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CATEGORY: The Nature of Time Essay Contest (2008) [back]
TOPIC: Let's benefit from special mathematics for elapsed time by Eckard Blumschein [refresh]
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Eckard Blumschein wrote on Dec. 2, 2008 @ 10:41 GMT
Essay Abstract

The best way to a better understanding of the notion time might be to benefit in practice from getting rid of illusions. This essay is presumably the first attempt to elucidate a lot of enigma by attributing causality to the past but merely expected determination to models. It considers ordinary time having lost its natural zero due to abstraction from elapsed time. Fourier analysis of one-sided variables like elapsed time and distance is known to require a trick by Heaviside. It looks as if the also required care in step by step using the related complex calculus was sometimes missing, in particular when quantum mechanics was invented. The strange time-symmetry, which is known to be exclusively attributed to the microscopic world, can be explained as a result of improper interpretation. Heisenberg’s canonical quantization condition is also claimed to be an admittedly reasonable artifact for a simple reason that was further substantiated by performing a spectral analysis not as a complex Fourier transform with -oo0. Already tangible benefits are reported from the application of cosine transform in particular for mimicking the function of the inner ear. A more natural spectrogram was obtained by means of simple but uncommon methods. In addition to more practical suggestions concerning mathematical methods, food for meta-mathematical thought is added. It relates not just to Buridan’s donkey and v. Neumann’s confession to not believe in Hilbert space any more but also to the numbers thought to completely constituting a continuous time scale. Hopefully, a suggested introduction of “irreal” numbers can contribute to a clarification.

Author Bio

Dr.-Ing. Eckard Blumschein is a retired teacher of Electrical Engineering. He was with to Otto von Guericke University of Magdeburg since 1966. There he developed inverter control of arc welding. Because welding by ear still outperforms complex signal processing, and the usual spectrograms has notorious imperfections, he asked for reasons and revealed arbitrary redundancies. He managed mimicking spectral analysis within the cochlea by cosine transform and suspects improper interpretation of complex calculus in quantum mechanics, too. Meanwhile he feels forced to deal with basic notions like time, number, and continuum.

Download Essay PDF File

Ryan Westafer wrote on Dec. 2, 2008 @ 17:07 GMT
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!

Eckard Blumschein wrote on Dec. 2, 2008 @ 22:27 GMT
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 and other messages ranging up to M285. Currently there is a discussion on cochlear amplifier managed by Matt Flax.

Peter Morgan wrote on Dec. 4, 2008 @ 04:56 GMT
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.


Eckard Blumschein wrote on Dec. 4, 2008 @ 15:21 GMT
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.



Eckard Blumschein wrote on Dec. 5, 2008 @ 07:11 GMT
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

T H Ray wrote on Dec. 5, 2008 @ 14:11 GMT

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.


Eckard Blumschein wrote on Dec. 5, 2008 @ 17:08 GMT

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,


T H Ray wrote on Dec. 6, 2008 @ 01:10 GMT
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.


Eckard Blumschein wrote on Dec. 6, 2008 @ 11:33 GMT

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:


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:

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.



Eckard Blumschein wrote on Dec. 6, 2008 @ 11:41 GMT
I am sorry, the attached file was too large (7.4 MB).

You might find it at



Eckard Blumschein wrote on Dec. 11, 2008 @ 07:32 GMT
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

Eckard Blumschein wrote on Dec. 12, 2008 @ 13:55 GMT
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.


Eckard Blumschein

Eckard Blumschein wrote on Dec. 13, 2008 @ 08:53 GMT
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...

view entire post

Eckard Blumschein wrote on Dec. 13, 2008 @ 08:58 GMT
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

Eckard Blumschein wrote on Dec. 13, 2008 @ 16:28 GMT
Hopefully this will not be cut:

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

Eckard Blumschein wrote on Dec. 14, 2008 @ 00:33 GMT
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

Eckard Blumschein

Armin Nikkhah Shirazi wrote on Dec. 17, 2008 @ 04:19 GMT

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.


Eckard Blumschein wrote on Dec. 18, 2008 @ 01:10 GMT
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?"



attachments: Microsoft_Word__How_do_negative_and_imaginary.pdf

F. Le Rouge wrote on Dec. 18, 2008 @ 08:59 GMT
'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...

view entire post

Eckard Blumschein wrote on Dec. 18, 2008 @ 17:31 GMT
Dear Frenchman,

Since we agree in important issues, I will tell you that both me as a German and you as a Frenchman do not not have a perfect command of English. Maybe, this contributes to the lacking awareness of the majority to what we have to announce.

