Dear Akinbo,

I agree with you that if any of the two main postulates of SR are falsified the theory will be falsified. However, I am not aware of conclusive evidence that falsifies either. As I said I do not know every little detail. Please note that regarding SR and QM I have not expressed personal views but those that are accepted. However, my objective was not to promote any theory but to discuss the role of mathematics that is the same regardless postulates. Note that I admit the SR predictions are equivalent with a large class of theories that do not adhere to the speed of light constancy. Therefore, as I note in my essay and maybe not too successfully, the metaphysical commitments vary. I also made a note that many scientists are not ready to adhere to the metaphysical commitments of SR. Also I want to be honest and tell you that I believe that Einstein was correct about the light postulate but I hope he will be proven wrong for some reasons that are hard to explain now but deal with free will. I am open to all possibilities but I have a high regard for Einstein. Even if he was wrong, he challenged us with alternatives. According to pessimistic meta-induction, at the end, we will be all wrong with high probability.

Since the relativity subject is controversial, it may be better to stick to the essay subject, which is about the role of mathematics in physics. I hope there will be another contest about relativity and we can discuss these matters in more detail. Thanks.

Note that F = ma is referred to as Newton's second law but it is not, according to the statements in Principia. I think Euler stated that law and it happens to correspond to Newton's law when the mass is constant, F = dp/dt

I am not sure time is a geometric parameter. Actually, I have no idea what it means other that it is a reading of a clock. Thus, there is some physics in both sides of the equation but also metaphysics. I see nothing wrong about that as long as it works and it does in weak-field limit. After that one must use general relativity or equivalent and maybe there are no forces, i.e., the metaphysical commitments may change.

Thanks LC

Thanks. The explanation of relativity is not mine. See related reference in the essay that gives credit where it is due.

Thank you Joe. If I said anything else, i.e., about accurate predictions, I would be wrong given that Newton's law applied to free fall was tested to be accurate to about 1 part in a trillion and Einstein's equivalence was tested to even better accuracy. But as I write, there is a lot of metaphysics behind the math. I sense you did not read the whole essay, just the abstract.

    Dear Dr. Harokopos,

    You sense wrong. I read all of your essay. Newton's abstract law applied to abstract free fall of what? All real surfaces must travel at the same constant speed. You apparently only understand codswallop abstractions.

    Warm regards,

    Joe Fisher

    If I am correct about only surface having the ability to travel at a constant speed, it means that scientists attempting to build a spaceship that would have a physical surface that could travel "faster" than that of a surface of a garbage can are engaged in an act of utter futility.

    Warm Regards,

    Joe Fisher

    24 days later

    Dear Efthimios Harokopos,

    Thank you for a very readable essay touching on some basic concepts.

    If I understand you correctly, the primary evidence of physics (experimental results) coupled with mathematical expressions (or equations) constitute the primitive ontological basis of physics. The nomological variables are more the interpretation of the experimental results and need to include abstract concepts, which are the meta-physical pieces.

    In considering difficulties with our current interpretations, two directions (at least) come to mind:

    That our abstractions (our metaphysical concepts) are incorrect or inadequate or that our tools (by which we generate the primitive ontology) are insufficient.

    It seems quite possible that, given the apparent accuracy of current physics, both of these situations might be the case. What we measure as accuracy (primitive ontology) might be a misconstruing of the metaphysical concepts involved, so that we mislead ourselves concerning how accurate we really are in defining nature.

    As an example, take the metaphysical concept that all action stems from the very small and that all larger objects are simply aggregates of actions of the very small. It would appear that intelligence is a counter example to this concept, since the intelligence to understand the very small does not occur at the level of the very small, but requires animate beings at our level for this activity to occur. This means activities at our level act upon objects of the very small (our experiments) - countering a basic metaphysical concept of current physics. Why our very accurate measurements should appear to corroborate our metaphysical concept of action only at the very small is due to that same metaphysical concept that accuracy, down to very small measurements, is an appropriate measure of how 'good' our theories are. If actions at our level do impact actions at the very small, then this measure is no longer an appropriate one for how 'good' our theory is.

