Dear Stefan,

I appreciate your kind remarks! Regarding your impression of my approach as largely involving reinterpretation, I would prefer to think of it in the way you describe than to think of it in terms of simply throwing out all that we've learned over the last 500 years and starting over. There are often many steps separating original physical ideas from the formal theories eventually used to describe them, and I think that a lot of the great scientists of previous eras had many physical ideas more or less perfectly correct without necessarily having the tools necessary to make them precise.

Regarding the mathematical nature of my approach, through my many discussions here I have come to realize that to some extent I have failed to communicate what I view as the proper perspective on the relationship between the physical and mathematical ideas involved. As a mathematician trying to do physics, my goal is to not allow mathematics to be a limiting factor in the expression and description of physical ideas. In other words, I have tried not to be influenced by the mathematical convenience of particular models, but rather by which models I feel express the physical ideas in the purest way and with the least baggage. One possible result of abandoning mathematical convenience is, of course, that the mathematics can become very difficult and can lead into mathematical fields and topics that most people, including myself, have never heard of before. For this reason, the whole approach can create the false impression of focusing too much on the mathematics itself. The intention, however, is just the opposite: to begin with the simplest of physical ideas (such as cause and effect) and then simply bring to bear whatever mathematical machinery is necessary to adequately describe the resulting theory. Take care,

Ben

Dear Ben,

You have gone through my paper extentsively. Thanks. Pls give me some time to go through yours once again and make my comments.

I will have to respond to your comments part by part, since the posts cannot be too long. In this post I will take up your comment about "Lorentz invariance".

You wrote: "5. I agree that Lorentz invariance as Einstein conceived it is not exactly right, but it is close enough to being right that I prefer to regard it as an approximation of the correct principle. This is what I mean when I discuss "reinterpreting the principle of covariance" in my essay. "Covariance" is usually understood to mean "Lorentz invariance," i.e., group symmetry. I do not think group symmetry is the right way to think about this principle".

Let us look at this issue from a historical point of view. And also let me quote Einstein in regard to his own views on evolutions of concepts.

'The concepts originate from experience by way of 'abstraction' i.e. through omission of a part of its content... (They) easily achieve so much authority over us that we forget their earthly origin and take them for something immutably given. They are then stamped as 'necessities of thought', 'a priori given', and so on. The path to scientific progress is often obstructed by these errors for a long period of time. It is therefore no idle amusement at all, when we are preoccupied with analysis of concepts that have been current for a long time and with showing, upon what circumstances are dependent their justification and utility and how they emerge, individually, from experiential data. Thereby their excessively great authority is broken down. They are omitted, if they cannot be made properly legitimate; corrected, if their co-ordination with the given objects was too carelessly established; or replaced, if it is possible to construct a new system which we, for some reason prefer" (4, p.19).

There are a lot of mathematical baggage that has been overlaid in trying to interpret the EMPIRICAL EQUATION for the DISPLACEMENT that Lorentz discerned by TRIAL AND ERROR by ITERATING the data of Kaufman's experiments on fast moving electrons. By 'interpret' I mean what mainly Poincare (and Einstein too) did to give it a twist to make it fit into his line fictitious thinking of about the "nature of SPACE and TIME". (Note: Displacement is what is measured directly, "SPACE" is where the displacement occurs). Now people have been so indoctrinated that they cannot discuss LT in simple terms as an expression for displacement, without getting confused into using this mathematical baggage concerning the 'nature of space'.

So if we are to understand what Lorentz transformation really means, we must forget all the interpretations that have been assigned to it, and consider its point of birth by 'curve fitting' of data, " showing, upon what circumstances are dependent its justification and utility and how it emerged, individually, from experiential data".

What has happened is when Lorentz curve fitted data for particles moving at NEAR LIGHT VELOCITIES (v/c tending to 1) he had unknowingly missed out the term v/c which should have belonged to that empirical equation. Then this equation with the v/c term deficient was taken over by Einstein as true and perfect and made it into a postulate of the theory.

If you consider the equation x' = gamma (x - ut), it gives very accurate results when v/c is almost equal to one. As a result when the empirical equation of Lorentz conforms to the DISPLACEMENTS of particles at very fast velocities, the credit goes to SRT. But everybody forgets that every time x' gets confirmed, time does not correspond to t' = gamma. t(1- ux/c2) as SRT contends, but SRT gets a free pass on this.

