Dear Sean,

I hope you and your group publish a textbook on shape dynamics. You are all such superior geometers that one cannot go away without learning something new, or at the least looking at current knowledge in a new way. I now have a clearer idea of the assumptions underlying your research program.

As much as I thoroughly enjoyed your essay -- and certainly, my high rating will reflect it -- I have to agree with Carlo Rovelli that QFT degrees of freedom are discrete and therefore static, not dynamic. For this reason, I think that attempts to found quantum gravity in a continuum theory favors models like those of 't Hooft and Corda. These models work with scale invariance, too, and at the black hole extreme condition I think better explain the meaning of the time-dependent Schrodinger equation. Nevertheless, in free space, I can see that shape dynamics is a beautiful and useful model.

All best in the competition, and I do hope you can visit my essay before the curtain closes.

Tom

    Hi Sean,

    I read your essay and I finally understood the basics of shape dynamics. Although this is about your essay(very nicely written), I would like to discuss it from my essay point of view. My theory is just like yours is scale invariant of a sort. My theory is both scale invariant for reals and integer for large scale but for small scale the reals and integer diverge.

    But the interesting part which I like to ask you if shape dynamics agree with is that although my system is scale free but the constants c,h_bar, charge e are all constant since they are generated from ratios. The same thing is with mass ratios. but not absolute mass.

    All this is apparent from the curves that you see for the electron mass from my essay. If you look at them you see the mass of electron in au units which does not make sense. In fact this is just a coincidence because of the scale of the simulations, you can find the proton to electron mass ratio at any scale.

    I am sorry for being brief, I will explain more.

    http://fqxi.org/community/forum/topic/1877

    Thank you.

    Adel

      Dear Howard,

      Sorry for the delay in my reply. I've just finished 2 intense conferences and then a couple of days of hiking through the Alps. I hope you'll forgive my silence.

      To answer your question, there is definitely some relevance to the usual ads/cft correspondence here. Me and a couple of coauthors have been investigating the link between the ads/cft correspondence and shape dynamics in a couple of papers (the most recent being: http://arxiv.org/abs/1305.6315).

      Indeed, I think there are more direct connections with the dS/cft correspondence being explored by Skenderis and collaborators over the past few years. I'm working on a paper right now that will compliment the essay and try to make these connections more clear.

      Glad you enjoyed the essay and best of luck in the competition!

      Sean.

      Dear Stephen,

      Apologies for the delay in the response. I will try to read through this and send some comments if I have any.

      Best of luck in the competition!

      Sean.

      Dear Paul,

      I'm glad you enjoyed this essay and the last one.

      Yes, these are definitely interesting questions. As I said in my essay though, I was using a definition of countability that is completely ignorant to practical issues. You're very right that some things things that are, in principle, countable may, in practice, not be possible to count or one may just go on counting forever. For my purposes, all these things are "countable" (at least in principle). However, it is very interesting to consider the more realistic case of things that are practically countable.

      Take care,

      Sean.

      Dear Michel,

      Sounds interesting. Thanks for pointing my attention to this.

      Sean.

      Dear Torsten,

      Thanks for your interest in my essay and my other work.

      I don't know much about Mostow rigidity but it sounds like an interesting idea to pursue. I'll try to take a look at your essay.

      Good luck in the competition!

      Sean.

      Dear Akinbo,

      I think there is certainly a sense in which Mach would have agreed that the motions and forces felt by a body should be thought of as being influenced by the relations between everything in the Universe. However, Mach didn't know that things and information can't travel faster than light, so this changes the story slightly.

      Hope that helps answer your question.

      Sean.

      Dear Ram,

      Thanks for bringing this to my attention.

      Sean.

      Dear Doug,

      Thank you for your thoughtful comments. I wasn't aware of the Aldrovandi and Pereira paper but it certainly looks relevant to what we are trying to do. Thanks for the reference. I was aware of the Fermi data which I think everyone working on quantum gravity should be following closely. Experimental probes of quantum gravity effects are rare and you are very right that experiments are really the correct way to settle these kinds of issues.

      In regards to your last comment, it is true that, if we find a candidate for a UV fixed point we will need some parameter to break conformal invariance. I'm not really sure at this point how this will ultimately work but, at some point, something like the ratio of the cosmological constant to the Newton constant should emerge from the theory. It's still very early on so I can't give a definite answer right now. Nevertheless, it is a great question and exactly the kind of thing we should be thinking about.

      Good luck!

      Sean.

      Thanks! Your topic looks interesting.

      Good luck in the competition!

      Sean.

      Dear Wilhelmus,

      Apologies for the delay in my response. You are very right: I've been hiking through the Alps over the last couple of days and haven't had email access. Also, before that I was extremely busy with two very intense conferences. It is a bad idea to schedule an essay contest in the middle of the summer: it is the height of holiday and conference season!!

      In regards to your questions, I am very happy that you were able to read through the essay carefully and gets some ideas for your own thoughts about the world. You're right that many of these mathematical structures are just conventions. In the end, they are only useful if they can be used to model real-world experiments. I will admit that the model Universe that I give here is very idealized. But, I still think it could be interesting to give us some clues as to what our real Universe might be doing. The spheres are meant to stay spheres in the infinite future but this is somewhat of an idealization too.

      I am really enjoying my time in Holland. It is a very nice country!

      All the best,

      Sean.

      Dear Vladimir,

      Thank you for the nice comments about the essay.

      I think you are right that scale invariance seems to be in conflict with Loop Quantum Gravity and other lattice approaches to quantization.

      All the best,

      Sean.

      Dear Ralph,

      Thank you for these very flattering remarks. I am really happy that you were able to take something useful out of the essay. You are too kind.

      All the best,

      Sean.

      Best of luck in the competition. I will try to take a look at your essay.

      Sean.

      Dear Leo,

      Thank you for these thoughtful comments.

      I will have to look into this in more detail before making a definite opinion of how my work might relate to yours.

      Best of luck in the competition!

      Sean.

      Dear Unnikrishnan,

      Thanks for the question.

      The relation is between space and time and information. Since space and time provide the fundamental arena in which relationships between matter can be described, the essay addresses whether it's possible for matter to be fundamentally describable solely through information. My suggestion is 'no', because the standard arguments for the discretization of spacetime can be replaced by fundamental scale invariance. I thus don't find the arguments that matter can be described primarily by information particularly compelling.

      All the best,

      Sean.

      Dear Tom,

      Thanks for your nice comments on the essay. I will definitely try to have a look (very soon) at your essay.

      Regarding Rovelli, I'm not sure I immediately see why QFT degrees of freedom are discrete or what it means for them to be static. After all, things DO HAPPEN in QCD, which seems to me to indicate some sort of notion of dynamics. On the other hand, I do agree that 't Hooft's conformal gravity stuff is very interesting and promising. I'm not too familiar with Corda.

      All the best,

      Sean.