    Take care,

    Donald

      Dear Donald,

      Thank you very much for an interesting comment. I admit I have not thought of things this way. Your thinking is quite original. I talked about the accuracy of special relativity and quantum mechanics. Apparently, I paid for this mistake and have received low marks because this contest is flooded with cranks of all kinds that have no connection to math and physics whatsoever but are under a severe state of delusion.

      Having said that, high accuracy does not mean a theory is "true", i.e., a true representation of physical reality and this is also part of the puzzle. Theories are underdetermined by empirical observations because there are unobservables. More importantly, when we talk about primitive ontology, such a particles for example, please note that experimentation will never "see" those particles but only their effects. For example, it is claimed that the Higgs was found but actually that was a statistical computation at 4.5 sigma I believe (1 in a million of being wrong or about).The primitive ontology cannot be observed. In Newtonian physics the primitive ontology is the particles that in turn form bodies that have mass and extension. The nomological variable in the case is momentum and it is an empirical quantity. The metaphysics is that forces cause the particles to change their state of motion. One could write Newton's law as follows:

      Action of God = ma

      and then say that the Action of God is what changes the state of motion. This is an equivalent theory. It works the same as Newtonian mechanics. Instead of forces we have the Action of God. The law of inertia is

      If the Action of God is zero, a particle maintains its state of uniform linear motion. This works, you only have to calculate the Action of God.

      "As an example, take the metaphysical concept that all action stems from the very small and that all larger objects are simply aggregates of actions of the very small."

      You gave a good example. Nobody knows how the macro emerges from the micro. Actually, the micro may be emerging from the macro. This is what quantum mechanics may be saying in a way. I have no idea honestly. But you raised one of the most important questions in physics: how is the macro world of determinism emerging from the indeterministic world of quantum mechanics? Either what we see is an illusion or quantum mechanics is wrong or deterministic.

      "If actions at our level do impact actions at the very small, then this measure is no longer an appropriate one for how 'good' our theory is."

      Interesting thought. This is related to the quantum mechanics measurement problem. There is no solution that can combine locality with counterfactual definitiveness. Actually you are saying that our physical theories are corroborated because we impact the world in a way that corroborates them. Maybe we always find what we are looking for.

      Thanks and regards,

      E. Harokopos

      4 days later

      Dear Efthimios,

      I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

      All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

      Joe Fisher

      8 days later

      Dear Efthimios,

      It was refreshing to read a paper on the connection between physics and mathematics that made explicit that the manifestation of this connection in different domains involves metaphysical commitments that are often not sufficiently acknowledged.

      I think you are right the choice of a particular mathematical formalism to represent an aspect of reality entails a metaphysical commitment, and the example in classical mechanics this is most obvious to me when considering, say the Lagrangian vs. the Hamiltonian Formulation. I was not familiar with your paper in which you take power as the cause of motion. I had a quick look at it and found it interesting. Some comments, on that paper, if you allow:

      In addition to the problem of action-at-distance I would also take the prediction of classical mechanics that perfectly rigid extended objects can exist as another problem (really, it's just another facet of the same problem, that influences are permitted to travel infinitely fast).

      Concerning your axiom of motion, I must say, as metaphysical as "Force" is, it seems in some sense more concrete than Power. I don't know if this is an artifact of my education, having used and thereby attained much greater familiarity with the former than the latter, but nonetheless, I would say that if there was a way to intuitively conceptualize Power as easily (or even more so) as Force, then your approach might attract more attention.

      Your finding that the metaphysics of your approach permits a zero of the cause of motion to be associated with uniform circular motion reminded me of the fact that Galileo seemed to consider this type of motion to be inertial, which suggests that his metaphysics might have been closer to yours than to Newton's.

      I found the analogy you gave between power in Leibniz's system and Force in Newton's system surprising and interesting. I had not looked at their different metaphysics from this perspective. To anyone unaware of this way of looking at things, I'm afraid, the term "substantival relationism" will sound like an oxymoron. Equation (27) in that paper reminds me a little of equation (15) in this paper of mine, the classical mechanics portion of which you may find interesting.

      I have to think some more about the robustness of your arguments concerning the emergence of an arrow of time and the notion of spacetime as a substance. I tend to agree with the latter, but ascribe this more to the Lorentzian signature which leads to a geometry for which we do not have good intuitions (particularly the notion of a definite-negative metric interval).

