GW

The rules of canonical quantization fixed about 1930 are the foundation of quantization. One rule is postulated, namely the choice of Cartesian coordinates and momenta, is adopted as a necessary assumption. However, such phase space coordinates do not have a metric to choose Cartesian variables. The procedures under the heading of enhanced quantization provide a very different connection between classical and quantum variables and happily it identifies Cartesian variables to confirm their use in Quantization. The new connection permits arbitrary contact transformations which canonical quantization fails to achieve. An added bonus of the new approach not mentioned in my essay is the fact that certain models that fail to have successful canonical quantizations do have successful enhanced quantizations.

JK

    5 days later

    Dear Professor John R. Klauder,

    My research has concluded that Nature must have devised the only permanent real structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

    Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

    JF

    Thanks for your views. I sympathize with the idea of a single universe that can survive the time and events there in. I would include what we can see and what we can not see. If I understand you correctly, I would have difficulty in admittting only a single dimension, however, because the naked eye as well as the many telescopes offer us a three dimensional view of objects within our Universe.

    JK

      • [deleted]

      • Post #25

      Dear Professor John R. Klauder,

      Thank you for your courteous reply. Nobody has ever seen a ball. All observations and photographs of a ball will only ever show it to appear as a flat filled-in disk. That is why the sun, a full moon, and all of the planets always appear as flat filled in disks. Nobody has ever seen a cube. That is why photographs of the New York city skyline always appear to show squares, rectangles, and parallelograms. Nobody has ever seen a supposedly three-dimensional pyramid. Every photograph taken of the Pyramids at Giza only shows them to appear triangular.

      There are no finite dimensions of length, width, depth and time. There only am one single infinite dimension.

      Joe Fisher, Realist

      Dear Professor John R. Klauder,

      Thank you for your courteous reply. Nobody has ever seen a ball. All observations and photographs of a ball will only ever show it to appear as a flat filled-in disk. That is why the sun, a full moon, and all of the planets always appear as flat filled in disks. Nobody has ever seen a cube. That is why photographs of the New York city skyline always appear to show squares, rectangles, and parallelograms. Nobody has ever seen a supposedly three-dimensional pyramid. Every photograph taken of the Pyramids at Giza only shows them to appear triangular.

      There are no finite dimensions of length, width, depth and time. There only am one single infinite dimension.

      Joe Fisher, Realist

      JF

      If we had only 2 dimensional pictures of a ball at a single moment of time I would support your view.

      But for a ball or for a picture of you Joe we can feel the object and know it is really three dimensional. Photos at different times or even a movie are seen as 2dimensional but they may also show different photos as you, say, turn around. We accept that part of you is not visible after you turn around from a position where that part of you was visible. That is easy to understand if you are 3dimensional but not so clear if you accept only 2 dimensional views. Likewise we can see Jupiter and it's multiple moons as moving around that planet as photos and sometimes do not show some moons that were visible in other photos taken at different times. This sight led Galileo to suggest that the planets including the Earth rotate around the Sun.

      I doubt that my words will change your views, but I am just citing additional data from which one can decide what 2 dimensional information observed over time is able to provide a reasonable interpretation of what may be seen.

      JK

        Dear John Rider Klauder,

        Please forget about finite dimensions. A picture of a ball, or a picture of me can be of infinite size. You can only touch the surface of a ball with the surface of your fingers, because I have concluded from my deep research that Nature must have devised the only permanent real structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

        Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

        Dear John Rider Klauder,

        In response to a comment above, you note that "the current rule sometimes leads to nonsense." and elsewhere,

        "The usual rule of the relation of a classical/quantum connection fails sometimes."

        I confess not to have followed your complete argument, however it seems to derive from Dirac's interpretation of all contact transformations in which the classical transformation has a role to play in the quantum theory.

        The classical variable is either random or varies with respect to something. If it varies with respect to something, say z, then we typically form an 'operator' of the form O ~ d/dz, and the formalism that results (incorporating h) is a quantum theory. It is difficult to see how the quantum operator could possibly be more fundamental than the classical variable from which it is derived, and, in fact, the correspondence principle insists that the quantum operator equations must be derived from the appropriate classical Hamiltonian. This seems compatible with your statement that

        "The Hamiltonian operator is the same function of P and Q as the classical Hamiltonian is of p and q ... [plus o(h)]..

        I will not repeat your logic but will say that I agree with your conclusion that

        "The special role played by Cartesian coordinates in canonical quantization is essential."

        Your goal, as I understand it, is "an alternative quantization procedure relating classical and quantum variables to each other", and your derivation of equation (5) seems to yield the correct classical action function without the need to modify the quantum operators at all.

        I did not follow your switch to affine variables, but, to return to your point that "the current rule sometimes leads to nonsense", I would note that Steven Kauffmann (viXra:1707.0116) has shown that the Dirac equation was not derived from a classical Hamiltonian, but was instead influenced by 'space-time symmetry' considerations, and, accordingly, leads to some nonsense results, such as particle speed ~1.7c. Additionally, the result of Dirac's equation is a spin that differs from Pauli's eigenvalue spin; in fact Dirac does not have a spin eigenvalue equation, and such is obtained only after a Foldy-Wouthuysen transformation smears a spin over an extended region (viXra:1411.0096 ).