I do not understand your word Looming. One says that something looms when it appears as a tall, unclear shape, often in a frightening way.

You are calling it "the" key point that mirroring creates redundancy. I am claiming having found several obvious mistakes. The most uncommon insight of mine is perhaps that our usual notion of time is secondary with respect to the primary because reality bound already elapsed time.

If you have any question or comment to the attachment to my last post, please tell it to us. I will include it in the second part.

By the way, we should not suspect Professor Rovelli a conjurer just because his name reminds of circus. And besides Descartes, there are many other very famous French mathematicians who are related to how we deal with time. Let me just mention a few: Buridan, Fermat, Laplace, Fourier, Cauchy, Dirichlet, Meray

Thank you in advance,


Eckard Blumschein wrote on Dec. 20, 2008 @ 00:13 GMT
Please find attached part 2.

attachments: Microsoft_Word__How_do_part_2.pdf

F. Le Rouge wrote on Dec. 20, 2008 @ 20:34 GMT
- In the nautical language 'looming' is a mirage.

- P. Fermat is no doubt a better Scientists than R. Descartes; he is pointing for example some mistakes of Galileo that Descartes did not even noticed. But I am afraid that the influence of Descartes on European Science was far more big than Fermat.

Therefore Descartes is more complete than Newton or Huygens. You can compare his metaphysics to his science easily, what is more difficult with Newton. The big change that is determining Rovelli and C. Stoica is in Descartes' method already. Before Descartes -Galileo for instance- Scientists had a Metaphysics that they were extending to Physics. Big change is that -starting from Descartes- Physics becomes Metaphysics (Proved by the fact that Newton or Einstein became sort of new Saints.)

Why? Because Descartes wanted to forget Time and speed that is to say Metaphysics in his ballistic Science! The today entanglement is coming from the willing of Descartes to be clearer. Splitting Physics from Metaphysics he contributed to kill the second one and to the big confusion in Modern Physics that is breaking the surface here because Time question is like Pandora's box.

Behind Einstein's Algebra there is an attempt to put more Time or Idea or Metaphysics in Science that some Scientists or Ingeneers do not even see.

In the LHC experience one want to understand the World with ballistic laws what would have been for sure a shock for Descartes or Newton.

Eckard Blumschein wrote on Dec. 21, 2008 @ 21:26 GMT
I was told, Fermat invented what led to dx/dt when he calculated extrema. This was 35 years before Newton in 1629.

Metaphysics originally meant an addition to physics.

Aren't functions of time and functions of frequency/energy equivalent?

Narendra nath wrote on Dec. 28, 2008 @ 04:59 GMT
Dear Eckard,

i have just gone through your postings and have yet to go through the full text of the essay. May i say that i am fully with you and Frenchman, Le Rouge , with whom i had interactions on my essay too. Let me say that innovations are something that are hard to digest by the conventional carrer scientists or even other professionals. if you permit i have bad experiences of many rejections in my professional work. i have a strong tendency towards enginnering in Physics and have 3/4 Patents too. Very rarely mt normal Physicists colleagues say that you are doing 'useless'things and even wasting your time. But i have noted at my age (76 yrs. ) that persistence pays, more if it gets coupled with humility and silence against 'casual' criticism. Please continue with what you are sure of as if nothing matters in this world but sincere work, diligence in a selfless manner. No sermons, please excuse me. Carlo has beaten me in votes and i am very happy for it, please blieve me. Nature is far far above science/rechnology and so is humanity. et us bow before the Nature and its secrets and continue to unravel these 'secrets ' to the best of our ability and experience.

