must of course be discrete and vice versa.

Complex integral transformation is not metaphysical but necessarily unphysical.

Hermitian symmetry is not a physical phenomenon but relates mathematically to algebraic continuation of what is called a semigroup into the void "half"-plane.

Mirroring just creates redundancies.

The complex representation is not a richer one if it originates from a real-valued one.

Well, this statement of mine is at odds with putative essentials of quantum mechanics and most of its trouble with itself.

I published more than 50 papers. Some of them dealt with dualities in particular in power electronic circuits.

I uttered the conjecture that a check of duality may help to reveal imperfections in theory. So far this seems to be true. Cantor's paradise fails the check. I collected mounting indications that confirm my suspicion: Cantor was wrong.

Well, I was shocked when I read how Schroedinger impressed his 14 years old pupil Itha Junger by telling her to expect getting the Nobel price, made she his lover, promised care but refused to divorce from his wife when Itha got pregnant.

I was also shocked when it got more and more obvious to me how carelessly Schroedinger, Heisenberg, and others dealt with the innocent complex calculus.

Instead of hand-weaving, you might look at the results of some simulations:

http://home.arcor.de/eckard.blumschein/M283.html

http://home.arcor.de/eckard.blumschein/M284.html

http://home.arcor.de/eckard.blumschein/M285.html

I apologize for not yet providing the due explanations there. Experts should nonetheless be in position to understand my argument.

My basic insight is: The reality of any physical process is restricted to elapsed time. I derive serious consequences from that restriction.

Read again: fqxi.org/community/forum/topic/369

To those physicists who are interested I will make already available

"A still valid argument by Ritz" (8 pages).

Non-physicists, in particular physicians, might rather look at the attached file.

Regards,

Eckard

I am sorry, the attached file was too large (7.4 MB).

You might find it at

http://home arcor.de/eckard.blumschein/M277.html

Eckard

Someone who pretended to agree with Mc Gucken, essay 238 reiterated what I consider not justified: He used the imaginary unit i without careful distinction between mathematical identities and arbitrary transforms into a complex domain. While I appreciate that he gave a translation of Einstein's utterance on past, present and future that might be more eloquent as compared to the translation given in the book by Zeh, and I agree with a few of his statements, I see him unable to escape possibly wrong tenets. For instance, he wrote "processes that evolve in time" and "all things in nature from the big bang onwards".

He glorified the "Platonic realm of mathematics".

While I prefer to share Platon's view that the laws of mathematics are discovered rather than invented, I do not share his belief that anything is a priori given by numbers.

Eckard Blumschein

Dear all,

If I recall correctly, at least Le Rouge and Lynds promised to read my essay soon. As I promised, I will take issue concerning several ideas now.

Yuri Rylov uttered: "Find and correct mistakes! New ideas are needless!" I would like to add that I am claiming having found cardinal mistakes, and consider it necessary to check whether or not I am correct. The possible consequences seem to hurt those who like Carlo Rovelli are trying to escape problems that were made perhaps most understandably obvious by Kiefer's essay.

F. Le Rouge mentioned the potential infinity. I understood the Fourier transform as based on the more ideal notion of actual infinity while the cosine transform fits better to reality in that, the considered variable, no matter whether temporal or spatial distance is limited at least at one side. Temporal distance is also called elapsed time while spatial distance is called radius. It would be formally possible but pontless for physics to count these sign-less variables backwards. Also it does not matter whether or not they are considered finite or not. Infinite distances are pointless.

Yuri Rylov raised the issue of partly continuous, partly discrete. This is almost boring to those who are familiar with signal processing. Fourier transform as well as cosine transform change the continuous component of a function into a discrete one and vice versa.

Peter Lynds defended the essays by Ravelli and Stoica. Well, both offer in an impressing manner to escape an admitted mess. A third favorite of public voters seem to emphasize the likewise impressing evidence for the mess. If my suspicion is correct then we will need alternative explanations in particular concerning entanglement and decoherence. Those who like Goldstein favor Bohm are facing the same distrust.

My radical exclusion of time in excess of concrete consideration will hopefully shed new light into some putatively compelling evidences. As well known, Nimtz proved that signals can propagate faster than light. While serious scientists did never believe him, it was, so far, difficult to prove him wrong.

Regards,

Eckard Blumschein

Elliot McGucken,

My reply to you at 238 was mutilated when I begun to explain what essential details you are not aware of. Then you quoted Born in order to lecture me. However, as I suspected Born and obviously also the other ones who introduced quantum mechanics did not mention what I learned as a student in Dresden and thousands of my students learned from me:

One correctly arrives at the complex frequency domain and correctly returns only via several steps of a transform and inverse transform, respectively, while it is common practice to skip several steps for convenience.

Given, a physical quantity could be described with a function cos(x) with -oo < x < +oo, then Euler's identity

yields 2 cos(x) = exp(ix) + exp(-ix). The two exp functions represent two phasors, which are rotating in complex plane anti-clockwise and clockwise, respectably. Transform into a complex domain means to arbitrarily omit either exp(x) or exp(-ix). It can also be considered like an arbitrary addition of either i sin(x) or -i sin(x). Electrical engineers decided roughly one hundred years ago to use a more reasonable sign. As a result, their transform is different from the originally chosen one which is still preferred in mechanics.

The transform into complex plane is tacitly performed with a complex integral transform, in particular with Fourier transform by multiplication with the complex kernel. Fourier Transform of a real function of time yields a complex function of positive as well as negative frequency. Likewise Fourier transform of a real function of frequency would provide a complex function of negative as well as positive time. The same is true for the pair distance and wave number. Some people are calling wave numbers spatial frequencies.

