Thanks, Tom. I have almost dealt with the most urgent issues that have accumulated during my absence and will soon start reading essays.

Best,

Vesselin

Dear Janko,

I am afraid I cannot answer what you ask since I share the views expressed by:

J.L. Synge in his excellent General relativity book: "The Principle of Equivalence performed the essential office of midwife at the birth of general relativity... I suggest that the midwife be now buried with appropriate honours and the facts of absolute space-time faced."

Einstein himself, later in his life, changed his opinion of Mach's principle and wrote: "Actually, one should no longer speak of Mach's principle at all."

And here is why I think Mach's ideas contradict spacetime physics (properly understood in terms of Minkowski's four-dimensional formulation of Einstein's special relativity). Only two examples:

1. According to Mach, if there existed a single particle in the universe, one could not say anything about its motion (e.g., whether it is moving with constant velocity or is accelerating). That is true in Einstein's original special relativity, but clearly wrong in its accepted Minkowski's formulation: if there existed a single particle in the universe, its worldline would be either straight (which, in three-dimensional language, means that the particle is moving with constant velocity) or curved (representing accelerated motion).

2. According to Mach, one cannot distinguish between the Copernican and the Ptolemaic systems because, on Mach's view, it is not clear what orbits what. This is plain wrong in spacetime physics because the worldlines (rather worldtubes) of the planets are helixes around the worldtube of the Sun (which, in three-dimensional language, means that it is the planet that orbit the Sun).

Best,

Vesselin

Thanks a lot, Cristi. I see we agree on a lot of issues related to the interpretation of general relativity and to quantum gravity. Thank you also for the link to your paper in Annals of Physics.

In fact, regarding your PhD thesis, if you are planning to publish it, would you also consider the new academic publisher - the Minkowski Institute Press; we have a special Doctoral Theses Series. You can always contact me at the email address given at my webpage.

Dear Vesselin Petkov

I agree with your answer about Mach principle, but I thought on more wide definition of Mach principle, where one option is Mach7 rule: ''If all matter is removed from our universe, universe does not exist any more''. What is your opinion? I expect that this dissagrees with your view? On this view it is also based the graph theory of Fotini Markopolou. I think that gravity is quantized also because G helps to give that physics is dimensionless (similarly as Planck constant helps this.)

I intuitively like the idea that gravity is not a force, but I also like the Mach7 rule. So it seems that the elegant solution is that the virtual graviton does not exist.

Otherwise, I also like your opinion and example that mathematics is not only description in physics. I also mainly agree wih Stoica opinion about your essay, except that I think that spacetime is discretized on some way.

My essay

Best regards

Janko Kokosar

    Dear Janko,

    Regarding your question (at the end):

    Mach7 rule: ''If all matter is removed from our universe, universe does not exist any more''. What is your opinion?

    You know that there exist matter-free universe solutions of Einstein's equations. And it is not trivial at all to decide which solutions are "physical".

    However, I think it is, to a larger extent, a matter of what we will call matter - if we regard as matter everything that exists in the universe, the answer to your question is self-evident.

    Best wishes,

    Vesselin

    Dear Vesselin,

    Thank you for your very interesting essay, one of the best in the contest. I have nothing to add to your essay's conclusions, especially: "the exciting art of doing physics is to determine which mathematical entities have counterparts in the physical world."

    I take the opportunity and propose the mathematical entities and their counterparts in my essay, engaging the set of Thurston geometries (the geometrization conjecture ) with metrics. I treat them as a space-like, totally geodesic submanifolds of a 3+1 dimensional spacetime. In three dimensions, it is not always possible to assign a single geometry to a whole space. So, the geometrization conjecture states that every closed 3-manifold can be decomposed into pieces that each have one of eight types of geometric structure, resulting in an emergence of some attributes that we can observe. As you probably know, Thurston geometries include: S3, E3, H3, S2 ﾃ-- R, H2 ﾃ-- R, SL(2, R), Nil and Solv geometry. The constant curvature geometries arise as steady states of the Ricci flow, the other five arise naturally where the dynamics of the Ricci flow is more complicated and where topological changes (neck pinching or surgery) happen. I have tried to attribute the geometries to interactions and fermions, except of five exotic ones (so far). You will probably find interesting Torsten Asselmeyer-Maluga's publications that deal with details of similar approach. Interesting is also the proof of the geometrization conjecture, sketched in 2003 by Grigori Perelman, showing that the Ricci flow can be continued past the singularities.

    If you are interested you can find details in my essay.

    I would appreciate your comments however I would understand if you were tired with the contest. You deserve the high rating what you can observe in a moment.

    Jacek

      Vesselin,

      Nice to hear from you again. In your essay, you wrote/spoke like a true physicist. Physics is the study of this special relationship between the observer and his reality that we call "experience".

      This experience only exists by the interaction between the observer and what is really out there, the substance. By opposition to "experience", the substance of the universe does not need us in order to exist.

