Dear Efthimios Harokopos,

I very much enjoyed your well-written essay. Unless I have forgotten someone, I do not believe any other essays maintain such a clear focus on linking physics and metaphysics through math, and it seems quite an appropriate undertaking. What is most interesting is that you managed to do so using the most basic concepts and beginning with Newton. The math is simple, the ideas are simple, but the significance is very large I think. Your equation (9) is so clean and yet I have never seen it written in this way. Very clearly thought out - I congratulate you. Your equation (10) and your discussion of autonomous versus non-autonomous is also interesting and worth thinking about. And after discussing what you view as possible with regards to the existence of a 'meta-mathematical' framework, you properly leave the question open, and did not cloud the issue with hypotheticals.

I invite you to read my essay and invite your comments.

Edwin Eugene Klingman

Dear Edwin Eugene Klingman,

I truly appreciate your good words about my essay. However, I have a problem with your invitation to read your essay as follows:

Before your comments my community rating was at 6.0 based on two votes. Afterwards, it dropped to 5.0 based on a single vote. This means that someone rate it at 3. There are two possibilities then

(1) Either you rated my essay at 3 despite your good words, or

(2) You did not rate my essay despite your good words.

In either case, I will not read you essay and as a matter of fact I will refrain from judging other essays because such judgment cannot be objective anyway. I will read several essays but not rate.

Thank you. I am not here to get a prize but just to participate and convey my thoughts. I know the process since last time I participated in 2011. My essay was first for two weeks and then in just a few days I got a series of low marks. It ended up in the 35 essays sent for review but to see how some people acted was quite disappointing. I just wish FQXi would use an independent panel of judges and pay no attention to ratings. I think they are smarter than that.

    Dear Efthimios,

    I just replied you on my blog. Also I just read your 2011 Essay and your discussion of Zeno's Dichotomy paradox. I see that you desire to make spacetime as the foundation of your proposed solutions. Please be careful about this.

    When you say, "I'm not aware of any experiment that falsifies special relativity", are you aware of observations and experiments that falsify the postulates that form the basis for special relativity theory? I mean special relativity for example implies that motion of an observer has no effect on the arrival time of incoming light, i.e. the resultant velocity of light is constant. This postulate depends on what Michelson and Morley found out in their 1887 experiment.

    However, are you not aware that in some other experiments, like Pulsar timing observations, Lunar Laser Ranging, Global Positioning System, motion of the observer affects the arrival time of incoming light signals?

    How can these two discordant findings be reconciled? Can an observer's motion hasten incoming light arrival or not? You may check my humble suggestion HERE in your free time. Please note that I am not quarreling with your statement, "...testable predictions that have been verified in laboratories numerous times. So far, none of the predictions made by special relativity have been falsified in a laboratory experiment", but with the postulate on which SR rests on, which if false there is no basis for SR to be held as true. Or can a postulate of a theory be false and the theory be true?

    Finally, I would like to ask in view of our cosmological model, the Big Bang, whether your 4-dimensional block universe can perish or is it eternally existing?

    Regards,

    Akinbo

    *Sorry about the rating system in the essay contest. It is absurd to receive a 10 and a 1 on the same essay as I received myself. Let us just continue and benefit from the intellectual exchange.

    Efthimios,

    I think something has happened to your .pdf file. I have attempted to download your essay several times and it is blank. Obviously from comments above, your essay was present in the system. I have downloaded other essays, so I am not sure what has changed. Perhaps the file has become corrupted or perhaps my Adobe Reader has become corrupted. Also, I have Windows 8. It is junk.

    Regarding rating ... get over it. I have been given 3 ones and 1 two. I have also been given a ten, an eight, and enough other positive votes to average a five point zero. Some people give ones just to knock scores down ... no other reason. And they don't bother giving comments ... after the one votes I received there were no comments to state what they did not like or agree with ... I doubt if Dr. Klingman voted you down. He has BEEN voted down himself but he has gotten enough positive votes to over-come the haters.

    I'll keep trying to get your essay.

    Best Regards,

    Gary Simpson

    Efthimios,

    False alarm on my part. It appears that somehow my Adobe Acrobat .pdf reader became corrupt.

    In your statement of Newton's 2'nd Law, you implicitly assume that the force and the resulting change in motion are collinear. This is the standard understanding. What would you do if they were not collinear? The reason for my question is that I can use Hamilton to produce an equation of motion that is circular but requires no force. I had not considered a constant kinetic energy reference frame.

    As a minor point, near the middle of page 3 you reference (Newton, 1952). Is this a typo or is there another guy named Newton?

    Your Figure 1 captures the essence of this essay contest I think.

    Best Regards and Good Luck,

    Gary Simpson

      Hi Gary,

      By "change in motion" it is meant change in momentum vector mv. This is the meaning of "motion" in Newton's law. In circular motion the change in momentum dp/dt is along the direction of the center of the path. Thus, a centripetal acceleration is generated and a centripetal force. By definition, these are collinear.

      You said:

      "The reason for my question is that I can use Hamilton to produce an equation of motion that is circular but requires no force"

      There is no way that I know to get circular motion without a force that is directed towards the center of motion, the centripetal force. But I do not claim to know everything.

      It is often confusing because when a particle is on circular motion there is no applied external force but there is a force generated due to the motion that is directed towards the center of the path. This force has a "stretched" causality with acceleration and this is what has prompted some scientists to question the causality in Newton's Law. Specifically, in his graduate text Principle of Dynamics, Greenwood specifically mentions this problem.

      (Newton, 1952) is the book written by Newton (Principia) translated in 1952. It also means that Newton will be always alive (in physics):)

      Thank you for your comments.

      I do not understand the part about power and cause-free motion but the rest is an honest attempt to answer the essay questions. First time I read a concise explanation of relativity theory. Good essay.

        Dear Efthimios Harokopos,

        I saw your complaint about scoring on your thread before I commented on your essay, so I knew that you were already upset about scoring. What I had not realized was that you think you can, in general, correlate comments with voting behavior. It is upsetting when low scores are received for no apparent reason. During the first weeks of this contest I was the top paper with a 10 (every time I looked at it I reminded myself that there was nowhere to go but down) and then I received at least two 1s and a couple of 2s. I was of course not happy about this.

        There are no rules for how one "should vote". After several essay contests I have a voting strategy that I think is most effective. I typically wish to see all essays before I decide how they should be ranked. I think it is presumptuous for you to assume that my voting behavior should match your ideas of voting but if you are hostile over this point it's probably best you not read my essay.

        You have written an essay in an earlier contest, and you should therefore be aware that no one is happy with FQXi voting. There is always some vote trading going on and the best policy is not to discuss votes in comments and not to combine the timing of comments and votes to 'send messages'.

        Your implication that I would give high praise and low scores is unwarranted, and there is no basis for you even to suggest this. The fact is that I have not scored your essay, nor most essays, as I have my own policy or voting strategy. I think your complaint about voting is valid, but your assumptions about how I should vote are invalid and not appreciated.

        Edwin Eugene Klingman

        PS, After you posted your unhappy comment on my thread, someone gave me a 3 vote. By your logic I should suspect you, but I don't think your logic is good. I also note that the other top-rated essays seem to have received low votes at the same time, so it's probably someone either trying to pull the top down as a way of raising their own status, or it could be simply someone who resents anyone having a higher score. My point is, there is no way of knowing, and it is inappropriate to make the suggestion you did that I would give high praise and low scores. That is personalizing an issue in a very uncalled for manner.

        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