Essay Abstract

To think about mysterious connection between physics and mathematics we need first to understand what mathematics is and what physics is. I see mathematics as a reflection of universal hidden order (in the meaning proposed by David Bohm) in the human rational mind. Physics is the model of the universe created by the human rational mind. The subject of this essay is how to use realize Einstein vision on completeness theorem according to which each element of the physical universe corresponds exactly to the one element of the model. To realize this vision of we apply bijective function of set theory. We build a model the universe in which each mathematical element represents exactly one element of the physical universe.

Author Bio

Amrit Sorli Studied at University of Ljubljana, Slovenia, physics, geodesy, philosophy of science, epistemology, psychology. Amrit is Independent Researcher, co-founder and member of SpaceLife Institute back in 2000 and founder of Foundation of Physics Research Institute - FOPI in 2013. He publish several scientific papers and books. See more on ORCID ID http://orcid.org/0000-0001-6711-4844

Download Essay PDF File

``However out of pure mathematical laws we cannot deduce physical laws.''

We disagree.

    The Noether Theorem regarding the basis for conservation laws is a pretty good example of there at least being a correspondence between mathematical law and physical law.

    Best Regards,

    Gary Simpson

    I am interested in what you say about "Einstein's Completeness Theorem" Where did you find Einstein's definition of completeness of a physical theory? Was this something he wrote about specifically or is it your interpretation of his methods?

    Hi Philip, see that link. yours Amrit

    http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters_2015_Jan_1/quantum_theory_completeness/index.html

    Amrit Sorli's effort to validate "Einstein vision on completeness theorem according to which each element of the physical universe corresponds exactly to the one element of the model" using bijective function of set theory is important. It would have implications for the foundations of quantum theory and may provide explanations for entanglement and similar phenomenon. Let's see where he goes with this.

    Looking forward to additional comments on these important ideas.

    Gus Koehler

    Hi Amrit,

    You argue, as I understand it, to replace time by "change sequence" or numerical order of changes which run in space. Time then has only mathematical existence instead of physical reality. But then on page 2 you introduce Planck time and duration as emergent time. I'm confused at this point and wonder if you could clarify this point for me here.

    Thanks for reading and commenting on my essay, and thanks for contributing your own thoughts.

    Best regards,

    Edwin Eugene Klingman

    Hi Edvin,

    Fundamental time is numerical order of change. When we measure this numerical order with clocks we get emergent time which is duration. Duration is a sum of numerical order. Without measurement of the observer there is no duration. See our article published in Foundations of Physics: Perspectives of the Numerical Order of Material Changes in Timeless Approaches in Physics

    http://link.springer.com/article/10.1007/s10701-014-9840-y

    yours amrit

    I cannot attach article here, but I can send it to you. Write me on my mail sorli.amrit@gmail.com

    8 days later

    Dear Amrit Srecko Sorli:

    First of all, I admire the effort that goes into making a submission. That applies to your article. I liked the idea of a bijective relationship between elements of a physical theory and a mathematical theory because it seems like a fresh take. Is there not a difficulty in this approach though: how does one determine what an element is, whether for physics or math? Is there an explanation of what energy is, or how it arises, sufficient for us to consider it as an element? You can see the effects of electromagnetic energy, but do you see the energy directly? I suspect that counting relates to some deep aspect of the structure of the universe, which is why we see it in so many contexts and your emphasis of counting in the introduction seems right. On your conclusion "out of pure mathematical laws we cannot deduce physical laws" would the prediction of the positron based on Dirac's math be a counterexample?

    Bob Shour

    Dear Bob,

    with mathematics is all fine. It is perfect.

    Just in physics we have to apply it in a proper way.

    This is the outcome of bijective epistemology.

    Mass and gravity have origin in diminished energy density of quantum vacuum. Higgs boson is a momentary flux of energy of quntum vacuum, not mmore. Has no real impact on particles mass. The whole theory of Higgs is simply not right. It has no bijective correspondence with physical reality.

    Yours AmritAttachment #1: 2_Gravity_originates_from_variable_energy_density_of_quantum_vacuum.pdf

    DEar Joe, thanks, very good comment,

    there is no "hidden order",

    there is just ORDER that common mind is not able to grasp.

    Please give good vote to my paper.

    Thanks.

    Amrit

    Amrit,

    Thank you for contributing your views on this topic. I do however believe we do not gain any insights into a greater understanding of reality by rejecting one model in replace of another. The fundamental idea in question is our ability to define an event or observation (using whatever model) and to predict future occurrences in an effort to validate our understandings of this physical interpretation or description of nature.