In particular the negative frequencies puzzled engineers as well mas physicists when quantum physics was introduced. Dirac explicitly wrote what all others thought: Frequencies cannot be negative. Indeed, negative frequencies are just an artifact of transform from physically correct original time domain into a complex frequency domain. They vanish with the return by performing inverse transform.

Undoubtedly advantageous interpretation of complex quantities like impedance and permeability in electrical engineering was tempting. Those who did not like demanding careful work were ready to forgot that complex frequency domain (or also complex time domain) does strictly speaking not allow immediate physical interpretation. Instead of being aware of performing any transform they made an ansatz immediately in complex domain and did not even know that complex frequency domain is different from complex time domain.

They felt supported by mathematicians who referred to complex plane, not to a special tool of physicists and engineers when they correctly confirmed that the complex numbers enriched the ordinary ones, and the complex representation is the more general one.

Now I will point to a decisive peculiarity: Fourier's transform demands x either to range from -oo to +oo or to be included within perfect mirrors. Fourier himself dealt with a closed ring. Quantities like temporal or spatial distance do not make sense if one demands them to be actually infinite. Radius and elapsed time are reasonably limited to merely positive values. Oliver Heaviside, who incidentally also found the final Maxwell equations, found a sokution that boosted technology. He continued the function f(x>0) into the negative half-plane x

My last post was cut. This continues it:

Oliver Heaviside, who incidentally also found the final Maxwell equations, found a solution that boosted technology. He continued the function f(x>0) into the negative half-plane x

Hopefully this will not be cut:

He continued the function f(x>0) into the negative half-plane x

It looks as if a referee has begun to understand that my essay is at odds with deeply rooted tenets and therefore unwelcome. Those who got curious might be patient until I posted what was cut at http://home.arcor.de/eckard.blumschein/M286.html

Eckard Blumschein

Eckard,

I think that your post was cut because the software truncates text following certain symbols. This happened to me when I used the 'less than' sign. Try avoiding the symbol you were using at the location at which your text was cut.

Given that the the text is immediately posted, I find it highly doubtful, if not impossible, that a referee could read a post so quick as to do anything about it.

Armin

Thank you Armin.

I did indeed use such symbols.

Nonetheless, someone hoped I might be wrong.

This is understandable because my criticism would imply serious consequences.

Please find attached a hopefully readable and understandable pdf file

"How do negative and imaginary numbers relate to reality?"

Regards,

EckardAttachment #1: Microsoft_Word__How_do_negative_and_imaginary.pdf

'Mirroring just creates redundancy': this is the key point.

One can add that each Time that a Symmetry is 'observed', there is no Physics, no Observation but just Language. At the end of his life, Bertrand Russell discovered that he was wrong before and that Algebra was not 'pure water'.

Speaking about 'redundancy' one have to mention Wittgenstein here who fighted against Russell using lots of redundancy.

Modern Physics and its 'Black Holes', 'String Theory', 'Expansible World', 'Non-Euclidian Geometry' is just a Looming.

Even if it is the most politically uncorrect subject-matter here, problem of Engineers must be boarded.

I am including G. Galileo and R. Descartes because of their ballistic Science that drives to 'Scale Ideology' that swallows Matter like the Sea is swallowing the Sun at the Sunset. I do insist on the comparison with the sunset because the Looming I am speaking about is a Sailor's ideology (I was listening to a French sailor recently who crossed the Oceans many times and he was explaining that everything on the Sea is a question of Sound.)

Difference between Descartes and today engineers is that Descartes does know that the 'String Theory' comes FROM Sound and Music although today String Scientists think that their theory is going TOWARD poetry and music. They went across the Mirror. Exactly like the young guy that played video games too much and does not know anymore exactly where the reality is. In or out of the Game? In front of him or behind him?

Einstein was obviously disturbed by the fact that the Empiricism/Ballistic Science does not correspond to his own intimate idea of 'flowing' Time. But he is exchanging the right mirror against a concave one which is not less static but gives only the IDEA of flow and wave.

See C. Rovelli's essay for instance: at his turn he is disturbed by Einstein intimate idea and its consequences on Ballistics. So he is letting Einstein's idea on one side like Descartes did more than three hundred years ago. What sounds incredible to me is that contrarily to Descartes Rovelli is forgetting the Time but keeping the Time Dimension!!

This difference between Descartes and Rovelli is coming from the fact that Descartes is one of the fathers of the Algebraic Geometry and the Trigonometry. He does understand it better than his followers and especially the entanglement between Physics and Metaphysics.

But Rovelli is still in Descartes' reference as Einstein and Poincaré were.

Descartes is somewhere mixing Physics and the language... as Rovelli does. But therefore Rovelli is mixing Metaphysics and Physics without beeing aware of this, contrarily to Descartes. Descartes' Rationalism drives to Rovelli's Irrationalism.

So, I have two suggestions for today engineers:

-First one is to solve the problem at Descartes' level: all the paradoxes are still in Descartes' 'Natural Philosophy' and the ball is not as much entangled as it is now after Schrödinger's cat, Feynman's jokes, and all that stuff.

-And if it is just a problem of rules, scales, nothing about Physics, engineers should just organize a poll to decide to choose 'arrows' or 'blocks' to play the game, not blocks and arrows together, what Father Descartes would have condemned for sure himself as a deviation. Because you cannot square the Circle with the tools that are made for cubing one Sphere.

(Comment on my own forum is the same.)