        If you're wondering where this extended comment is leading, it is the fact that Dirac based his equation on space-time symmetry considerations and my current essay treats the development of space-time symmetry concept. I hope you will read my essay and comment on it.

        Thanks for a very interesting essay,

        My best regards

        Edwin Eugene Klingman

        EK

        The lack of all canonical transformations finding a place within conventional canonical quantization is a minor failure suitable for such an essay. But the real failure, which is not discussed in my essay, is illustrated by the following property. Namely, in canonical quantization the classical Hamiltonian H(p,q) is promoted to a quantum Hamiltonian £(P,Q) which, in the classical limit (h =0) recovers the original classical Hamiltonian H(p,q). I now offer an example in which this criterion fails. Let the classical Hamiltonian be given by (using p= p1, p2, p3,..., q=q1,q2, q3,..., p^2=p1^2+p^2+p^3 + ...,

        and q^2=q1^2+q^2+q^2+..., where the sums run to infinity). We choose

        H(p,q) = a p^2+ b q^2 + c(q^2)^2

        where a, b and c are positive real constants. The quantum Hamiltonian for such a model is given by

        £(P,Q) = a P^2 + b Q^2 + c(Q^2)^2 + ...

        Where Q and P represent a string of conventional canonical quantum operators. Now we ask what is the classical limit of this proposed quantum Hamiltonian and the answer has the form

        H(p,q) = a p^2. + b' q^2

        NAMELY THE QUARTIC INTERACTION TERM HAS VANISHED ANd A NEW COEFFICIENT b'

        HAS BEEN INTRODUCED. This is what I mean that conventional canonical quantization 9has

        FAILED. There are many examples that fail in this manner. I also add the fact that our new procedures in the essay do NOT fail and lead to a satisfactory solution for such problems. I only illustrated the problems with canonical transformations because proving the failure as illustrated here was too complex for an essay.

        JK

        Some errors in the equations of the preceding comment. I put the correct equations below

        p^2= p1^2+p2^2+p3^2 ...

        q^2=q1^2+q2^2+q3^2...

        It's good to see you here John...

        My experience, hearing your lecture at FFP15, was uplifting and enlightening. I felt like the top of my head popped open, at one point, and the heavens opened up so that new knowledge could pour in. I've had that kind of experience only from the best of the world's best scholars before, so I put you in the same category.

        I would add that a visual metaphor was helpful for me to understand this work. An infinite-dimensional Hilbert space provides plenty of room for the Quantum action, and the Classical action can be seen as interactions on a specific restricted subset - a bounded 2-d surface. However; if we vary the characteristics of the restricted target space, we may derive an enhanced quantization rule that lets us obtain results even where that would not otherwise be possible.

        I see this methodology as having great potential for studying the boundary between quantum and classical, automatic reduction vs. no-collapse models, and so on. This might even provide insights for the material covered in my essay (yet to post), which talks about thermodynamic models of gravitation, because I also deal with issues on the quantum-classical boundary.

        All the Best,

        Jonathan

        JD

        I support your view and applaude potential expansion of enhanced quantization.Thanks for your comments.

        JK

          Then let me extemporize...

          The reason I think your work represents an advancement in fundamental Physics is that it provides the missing piece to bring the search full-circle, and so could be a kind of holy grail for QM researchers. My thinking is that it is ill-advised to try to reduce the descriptive vocabulary for QM phenomena too far, because the core of what the subject is about resides in nature's optiony.

          I had the privilege to correspond with Philip Pearle, when he first introduced statevector reduction theory, and I even have a typewritten manuscript of his 'gambler's ruin' paper. But I later became an advocate for no-collapse models, having studied and identifying with decoherence theory in its pure form, and had extended correspondence with H.D. Zeh and briefly with Joos.

          I have more recently come to take seriously the idea that QM is more like a compass with a range of options of different formulations, depending on the kinds of information you have and are hoping to extract. This makes both automatic collapse as in CSL and no-collapse as in decoherence theory relevant to a full understanding of QM. All points on the compass are real, and only the pointer reveals the truth.

          In this context; your enhanced quantization methodology is the missing link.

          All the Best,

          Jonathan

          Hi John Rider Klauder

          You said "This failure is due to the rigid connection of quantum variables arising by promoting the corresponding classical variable from a c-number to a q-number....When Canonical Quantization Fails, Here is How to Fix It ....wonderful solutions, you have very vast experience also sir John Rider Klauder.......wow............. very nice idea.... I highly appreciate your essay and hope for reciprocity.

