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

        I agree with your intuition about the importance of the cosmological constant at the fixed point. As the universe continues to expand, the cosmological constant starts to dominate the dynamics of the universe. In our scenario, the infinite future corresponds to the fixed point. This means that the cosmological constant dominates the behaviour of the system near the fixed point. We've investigated some of this in:

        http://arxiv.org/abs/1105.0938 ,

        where we compare some results of shape dynamics with some well known results from AdS/CFT (we will be updating this paper shortly). As we point out in the paper, there are similarities between the cosmological constant and the trace anomaly in the CFT (i.e., the expectation value of the trace of the energy momentum tensor of the CFT). However, I'm not sure if this is related to your comments about the energy momentum tensor.

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        • Post #26

        Yes it is related but I would be some ways from being able to give you a comparison of a reinterpretation of the EFE (my essay) into shape theory, but it is very closely related to AdS/CFT. There are some concepts in your paper and essay that may be helpful to me.

        Hopefully! When the volume of space is large, there is not much difference between the SD Hamiltonian and the GR Hamiltonian (they converge to the same thing). That might help. Glad to hear your interested in these ideas.

        Sean.

        ps. I don't know why the last post came up as "anonymous"... I should have been logged in. Sorry about that.

        I would like you to read my essay "Billy Pilgrim Blues". I cover the same issues as your essay, but in a very different way. Please honestly tell me what you think.

          You're right that we are tackling similar issues from a very different perspective.

          In our proposal, there might be a way to relate time, as a renormalization group flow time, to a measure of complexity. This could indeed be a kind of entropy of configurations. However, I believe this is quite different from the kind of relationship you are suggesting.

          I don't agree with your statement that "entropy is needed to define time". Your pendulum example is misleading because clocks don't have to be cyclic. In Julian Barbour 2009 essay: The nature of time, he describes a relational notion of time that is perfectly well defined without a notion of entropy. This is what astronomers use to define time. So I don't understand your argument.

          Best,

          Sean.

          Sean,

          Thank you for your comments and taking the time to read my essay.

          Clocks do not have to be cyclic. I used the example of a perfect cyclic timepiece to isolate time from all other factors. The Earth spins on its axis and the stars move in relationship to each other, but the Earth is different each day and the stars burn a little of their store of hydrogen each momentum. Entropy is very much a part of Astronomy. At the quantum scale, when enthopy change is harder to come by, postion relationships between indivual particles are uncertain. Please show me a way to mark time that does not change enthopy.

          All the best,

          Jeff

          You need to define entropy more precisely. In particular, if you're talking about thermodynamic entropy then this is not even defined for systems outside of thermodynamics equilibrium. Surely you are not suggesting that time is not defined for systems (such as the sun and humans) far from equilibrium?