Dear Sean and Flavio

First of all, congratulations. You have written a very clear essay, and I´m deeply impressed by your proposals. The definition of entropy in shape space is very compelling and the derivation of the entropy formula is fantastic. It will be very interesting to investigate in full details your idea of linking measurement and time.

Flavio, you may remind of me, I´m the brazilian student that visited Julian Barbour earlier this year in college farm.

The most interesting aspect of your idea is that it all comes from questioning few very natural assumptions. A (close minded) string theorist could argue that our world is simply too bizarre for mundane conceptual questioning like asking what is space, time and motion, and would look solely for ''mathematical hints'' for building a theory of QG. But upon these first questions, one may choose to build physics on shape space and once this happens the whole mathematical structure, and consequently, the whole theory is changed. As a result, you may get new path to quantum gravity by changing its concepts, or ''building blocks'' at the classical limit.

It is then evident how different conceptions of motion at the classical level may lead to new physics. I feel shape space is a more natural arena for building physics then the traditional configuration space.

In my essay Absolute or Relative Motion... or Something Else? I propose the following question: how can we conceptually conceive motion? I argue that Machian´s philosophy (which leads to Barbour´s relational physics) may be part of something bigger and give hints on how to take these questions foward. You may find it interesting.

Good luck in the contest, and once again, congratulations for one of the best essays I´ve read so far.

Daniel

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    • Post #3

    Sean, Flavio,

    You wrote: "...it is still true that the spacetime framework is incredibly useful and, as far as we know, correct."

    Incredibly useful for what? If you mean the destruction of human rationality - yes, I agree:

    http://www.nytimes.com/2004/01/01/opinion/the-time-we-thought-we-knew.html

    Brian Greene: "Now, however, modern physics' notion of time is clearly at odds with the one most of us have internalized. Einstein greeted the failure of science to confirm the familiar experience of time with "painful but inevitable resignation." The developments since his era have only widened the disparity between common experience and scientific knowledge. Most physicists cope with this disparity by compartmentalizing: there's time as understood scientifically, and then there's time as experienced intuitively. For decades, I've struggled to bring my experience closer to my understanding. In my everyday routines, I delight in what I know is the individual's power, however imperceptible, to affect time's passage. In my mind's eye, I often conjure a kaleidoscopic image of time in which, with every step, I further fracture Newton's pristine and uniform conception. And in moments of loss I've taken comfort from the knowledge that all events exist eternally in the expanse of space and time, with the partition into past, present and future being a useful but subjective organization."

    http://www.liferesearchuniversal.com/1984-22

    George Orwell: "He set to work to exercise himself in crimestop. He presented himself with propositions - "the Party says the earth is flat", "the party says that ice is heavier than water" - and trained himself in not seeing or not understanding the arguments that contradicted them. It was not easy. It needed great powers of reasoning and improvisation. The arithmetical problems raised, for instance, by such a statement as "two and two make five" were beyond his intellectual grasp. It needed also a sort of athleticism of mind, an ability at one moment to make the most delicate use of logic and at the next to be unconscious of the crudest logical errors. Stupidity was as necessary as intelligence, and as difficult to attain."

    Pentcho Valev pvalev@yahoo.com

      Dear Sean and Flavio

      a very interesting essay. I applaud your emphasis on coarse graining, a key process in understanding how physics works in practice, as well as on the measurement problem and the limitations of theories of the universe as a whole. I also agree on the central importance of conformal degrees of freedom for gravity.

      However I don't get one thing. You say time can come from coarse graining. Now I agree that time and measurement are inseparable, provided one means by "measurement" any interaction with a well-defined outcome. But I could not see in sections 3.2 and 4, where time actually emerged. You derive expressions for entropy but never for time.

      Please can you clarify where/how time emerges?

      thanks

      George Ellis

        Dear Daniel,

        Thanks for your enthusiastic comments. I am happy to see other young people interested in these foundational issues. I certainly agree with the relative merits of Shape Space. The real question is: what new physics can we hope to see and what could shape dynamics teach us about the quantum theory?

        I will take a look at your essay, which seems very interesting. I hope to see you some time soon!

        Sean.

        Dear Pentcho,

        I take your point that there are aspects of the spacetime picture that appear to be at odds with our experience of reality. The purpose of this statement was to make the simple observation that the predictions of the spacetime picture are extremely well tested and cannot be ignored, even if the spacetime picture turns out to be problematic. Any alternative way of viewing reality must reproduce these observed phenomena. Shape Dynamics achieves this and so do other approaches either exactly or in some limit (like Horava gravity, for instance).

        Sean.

        Dear Prof. Ellis,

        Thank you for your comments. I am glad for your interest in these ideas.