      We have known this long enough to stop beating around the "black box" and guess right away what's in it. The truth is not something to look for anymore. It is something we have to be able to look at.

      All the bests,

      Marcel,

        Thanks a lot for your comments, Jacek.

        I have hardly started to read essays this weekend and I am indeed interested in seeing more on what you wrote in your comments here.

        Best wishes,

        Vesselin

        Marcel,

        Nice to hear from you too. Regarding your:

        "In your essay, you wrote/spoke like a true physicist. "

        I hope you meant as, not like. English is not my first language either, but I have always tried hard to learn such delicate differences.

        However, if you did mean like, then you could consult my webpage given above,

        Best wishes,

        Vesselin

        Vesselin,

        Besides the essay itself, I hope you will read my defense of the physical reality of Minkowski space in a series of posts & attachments beginning 2 April. Thanks.

        All best,

        Tom

        Dear Vesselin,

        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

        7 days later

        Dear Vesselin,

        I read with great interest your depth analytical essays in the spirit of the Cartesian doubt with extremely important conclusion, which I fully agree:

        "...mathematics in physics is not merely a description and that part of the exciting art of doing physics is to determine which mathematical entities have counterparts in the physical world. Also, despite that the issue of the nature and role of the mathematical formalism in physics is a metatheoretical issue, physicists should deal with it because misconceptions about this issue might delay the advancement of fundamental physics. " My high score.

        Tthe basic science is in a deep existential crisis, "crisis of understanding" ("Advances in Physical Sciences" K.Kopeykin "Souls" of atoms and "atoms" of soul: Wolfgang Ernst Pauli, Carl Gustav Jung and "three great problems of physics"), "crisis of interpretation and representation" (T.Romanovskaya "Sovremennaya phizika I sovremennoe iskuusstvo - paralleli stylya" / "Modern physics and contemporary art - parallels of style"). This profound existential crisis of basic science - universal human problems. Mathematics and physics require a deep ontological justification (basification). In fundamental physics is necessary to introduce an Ontological standard of justification (basification) along with the Empirical standard.

        I invite you to see my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing of the primordial generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - the ontological (structural, cosmic) memory. I believe that the scientific picture of the world should be the same rich senses of the "LifeWorld" (E.Husserl), as a picture of the world poets and philosophers.Today, more than ever, are relevant philosophical covenant of J. Wheeler: "Philosophy is too important to be left to the philosophers."

        Kind regards,

        Vladimir

        Dear Vesselin,

        You make a compelling case as to how equivalent theories contribute to hiding the nature of the foundational properties of the physical world. I found enlightening the idea that one may have equally correct theories but only one of them is closer to the heart of things and can be used as a foundation for future research. It's an idea that feels true. You have a very enjoyable and clear writing style which benefits the presentation very much. I am very enthusiastic about your essay. One thing I found a bit confusing is that I always though that relativity implies that there is no interaction but only geometry, however you seem to say something a bit different (page 8, the last paragraph "Had he lived longer, Minkowski himself might have arrived at this radical possibility"). But maybe I'm just reading it wrong.

        Anyway, I loved your idea and your writing style so I am rating this essay accordingly. Should you have the necessary time, do read my essay and let me know what you think.

        Warm regards,

        Alma

        You are very much gelled with the concepts.

        Great.

        - Sincerely

        Miss. Sujatha Jagannathan

        Thank you all for your comments. Due to some urgent issues in the last ten days and this week I hope to be able to do something enjoyable next weekend - reading essays.

        Vesselin Petkov

        P.S. Thanks a lot Alma. What I meant is that if Minkowski had lived to see the advent of general relativity, he would have realized, as a mathematician, that the mathematical formalism of general relativity implies that gravitational phenomena are merely manifestation of the non-Euclidean geometry of spacetime (not an interaction). Einstein made a gigantic step by linking gravity with spacetime geometry, but even he was unable to overcome the seemingly self-evident "fact" that gravitational phenomena are caused by gravitational interaction (which, unfortunately, is still the accepted view in physics).

          Dear Vesselin,

          Thank you very much for explaining, now it makes perfect sense. I did suspect I misunderstood what you meant. I wish you good luck and I hope the issues you are attending will be resolved soon!

          Have a great day and a successful week!

          Alma

          Vesselin,

          Great essay. Tom flagged it up for me. It was on my list but I've failed to hit my target so got promotion! (and a top score), but only a 'speed read' so lowfi and I've marked it for a return.

          I'm sure you'll like mine, no worries on scoring, but I'd greatly appreciate your views. There's a link to the main paper co-authored with John Minkowski. Our main work has been in the 'discrete field' model of SR, but this is a result of the implications of that model on QM.

          There's also a short video on my string I hope you'll look at and discuss.

          best wishes.

          Peter

          a month later

          Dear Vesselin,

          I very much enjoyed your essay! You offer convincing arguments that mathematics in physics is not merely a description. I agree with your opinion that metatheoretical misconceptions might delay the advancement of fundamental physics.

          Best regards and good luck,

          Milen

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