However, as the velocity declines to 0.9c, 0.8c, 0.7c there is a progressive degeneration of the accuracy x' in a non-linear manner. Below 0.5c the degeneration becomes more marked. And at much lower velocities the degeneration of results reach exponential proportions.

We can now understand why the theory has been named "special" theory. It is valid only for the special condition of v/c tending to 1. So there is a schism in physics, SRT [meaning displacement x' = gamma(x -ut) and gamma' F for force] for very fast motion and Newtonian mechanics (meaning x= vt for displacement and F for force). But this leaves out the vast middle ground between very slow and very fast motion. Should not there be an equation that covers the whole range of velocities from very slow to very fast?

From the above observations (about the degeneration of results with declining velocities) we can re-construct the equation to be valid for all velocities v by following simple logic. If the LT equation is valid for the condition v/c = 1, then the equation that will be valid for all values of v will be

x' = gamma. (v/c)(x - ut) or x' = gamma .vt(1- u/c).

This then is the general equation of motion valid for all velocities. It can be verified by the computer analysis of all the relevant experiments done in the last century.

Your next comment: "6. I agree that "all inertial frames are not equivalent, but..." is closely connected with why the discrepancy (wrt classical x = vt) in a straightforward displacement measurement had to be interpreted as arising from the "nature of space and time". I will touch upon this in my next post.

(My essay: : http://fqxi.org/community/forum/topic/1549)

Best regards,

Viraj

    Ben,

    You wrote: "Regarding the constancy of the speed of light, my guess would be that a concept like this only makes sense at sufficiently large scales. (...) You'll have to remember that my background is mostly mathematical, and therefore I'm inclined to consider the possibility of things that most physicists "know" are wrong. This might be useful in some cases; in others it only reflects my own ignorance."

    Insofar as "the constancy of the speed of light" is concerned, I am afraid your last statement is relevant, Ben.

    Pentcho Valev

    Hello Ben,

    I thank you for the gracious comments you left on my essay forum page. I'll answer your queries shortly. Your points are well taken and very much appreciated. Unfortunately; I've been sidelined with unexpected responsibilities, but I do hope to get to read your essay soon and respond to your comments sooner. However I am still catching up elsewhere, so it may be a little bit.

    All the best,

    Jonathan

      Dear Sergey and Benjamin

      A lot of fascinating ideas seem to have emerged and are emerging in Russia - but unfortunately I do not have the language either! I have newly discovered that entropy emerges naturally in the same mechanism - diffusion - explaining uncertainty and probability) in my Beautiful Universe model, where also e/m and gravity are realized in local causal building blocks of a universal lattice.

      Vladimir

      Hi Ben and thanks for a very interesting essay.

      I realise I share your view of the universe in some key aspects of your hypothesis and must read it once more to give you some useful comments on it. Here is a first:

      "...the metric properties of classical spacetime, up to overall scale, arise from a binary relation, which I will call a causal relation, on a set..."

      Well formulated !

      The problem I have in accepting it is not that it contradicts observations, but the mind-nuking number of "binary relations" involved. Intuition tells me this cannot be right and that there has to be a simpler model, but then again, I do not trust intuition very strongly in these matters.

      If you have an hour of lesure time, I think you would enjoy this youtube-video:

      http://www.youtube.com/watch?v=YfYon2WdR40

      PS.

      My first impression of you, extrapolated from your written posts on several essays, was that you were 60 years old. But since you present yourself as a Ph.D student, I suspect that is not the case.

        No, I am sorry but there are a lot of probelms. Indeed I am parano. and you know it all. I have known FQXi at the begining. I have shared my theory in a total transparence. I don't understand the comportment of Tom, Joy, Christi,Jonathan Dickay, Brendan, Lawrence, and friends , I am stopping there for the names. I beleive in fact that it is a team trying for their vanity and hormons.Probably that they like this play. The Universal integrity is more than these comportments with superimposed algorythms for the confusions and the strategy. I continue even with your strategy. In fact, all is false. You have made a bad thing. For your knowledge, the laws exist and it is important for the good governances. The real integrity is essential. If these persons trying to discriminate, or to profit, or to steal, or to superimpose the algorythms are in a bad boat, it is not my probelm. The lawz are the laws. You are not generalists, just persons competent for the computing, it is totally different. Me without tools and strategy and alone, and you with all that.let me laugh , frankly it is ironical. I know the team behind. it is what the probelm, they want the nobel, because they need funds and investments, because they are not able to ponder works like mine, it is what the probelm?