    Fortunately we have gained many pieces to this very complicated puzzle, now we must arrange these pieces into a coherent manner that effectively defines reality. This is the current state in physics. Its not that the concept of using physics is wrong neither is the method you advocate. I believe they are both useful and will arrive at similar conclusions even if they are stated in different languages.

    You propose an excellent argument, suggesting the physics we are currently using is not a correct interpretation of mathematical laws. Perhaps we will uncover this complete idea soon.

    Best Regards,

    D.C.Adams

    Hi Adams, bijective epistemology goal is improving existent physics and see which elements are nonexistent. Physics is a strong building, we just have to adjust few elements. For exampla existent model of mass and gravity is not right. Our proposal model is respecting bijective function, see files attached. yours AmritAttachment #1: 5_Special_theory_of_relativity_postulated_on_homogeneity_of_space_and_time_and_on_relativity_principle.pdfAttachment #2: 3_Gravity_originates_from_variable_energy_density_of_quantum_vacuum.pdf

    15 days later

    Dear Amrit,

    A worthwhile essay to read. I have a problem that you may want to try your tool: Bijective function of set theory on.

    What does a line consist of and how can you cut a line?

    Best regards,

    Akinbo Ojo

    Dear Ojo,

    the "point" is that we esablish bijective function between what we perceive and what we imagine.

    yours amrit

    The Main Power of Physics is Creative Imagination based on Experimemtal Data.

    7 days later

    There is completeness to your subject on relative kind of matter.

    Sincerely,

    Miss. Sujatha Jagannathan

    6 days later

    Dear Sir,

    We thoroughly enjoyed your ideas. It stands at a different footing from most essays. We extend your ideas as follows.

    Your classification resembles ancient Indian system of classification of fundamental entities - Matter (prithwi), change that induces inertia (ap), heat energy (teja), non-heat energy (marut) and space (vyoma), where the others are sequential order emergent derivatives of space, which itself is an emergent derivative of time. The observer (purusha) is independent of all these. They also believed spontaneous creation of mass particles from the background structure, which did not disappear, but got transformed into other forms. The Planck time was known as kshana and "duration (which is emergent time and requires measurement of the observer) is a sum of a numerical order of a given change". Time is a non-physical mental construction (buddhinirmana) perceived through alternative symbolism (vikalpana) of the order of events (vastupatita). But arrow of time is established - Past, Present and future are segments of these sequences of intervals that are strictly ordered - all of future always follows present. The same sequence is not true for past, because any past event can be linked to the present bypassing the specific sequence of its occurrence but you cannot move from past to future violating the sequence. Thus, time travel is fiction. Twin paradox arises out of Einstein's misplaced interpretation of simultaneity, which actually is synchronization.

    Relativity is an operational concept, but not an existential concept. The equations apply to data and not to particles. When we approach a mountain from a distance, its volume appears to increase. What this means is that the visual perception of volume (scaling up of the angle of incoming radiation) changes at a particular rate. But locally, there is no such impact on the mountain. It exists as it was. The same principle applies to the perception of objects with high velocities. The changing volume is perceived at different times depending upon our relative velocity. If we move fast, it appears earlier. If we move slowly, it appears later. Our differential perception is related to changing angles of radiation and not the changing states of the object. It does not apply to locality. Einstein has also admitted this. But the Standard model treats these as absolute changes that not only change the perceptions, but change the particle also!

    One caveat with Barbour's view is that they assume total energy (potential plus kinetic) and the total angular momentum of the system to be zero. Though this is a valid assumption, it expects some initial mechanism to break the equilibrium. Bijective function is inherent in conservation laws and Newton's third law. When the equilibrium is broken, it resolves into equal motion in two opposite directions. You can call one of these as the corresponding negative energy. When such motion is through a medium at rest, it creates a bow-shock effect. This reduces motion till it comes to rest after certain distance. In ancient India, this was the mechanism of creation - a bounded sphere (there may be many unconnected spheres or universes which cannot be approached as no motion is possible in the space between them). The medium is now called dark energy.

    Hawking's idea of light cone and event horizon is not correct as explained in our essay.Also, the terms energy of matter and gravitational energy need to be precisely defined (there are many unsettled questions relating to gravitation including whether graviton exists at all). All particles were considered bijective in ancient India (agni-somaatmaka jagat). We will discuss these separately.

    Regards,

    mbasudeba@gmail.com