Gordon,

I hope we will help each other to get more attention for our essays. Please don't mistake my criticism of improper use of FT as lacking knowledge. Let me remind of a few of my common sense views which I consider most fundamental "prejudice" (as called by Del Santo from his questionable to me perspective):

- Measured data are fundamental to expected ones, not the other way round.

- Hairs may curl but never truly form closed loops. The same holds for time.

- Accordingly, so called frog's view is basic to the bird's view.

- The barber's paradox worried Frege because he confused frogs with birds.

- Restrictions to elapsed time and cosine transformations fit to frog's views.

- A frog like me (and you?) cannot look backward and forward in time at a time.

Eckard Blumschein

Gordon,

I wrote: ... Dirac possibly ... believed "that this concept of the probability amplitude is perhaps the most fundamental concept of quantum theory"? If my doubt is justified, then it is even more fundamental.

You added in parentheses [the Fourier-based R-F theorem; RFT] after "it".

I agree on that the R-F theorem shows that probability is just a mathematically equivalent option of interpretation.

However, my "it" referred to a much more radical doubt that I tried to express in my essay.

While have to I expect you not immediately agreeing with me in this case, I nonetheless hope for getting treated fair.

Eckard

Stefan Weckbach's essay challenged me to better explain how I interpret the notions fundamental, frog's view, and causality.

As the title of my essay "semi-fundamental structures" indicates, my boss understood fundamental as do I and as does my dictionary too: "very important or basic" (as is the trunk of a tree structure in comparison with less fundamental branches and roots).

To me existence is not "the most fundamental 'fundamental' one can imagine. This is obvious to me in mathematics, see A infinity and B infinities. Does a real number really exist? Do transfinte cardinalities exist? ...

To me causality, except for Aristotle's fourth case, is most fundamental.

I see his causa finalis due to confusion of the basic Frog's view with the abstracted from it birds view.

Eckard Blumschein

Eckard,

Reading your -- "Dirac possibly ... believed that this concept of the probability amplitude is perhaps the most fundamental concept of quantum theory? If my doubt is justified, then it is even more fundamental" --

I took the "it" to refer to Dirac's opinion about the probability amplitude. Hence my comment in the context of the more fundamental R-F theorem.

I see now (and somewhat surprised by your accompanying doubt), that your "it" here "referred to a much more radical doubt that I tried to express in my essay."

Please, what is that radical doubt? I did not see such a thought in your essay; perhaps I am a less-doubting radical?

Thus: there is so much that I agree with in your essay, I truly wonder where your doubt arises. Are you referring to this: "Therefore, some putative pillars of science are suspected to be just semi-fundamental constructs on a shaky basis. Judge yourself." ??

I (see my essay) would strengthen you claim to this (and without doubt): "Some supposed pillars of science are false. Judge for yourself. See how far we advance by rejecting the ubiquitous and unqualified (but primitive) notion of REALISM in physics (it is NAIVE REALISM). That is: simply replace NAIVE REALISM by TRUE REALISM* (the insistence that some existents may change interactively), and see quantum theory derived classically." [Then, relatedly, there is Bell's theorem; as in my essay's Appendix!]

* With such true realism known to me since the age of two, with a photo for proof (me with my rail-spike-for-a-hammer beside a newly-fitted but now smashed porcelain toilet bowl), me having imitated the plumber who (10 minutes earlier) had gently tapped the bowl into the fresh cement with his own steel hammer! dink-dink-dink, I can still hear it! [Me, as ever, trying to make sure things are right ... kaboom.]

This story for you: some light-relief as to why you should, today,** NOT be tense and NOT harbour any doubt, radical or otherwise!

** Given your own analyses, with my essay.

PS: You say, "There is one reality." In agreement, I add, "Reality makes sense and we can understand it." Against Bell, I add, "Correlated tests on correlated things produce correlated results without mystery." To you, I say, "Only the impossible is impossible."

HTH; and loving your very deep essay,

Gordon Watson

More realistic fundamentals: quantum theory from one premiss.

Dear Gordon,

"what is that radical doubt?"

Because the usual notion of time refers to an arbitrarily chosen point t=0 of reference, I doubt that it is an appropriate basis in this case.

This usual scale of time extends from minus infinity to plus infinity and implies therefore the complex Fourier transformation.

Alternatively, the elapsed time refers to something that is non-arbitrary, the actual moment. This scale is always positive, it does permanently slide with respect to the usual scale, and it corresponds to an equivalent real-valued cosine transformation instead FT.