        I love FQXi , it is important for me,I respect Mr Wilszec,Mr Tegmark,Mr Witten,Mr Guth and friends. So don't try with your discriminations between Canada,USA and Netherlands.

        You know, you do not imagine how I forgive this play of Tom, Jonathan ,joy and friends. and if people utilizes false names, be sure that I see it .No probelm dear team. each thing at its times.

        They have hacked my computer, they check all.and what? where is the probelm?

        You know Ben, I have been already lsot in the past in my country, due to bad people, they have caused me a bankrupcy. I have worked hard for my theory of spherization,I have learned a lot.and always I have people who are bad with me.always I have been nice and kind, always Ben. My economical situation, my health, mysocial situation are catastrophic.My state of mind is very weak. I am not well. I am isolated at home without job. This society disgusts me you know. I am tired.My theory is all my life.I just would sharing it in a total transparence.I would simply find partners and friends.I would like just finding a job also.I just would a little of recognizing for my works.and even on net, it is corrupted.Oh my god, but what is this circus. I am shocked by this planet. I have found FQXi and I said me, it is cool, a platform of physics for the theoretical physics. I am happy, I will can show my theory and I will find a job and coachs and mentors. and I see all this play from a team. It is sad. The technology of information is a tool, and this tool must be utilized with wisdom and universality. The cyber criminality msut be punished for the well of all in fact.

        But where are the good persons ? on an other planet or what ?

        I have 48 inventions ben and my theory of spherization, a revolutionary theory, general and rational and deterministic. I just want to evolve correctly with good persons. I search even my mentor. I need to learn more.Personally I will be honored if Mr Penrose, Mr Hawking, Mr Solomon or Mr Wilcszec could be my mentor. I need to evolve, there I don't evolve. I just decrease my health. I must move. I become crazy in fact there at home with my problems.

        FqxI is a wonderful platform. so why ?

        Dear Andreas,

        Haha... well, actually I'm 32, which I admit is a bit long in the tooth for a graduate student, but I've had a rather interesting and non-traditional journey to this point.

        Thanks for the feedback and the video suggestion...I will be sure to take a look!

        Regarding the number of relations, one must make a distinction between "binary relation," of which there is precisely one for each classical alternative in my approach (and a single higher-level binary relation for the entire quantum picture), and "relation between elements," which refers to a particular ordered pair of elements which are "related" by the binary relation.

        I'm not sure what could be simpler than cause and effect as a basic building block for physical interactions. Of course, there are going to be a huge number of cause-and-effect relationships, but this will be true in practically any model you can think of, whether that model takes causality to be fundamental or not. In particular, if the universe is infinite, its hard to imagine how there could not be an infinite number of causal relationships.

        If you mean that the number of "classical universes," each with its own binary relation, is large, then yes, there is an infinite number of such binary relations, representing the infinite number of possible histories. I call these "classical universes" not in the sense of "THE Universe," but in the sense that each is self-contained as a classical causal network. Then entire ensemble of these possible classical histories is a way of talking about THE Universe in my view.

        Again, on the subject of simplicity, I believe that the sum-over-histories view is by far the most conceptually simple view of quantum theory. Without it, you have to take for granted mathematical objects like Hilbert spaces and operator algebras. Of course, many people would still like to believe that quantum theory is somehow wrong, and that a single deterministic picture underlies everything. While I can understand and sympathize with this view, my own opinion is that quantum theory really does play a fundamental role,and that trying to do without it raises much worse problems, particularly in the philosophy of science.

        Anyway, thanks again for the feedback! Take care,

        Ben

        Dear Ben

        Thanks so much for your comments on my submission discussing Riemann's concept of density. I believe everything in your submission, up to its last sentence on "energy density," reflects rigorously much of what I discuss at a different level. And it does so a hundred times better.

        I've also often wished that Einstein had met Riemann. Einstein and Planck borrowed a lot from Riemann, from the zeta function to "their" term quantum. But I agree, they did not borrow enough. And, as you show, the problem lies in foundational assumptions. I discuss some of their assumptions in my European Journal of Physics article http://iopscience.iop.org/0143-0807/30/4/014. But I think your essay already identifies them.

