Philip,

There is an issue with gravity flux through a closed surface.

For comparison, let's start with Gauss's law used in electrostatics. If I had two co-centric metal spheres both with charge +Q, I could make a closed surface between the inner and outer spheres. A test charge on that closed surface would experience a force due to the electric field. The electric field lines would start at the surface of the inner sphere and end at the induced negative charge on the inside of the outer sphere. Using the correct surface integral I could find the charge +Q on the inner sphere.

If I did the same thing with two co-centric spheres of mass M and a small test mass to find the gravitational field, I could be disappointed. Since there is no anti-gravity there is no induced anti-gravity charge on the inside surface of the outer sphere. I could place the test mass at a radial distance, r, between the inner and outer spheres where the force due to gravity of the two spheres would cancel. A surface integral at the closed surface at radial distance, r, will find no mass for the enclosed inner mass. This means that some of the information contained within a closed surface is not reflected in the flux through that surface.

Gravity does effect time. Since the above is a statics problem and therefore time independent, this effect on time should not be an issue.

Jeff

    Jeff, thanks for your observations. However, Gauss law does not depend on the possibility of charges moving to the inside of a sphere so that field lines end there. This would only happen in the spheres are conductors, yet Gauss law works equally well for static charges if the spheres are non-conducting.

    Philip,

    An insulator or dielectric will have an electric dipole moment per unit volume or polarization. This induced dipole will be were the field lines effectively end.

    Since there is no negative gravity, there is no gravity dipole.

    Jeff

    Hello Philip

    You suggest that the lesson to be taken from holography is that there is a huge hidden symmetry in physics that nobody has yet appreciated. It may be only visible in an algebraic pregeometric theory from which space time emerges. My essay shows the foundation of such a pregeometry, and its nature. I would very much appreciate it if you might look at my paper and consider how it might inform your efforts. My essay is endpoint abstract, but otherwise not too hard to follow. After all, how did the universe know it was going to match some very heavy and complicated mathematics when it came into existence, figuratively speaking.

    As a matter of intellectual honesty, I don't feel qualified to rate your paper (so I won't, to be fair to you). While your essay deals with many areas dear to me, I found it very heavy going, and it took me a long time to get through. It required the reader to know some very advanced mathematics, Noether's theorem, gauge theory...you name it. With so much assumed foundation (of the nature of what there is) the foundational aspect of the essay is obscure to me. I have specialist knowledge of mathematics and physics relating to foundations, but would need another five or six years intensive study to fully appreciate it.

    Sorry I have been very busy and will be for the next few weeks

    Dear Philip,

    One can see the holographic principle in Plato's cave; indeed it defines the unsolvable reverse problem of observation. Consider the closed 2d surface surrounding you. The information written on this surface is all you know about the universe outside (or indeed, about the universe inside either). The changing pattern of information is what we call (perhaps in our conceit) "asking yes-no questions." The universe outside is, from your perspective, perfectly symmetrical under any transformations that write the same information on your boundary.

    Now imagine moving this closed boundary moving from your skin outward into space. The boundary encodes different information at every location. But the "boundary" here is purely notional; the physics - what is going on - does not depend on where the boundary has been located. This is also true as the boundary collapses inward to some point in the center of your body. At the (classical) limit, the boundary encodes no (classical) information, but this means nothing for the dynamics going on outside.

    So we have a "holographic information paradox" at every closed boundary. What the black hole knows about the universe is the same as what the universe knows about the black hole, and in neither case does this information pin down the dynamics.

    Cheers,

    Chris

      Hello Philip

      Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html)

      said: "It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but with a little mathematical fiddling you can show the relationship. And example of this is the Schrodinger equation and the Heisenberg formulation of quantum mechanics. I don't know why that is - it remains a mystery, but it was something I learned from experience. There is always another way to say the same thing that doesn't look at all like the way you said it before. I don't know what the reason for this is. I think it is somehow a representation of the simplicity of nature."

      I too believe in the simplicity of nature, and I am glad that Richard Feynman, a Nobel-winning famous physicist, also believe in the same thing I do, but I had come to my belief long before I knew about that particular statement.

      The belief that "Nature is simple" is however being expressed differently in my essay "Analogical Engine" linked to http://fqxi.org/community/forum/topic/1865 .