      Regarding the notion of causal influences originating from outside spacetime, you may find Gisin's paper of interest. I believe that he is onto something, and in fact in my own work am (among many other things) attempting to formulate a firm mathematical grounding for such an idea (within the context of QM) in terms of something I call an "incomplete embedding".

      Returning to your current essay entry, I applaud your effort to make the metaphysical commitments of particular mathematical formulations of physical theories more explicit. This is a subject that I believe physicists in general do not spend enough time thinking about. As for the power of mathematics,bas far along as we have come since, say, Newton's epoch, I think we have still barely scratched the surface in terms of what is possible to do with mathematics.

      My view on this arises out of the fact that contemporary mathematics is at its heart based on classical logic. But if you peruse, say, the philosophical handbook of logic, which at 20 or so volumes of several hundred pages of small text per volume outlines so many of the possibilities to go beyond classical logic, each of which in and of itself could serve to extend the foundations of mathematics, then you may find that the possibilities of enlarging mathematics by building mathematical structures based on these are truly staggering. I am myself making an attempt in this direction by incorporating two non-classical logics into its foundation in the hope of increasing the expressive power of mathematics beyond what is possible at present, in order to arrive at a model of quantum mechanics that accomodates a distinction current theory doesn't and thereby illuminate what it says about the world. The analogy of the difference between contemporary mathematics and what I just hinted at to that between black and white and color vision seems hardly more appropriate here.

      Hope you found my feedback useful.

      Best wishes,

      Armin

        Hello Armin,

        I appreciate your comments and they are indeed useful.

        Here are my comments:

        "Concerning your axiom of motion, I must say, as metaphysical as "Force" is, it seems in some sense more concrete than Power. I don't know if this is an artifact of my education,"

        It may be more concrete because it has already become common sense through education. But the notion of force is puzzling as much as power. However, in many cases people use power: "this car has a lot of power", "that was a powerful storm", etc.

        "I would say that if there was a way to intuitively conceptualize Power as easily (or even more so) as Force, then your approach might attract more attention."

        This is a good point. The way for people to conceptualize comes from education and solving problems. However, my intention was not to replace Newtonian mechanics but only to show that there can be alternative foundations. The key here is that the notion of force is compatible with a materialistic universe, where the notion of power sounds more "spiritual": Powerful God, powerful feelings, etc. Given that the goal of science is to preserve material autonomy, the notion of force is more appropriate for that, I agree.

        "Your finding that the metaphysics of your approach permits a zero of the cause of motion to be associated with uniform circular motion reminded me of the fact that Galileo seemed to consider this type of motion to be inertial, which suggests that his metaphysics might have been closer to yours than to Newton's."

        Actually in relativity such motion is also inertial because there are no forces that cause motion. One problem with circular motion is that it imposes stretched causality: If a stone is attached to a string and rotated, there is a centripetal force directed towards the center of motion. Does the force cause the motion of the stone, or the motion of the stone causes the force. Greenwood in his excellent textbook says he does not know the answer. More importantly, if power is the cause of motion, no fictitious causes must be considered in non-inertial frames as it is the case with force and centrifugal and Coriolis inertial forces.

        "I have to think some more about the robustness of your arguments concerning the emergence of an arrow of time and the notion of spacetime as a substance. I tend to agree with the latter, but ascribe this more to the Lorentzian signature which leads to a geometry for which we do not have good intuitions (particularly the notion of a definite-negative metric interval). "

        The arrow of time is a hypothesis that emerges from the notion of universal time in an occasionalist sense. I tend to look at geometry more as a convention rather than ontology.

        "Regarding the notion of causal influences originating from outside spacetime, you may find Gisin's paper of interest. I believe that he is onto something, and in fact in my own work am (among many other things) attempting to formulate a firm mathematical grounding for such an idea (within the context of QM) in terms of something I call an "incomplete embedding"."

        One problem here is to have a theory that generates some new and unique predictions based on this hypothesis.