        You're absolutely right: Riemann himself did not take continuum manifolds for granted as a basis for physics. His unpublished notes reveal an approach closer to your paper's causal structures. I will spend more time on your immensely insightful proposal. It deserves better thoughts than the following. I'll send you an improved response but for now just a few "brainstorms:"

        I believe Riemann's concept of manifold is not the one you reject as "the manifold structure of spacetime." I'm working on a paper like my one on the concept of density, except on Riemann's concept of manifold (Mannigfaltigkeit). Few people remember Cantor's Riemannian manifold -theory (Mannigfaltigkeitlehre), later known as set theory. I learned from your paper about "causal set theory." The term reminded me of Cantor's late research on set-theoretical "physics."

        Like you, Riemann would also reject the "evolution of systems with respect to an independent time parameter." As he tells us, the reigning paradigm was mostly Kantian. If you view time as a way of talking about causality then you come close to his "neo-Kantian" approach, i.e. space and time as somehow mathematically observer-dependent. He never finished this late work.

        As for the "commutativity of spacetime" I believe Riemann held space and time to be dual, i.e. just like the particle-wave duality, but somehow commutative-noncommutative.

        As for your promising causal metric hypothesis, I believe you may find philosophical/foundational support in what Hermann Weyl wrote about Riemann, specifically in Weyl's recently reprinted books.

        "In the universe of scientific thought, ideas from mathematics, philosophy, and the empirical

        realm combine in the form of general physical principles, which crystallize into the formal

        postulates of physical theories, while remaining colored and sometimes distorted by the interpretations

        and prejudices of their intellectual environment." Riemann could not have put it better than that!

        A few of Riemann's contemporaries did not formalize causality as an irreflexive, acyclic, transitive binary relation on the set of spacetime events. I think you implicitly mention them. As I read them, Gauss' reciprocity laws and Riemann's reciprocal numbers "arythmos," were interpreted as rythmic, oscillatory, cyclic, reflexive, causal (force-effect) relations inextricable from space, time or gravity. A more technical version of my paper would say that the inverse square and quadratic reciprocity law were not separate into "physical" and "mathematical" laws. One can see that just from the laws' names. ...(cont.)

          ...From my European Journal of Physics article perhaps you could guess that I would find exciting any research concerning your "universal Schrodinger equation." Keep it up!

          "Mathematical tools necessary to implement these ideas include a synthesis of multicategory theory and categorization in abstract algebra, involving interchangeability of objects, morphisms, elements, and relations." The seeds of those tools are in Gauss Disquisitiones Arithmeticae and Riemann's "Natural Philosophy." I believe Grothendieck's use of category theory re-discovered a few ideas already present in Gauss, and even more, Riemann.

          "For example, zeta functions, and hence the Riemann hypothesis, are connected to

          quantum field theory via noncommutative geometry and the theory of motives " You've read the book "Zeta and Modular Physics (2010)"? Maybe the link to relativity is there. I would link their discussion to Riemann's approach to Dirichlet.

          Thanks for the reference to Connes. I've only read his earlier work on Riemann's hypothesis. If you ever want to win a million dollars you should try to prove Riemann's hypothesis. You could apply your ideas to Connes' proof and/or your paper's "complex Hilbert spaces whose elements represent probability amplitudes of point particles, self-adjoint operators whose eigenvalues are interpreted as the possible values of measurements, and time evolution according to the Schrodinger equation." I would approach the Hilbert-Polya conjecture through Heisenberg/ Von Neumann's "mathematical causation" and Von Neumann/Wigner's "observational algebra."

          Riemann wrote down he proved "Riemann's hypothesis" and only needed to "simplify the expression." But from my paper you know what he meant by "expression." Still, if you pay close attention to what Riemann thought about his hypothesis, i.e. pay attention to the historical-foundational context, you could come up with the proof. You certainly have the required talent.

          Hope at least some of this helps. I'll give it more thought and send you comments that are not half-baked. I look forward to read more of your work. Best, Juan.

          Great Article. I will reread again -

          Regarding the ending, quoted as follows:

          "Finally, the dimension of space as well as its curvature might vary

          with \energy density," though the effect might be immeasurably small"

          This appears consistent with CIG: www.CIGTheory.com in that the volume of Space (i.e. dimension of Space) is tied to energy density / / / Full curvature = black hole; no curvature = vacuum energy/Dark Energy; partial curvature = Dark Matter, and each is all %"c" dependent

          THX

          doug (comments still welcome)

            Dear Ben,

            I will prepare an article on detailed derivation of spacetimes from generalized formulation in Liouville space.