      Specifically though, I said "Planck constant is the Mother of All Dualities" and I put it schematically as: wave-particle ~ quantum-classical ~ gene-protein ~ analogy- reasoning ~ linear-nonlinear ~ connected-notconnected ~ computable-notcomputable ~ mind-body ~ Bit-It ~ variation-selection ~ freedom-determinism ... and so on.

      Taken two at a time, it can be read as "what quantum is to classical" is similar to (~) "what wave is to particle." You can choose any two from among the multitudes that can be found in our discourses.

      I could have put Schrodinger wave ontology-Heisenberg particle ontology duality in the list had it comes to my mind!

      Since "Nature is Analogical", we are free to probe nature in so many different ways. And you have touched some corners of it.

      Regards and Good luck!

      Than Tin

        Dear Philip,

        For completeness, kindly indulge me an answer to the question even though it may not be your essay topic. But being a professional I will value your opinion:

        Is it being implied by the relational view of space and as suggested by Mach's principle that what decides whether a centrifugal force would act between two bodies in *constant relation*, would not be the bodies themselves, since they are at fixed distance to each other, nor the space in which they are located since it is a nothing, but by a distant sub-atomic particle light-years away in one of the fixed stars in whose reference frame the *constantly related* bodies are in circular motion?

        You can reply me here or on my blog. And please pardon my naive view of physics.

        Accept my best regards,

        Akinbo

          It's trivky to answer questions in terms of Mach's principle because Mach only gave a vahue idea of what he meant and it does not correspond to the way we think about gravity and inertia since general relativity. I can only really answer the question in terms of what we know now.

          In general relativity it is not correct to say that rotation is measured relative to distant stars. Rotation is relative to a local inertial reference frame. In normal circumstances local rotation in an inertial frame is very close to the fixed frame defined by the distant stars but it does differ slightly due to the geodetic effect and frame dragging. This means that it is not really correct to talk about rotation in terms of direct relationships between objects at very large distances. Instead of the "action at a distance" idea of Newtonian mechanics we must now think in terms of matter affecting and being affected by the gravitational field whose effect propagates at the speed of light.

          However, there is still possibly some mileage to be had from relational ideas in quantum gravity at small scales.

          I agree fully with what Feynman said and it always influences my thinking. It is why I do not dismiss different ways of looking at things. For example I am always promoting the idea that string theroy and loop quantum gravity are not contradictory alternative ideas. They are more likely different (but incomplete) ways to look at the same things. The concept of dualities has become even more important in recent times and is a dramatic example of his thinking.

          Another side to this is that even different philosophical approaches can turn out to be equally valid. e.g. "It from Bit" vs "Bit from It", but I think that the "It from Bit" viewpoint is more useful in our current state of knowledge.

          Chris, I am sorry I am having trouble forming a good answer to this because I dont see clearly what you mean. As the sphere expands there is more information inside the volume and more area on the boundary. vice versa as it shrinks. I dont see where this poses a problem for the holographic principle. It is probably my misunderstanding of your point that is the problem.

          Phil

          I appreciate your reply and very sorry to be troubling you. Trying to know what you physicists have in mind. Answering the question in terms of what we know now:

          1)Between those two bodies where will the local inertial reference frame be located? In the middle point of the line joining them, being the only two local objects, there will still be no way of knowing of their rotation without reference to a third object. So in what frame will this rotation be observable? Note apart from that distant star these are the only two objects in the universe!

          2) Let us not assume that these two objects are bound by gravity. It may be electromagnetism or a string binding them. This is to avoid complicating the picture by geodesics and frame dragging. The question is how can we know they are rotating? We know this by experiencing centrifugal force. But then rotating with respect to what?

          It seems to me without preempting you that space may not be relational but substantial, don't you think? Then someone referred me to a talk by Paul Davies in which moving objects in space experience an Unruh effect.

          In the absence of any reference frame to distinguish circular from linear motion, then it appears we have only Newton's space to decide our reference frame? Or do you disagree? Where can you be located to observe the rotation if it is occurring?

          Thanks for your time. Much appreciated.

          Akinbo

          Gibbs,

          I have a few questions or comments/opinions if you will.