Narendra nath wrote on Dec. 28, 2008 @ 05:42 GMT
Read the text of the essay. To me, it is a nice exposition. i use to wonder why when we use Maths in Physics faithfully, we neglect the unphysical solutions. Are we missing something in the process? i also wonder about the significance of numbers in Physicsreality. To me there are just two numbers and the rest are all derivable from these two, 0 and 1, either through summation or raising the power. In this context, i wonder what is the significance of exponential? I realized that is what is a fact when a quantity decreses or increases under pure random or 'chance' environments. About negative numbers, in Physics, we start to talk of 'vacuum' as containing all such negative energy states that are full.Only a vacancy in any of these appears as a physical reality--Dirac.Thus, we see greated significance for what we mean by the number 0. We can't call it as nothing in Physics. Vacuum is not nothing. It has a meaning. Even, physically can we ever attain perfect vacuum? Does it exist even in our universe where apparently there is no matter! In the atom alsowe have a similar sitaution. Only the nucleus is occupied by mass and the rest is very very good vacuum, for all practical purposes. Then, see the particle structure as the Theory of Strings/Super strings. It is just vibrations and nothing else. Thus mass/energy are just mere vibrations in space, nothing concrete as we imagine as an ordinary person. Thus, everything appears to be all 'illusionary' What is the reality! May be there is a non-physical thing called 'consciousness'. It becomes physical as soon as it vibrates, otherwise it remains unobservable! We all know of 'awreness'. may i say that 'consciousness' has various levels of 'awareness', even beyond what we humans feel through our body sensors through the brain. i also wondered what the term 'mind' means. The only way ican understand is to go beyond the ususl human sensors, as mind is not analogous to any body organ. Let me say, the mind projects our individual consciousness that has extension beyond our body too. Thus, there will be lots of individual consciousness and these exist along with the 'pure' or vibration-free consciuosness.

These are all conjectures too, as science can never confirm something that is non-physical in nature!

in typing i commit many spelling omissions that may be excused!

Eckard Blumschein wrote on Dec. 28, 2008 @ 22:21 GMT
Dear Narendra Nath,

Thank you for reading my essay. You wrote: "I use to wonder why ... we neglect the unphysical solutions." You did not write I used to... Perhaps, I have to apologize for not clearly enough explaining that the differential equations do not at all correctly describe the basic relationship in reality. Any step min a process in reality is the sum of already real influences.

Therefore, reality is most closely described by integration, not by derivatives. Abstraction from reality to the abstract "physical" quantity time gets rid of the so called arrow of time. The abstracted Christian time is negative BC and positive AC (after birth of Christ). I hope that at least non-Christian scientists will admit that this choice is arbitrary.

The price for such decision at will is ambiguity. That's why the advanced solution is unrealistic and must be excluded.

With pleasure I would like to add scores of further comments after this detail has been fully accepted.



Narendra wrote on Dec. 30, 2008 @ 04:36 GMT
Dear Eckard,

i have put up a response to your post on my essay site. Hope it makes up any misunderstanind,as i feel alike with you. Let us understand that our imagination demands 'absolute truth' but science can only provide better and better relative truths. In fact science ends when the absolute truth is realized!Let us persue both and remain as broadminded as we possibly can. This will help in uniting us all and realize that universal love is the most sacred thing that exists in the universe.

Eckard Blumschein wrote on Dec. 30, 2008 @ 10:47 GMT
Dear Narendra,

As Popper pointed out, falsification is mostly more reliable than verification. In this sense I hope to have provided at least an attempt to solve some putative enigma.

What about universal love, do you know G. E. Lessing's "Ringparabel"?

Eckard Blumschein wrote on Dec. 31, 2008 @ 04:00 GMT
This is a reply of me, Eckard Blumschein, to what Narendra wrote in his thread. Those who might feel offended by criticism on religions should not read it.

Was there really a creation = Big Bang? Is there a block universe? Does spacetime include future time?

Religions suggest a confirming answer. We all learned to integrate from minus infinity to plus infinity.

Let me start with Adam and Eve. I see this story perhaps wrong for meanwhile evident genetic reasons and just an illustration for the idea of an almighty god.

Religion tells that god created the man as a copy of himself. Actually men created the understandably instrumental idol god like a copy of a superman.

My point is the perverting confusion in this case. Likewise the elapsed time and an abstract time were confused. Infinity alias eternity was attributed to god. The tangible elapsed time was perverted to something allegedly illusionary. While nobody has problems to understand that his own age steadily increases, the usual abstract notion of time has reached priority and dominated even modern physics regardless of the fact that it cannot be measured at all.

What about eternity, the religions attribute it only to god. Anything else is declared doomed to die. Indeed, life of any individual and any physical object is limited. Death and life mutually complement each other. Religions asked for a perverse while understandable from intention question: Is there life after the death? They even suggested eternal life in heaven or rebirth.

In all, religious tenets have proven to freeze obviously wrong ideas that have a clearly intentional background.

Isn't the desire to foresee future understandable? Isn't it tempting blurring the difference between past and future?

Narendra wrote on Dec. 31, 2008 @ 04:05 GMT
hanks , Eckard for your interactions. All my best wishes in your endevours.

Eckard Blumschein wrote on Dec. 31, 2008 @ 10:19 GMT
While I respect the role of religion in social life, I cannot confirm any reproducible evidence and positive significance of the belief in god for physics.

