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.

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          • Post #22

          Originally the Michelson-Morley experiment confirmed Newton's emission theory of light:

          http://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768

          Relativity and Its Roots, Banesh Hoffmann: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."

          http://www.aip.org/history/einstein/essay-einstein-relativity.htm

          John Stachel: "An emission theory is perfectly compatible with the relativity principle. Thus, the M-M experiment presented no problem; nor is stellar abberration difficult to explain on this basis."

          http://www.philoscience.unibe.ch/documents/kursarchiv/SS07/Norton.pdf

          John Norton: "These efforts were long misled by an exaggeration of the importance of one experiment, the Michelson-Morley experiment, even though Einstein later had trouble recalling if he even knew of the experiment prior to his 1905 paper. This one experiment, in isolation, has little force. Its null result happened to be fully compatible with Newton's own emission theory of light. Located in the context of late 19th century electrodynamics when ether-based, wave theories of light predominated, however, it presented a serious problem that exercised the greatest theoretician of the day."

          http://philsci-archive.pitt.edu/1743/2/Norton.pdf

          John Norton: "In addition to his work as editor of the Einstein papers in finding source material, Stachel assembled the many small clues that reveal Einstein's serious consideration of an emission theory of light; and he gave us the crucial insight that Einstein regarded the Michelson-Morley experiment as evidence for the principle of relativity, whereas later writers almost universally use it as support for the light postulate of special relativity. Even today, this point needs emphasis. The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."

          Pentcho Valev pvalev@yahoo.com

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          • Post #23

          Sean,

          I think the traditional emphasis on measurement only compounds the confusion about time. We perceive time as a series of events and measurement only re-enforces this perception, but physics is supposed to be about understanding the underlaying dynamic processes, not just how to model them. It is not that reality consists of a four dimensional geometry in which all events are somehow suspended, but that the changing configuration of what is, turns future potential into actual events, then replaces them. To wit, the earth doesn't travel a fourth dimension from yesterday to tomorrow, but that tomorrow becomes yesterday because the earth rotates.

          Einstein said time is what you measure with a clock and a clock consists of two components, the hands, representing the present and the face, representing the events. Blocktime, as a declarative explanation of spacetime, argues only the face is real and all those events simply exist as their own present. It says time is like a book or dvd, where all the scenes already exist and it's simply a matter of where you are in that four dimensional geometry.

          It's not the face, the events, which are real and the present is an illusion, but the present, that which exists, that is real and the events which are transitory. So it's not the hands moving around the face, but the events coming into being and being replaced. An example I go into is Schrodinger's cat; Quantum theory uses an external timeline, ie, going from past to future. But that pushes a determined past onto a probabilistic future and it branches out into multiple realities. If we eliminate that external timeline and just let time emerge from the process, then it is the actual occurrence of the events which determines the fate of the cat. To use a less loaded example, prior to a race, there are as many potential winners as runners, but after the race has occurred and the events reduced the possible outcomes to one, there is only one result.

          The present isn't some dimensionless point on a timeline, because duration doesn't exist external to the present, but is the state of the present between measured events.

          It is a dynamic reality, much of which is traveling at the speed of light and much of which is seemingly stable for periods far longer than our lives. Out of this flood of input, our minds select very limited bits of information to coalesce into each thought, thus the sense of the present as a frozen moment.

          John Merryman

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          • Post #24

          Sean and Flavio,

          Interesting essay.

          "Consider a world with no scale and no time. In this world, only 3 dimensional Platonic shapes exist. This kind of world has a technical name, it is a fixed point of renormalization {"fixed" because such a world does not flow since the renormalization scale is meaningless. This cannot yet be our world because nothing happens in this world. Now, allow for something to happen and call this "something" a measurement. One thing we know about measurements is that they can never be perfect. We can only compare the smallest objects of our device to larger objects and coarse grain the rest. Try as we may, we can never fully resolve the Platonic shapes of the fi xed point. Thus, coarse graining by real measurements produces ow away from the xed point."

          This quote makes me think of the cosmological constant as the fixed point of renormalization and the accompanying dynamic stress energy tensor as your measurement. As Eddington stated:

          "matter does not cause the curvature of space-time. It is the curvature"

          I look forward to reading more in depth. We may have quite a bit in common.

          Regards,

          Jeff