Essay Abstract

The purpose of this paper is to show that the study of physics is limited when only mathematics is used to explain the phenomena in the world around us. The thrust of this paper is to suggest that mathematics is a language, like English, that describes reality but does not represent it. This paper further suggests appropriate behavior would be to use reality, modeling, and mathematics to study the phenomena that surrounds us. Two mental experiments are presented to bring this idea home. One is of a king's roses and the other examines special relativity from an alternate point of view.

Author Bio

Al Schneider began his interest in physics when eleven years old upon reading "ABC of Relativity" by Bertrand Russell. The study of theoretical physics became a lifelong interest. He acquired a B. S. in Physics from Wayne State University, Detroit, in 1969. Professionally he was a programmer working in industrial and scientific circles until retiring.

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Hi, thanks for your essay. They are many points to look at. I tried to look at your main idea and questions came up to me.

In your essay:

"The first to look at is that the model universe contains only photons moving about. This makes the statement that our real universe is made only of photons. .... Another consequence: the appearance of virtual particles now becomes clear. Photons can randomly come together to form a particle if the area of photons is dense enough."

Here are my questions:

1. If the universe is made only of photon, what makes photon comes together?

2. If the universe is made only of photon, what is between photon so sometimes they are together or not?

A secondary goal of this essay was to present a model of a universe that supports special relativity. To me, that model is a thread to a rug called universe. Once pulled the rug unravels. Let's call the end of that thread concept A. Once A is mastered then one proceeds to B. Then C and so on. There are answers to both questions however; they are concepts like G and H. There is not space to go over B, C, D, E, F, G, and H. So answering the questions is difficult. However, with that restraint, here are the answers.

Answer 1 is random action.

Consider the force on molecules causing heat transfer. What force is there causing high energy molecules to move to a low energy space. There is none. Entropy is due to random action. Theoretically, at some point in time, electrons and protons did not exist. Then the body of photons was like a thick soup. The high density of photons enabled random action to cause photons to clump and form electrons and protons. Then the density of photons between

electrons and protons became low. Now, only a few photons are capable of clustering into virtual particles that decay soon.

The idea that there are only photons in the universe suggests that the universe consists of a photon gas. The photons interact much the same as molecules in a gas structure. However, the rules of interaction of photons are considerably different than the rules of molecular interaction. The description of that comes in at about F.

Elsewhere I have described the interaction of photons to a limited extent. This is somewhat similar to the Newton's laws. He had the math but could not explain what happened between the mass particles to explain why the math expressed said events.

Answer 2 is subspace.

Subspace is defined somewhere between A and G.

All of this is detailed in a book I have published and have for sale on Amazon dot com titled, New Age Quantum Physics. The purpose of the book is to present the history of quantum mechanics and forward the new concepts from A to Z.

    My questions were on second part of your essay because I was curious to see more in details your arguments.

    I value constructive models over relativism. In the first part of your essay, I found that you introduced a lot of relativism on mathematics. In the second part, you introduced a model.

    In your book, is there a chapter where you explain your idea that entropy is due to random action? It is an idea that I would be very interested to read.

    Christophe Tournayre

    My book does not do well with this subject. The idea that entropy is due to random action comes from the study of entropy in standard texts on the subject. It also comes from a study of Boltzmann's theories of the subject. In essence, consider an ideal gas: space between little hard balls that are perfectly elastic in an elastic container. There are many combinations of position and speed of these particles. Consider all of the gas in one half of the container. There are many more combinations of gas distributed throughout the container than in one half of the container. Therefore, through random action, the gas will fill the container and entropy increases (The gas losses its ability to do work.). That is a snapshot of it all and a basis for the laws of thermodynamics. I may error in this and hope there is someone reading this that can clarify it better. I believe that Boltzmann's concepts are vital to an understanding of the universe and extremely fascinating.

    Al Schneider

    20 days later

    Dear Sir,

    Congratulation for such a brilliant essay. You deserve the best.

    Though our views of numbers, infinity and zero (discussed elaborately in our essay) are different from that of Deepak Chopra, we hold that infinities are real and not a very big number. The number of infinities is not infinite, but only four. Zero is the absence of something at here-now that is known to exist elsewhere (hence real; otherwise we will not perceive its absence at all). Since all measurement/perception are done at here-now, the concepts of the objects (information about it) only are available and not the real objects. To that extent you can call it unreal. Infinities are everywhere; hence it is not like zero. You are using the term infinity for very big numbers, which is not its proper definition.