Eckard Blumschein wrote on Jan. 11, 2009 @ 00:12 GMT
Dear Elliot,

As promised, I will reply here for the sake of readability.

Having experienced bad things due to a „heroic thinking leader of a nation“, I do not share the widespread desire to idolize people. On the contrary, I suspected Minkowski was not as sure as he pretended to be about his two symmetrical cones.

I agree that the laws of physics will certainly be valid...

view entire post

Brian Beverly wrote on Jan. 18, 2009 @ 03:32 GMT
Hey Eckard,

I want our discussion of complex analysis on as many essay forums that will allow it. The measurement problem in physics is where it is implied that imaginary time is ordered:


The mathematical axioms tell us that complex numbers can not be ordered.

Order Axioms:

1) A number can not be less than itself

2) x > y, x < y, or x = y

3) if x > 0 and y > 0, then xy > 0

4) if x < y, then for all z, x + z < z + y

5) if x < y, then for all z, xz < yz

set x = i and y = 2i and z= 2 + i

1) makes sense

2) i < 2i makes sense

3) a bit tricky:

0 = 0 + 0i and i = 0 +1i therefore i>0 and 2i>0

(i)(2i) > 0 ---> -2 > 0 FALSE!

4) 2 + 2i < 2 + 3i (complex # is of the form a + bi)

5) This is the key axiom!

xz = what exactly? xz or x*z (* is complex conjugate i*=-i)

If we distribute xz as we do for real numbers then axiom 5 is false. If we take the complex conjugate x*z then axiom 5 is true.

Quantum mechanics relies on C* algebra which is ordered. What is the big idea of C* algebra? C*C, multiply a complex number by a complex conjugate and you end up with a real order/countable number.

By the axioms of math the measurement problem does not exist in physics.

Brian Beverly wrote on Jan. 18, 2009 @ 03:36 GMT
I almost forgot I found an interesting paragraph on Wolfram's mathworld:

storically, the geometric representation of a complex number as simply a point in the plane was important because it made the whole idea of a complex number more acceptable. In particular, "imaginary" numbers became accepted partly through their visualization. Unlike real numbers, complex numbers do not have a natural ordering, so there is no analog of complex-valued inequalities. This property is not so surprising however when they are viewed as being elements in the complex plane, since points in a plane also lack a natural ordering."

Eckard Blumschein wrote on Jan. 19, 2009 @ 08:18 GMT

If the dilemma between either poor time resolution or poor frequency resolution was due to complex representation, then it would be restricted to complex Fourier transform. However, this is not the case. Uncertainty also belongs to the real-valued cosine transform.

By the way, I would like to add to 2) x > y, x = y, x < y the so called 4th logical possibility x || y.

Already Brouwer claimed that trichotomy does not hold for real numbers. The notion real number has been rubber-like defined as to cover the quite different meanings of rational and irrational numbers.

That's why I suggested to call the uncountable numbers, which can be thought to constitute the genuine continuum every part of which has parts, "irreal" instead of real.

Incidentally, Cantor used his first diagonal argument in order to demonstrate that points in a plane are countable according to his definition. He "ordered" the rationals.

I found out that the decisive distinction to be made is between continuum and discrete points. Functions of a quantity that related to a so called conjugate one like e.g. radius to wave number or elapsed time to frequency are continuous in one domain while necessarily discrete in the complementary one and the other way round.

As I already mentioned elsewhere I do not have problems with complex representation but would appreciate you to explain to me why Einstein believed that Ritz was wrong when he stressed that the future cannot influence the past.


Eckard Blumschein

Don't worry about the

Eckard Blumschein wrote on Jan. 24, 2009 @ 18:02 GMT
Thank you Brian,

You put two replies as pdf on your thread.

I am not sure, maybe the agreement to disagree was indeed based on mistakes on both sides.

Ritz was obviously correct in that the future cannot influence the past while his own theory was flawed.

Einstein was obviously correct in that entropy can be explained by the combination of a huge number of superpositions and appropriately calculated by means of probabilistic methods although he later uttered god does not play dice.

However, I consider it Einstein's mistake to assume in 1907 a model for solids composed of harmonic oscillators, oscillating forever. This belief hindered him for his lifetime to get rid of the notion of an eternal and a priori god-given time.

When I briefly looked at

I was disappointed because apparently nobody so far was ready to distinguish between the physically real past time and the abstract notion that is usually called time.

Maybe, I will find something that comes close among the tensed theories of time.