        "Returning to your current essay entry, I applaud your effort to make the metaphysical commitments of particular mathematical formulations of physical theories more explicit. This is a subject that I believe physicists in general do not spend enough time thinking about. As for the power of mathematics,bas far along as we have come since, say, Newton's epoch, I think we have still barely scratched the surface in terms of what is possible to do with mathematics."

        Thank you and I agree about the power of mathematics.

        " I am myself making an attempt in this direction by incorporating two non-classical logics into its foundation in the hope of increasing the expressive power of mathematics beyond what is possible at present, in order to arrive at a model of quantum mechanics that accomodates a distinction current theory doesn't and thereby illuminate what it says about the world."

        This sounds interesting and the way to escape from the circle the same way that mathematicians escaped from Euclidean geometry after hundre4ds of years of trying to wither defeat or prove the fifth postulate. Good luck to you.

        All the best.

        Efthimios

        5 days later

        Efthimios,

        Excellent paper indeed! A real understanding touching the crux of the problem; the lack of substance. The bridge that mathematics provide between our reality and the metaphysical one.

        A theory of everything will be a symbiosis between physics and metaphysics with a mathematical bridge. Natural Metaphysics runs on a logical engine with the rule of non-contradiction as starting impossibility, evolving/exploding time at a certain rate as substance, any differential in the time rate as a cause. Yep! Good old substance and cause. Physics can always say how it happens, metaphysics will tell why. They are complementary but mutually exclusive components of knowledge.

        Bests,

        Marcel,

          Efthimios,

          Calculus allowed us to remove time so that we could write equation on paper which is not the passing time background we live in. All our notions of physics are over integrated in time by one order. What concerns us on paper is energy. But what concerns the universe is power. Energy is a dimension of knowing the final result or a form of accounting. Power is a dimension of happening, what it is like out there.

          Marcel,

            Thanks.

            However, "mainstream" physics may not agree. They are immersed in "math games". Billions have been spent in string theory math research although it does not produce a single unique prediction. After all, one task of modern physics has been obscuring issues and a focusing on epistemology. Fitch's paradox is a slap on science face. The price for mentioning it in my paper is the low "community" grade. Most scientists are naive enough to believe that a theory of everything will be obtained through math alone without requiring omniscience, i.e., man becoming God.

            Thanks.

            However, "mainstream" physics may not agree. They are immersed in "math games". Billions have been spent in string theory math research although it does not produce a single unique prediction. After all, one task of modern physics has been obscuring issues and a focusing on epistemology. Fitch's paradox is a slap on science face. The price for mentioning it in my paper is the low "community" grade. Most scientists are naive enough to believe that a theory of everything will be obtained through math alone without requiring omniscience, i.e., man becoming God.

            Yes, or put it in math language, power is the rate of change of energy, i.e. the flow of energy in time. In your house you get power and you pay for its integral, energy. No one cares how much work was done. You may as well dissipate all energy back in space. Power is the single most important concept in physics. When I published my paper on the laws on motion based on power in 2005, I received many emails from physicists around the world that were excited but ask me not to mention them because they were possibly afraid of consequences. There has been no rebuttal since but mainstream journals have refused publishing articles on it, considering the case closed in favor of force. There is a fundamental reason for that struggle, it will be explained ion my soon to be published book. In a nutshell, behind any theory in since, even math, a certain ideology hides, often of sociopolitical nature. Science nowadays is indistinguishable from politics. Physics is becoming like economics: there are many truths but no one knows which one applies at a given moment or the choice is based on ideology. If you believe in locality, you adhere to that one QM theory and if you believe in non-locality you adhere to the other theory but surprise! They all generate the same predictions. Isn't that funny?

            Thanks and all the best.

            This is a fascinating paper. This is the first time I read that power could take the place of force in mechanics and yield laws of motion.

            Jason

            Efthimios,

            That's a big oups! The word "God" is out of context! Anyone seeing that may think that there are other words or concepts out of context and dismiss the whole paper. My opinion is that this extension of "omniscience to God" opens up a whole can of worms which is not your first intent, which is physics and mathematics. Give yourself a chance and leave that one out. It is like pulling down your shirt and asking for flogging.

            Just my opinion.

            Thanks,

            Marcel,

              3 months later
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