    Your statement that "dx could be part of an equation describing that beautiful curve" is partially correct, as no equation can describe beauty. A smile is not the same as curvature of the lips - snide also has the same characteristic. Newton and Leibniz evolved calculus from charts prepared from the power series, based on the binomial expansion. The binomial expansion is supposed to be an infinite series expansion of a complex differential that approached zero. But this involved the problems of the tangent to the curve and the area of the quadrature. In Lemma VII in Principia, Newton states that at the limit (when the interval between two points goes to zero), the arc, the chord and the tangent are all equal. But if this is true, then both his diagonal and the versine must be zero. In that case, he is talking about a point with no spatial dimensions. In case it is a line, then they are all equal. In that case, neither the versine equation nor the Pythagorean Theorem applies. Hence it cannot be used in calculus for summing up an area with spatial dimensions.

    Newton and Leibniz found the solution to the calculus while studying the "chityuttara" principle of ancient India, which is now called Pascal's differential triangle. To solve the problem of the tangent, this triangle must be made smaller and smaller. We must move from x to ﾎ"x. But can it be mathematically represented? No point on any possible graph can stand for a point in space or an instant in time. A point on a graph stands for two distances from the origin on the two axes. To graph a straight line in space, only one axes is needed. For a point in space, zero axes are needed. Either you perceive it directly without reference to any origin or it is non-existent. Only during measurement, some reference is needed.

    Your point about roses was uniquely enjoyable, but we hoped you would end it in a more realistic manner. After the bill for 400 hundred roses was paid, the driver should have taken those away in the other truck and claimed another bill for the -400 (lack of 400, which used to be there) roses. Tachyon roses are somewhat imaginary. You are correct that in SR, the squared velocity yields tachyons as one of the possibilities, if v is negative. We have discussed many other aspects of SR (including wrong mathematics) in our essay.

    We are reminded of an anecdote relating to a famous scientist, who once directed two of his students to precisely measure the wave-length of sodium light. The students returned with two different results - one resembling the normally accepted value and the other a different value. Upon enquiry, the other student replied that he had also come up with the same result as the accepted value, but since everything including the Earth and the scale on it is moving, for precision measurement he applied length contraction to the scale treating the star Betelgeuse as a reference point. This changed the result. The scientist told him to treat the scale and the object to be measured as moving with the same velocity and recalculate the wave-length of light again without any reference to Betelgeuse. After sometime, both the students returned to tell that the wave-length of sodium light is infinite. To a surprised scientist, they explained that since the scale is moving with light, its length would shrink to zero. Hence it will require an infinite number of scales to measure the wave-length of sodium light! Then consequences of the model are extrapolated - as you say.

    Your statement that: "in observing particles that decay and experiments in super-colliders: all particles decay into energy which consists of photons moving away from the site of decay. All except neutrinos" is true. Also "Photons can randomly come together to form a particle if the area of photons is dense enough. The small number of photons gathering would be such that the particle would not persist and decay into its component photons. This is observed in the real universe". Yet, as you say, there are caveats.

    Regards,

    basudeba

      A beginning comment in your post is, "...we hold that infinities are real and not a very big number."

      "...we hold..." is not a mathematical nor physics form of science.

      There are many flaws in your following explanations. However, it suffices to point out that the phrase, "...infinities are real and not a very big number," indicates your unwillingness to face reality or the projection of consciousness that manifests what we call reality. Ergo, the remainder is null and void.

      I have reread your post several times. I am confused. Who is "we"? Is it the physics community or the Deepak community? Next, you have made a statement about infinity. It is presented as the ultimate fact, "...we hold..." Since the purpose of the contest is to discuss the aspects of mathematics, such a statement is inappropriate. I can understand stating your side but would it not be better to write up your opinion and submit it as I have.

      The third issue is about politeness on forums. Submitting a number of statements is inappropriate. This is a technique Deepak uses often in his discussions with others. He throws out a fistful of points or what he considers truths and the other party has no time to discuss any of them. Then he puffs his chest out as if he is the winner. It is very impolite.