As is obvious since the 1920th but already anchored a decade earlier, QM is based on the usual time scale and accordingly on the redundant complex Fourier view. It doesn't matter whether one prefers Hermitian square matrices or Schroedinger's complex iswave function.

This radicalism of mine is not restricted to QM but it arose from studies of signal processing, in particular of cochlear function.

Eckard

    Continuation:

    A key discrepance between the usual event-related scale and the object-related scale of elapsed time is an steadily growing phase angle between the two different reference points. In case of calculationof a usual spectrograms, one has to accordingly relocate the origin of the usual time scale again and sgain.

    Fröhner mentioned on p. 638 that the wave function is determined only up to a phase factor which is pulled out in his equation (2).

    "The superposition principle had been established first as a puzzling empirical feature of the quantum world, before M. Born recognized that the absolute square of the wave function can be interpreted as probability density." The superposition principle corresponds to the Riesz-Fejér theorem.

    I guess, cosine transform in IR+ with the natural reference point (elapsed time = 0) is also correct.

    Eckard

    MR. Blumschein,

    Nicely written!

    Read and rate it.

    Here is a relater (as far as I understood yours) essay, if you would like to read one (more)

    Corciovei Silviu,

    Hacking the brain is not so easy. Va doresc mult success.

    Perhaps you feel having understood my essay because you are not aware of contradictory theories which are seemingly fundamental in the sense of mandatory.

    You are correct, one may understand "What is fundamental" as a questionable question for a single ultimate fundament of physics.

    My boss, you and I understood "fundamental" differently as a pretty universal feature within a logical structure. My metaphore is a tree with many not fundamental roots and many not fundamental branches at its two ends.

    Toate Bune,

    Eckard

    Addendum:

    When I was a child who collected stamps I noticed the message "In God we trust".

    Weren't Adam and Eve fundamental to everybody? No, at least in this respect, the bible was fundamentally wrong. The same applies for Noah's Arc.

    Familiy trees ramify backwards. Just a single male and female individuum are not enough as to cope with occasional genetic defects.

    Eckard Blumschein

    Gordon Watson wrote:

    "Reality makes sense and we can understand it."

    In my understanding, this is a tautology because I am merely distinguishing between mysticism and conjectured reality of anything including the also comprehensive notion of the physical universe.

    Among the first ones who guided us to get a more fundamental in the sense of comprehensive understanding by consequently excluding mysticism was Lichtenberg (1742-1799),the same professor in Göttingen who coined the notions positive and negative electricity.

    His aphorisms include:

    - Praying in churches doesn't make the ligthning conductor on them unnecessary.

    - God created man to be similar to Him does probably mean, man created God similar to himself.

    Eckard Blumschein

      A religious believer asked me to further expand on this comment. Well, from the perspective of the 18th century, God is most fundamental. Newton argued:

      "God is more important than physics or mathematics. He created the world such as we see it now. Time and space are absolute. Space is the sensorium of God. God winds up the big clock again and again."

      Leibniz distinguished three levels of infinity:

      - the (currently preferred as mathematical) relative one

      - the logically absolute (potential) one

      - God as the highest one.

      Leibniz criticized the absolute space as too restrictive. He argued, God doesn't need winding up the created by Himself big clock, the universe. On behalf of Newton, Samuel Clark commented: This implies God is redundant, Leibniz is close to atheism.

      When I formulated the title of my essay "Semi-fundamental constructs", I was aware of the quite different meaning of the notion semi-fundamental in modern mathematics. With "semi" I rather meant a restriction to a fundament which needn't be straightforward correct but may possibly be of heuristical value.

      I anticipate that only people with common sense will be ready to accept that the age of something is more fundamental than its arbitarily attributed location in a human (e.g. Christian) time scale. Please don't mistake this as blasphemy.

      Only elapsed time, i.e. the age, can be measured.

      Eckard Blumschein

      Dear Eckard, Time is a synonym for universal total movement. Look at my essay, FQXi Fundamental in New Cartesian Physics by Dizhechko Boris Semyonovich Where I showed how radically the physics can change if it follows the principle of identity of space and matter of Descartes. Evaluate and leave your comment there. Then I'll give you a rating . Do not allow New Cartesian Physics go away into nothingness.

      Sincerely, Dizhechko Boris Semyonovich.

      Dorogoi Boric Semyonovich,

      Perhaps you mistook my utterance "time is (merely) a construct" which means it is semifundanental. I meant, ordinary time is not directly measurable on the tevel of reality. It is based on the truly fundamental elapsed time.