Best regards,


Brian Beverly wrote on Jan. 28, 2009 @ 00:50 GMT

I was surprised that Einstein argued that the arrow of time was due to probabilities too because he said "god does not play dice". Maybe it was because he became famous for relativity? Although it seems he felt a stochastic model for time is correct. As far as harmonic oscillators going forever this does in principle not happen. As the temperature cools a Bose-Einstein condensate will form. The oscillators are not an example of perpetual motion. Could you please clarify the difference between past time and abstract time?


Eckard Blumschein wrote on Jan. 28, 2009 @ 22:09 GMT

Let me begin with your question. I consider the order of all those events for in principle known that might have been contributed to the process of concern. This process can for instance be you or a measurement actually performed by you. In this sense, your past time is measured as your steadily growing age. Notice: It relates to the very moment from which you are looking back. While this choice is highly uncommon in science, I consider it the natural scale because it always includes anything that already got reality relative to your perspective. Any forecast does not matter if one relates to traces of events having influenced reality. You cannot shift this scale. It belongs to the process "you".

If you made a model of this order or more likely are using a model made by others, then this model of your past is something different. It can be compared with a movie of your life. Abstract time includes abstract past but it is not restricted to it. Future is always just an abstract model.

I consider physics naive as long as it does not distinguish between the reality itself and the more or less matching models of it.

What was the reason of so called crisis of banks? Overly intelligent, horribly clever people took the future for reality. They ignored that economy is not a closed system and therefore not a predictable one.

Einstein believed in "deep" laws of nature to be discovered. While he quickly grasped ideas by Boltzmann, Lorentz, Planck, etc., he firmly believed in causal order. It was Planck who made Einstein famous.

You are correct, in reality perhaps no oscillator will oscillate for ever. Therefore cosine and sine functions are merely approximations of reality. Any life is a span between birth and death. How much of it is already real past depends on the point of view.


Brian Beverly wrote on Jan. 29, 2009 @ 08:24 GMT
I will start with your first question, the problem with the banks was the central banks and greed. I still am not sure I understand the differene between your two descriptions fo time. Cosine and Sine are approximations but to what order of their taylor expansion?

Eckard Blumschein wrote on Jan. 31, 2009 @ 04:26 GMT

Usual time is not measurable. It is an abstraction. I do not have any reproach towards religions except for they demand to not question very basic tenets.

In church I learned: Our father in heaven, you were and will be in eternity. The intention is the same with regard to time and space. Our horizon is obviously limited. Anti-worlds and anti-time (strange transinfinite...

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Brian Beverly wrote on Jan. 31, 2009 @ 06:43 GMT

Well said.

I would like to see some of your work on complex signal processing so I can understand your ideas better. Do you have any links or documents?

Eckard Blumschein wrote on Jan. 31, 2009 @ 13:52 GMT

Did you already read my IEEE paper?


Brian Beverly wrote on Feb. 1, 2009 @ 05:25 GMT

Give me sometime to review your essay and two attachments again as well as review your IEEE paper. It will take me a little while because I have not examined Fourier analysis in depth for over 5 years.


Eckard Blumschein wrote on Feb. 2, 2009 @ 12:26 GMT

You are quite right. Careful work requires time. While my time is limited, I will also try and explain more in detail to engineers why restriction to functions of positive argument avoids notorious flaws in signal processing.

Many hoity-toity experts are just not ready to believe that my real-valued frequency-versus-time representation is correct. They cannot deny that is very similar to result of physiological measurement. But they learned and stubbornly believe that cosine transform is only a special case of Fourier transform. Among them is Dick Lyon, who wrote a paper "cochlea demystification". In a discussion group there are many mutually excluding explanations and everyone sticks on his own for decades.


Brian Beverly wrote on Feb. 26, 2009 @ 01:27 GMT
Dear Eckard,

I have reviewed Fourier analysis somewhat but reading your essay and papers again has reminded me of something I should be doing in quantum.

You mentioned something in your IEEE paper I absolutely agree with, “measurement that is based on complex analysis should generally be considered with precaution.”

If I understand acoustics correctly then any signal can be expressed as a series of terms of the fundamental and harmonics. This is very similar to the ground state and excited states of a quantum system. Eventually the measurement problem and collapse must be explained, how would you tackle these problems?

While I’m just barely competent, my gut feeling for the collapse of the wavefunction would be something similar to noise in a signal. I have read that a signal with high fidelity has a large coefficient for the important terms in the Fourier series. In quantum these coefficients are the probabilities, and when we measure the wavefunction (pass the signal through a network) we collapse it to an eigenvalue. In other words one of these coefficients becomes 1 and the others become zero (filtering?). Considering your lifetime of wisdom with signals and Fourier analysis it would be a crime if I didn't learn as much as I can from you.