      I am worried that if I respond to each of your comments you will respond to each with a multiplicity of responses. It is a cheap trick to bury someone without making progress.

      I would like to respond to your statements but not as if I am being attacked.

      Dear Sir,

      Decorum is a part of our culture. We beg to be excused if you feel otherwise. Our post did not "attack" you, but supported and expanded your views in many areas.

      You have rightly said that "the purpose of the contest is to discuss the aspects of mathematics". For this purpose, we want to keep out I from the discussion to make it a collective effort to find the truth. We would be grateful if you could educate us about our faults by justifying your statements.

      Regards,

      basudeba

      Dear Sir,

      On second thoughts we feel that our reference to smile and snide might have hurt your feelings. If so, we are deeply sorry and profusely apologize to you. It was totally unintentional and quoted from our essay. We were surprised at your reaction since we had written nothing against you and of all the essays we had rated, we had given you the highest score. We also do not know Dr. Deepak Chopra except for comments on him in the net. We have not studied his works. Hence cannot comment on it.

      Finally, before forming any opinion, we request you to kindly read our essay once.

      Regards,

      basudeba

      I would eagerly read your essay if I knew what it was.

      Second, I have essentially given up on this contest.

      It appeared that the popular authors were getting all the attention.

      I am honored that some have given me credit.

      Actually, I am ecstatic.

      If you would let me know which essay is yours, I will read it and we can continue.

      Now I am curious what you have to say.

      All the best.

        The purpose of this post is to reiterate the thesis of this essay.

        Present Operation:

        At present the physics community values real world experimental data and a mathematical explanation. It abhors mechanical models used to relate experimental data to the mathematics. This author believes that this breeds incomplete understanding.

        Desired Operation:

        Understanding can be improved by using experimental data, mechanical models, and mathematical descriptions.

        In this post, three scenarios are presented to attempt to bring this idea home.

        The first is the rose garden scenario from the essay and a post from basudeba. As pointed out, the truck drivers could have delivered the +400 roses then, to deliver the -400 roses, the +400 roses would be carted away. This is a very accurate assessment. However, this assessment is made due to the fact the truckers and gardener has a model from which to work with. That is, they can hold roses in their hand. That is, they have real world data, a model from which to work, and a mathematical understanding. The gardener did not process the model in his thought process. He thus thought there were some mysterious roses. The truck drivers understood the model and sold the gardener his mysterious roses.

        This is to mirror the way special relativity is treated. There, people have proposed tachyons. The "mathematics" proposes that tachyons are particles moving backward in time at a speed faster than the speed of light. This author proposes that this scenario is generated because the physics community abhors the idea there is a model that explains special relativity. The essay suggested (in the physics community this is considered a sin) a mechanical model that represents how special relativity works. The point is that once a model has been selected, many ramifications of the concept of special relativity can be drawn. Understandably, those ramifications can come under fire of skepticism and challenge. This is as it should be. The point is that without a model, further discussion does not exist.

        As a third attempt to explain the prime thesis of the essay, consider quantum wave collapse. Presently a quantum particle is considered a probability wave that upon observation collapses to occupy a specific position and time in space. This author believes this concept is due to no model or a false model. At present the physics community clings to the idea that particles are little hard balls that can appear randomly in locations in space adhering to quantum mathematics descriptions. Consider a different model. Perhaps particles are like oil drops that undulate as they move through space. Maybe we should consider a particle as a loop of string that undulates as it moves through space. The concept here is that the center of density of the particle is shifting up, down, left, right, forward, and backward.

        Now, the process of observation is the process of measuring the density of the particle at all points within the particle and finding the center of the density. The physicists of today will consider that is where the particle is at. As the physicists consider all these things hard little balls, they will declare that is where the ball is at, at a specific space and time. From this the concept is that quantum particles can move backward in time and experience Heisenberg Uncertainty.

        The point is that they are making a false assumption. They claim that the little ball can be mysteriously anywhere and mysteriously finds its location when observed. In reality, during observation, the averages of all parts of the particle are averaged to a specific point in space and time. The oil drop or string has no idea it has been observed, experiences no change in behavior, and just continues undulating along.

        One might ask, "OK, what do you mean we average the parts of the thing." Well, what happens when a beam is observed in a cloud chamber or we see splats of light on a piece of paper caused by some flying thing? We look at the center of the trail or locate the center of the splat and declare that is the things position in time and space. Thus we get the average of a position in time and space.