        Your question is fair and I wish I could provide a more concrete answer. We are currently investigating the details of our proposal, which is still very much open for discussion (an important reason for writing the essay). Nevertheless, the text, in hindsight, is a bit vague on this issue and I can certainly go into more detail now.

        We believe that it might be possible to relate Renormalization Group (RG) time to the spatial volume of a spatially closed universe in shape dynamics. That is, Hamiltonian flow of gravity in terms of the York time (which is canonically conjugate to the volume) would be canonically conjugate to RG flow time away from a 3d Euclidean Weyl invariant theory. The issue arises when trying to understand the role of the Weyl anomaly in shape dynamics. So far, we have made progress only on toy models (which will be published soon).

        The toy model is a 1/r^2 potential in an N-particle theory. This model is classically scale invariant but there is a Weyl anomaly in certain regions of the parameter space. In the anomalous regimes, scale invariance is broken by regularization, giving an emergent scale. If we promote the Hamiltonian of the system to a Hamiltonian constraint, then the emergent scale can be used as an internal clock for the system. The shape degrees of freedom then pick up a "time" evolution in terms of the emergent scale. The monotonicity of time is then a result of the irreversibility of the RG flow which is toward a conformal fixed point in the infinite future.

        There are a couple of obstacles to this approach. One of the most important is the regulator dependence of the evolution equations. This is why we are advocating that the measurement process itself should be key to the emergence of dynamics. Because the measuring apparatus provides a PHYSICAL coarse graining of the system, there is nothing, in principle, unphysical about the regulator dependence. Nevertheless, this picture would require a radical rethinking of notion of time and the role of measurement.

        I hope this helps! The picture is still emerging so it is difficult to illustrate in a simple way. Any input others could provide would be extremely valuable and welcome.

        Sean.

        Minkowski spacetime (more precisely, special relativity) implies that an arbitrarily long object can be trapped inside an arbitrarily short container, and that the bug from the bug-rivet paradox can be both dead (according to one observer) and alive (according to another). Does Shape Dynamics reproduce these predictions?

        http://math.ucr.edu/home/baez/physics/Relativity/SR/barn_pole.html

        "These are the props. You own a barn, 40m long, with automatic doors at either end, that can be opened and closed simultaneously by a switch. You also have a pole, 80m long, which of course won't fit in the barn. (...) If it does not explode under the strain and it is sufficiently elastic it will come to rest and start to spring back to its natural shape but since it is too big for the barn the other end is now going to crash into the back door and the rod will be trapped IN A COMPRESSED STATE inside the barn."

        http://www.quebecscience.qc.ca/Revolutions

        Stéphane Durand: "Ainsi, une fusée de 100 m passant à toute vitesse dans un tunnel de 60 m pourrait être entièrement contenue dans ce tunnel pendant une fraction de seconde, durant laquelle il serait possible de fermer des portes aux deux bouts! La fusée est donc réellement plus courte. Pourtant, il n'y a PAS DE COMPRESSION matérielle ou physique de l'engin."

        http://www.parabola.unsw.edu.au/vol35_no1/vol35_no1_2.pdf

        "Suppose you want to fit a 20m pole into a 10m barn. (...) Hence in both frames of reference, the pole fits inside the barn (and will presumably shatter when the doors are closed)."

        http://hyperphysics.phy-astr.gsu.edu/Hbase/Relativ/bugrivet.html

        "The bug-rivet paradox is a variation on the twin paradox and is similar to the pole-barn paradox.....The end of the rivet hits the bottom of the hole before the head of the rivet hits the wall. So it looks like the bug is squashed.....All this is nonsense from the bug's point of view. The rivet head hits the wall when the rivet end is just 0.35 cm down in the hole! The rivet doesn't get close to the bug....The paradox is not resolved."

        Pentcho Valev pvalev@yahoo.com

        For the same initial data, Shape Dynamics will make the same predictions as general relativity (there are some technical caveats that might be interesting for black holes but, more or less, this is true). The situation you are talking about is in special relativity where there are no accelerations and where one has rigid rods and clocks. I don't know what Shape Dynamics would look like with these unnatural assumptions so I can't answer your question directly.

        Sean.

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        • Post #11

        Sean,

        You wrote: "The situation you are talking about is in special relativity where there are no accelerations and where one has rigid rods and clocks. I don't know what Shape Dynamics would look like with these unnatural assumptions so I can't answer your question directly."

        Is Shape Dynamics incompatible with special relativity? Can you derive time dilation and length contraction in Shape Dynamics? Does the travelling twin return younger according to Shape Dynamics?