          Why are boundary conditions stressed? Yes, the surface area and Planck Unit-using formula say this is a relation between information and entropy, but I don't see the logical necessity of that function being at a particular point. I would think that such a fundamental looking math equation would describe a whole group of phenomenon, not just a particularly interesting black hole paradox. I'm getting at that maths being used for all region near this "boundary."

          Which leads me to note another peculiarity. You don't mention particles. I would think that they two would be fundamentally described with information, since it's appealing to think the same logic applied to black holes applies to all entities in the universe, big small or otherwise insignificant and completely ordinary.

          It was a very nice essay and showed two sides and gave a pretty thorough presentation or argument. Since such difficulties are arising when the best minds are working on these problems with strings and somewhat in the way you prescribed, and seem still not to be near resolution, I think a deeper assumption will be what breaks down. Hopefully this is before many physicists do!

          Appreciatively,

          Amos.

            Dear Philip,

            It was a privilege to read your essay, wherein you discuss many ideas at the very foundational level. Often you talk about the power of consistency. Let us consider the following three points in this context.

            (1) The energy-stress tensor is a redundant part of Einstein's equations as the material and the gravitational fields appear in the geometry through the metric field (see my essay in the present contest).

            (2) Recently it has been shown that the right hand side of Einstein's equations, i.e., the energy-stress tensor T^ik, has serious problems [arXiv:1204.1553].

            (3) The quantization of the right hand side of Einstein's equations, in a given spacetime, has yielded the interesting effects of the Hawking radiation.

            Do the requirements of the logical consistency then not render the Hawking results doubtful, which are obtained by using the stress-energy tensor?

            Best Regards.

            ___Ram

              Dear Ram, You have a very interesting essay. I also dispute some conventional wisdom concerning GR and the formulation of energy conservation, but not as radically as you. Good Luck, Phil

              Phil,

              I have the impression you are mixing up divergence with covariant divergence... I do not see anything in what you say that goes beyond what is written in all GR books about energy conservation in GR. There is a vast literature on this... The rest seems to me to be hanging on nothing ...

              carlo

                Dear Philip,

                One single principle leads the Universe.

                Every thing, every object, every phenomenon

                is under the influence of this principle.

                Nothing can exist if it is not born in the form of opposites.

                I simply invite you to discover this in a few words,

                but the main part is coming soon.

                Thank you, and good luck!

                I rated your essay accordingly to my appreciation.

                Please visit My essay.

                Carlo,

                As I am sure you know ordinary divergence and covariant divergence are simply related for vector fields

                [math]\sqrt{-g}J^\mu_{;\mu} = \frac{\partial \sqrt{-g} J^\mu}{\partial x^\mu}[/math]

                so the ordinary divergence theorem can be immediately translated to covariant form for vector currents. In what way then am I confusing divergence and covariant divergence?

                Please could you tell me which textbook treats energy conservation in covariant form without claiming that it works only in special cases? In particular can you tell me where my covariant formula for the energy current (or equivalent) is given by anyone else either in texts or papers, I will repeat it here because the equation editor mangled it in the essay,

                [math]J^\nu(\xi^\mu) = \xi^\mu T_\mu^\nu - \frac{1}{\kappa}(\xi^\mu G_\mu^\nu \xi^\nu\Lambda) \frac{1}{2}(\xi^{\mu;\nu}-\xi^{\nu;\mu})[/math]

                I am glad that you agree with my conclusions about energy conservation because I have been waging a one-man battle online for twenty years to convince people that energy conservation in GR works. I have been up against people such as Baez, Carroll, Carlip, Motl etc who all think that energy conservation does not work properly in GR. It would be very helpful if I could just reference a text book that agreed with me.

                As to your final statement, I am baffled. I have made a number of original points. If you don't agree with specific points that is one thing but to call it nothing just indicates that you have not understood.

                The boundary for the holographic principle can be any boundary. The information inside must be less than the area of the boundary. In the special case where the boundary is a black hole horizon, entropy is maximised and the information inside is equal to the area of the boundary. The holographic principle tells us that this is not just a bound but in fact the information can be determined from the state on the boundary. If that does not answer your question please clarify.

                About particles, in quantum field theory particles are fields are dual descriptions of the same quantised field. It does not matter if you think in terms of one or the other. Information is encoded in the spectrum of states whether you use the particle description of the field description.

                Thank you for your comments I have also enjoyed your essay