        Now one might refute the concepts illustrated here. The point is that differing models along with real measurements and descriptive mathematics will yield differing interpretations. Some will work together better than others. We then have a better chance of understanding the world around us.

        Hello Al,

        I love your conclusion section:

        Math is a language that can describe reality. When used to describe reality there should be a model accompanying the math. The model and math should be compared to reality to test the validity of the math and model. If these three things are not in harmony, we do not understand the phenomena and need more research.

        I totally agree and it is amazing that the interpretation of quantum theory has remained unresolved for so long.

        I have a great sense that Albert Einstein was outvoted and sidelined in the quantum theory debate when all along the issues that troubled him were totally valid.

        I hope you will get a chance to read 'Solving the mystery' where I have tried to provide a descriptive model that matches reality.

        Regards

        Richard

        I understand that Einstein, Schrodinger, and deBroglie believed there was something real about the equation and all were "outvoted". I suspect they were outvoted by a particular individual that had power and had his own ideas about the reality of the universe. It is incomprehensible to me that the three men that really made it all work were pushed aside. I get the feeling that if you are right you don't count. I have studied the history of physics and have found this common. I feel for people like Avagadro and Carnot. I am going to read "Solving the mystery."

          Dear Sir,

          Kindly see REASONABLE EFFECTIVENESS OF MATHEMATICS: by basudeba mishra @

          http://fqxi.org/community/forum/topic/2325

          We agree with your other comments.

          Regards,

          basudeba

          Dear Mr. Schneider,

          Your comment about Einstein, Schrodinger, and de Broglie echoes the introduction to my own essay, "Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory". I argue that premature adoption of an abstract mathematical framework prevented consideration of a simple, consistent, realistic model of quantum mechanics, avoiding paradoxes of indeterminacy, entanglement, and non-locality. What's more, this realistic model is directly testable using little more than Stern-Gerlach magnets.

          But questioning the foundations in this way is considered heretical, and is unpublishable in physics journals.

          Alan Kadin

          8 days later

          Dear Mr. Schneider

          Being myself involved in model theory, I read your article with great interest. And I fully agree with you that the understanding of physics is not exclusively a question of math. On the contrary, here in France and in Europe, many of us are grateful especially to Richard Feynman for his way to revolutionize the pedagogy of physics.

          However, if the understanding of physics is not exclusively question of math, the latter plays an essential role in the elucidation of physical reality, and at this level, there is a great mystery remaining until further notice.

          You say in your essay that math is a language like English. It is true that math, like English, can describe things that do not match reality, and that only experience determines if mathematical or English proposals correspond to the part of reality we try to describe. But I think that math has "something" than English or Spanish or Nipponese etc. do not have, and that this "something" plays an essential role in the relationship between math and physics.

          Let us consider cartography, a domain on the periphery of physics. Of course, we can try to replace a map by a description of the area in question in English, Spanish, Nipponese. But the semi-offshore amateur sailor I am - I do not like the term "yachtsman" - prefers a map. On a map, rather basic mathematical tools allow me to establish and correct my course, to determine my position etc. This would not be the case with an even meticulous English description of the waters where I am sailing. Being a projection of a spherical surface on a plane, a map always involves deformations. But mathematical tools depending from the adopted type of projection - in non-polar navigation it is usually the Mercator projection - allow to effectuate the necessary corrections. Here again, English or Spanish alone would not be of much help.

          On the other hand, in order to establish not a simple picture but a real map, the cartographer in turn needs mathematical tools, including differential geometry beginning with the famous ds, even if this ds does not exist in the physical reality.Let us now a bit of science fiction and imagine space-time relativistic cards destined for future and hypothetical space vessel diameter pilots traveling at a speed close to c. The establishment of these maps, necessarily computerized to be quickly accessible, requires the use of the imaginary number i, i2 = - 1, although the latter, by definition, in turn has no real existence.

          For all these reasons I think that math have "something" that other languages do not have. Regarding the nature of this "something", there is a great mystery, and this mystery is in my opinion the main motivation for the present contest.

