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.

Dear Adel,

It is certainly true in shape dynamics that only ratios of coupling constants have empirical meaning. However, it's not clear to me how much your ideas could be related to shape dynamics.

Best of luck in the competition!

Sean.

Sean,

Good to see another fine submission from you! I didn't have time to participate in the present contest, but I enjoyed your essay. Good luck with the contest, and take care,

Ben

    Thanks, Sean. I won't pretend to speak for Carlo Rovelli, though I think I do understand what he means by degrees of freedom in an n-particle state space (I would say n-dimension state space and use the Hilbert space) where things happen discontinuously because the field assumes t = 1 and time coordinates are therefore constant (static).

    In a continuous spacetime field, time changes with space -- dynamically, as you say. So I think what Carlo is saying, is that because a continuum theory such as shape dynamics cannot associate a definite dimensionless integer to a point of the space evolving in time, it is just as, if not more, meaningful to speak of the algebraic (Fock space) degrees of freedom as to speak of finite degrees of freedom in your continuously evolving system -- because the two descriptions, absent a simple time parameter of reversible trajectory, are equivalent.

    Personally, I don't agree with Carlo, though I understand the Fock space construction. At the end of the day, I think that if shape dynamics is mathematically complete, it allows relative degrees of freedom; i.e., time reversibility that guarantees conservation of information. That's what the 't Hooft and Corda references are all about.

    All best,

    Tom

    hmmm... I'm still not sure I understand what you're getting at. Of course, there is nothing wrong with having a Fock space in Shape Dynamics, but that doesn't mean that the degrees of freedom are discrete: the number of particles can be an integer but their energy spectrum can still be continuous. Just think of a scattering experiment. Perhaps there is something I am missing.

    Cheers,

    Sean.

    Thanks Ben!

    Hope things are well with you!

    Sean.

    Thanks Sean. I know it's extremely late, but even if you don't get a chance to look at it before the deadline I would appreciate you reviewing it at some point in the future. You seem to have an open mind, so I would value your thoughts.

    Best of luck to you in the finals.

    Ralph

    Hi Sean,

    It's just the difference between algebra and analysis. If one speaks of a continuous energy spectrum, there's no point in the spectrum at which any element (any measured state at any instant) is discontinuous from the line. If one speaks of a state of particle interactions ("state" means "static") all degrees of freedom are discontinuous from the line, thus discrete.

    The distinction is nontrivial, because finite degrees of freedom define particle states and predict an historical path (Feynman path integral). The ensemble transformation of a continuous measurement function such as you describe results, as you say, in the absence of fundamental discreteness -- so I think what Carlo is asking, is how can anything that is not fundamentally discrete be countable? One would apparently have to either eliminate the measurement function (and thus eliminate the physics), or allow that countable bits of spacetime are already described by evolution of the state vector in standard quantum theory.

    I'm on your side of the question, with a caveat: one must choose which element of continuous spacetime -- time or space -- is finite. General relativity conventionally chooses time (the universe has a finite beginning and a finite end). If one chooses space, which surely shape dynamics does, infinite varieties of time-dependent shapes of a finite space potentially describe a universally entangled wavefunction of continuous measurement values, without assuming discrete particles with discrete degrees of freedom.

    All best,

    Tom

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