Eckard Blumschein wrote on Mar. 4, 2009 @ 07:51 GMT
Dear Brian,

When I read the sentence you quoted, I was not cautious enough myself. If one knows how to correctly apply and interpret complex calculus then there is no reason for distrust.

My criticism with respect to quantum mechanics mainly focuses on the following details:

1) I did not found application to quantum mechanics of the complex ansatz exp(i omega t) before the paper by Kramers and Heisenberg in Z. Phys. 31, 681 (1925).

They even wrote:

The object of this work is to show how the careful application od correspondence ideas leads to the surprising result that the ansatz ... is very useful ...

To me, Kramers is known for his theory of dispersion and so called Kramers-Kronig relations.


to be continued

Eckard Blumschein wrote on Mar. 5, 2009 @ 08:36 GMT
2) Kramers expressed the real part n (phase velocity) as an integral of the imaginary part k (absorption). I did not find any indication that he was aware of the limitation for functions of time to either only positive or only negative values of time. This limitation is not just obvious for what already has been reality but also for the opposite point of view where for a closed ideal system the past does not matter.

3) While above mentioned paper was submitted in January 1925, Heisenberg submitted in July 1925 in Z. Phys. 33, 879 a paper that reveals: He intended to perform an inverse transform. At least he wrote for the last time Re for real part. He also correctly explained that a common phase is arbitrary and without physical significance.

4) to be continued

Brian Beverly wrote on Mar. 6, 2009 @ 04:43 GMT
Dear Eckard,

Thank you for 1-3 and I look forward to [4...n]. Your posts have become a priceless resource for me.

I'm working on something which is for the moment a very rough idea, but I think you will like it when it is completed and polished.

Eckard Blumschein wrote on Mar. 6, 2009 @ 15:09 GMT
4) Heisenberg wrote in letters to Pauli: On June 21, 1925: "Bohr's theory of hydrogen seems to me formally very much the same as Kramers' dispersions theory", on July 9: "My whole troubled efforts are intended to totally destroy the idea of the orbits.." and on July 9: "... Kramers called me the optimist".

Born received Heisenberg's manuscript on July 11, 1925 and wrote on July 15 to Einstein: "... looks very mysterious but is surely correct and deep". Born appreciated in particular Heisenberg's form of the quantization condition:

pq-qp=h/(i 2 pi).

When Pauli refused to join Born's team, Pauli said:"Yes, I know you are fond of tedious and complicated formalism. You are only going to spoil Heisenberg's physical ideas by your futile mathematics".

The paper of Sept. 27 by Born and Jordan in Z. Phys. 34, 858 (1925) gave credit to Heisenberg's assumption that the square of the magnitude of the element of the matrix representing the electric moment of the atom is a measure of the transition probability. It was motivated by Born's observation in 1924 that Einstein's emission probabilities correspond to squares of classical amplitudes.

This seems to answer my questions why Kramers' representation in terms of real and imaginary part was replaced by a representation in terms of magnitude and phase.

5) Born not only found out that Heisenberg effectively used matrix multiplication, and took the Hamiltonian point of view. He also underlined that pq and pq are not identical:

The matrices must be hermitian: q(nm)=q(mn)* for all real t.

6) to be continued

Eckard Blumschein wrote on Mar. 7, 2009 @ 13:05 GMT
6) In 5) m and n stand for quantum numbers. With omega(nm) = -omega(mn), cf. Equ. (26) in Born/Jordan Z. Phys. 34, 858 (1925), the matrices p and q must be hermitian, of course.

However, I did not find a compelling physical explanation why they must be hermitian. Why not admitting an expansion into cosine terms instead of complex exponential ones?

Born just borrowed the Hamiltonian from classical mechanics where complex calculus considerably facilitates the work but complex numbers are dispensable in principle.

Engineers know: Functions of time and functions of frequency are related to each other by Hermitian matrices if they are considered complex. Then the eigenvalues are real, and the eigenvectors are mutually orthogonal. They are related to each other via Fourier transform.

At least in classical physics, Fourier transform and cosine transform are equivalent to each other for the following reason: Since it would be absolutely nonsensical to have a result of analysis after all future at t=oo, the assumed end of integration is definitely always followed by something not yet existing.