          In my own paper "A Defense of Scientific Platonism without Metaphysical Presuppositions" (posted Feb. 25), I try - among others - to show that modeling of mathematics and modeling of physics by mathematics meet in both cases objectively given constraints and that this issue differs math from any other language and any other modeling procedure. In this connection my own paper defends a Platonic perspectiveand therefore a metaphysical position. But I try to show that any form of anti-Platonism is neither less nor more metaphysical than Platonism and that the latter is finally simpler and needs less (metaphysical and other) assumptions than its challenging theories, especially regarding the difference between existence within material reality and mathematical existence.

          Your paper and mine diametrically opposed positions express. But boths papers have a common denominator: they refer to the concept of modeling. Since the purpose of this contest is a constructive confrontation of ideas about a mystery where, in absolute terms, no one may be right, I would greatly appreciate to know your comments about my own essay.

          I would also like that this discussion could be continued for further, even after the closing of this contest.

          With best regards

          Peter Punin

            Peter Martin Punin:

            After reading this post and your essay, here is a few words that jump out at me.

            "For all these reasons I think that math have "something" that other languages do not have. Regarding the nature of this "something", there is a great mystery, and this mystery is in my opinion the main motivation for the present contest."

            I can explain this mystery. The many believe that math is the great and perfect descriptor of the all. Since it clearly fails, the many are dismayed, perceive a mystery, and search for some deeper meaning. There is none.

            In all of history, great leaders have gathered thousands of men and gone to war. Thousands on both sides in many battles have died. The great declare themselves the winner. Have those that died on the right side also won? It all depends upon one's point of view.

            All I am saying is that dependence on math does not automatically yield a correct description of reality. I am not questioning how it does it. Whether it is good or bad depends upon one's point of view.

            I have read your response and attempted to read your essay several times. Your education is superior to mine. I cannot extract understanding from the sophisticated language you use.

            Al Schneider

            Dear Al,

            You have presented the theme for this year's essay in a very entertaining and very informative way. In fact, if the remaining of the essay was as interesting and factual as the first five and a half pages, your essay would have been one of those to beat in this year's competition.

            The way you started by pointing out the scenes as the drama has unfolded was really good. Following that, your use of the parable of the "The King's Roses" to illustrate why math formula must correspond to reality makes the point clearly. This will spare us the various negative mass and negative velocities plaguing our physics today, which are the aftermath of the spell cast on our physics from Copenhagen.

            However, the euphoria I had from reading the early pages, reduced somewhat when in my opinion you went too deep into speculation in the latter part of the essay. For example, some things to ponder, if photons travel at c and are never at rest, how can they form a particle? Do they have an attraction force between them to bind them into a stable form? Your assumption does not take into consideration that light may be more of wave than particle. I will not tackle you on special relativity, which in my opinion you tried unsuccessfully to model. Special relativity cannot be modeled because it is not real, but as that is not the main focus of your essay, let me spare you the facts proving this (unless you want to discuss it on another forum on this site).

            Finally, under your Caveats, points of zero dimension are not a certainty. Indeed, in my 2013 essay I discussed the historical arguments between the Pythagoreans, Proclus and Aristotle on the one hand who held that the point had some minimum irreducible dimension and Plato who held that it was of zero dimension but not a "geometrical fiction". I continue on the same path in my essay this year, where I show that an infinite number of points on a line results in the kind of absurdity you demonstrated with your tale of the roses. I am sure you will like it because it contains things you have yourself pondered over and discuss in your essay. As a teaser, how do you propose to cut the kind of line on Deepak Chopra's hand as you mentioned, if the number of points are infinite and points are not things that are 'cuttable' into parts by definition?

            All the best in the competition.

            Akinbo

              Mr. Ojo:

              Thank you for responding to my essay. I am honored. I think you have pointed out that the beginning of my essay is on track. In viewing the second half you have pointed out what you think are flaws. In reaction to that, I would like to point out that when I talk of the things that are not modeled correctly, one would be the wave theory of light. In writing the paper I had considered addressing special relativity or the travesty of present understanding of light. I chose special relativity. I expect responses like yours and value it. Incidentally, the criticism of zero point particles was shown me by the director of a physics department of a significant university when I presented my idea to him. He didn't like my idea either.

              I will go take a look at your essay.

              Thank You

              Al Schneider

              Before I go however, I must point out that I wrote a book titled "New Age Quantum Physics" available on amazon dot com. It addresses the questions you have posed.