        Pentcho Valev pvalev@yahoo.com

          This is, of course, an important question and the final answer is basically 'yes'. The complete answer has a lot of technical and interpretational caveats that would require a full paper to properly explain. I haven't written such a paper yet but it is on my list. What I can do is give you a short answer and explain why the full answer is tricky.

          The simple answer is that Shape Dynamics (SD) can reproduce the same observable predictions as GR. As a result, Minkowski space is a solution to SD, but only in a preferred reference frame. Thus, all the physical predictions of special relativity - like the younger travelling twin and the fact that certain muons created in the upper atmosphere don't decay until they hit the surface of the earth - are reproduced. What we can't do is have scale invariance and, at the same time, allow ourselves to transform to different Lorentz frames. It's either Lorentz invariance or scale invariance. In SD we pick scale invariance so we can explain the PHYSICAL effects of time dilatation and length contraction but the interpretation is different because we have a preferred frame.

          The reason I wanted to dodge this question is because of the following issue: how do we decide which frame is preferred? This is tricky because special relativity is an approximate framework that makes assumptions that are not natural in SD. In particular, Minkowski space is spatially open, which means that one has to impose spatial boundary conditions to produce it as a solution to SD. It's these boundary conditions that give you a preferred frame. Thus, the selection of the preferred frame must have an external structure as an input and this is really non-Machian. A more realistic situation is to consider a homogeneous expanding Universe with a cosmological constant. Then, there are closed (Machian) solutions and there is a genuine preferred frame (i.e., the one that cosmologists use to quote the age of the universe). This happens to be exactly the preferred frame required for SD. I've always found this a rather compelling feature of SD. In this frame, SD and GR are indistinguishable.

          I hope this helps,

          Sean.

          After a night's sleep, I realize that there is a simpler way to answer your question. Time emerges through the following sequence of steps.

          1. Start with a theory with no time and no scale.

          2. Allow for measurements with finite precision.

          3. The coarse graining of these measurements breaks scale invariance.

          4. The emergent scale defines a natural preferred clock in the system.

          5. Time evolution emerges in terms of this preferred clock.

          We think that it is possible that the time evolution we will get from this procedure will match that of the SD Hamiltonian. This, of course, would be highly non-trivial but we think that principles like universality and locality will come to our rescue.

          Hope this is a better answer!

          Sean.

          ps. Steps 2 and 3 are necessary because of the expected Weyl anomaly.

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          • Post #14

          Sean

          Quote from your essay "i) time and space should be treated on the

          same footing, ..."

          My questions is next.

          I don't like 4-D space-time. I will try to explain .... Why are you went to bed, a night for all spatial scales changed in ten time.You are notice anything? Absolutely sure that no, but now the usual time period when you sleep, increase or decrease by 10 times. Did you notice this?

          The same footing?

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            • Post #15

            Sean,

            You wrote: "Minkowski space is a solution to SD, but only in a preferred reference frame. Thus, all the physical predictions of special relativity - like the younger travelling twin and the fact that certain muons created in the upper atmosphere don't decay until they hit the surface of the earth - are reproduced."

            Sounds confusing. Please elaborate. How is the younger travelling twin reproduced "only in a preferred reference frame"?

            Pentcho Valev

            I'm sorry I don't understand your question.

            However, the quote you gave is preceded by "We have questioned the basic assumptions that:" which means we are doubting whether this is true! The reasons are section 2.1 of our essay.

            Best,

            Sean.

            In the same way that modern either theories can reproduce the results of the travelling twin experiment. In SD, there is one frame where physics is scale invariant. That frame behaves much like an either.

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            • Post #18

            Sean: "In SD, there is one frame where physics is scale invariant. That frame behaves much like an either."

            Clever etherists know that, in a frame moving relative to the ether, the speed of light is variable:

            http://www.jstor.org/stable/3653092

            The Mystery of the Einstein-Poincaré Connection, Olivier Darrigol: "It is clear from the context that Poincaré meant here to apply the postulate [of constancy of the speed of light] only in an ether-bound frame, in which case he could indeed state that it had been "accepted by everybody." In 1900 and in later writings he defined the apparent time of a moving observer in such a way that the velocity of light measured by this observer would be the same as if he were at rest (with respect to the ether). This does not mean, however, that he meant the postulate to apply in any inertial frame. From his point of view, the true velocity of light in a moving frame was not a constant but was given by the Galilean law of addition of velocities."

            Does the same variation of the speed of light exist in Shape Dynamics?

            Pentcho Valev

              The results of the Michelson-Morley experiment are no different in SD then they are in GR. That's all that matters. Any words one would like to use to describe this prediction are nothing but a rose with another name!

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              • Post #20

              Sorry!

              It turns out we are allies in this matter

              http://fqxi.org/community/forum/topic/1413

              It seems we are, though our motivations are different.