Nobody at the time of Born already understood that complex representation is twice redundant. The sine and cosine function just differ in the arbitrary choice of the point t=0.

Eckard Blumschein wrote on Mar. 7, 2009 @ 22:45 GMT
7) I did not yet read Chapter 3 Connection with the Theory of the Eigenvalues of Hermitian Forms in Z. Phys 35, 557 (1926) by Born, Heisenberg, and Jordan. In Z. Phys. 43, 172 (1927) Heisenberg refers to "canonically conjugate dynamical variables" without however explaining the essence of this conjugacy. It is common tenet to attribute both the so called commutation relation pq-qp = h_bar/i and the uncertainty to them: "The more accurately the position is known, the less accurately the momentum is known and conversely."

I revealed that the same uncertainty also affects not only the Fourier transform pair f(t) and F(omega) with the conjugate variables time and frequency but also the cosine transform pair of the same while unilateral variables.

I conclude from this that the imaginary commutation relation must not be considered a quantization relation because imaginary values are precluded with cosine transform.

Plancks constant can be reckoned to the left side.

Heisenberg perhaps already understood that Bohmian guiding waves are fictitious envelopes.

In all I have to apologize for a horrible suspicion: Pauli was possibly not even wrong with his judgment on Born. Later he dealt without convincing result with the question whether and if so why quantum mechanics is the only field of physics that absolutely needs imaginary numbers.

I do not hide that I also tend to suspect: Georg Cantor misused Galileo Galilei's method of bijection, and Oppenheim made the idea of cepstrum by Tukey and others tedious and unnecessarily complicated. If we prefer to accept application as the final judge then it seems to be obvious that neither aleph_2 nor the complex cepstrum found any application so far.

What about quantum mechanics, it is my gut feeling that at least time-symmetry is for plausible reasons an aviodable artifact. Schroedinger repeatedly recommended to take the real part of psi: Naturwiss. 14, 664 (1926); Z. Phys. 4. Mitt. (1926). He still stuck on the traditional point of view where f(t) belongs to reality while F(omega) belongs to the complex domain. This is not compatible with a real and always positive Hamiltonian.

Eckard Blumschein wrote on Mar. 9, 2009 @ 13:00 GMT
8) Meanwhile I got aware of a paper by Schwarzschild, 1916 "Zur Quantenhypothese" where he used the Hamiltonian and the term "canonically conjugate", and he reported that already "Planck has noted that the elementary domains of phase space must be complete". WRT H Schwarzschild refers to Charlier, Mechanik des Himmels, Bd. I (Leipzig 1902).

Brian Beverly wrote on Apr. 14, 2009 @ 08:47 GMT

I'm not sure if you're still checking your forum but you should know that you've been very helpful and encouraging. I'm still working through this idea and I have had to overcome some major sticking points (more like fixed points). I hope to have something very solid in a month but finding the time to play and think about it has been difficult.

Eckard Blumschein wrote on Apr. 21, 2009 @ 17:51 GMT

Thank you for your encouraging words. I did not check fqxi on a regular basis. One reason for that was my effort to convince those who are still using the traditional theory in so called filterbank models of cochlear function, e.g. by Dick Lyon, Roy D. Patterson, or Frank Baumgarte that my method is not by chance superior. Even the physicist Dr. Strube tried to persuade me that my method is something like a special case of convolution.

The main obstacle seems to be ubiquitous thinking in terms of ergodicity. Not just Einstein imagined closed dynamical systems whose trajectories are given for good quasi by god. Consequently Einstein did not understand what he called the merely illusive separation into past, present and future.

I looked into Aseltine 'Transform Method in Linear System Analysis' NY: McGraw-Hill 1958. Already Fig. 2-1. showed "Three functions (of time) which have the same L-transform".

The late Einstein confessed that the Now worries him seriously, and there is something essential about the Now which is just outside the realm of (his) science.

I consider Claude Shannon refreshing the trivial insight that the past is closed while the future is open to influences.

In his quarrel with Ritz Einstein uttered his belief that one may restrict oneself without essentially restricting the generality of the consideration. He obviously missed the point.

Brian Beverly wrote on May. 15, 2009 @ 06:30 GMT
Eckard! Thanks for your feedback, ignore that idea because it needs about five more years of gestation. I hope to see another essay from you I suspect you have a lot of ideas about what is physically possible and impossible ;)

Eckard Blumschein wrote on May. 16, 2009 @ 22:06 GMT

While I feel not too old for obeying a piece of advice from someone perhaps considerably younger, I am not sure what "idea" of mine you are referring to.