          I request you please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance

          Some of the Main foundational points of Dynamic Universe Model :

          -No Isotropy

          -No Homogeneity

          -No Space-time continuum

          -Non-uniform density of matter, universe is lumpy

          -No singularities

          -No collisions between bodies

          -No blackholes

          -No warm holes

          -No Bigbang

          -No repulsion between distant Galaxies

          -Non-empty Universe

          -No imaginary or negative time axis

          -No imaginary X, Y, Z axes

          -No differential and Integral Equations mathematically

          -No General Relativity and Model does not reduce to GR on any condition

          -No Creation of matter like Bigbang or steady-state models

          -No many mini Bigbangs

          -No Missing Mass / Dark matter

          -No Dark energy

          -No Bigbang generated CMB detected

          -No Multi-verses

          Here:

          -Accelerating Expanding universe with 33% Blue shifted Galaxies

          -Newton's Gravitation law works everywhere in the same way

          -All bodies dynamically moving

          -All bodies move in dynamic Equilibrium

          -Closed universe model no light or bodies will go away from universe

          -Single Universe no baby universes

          -Time is linear as observed on earth, moving forward only

          -Independent x,y,z coordinate axes and Time axis no interdependencies between axes..

          -UGF (Universal Gravitational Force) calculated on every point-mass

          -Tensors (Linear) used for giving UNIQUE solutions for each time step

          -Uses everyday physics as achievable by engineering

          -21000 linear equations are used in an Excel sheet

          -Computerized calculations uses 16 decimal digit accuracy

          -Data mining and data warehousing techniques are used for data extraction from large amounts of data.

          - Many predictions of Dynamic Universe Model came true....Have a look at

          http://vaksdynamicuniversemodel.blogspot.in/p/blog-page_15.html

          I request you to please have a look at my essay also, and give some of your esteemed criticism for your information........

          Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes its in frequency and finally will convert into neutrinos (mass). We all know that there is no experiment or quest in this direction. Energy conversion happens from mass to energy with the famous E=mC2, the other side of this conversion was not thought off. This is a new fundamental prediction by Dynamic Universe Model, a foundational quest in the area of Astrophysics and Cosmology.

          In accordance with Dynamic Universe Model frequency shift happens on both the sides of spectrum when any electromagnetic radiation passes grazingly near gravitating mass. With this new verification, we will open a new frontier that will unlock a way for formation of the basis for continual Nucleosynthesis (continuous formation of elements) in our Universe. Amount of frequency shift will depend on relative velocity difference. All the papers of author can be downloaded from "http://vaksdynamicuniversemodel.blogspot.in/ "

          I request you to please post your reply in my essay also, so that I can get an intimation that you replied

          Best

          =snp

            JD

            I do not recognize CSL. Please explain. I like your compass picture, but I imagine that different directions reveal alternative formulations that all lead to the same conclusion. I assume your compass includes the Copenhagen view. I find that Copenhagen views can correctly deal with many problems but not all problems that arise in quantizing a given classical model. In a.response above I gave a classical interacting model that becomes non-interacting when quantized. This same model finds a good interacting quantum result using the enhanced quantization rules. I like to say that

            CQ (canonical quantization) is contained in EQ (enhanced quantization) I agree that EQ offers a kind of closure to CQ but surprisingly EQ can provide solutions that CQ cannot. One of these examples deals with covariant scalar fields with a quartic interaction in five and more space time dimensions for which CQ leads to a trivial (= free) solution while EQ leads to a satisfactory non-trivial solution.

            JK

              JD

              Let me propose a different story. For canonical quantization there is a building with a round central open space on the ground floor which has many doors that open to different formulations of CQ. However, we now can see there also is a first floor above with many doors that lead to different formulations of EQ.

              JK

              SNPG

              You cite many conditions that you would like to impose on your analysis. I wish you good luck in finding one or more solutions that fit your constraints.

              I will look at your essay.

              JK

              I am happy to be having this conversation...

              I like your alternative ending to the CQ story. CSL stands for Continuous Spontaneous Localization, and it is a logical endpoint of statevector reduction theory, by combining automatic reduction with gravity (i.e. - reduction by gravitation). I do agree that Copenhagen deserves a place on the compass, with the antipode being the notion that the fundamentals of QM and how a result is arrived at having equal relevance to 'shut up and calculate.'

              Beyond this; the idea of reduction being induced by gravitation may be seen to imply entropy or an entropic force associated with gravity. I presented a poster at FFP10 championing the idea of a common basis for thermodynamic entropy and non-local effects in QM, extending the ideas of spreading and sharing of energy as an entropy metaphor to include information.

              I based these assumptions largely on what I was learning about decoherence theory, but it turned out the pure formulation was ill-equipped to deal with dissipative phenomena or processes. On the other hand; I later learned Sandu Popescu was formulating a very similar picture in the same timeframe (2009) so I was actually more on-target than I imagined at the time.

              More later,

              Jonathan

              Dear John,

              Thank you for this essay, I was pleased to read it! I didn't know about enhanced quantization so far, but it seems to me that it fixes some problems already, and that even more significant results will probably follow. It seems more natural than the canonical quantization, and much better connected with the classical systems that are quantized. Maybe some of the developments will shed more light not only to QFT, but also to the problem of emergence of a classical world from the quantum one, and to the problems related to quantum gravity. I will follow with interest your work.

              Best wishes,

              Cristi