      I had two reasons for dealing a bit with what Descartes was teaching in the Netherlands.

      At first his speculation about space challenged Guericke to perform experiments instead.

      Secondly, Descartes combined ancient geometry with the pretty new use of negative numbers into Cartesian coordinates with extension from minus infinity to plus infinity. Ironically he didn't manage reaching as much freedom as possible because in Cartesioan coordinates one necessarily has to arbitrarily choose a point of reference. Hence, Cartesian coordinates are a mathematically perfect construct while not fundamental to physics.

      What about your New Cartesian Physics, I found some interesting claims. However, a more careful scrutiny will take more time. Did you deal with the three belonging experiments (1881, 1889, and 1923) by Michelson?

      Eckard Blumschein

        Dear Eckard Blumschein my attention to the concept of "time" due to the fact that I sometimes try to eliminate it from physics. I get it, but very cumbersome. Therefore, for brevity of presentation, we have to write "time". However, I don't like the phrase "space-time". I believe, that it is equivalent to the phrase "space-movement". The principle of identity of Descartes, then, would be: matter is space and space is matter that moves.

        I also have a claim to infinity from (-) to ( ) if this applies to the axes of the coordinate system, which are used as the inertial reference system in the theory of relativity. You are right that this leads to static. In the dynamics - this leads to existing paradoxes as if to say that in each inertial frame the speed of light is the same. I propose to separate geometrical space, where the statics of matter, from physical space, where the dynamics of matter. The geometric space may be associated with a coordinate system with an infinitely large axes, and each point of physical space you can put a coordinate system with only an infinitely small axes. This explains the results of experiments of Michelson. In geometrical space the speed of light depends on the velocity of the source. In the physical space, in points, of the trajectory of light are infinitesimal inertial frame of reference in which the speed of light is the same. Coming to the receiver, the light demonstrates the constancy of its speed.

        Dear Eckard, your high score I need to develop the New Cartesian Physics on. Visit my page and give your comment there, so I got a notice by e-mail and quickly respond.

        FQXi Fundamental in New Cartesian Physics by Dizhechko Boris Semyonovich

        Do not allow New Cartesian Physics go away into nothingness, which can to be the theory of everything OO.

        Sincerely, Dizhechko Boris Semyonovich.

        Hello Eckard,

        I find your essay relevant, a pleasure to see this redundance and how you interpret the maths and the physics which are different.

        ++++ :)

        Best Regards ; friendly

        Hello Steve,

        The word redundant might be a false friend. An Englishman warned me: Don't use it. I means "dismissed by your employer, out of job" (in German arbeitslos).

        What I intend to express is something quite different: the property of elements in a mathematical structure that are strictly speaking and with respect to an application unnecessary (= needless) in the sense of avoidable, in principle. Redundant elements increase the apparent volume of information. Hence I consider them and the structure that contains them definitely not fundamental.

        This view of mine collides with the also understandable but not always justified strive for more and more generalizing. Several essay authors hope for getting an ultimate fundament of physics by diving "deeper" and deeper. Actually, this strategy leeds to higher and higher levels of abstraction, being as a rule more remote from reality.

        What about my ++++, I enjoyed using the symbol box as long as it wasn't misused as to veil the fundamental difference between past and future. Our ancesters were in position to count elapsed days but not future ones. One can only abstract from fundamental observation, not he other way round.

        You got my essence. Thank you.

        With best regards,

        Eckard

          Some fundamental (historic) details from Lexikon der Antike:

          Jewish time counts from assumed creation of the world at 3761 BC. Greece counted from the first list of winners in panhellenic Olympic games in 776 BC. The Romans started with 753 BC (ab urbe condita). Some Roman provinces each referred to the begin of their Roman rule. Muslims refer to the year of Hedshra 622 AD.

          Abbot Dionysius Exiguus suggested referring to anno domini (AD). Carolus Magnus definitely died in 814 AD.

          The use of time before the birth of Christ (BC), i.e. negative time, goes back to the French theologian D. Petavius (1583-1652).

          Eckard Blumschein

          Dear Eckard,

          I highly appreciate your beautifully written essay.

          It is so close to me. «The alternative dynamic view has proved the more appropriate basis: In reality, in contrast to closed models of processes, the future is more or less open to erratic influences and evades therefore complete prediction».

          «Causality is most fundamental to reality»

          I hope that my modest achievements can be information for reflection for you.

          Vladimir Fedorov

          https://fqxi.org/community/forum/topic/3080