What about my criticism concerning the belief in the cochlear traveling wave model which was selected by v. Bekesy and cast in hydro-mathematics by Lighthill, Tianying Ren recently provided direct evidence that there is no backwards traveling wave while the proponents still are claiming the opposite. Referees tend to defend opinions that were awarded by a Nobel price no matter whether or not they are tenable. Several experimental findings by Ren challenged the old tenets. Prof. Ren repeatedly managed to publish unwelcome results in PNAS and Nature neuroscience. However he was unable to publish all data and in particular papers in JASA.

What about the not yet existing future, I see it related, and my criticism of sometimes dirty use of complex numbers is well founded. At least, nobody so far could refute my arguments, and I conclude from obviously unresolved incompatibilities between quantum physics and other putative fundamentals of physics that there is still room for a basic correction. The ultimate argument of physicists against my hints was: This is a matter of philosophy rather than physics. I do not think so.

Brian Beverly wrote on May. 27, 2009 @ 00:00 GMT

My apologies, I didn't mean ignore your ideas because I know they are legitimate. I meant ignore my idea about space and time with the convergent fixed point of the cosine function. It was a random thought and I'm going to have to spend a lot of time thinking it through.

Physics will benefit from my of your "ideas":


"Tianying Ren recently provided direct evidence that there is no backwards traveling wave while the proponents still are claiming the opposite."

Physics uses a similar idea of the backward travelling wave to explain the quantum tunneling in the finite square well. I'm glad you mentioned it because I always accepted it and now I'm curious if it is the right explanation.


"What about the not yet existing future, I see it related, and my criticism of sometimes dirty use of complex numbers is well founded."

I agree Eckard in my essay I wanted to rid the wavefunction of imaginary numbers because physicists use them to justify the multiverse and other ridiculous interpretations. I also wanted to show how the future does not yet exist by connecting it to entropy, combinatorics and probability theory. The imaginary numbers violate the axiom of additivity in probability and the theory is still accepted as fact!


"The ultimate argument of physicists against my hint was: This is a matter of philosophy rather than physics. I do not think so."

Eckard who are referring these journals and how are they qualified? If a theory is axiomatically unacceptable it is not some sort of philosophical interpretation! If experiments contradict the current theory then we are not debating philosophy, it is a cold hard fact of reality (we shouldn't even call it realism because it will be used to justifity philosophical arguments as valid). Historians have a name for the period of time when philosophies were above science. They call it the dark ages. Experiments are the reality check, so fuck them and their philosophies.

My only young advice that you should consider is that when the theory is mathematically unacceptable, and experiments explicitly prove it, then it is your duty as a scientist to rebel against the dominant paradigm.

Every great scientist has been censored I try to think of it as a rite of passage.

Eckard Blumschein wrote on May. 27, 2009 @ 10:35 GMT

You wrote:

1) Physics uses a similar idea of the backward travelling wave to explain the quantum tunneling in the finite square well.

----In case of cochlea, there is compelling evidence against reflection, and therefore the TW must not be considered a genuine wave.

Sommerfield's radiation condition says: Infinity does not reflect waves. I offer a modified...

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Brian Beverly wrote on Jun. 17, 2009 @ 01:50 GMT

I'm not sure I can comment on whether or not we will find the Higgs. My gut feeling is no, but when I did the derivation of the Higgs mechanism my professor was helping me a great deal. I derived it nearly two years ago and now all of the standard model seems like a blur of lagrangians. What I have seen looks like background dependence and that makes me skeptic.

Michel Planat wrote on Apr. 3, 2015 @ 15:40 GMT
Dear Eckard,

I totally agree with the first sentence of your abstract "Some seemingly mysterious interpretations of mathematics by physicists are just unwarranted" and most of what you are writing afterwards. My longstanding interest is to recognize and possibly expand the right mathematics appropriate to a seemingly paradoxal subject. I did it by using number theory for explaining the non-orthodox statistics one find in the so-called 1/f noise that you may know because you worked in signal processing. I do it now by using group concepts for understanding the deep nature of quantum paradoxes such as EPR.

I like that you put the development of mathematics in an historic perspective on p.2 and afterwards and criticize the false ideas that have appeared and have been corrected by the appropriate maths.

I disagree with "physics must be fully consistent with the premise of only one causally connected real world", where this requirement (that reminds the requirement of the preexistence of a space-time) comes from? For example, quantum theory don't need space-time and is acausal.

Finally, I enjoyed reading you and I hope you take the time to read my essay as well.



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