            Here t-causality is associated to the approximated Hamiltonians used in general relativity and quantum field theory, whereas tau-causality is associated to the fundamental Hamiltonian. The distinction between "tau" and "t" is mentioned in my essay. A more detailed discussion of both and of the limits of the use of coordinate time "t" is given in the monograph by Pavsic --reference [3] in my essay--. E.g., Pavsic denotes the fundamental Hamiltonian by H and the approximated Hamiltonian used in quantum field theory by H_0.

            Regards

            Hello Ben,

            Thank you again for your comments on my essay, which to me are among the most valued of all the comments I've had.

            I saw your recent point about objects ageing, in relation to the point I made about the residual effects of time dilation. The emphasis in my essay is simply to set out the clues we have, and draw broad conclusions from them, rather than going into detailed attempts to interpret them. Because I think it's possible to arrive at a conclusion that way, and to reject block time via simple deduction, it seemed a good way of keeping the essay simple. But of course these questions can be examined in far more detail, and from there it's a case of choosing between two or three initial avenues.

            I've read your essay today, will read it again, I found it excellent in a number of ways. The overview of the whole landscape of physics you give in the first half is important and very useful, particularly at a time when things are getting a bit fragmented. It not only helps that you've summed up the landscape as a whole, but - like myself and not too many others - you've included comments on the mindset of the physics community over the 20th century, which helps with understanding about attitudes, and how and why the general view has shifted over time.

            In relation to the second half of your essay, what I'll say now is simply a personal opinion, not a criticism of your particular view. And I tend to agree on the assumptions you reject. But I suspect that the way forward, when we find it, rather than involving shuffling the underlying principles and making some go from fundamental to emergent, while others go from emergent to fundamental - which several essays here do, though none better than yours - will instead involve finding some truly new concepts. However, it may be that rearranging the bits of the puzzle we have will also be needed, and I do see that you bring in new principles, and that you may recover established physics from them. So it's certainly too early to tell, and I very much wish you luck with it, and with your essay.

            Best wishes, Jonathan

              Dear Juan,

              I appreciate the kind remarks. I'm beginning to feel as if it is difficult to be a competent physicist or mathematician without being a rather avid historian! Your comments are particularly valuable to me because you evidently possess a rare grasp of historical context in regard to foundational issues. The phrase "before his time" is overused, but it undoubtedly applies to Riemann. In many cases, the most fertile period for an idea seems to occur shortly after its inception, before certain arbitrary choices have hardened into orthodoxy, and if the community is unready to use an idea at the time it is introduced, it may be many years before it is fully exploited. I believe this has occurred with many of the ideas of Gauss and Riemann, and I'm only dimly becoming aware that the potential seeds of new advances may be lying dormant not in the last few generations, but a hundred years earlier!

              I will certainly read your European Journal of Physics article with interest. For myself, I have several volumes of unpublished work on foundational topics in physics, but this is my first small effort to make any of it public. I prefer Gauss's philosophy of "few, but ripe" to the current creed of "publish or perish." Also, I am coming from the mathematical side, and don't yet feel comfortable with my grasp of what is already known.

              I was unaware of the close connection between Cantor and Riemann, but Cantorian ideas do arise unavoidably in the approach I have been working on. I even named an important counterexample the "Cantor graph." The axiom of choice and the continuum hypothesis also become significant.

              I will have to look at the early notions of causality you mention. One thing I have learned from reading Grothendieck is the importance of properly organizing local and global data, and in regard to causality, this has led me to define things somewhat differently from the usual notions. In particular, "interpolative" properties like "interval finiteness" and transitivity play less of a role than legitimately local properties.

              Thanks again for the helpful comments! Take care,

              Ben

              Dear Jonathan,

              Thanks for the feedback! I understand that your essay doesn't represent the whole of your thinking about fundamental physics, and I agree that the ideas you consider are sufficient for the point you are making. Conciseness and clarity are particularly important in the present context.

              Nevertheless, I am interested to know what your ideas about the fundamental structure of spacetime are. You say that you "suspect that the way forward, when we find it... will instead involve finding some truly new concepts." Do you have any favorite conjectures for what those "new concepts" might be? Take care,

              Ben