Dear Ernst Fischer,

I enjoyed your fascinating essay. Your reasoning seems sound and your conclusions reasonable. It's difficult to believe that no one has taken potential energy into account, and I guess I assumed that this energy or its equivalent was somehow factored into the stress energy tensor. I hope some general relativity experts will comment.

You make a number of interesting statements and many of them refer to local mass density, which I understand to be ill-defined in general relativity. Your assumption about particle rest mass in a volume element seems quite reasonable so it would seem that the correctness of your conclusions depends upon your definition of potential energy and your approach to incorporating curvature into the definition of density.

You conclude that "the Schwarzschild radius must be regarded as a purely mathematical quantity." Quite a statement!

I recently read that the matter in a spinning black hole is regarded as having one degree of freedom. Would you make the same assumption for the particles in your model?

Thanks for a well written, well thought out analysis of very basic assumptions, as FQXi asked us to do. I hope your model stands up well to criticisms.

I invite you to read my essay, The Nature of the Wave Function, and comment on it.

Edwin Eugene Klingman

    Dear Dr. Ernst Fischer

    Knowing the limitations in my understanding of the mathematics of GR I skimmed your essay and 'read between the lines' to try to understand your meaning. Are you suggesting that gravitational collapse not only compresses atoms nearer to each other, but also changes their internal density? In my Beautiful Universe theory I have embraces Eddington's 1920 suggestion for a density of space itself. That means the energy of the gravitational field immediately outside the star carries potential energy and should be considered in keeping a balanced account of the energy as the star collapses.

    Again thank you for a difficult (for me) but stimulating essay.

    Vladimir

      Dear Ernst,

      Approaching things from a completely different direction, just by considering things from a philosophical point of view, in my essay I come to similar conclusions as you do.

      Anton

      Hi Ernst,

      Thank you for considering my idea. I think that the model of nuclear fusion and the interior of stars must be wrong. How do you feel about the concept of 'saturated maximum energy density matter' who's gravitational attraction is dependent on it's x-sectional area, rather than the amount of material?? This assumes that the surface can't emit any more force carrying particles and is at it's maximum limit, so therefore it doesn't matter how much material is behind it at that moment relative to another body of maximum energy density material. This is at the crux of my idea for additional exotic matter tidal forcing.

      Here's a quick doodle which is my explanation for the extra 20% Spring Tides which occur every two weeks when the moon is on the Earth's equator. It's due to additional exotic matter tides which increase with increasing surface areas 'seen' by the two bodies.Attachment #1: 2_Exotic_Cores.jpg

      Dear Edwin Eugene Klingman,

      I agree that it is the definition of potential energy, which is essential for the conclusions presented in my essay. But this definition is based on the fact that quantities like particle number should be conserved in curved space and that the particles, which constitute the sources of gravitation, have an invariant property, their rest mass. Under this proposition in any theoretical model, based on the covariant geometrical description of gravity, a correction term of the form given in my essay must be included in the energy tensor to account for the deviation of volume from Euclidean space. That this term can be identified with the potential energy of Newtonian theory makes it easier to understand its role in the purely geometrical context of GRT.

      You remark that in a spinning black hole matter has one degree of freedom. I think that you will say that in this case rotational energy gives an additional contribution to the energy tensor, so that the geometry is not fixed by the total mass alone. This is true, of course, also if the matter or energy distribution is corrected for the influence of curvature. Modeling of such spinning black holes would be of high interest, as it is the basis to understand the cosmic jets emanating from collapsed systems. There remains much to do, but at least with the correct model of the spherically symmetric case we have a sound basis to attack this problem.

      Best regards,

      Ernst Fischer

      Ernst,

      This is an essay I am going to have to read more than once to make an intelligent comment. The discussion with Edwin of spinning black holes, though, piques my interest -- Bekenstein-Mayo described black holes as one-dimensional, which I guess is what Edwin means by one degree of freedom (by vector orientation in opposite directions), which I think imparts meaning to the cosmic jets -- because a vector that avoids a naked singularity is compelled to eject matter if what you say about the Schwarzchild radius is true. I think you're approaching something deep here. (My own essay explains why the singularity has to be avoided in any physical measurement scheme.)

      All best wishes for success in the competition,

      Tom

      "the 'black hole' in the center is not a matter concentration on the other side

      of some semi-permeable horizon, but an accumulation of nuclear matter, which

      can be recycled into the universe under suitable conditions."

      Are those suitable conditions the jets escaping from black holes (BH) and/or a final dissipation of the BH sometime in the future?

      Certainly the potential energy you speak of seems like a logical omission by others.

      Jim

        Hi Ernst

        I read your essay with great interest. A radical approach to the problem you consider was taken by Vladimir Majernik in "Energy conservation at the gravitational collapse", arXiv:astro-ph/0609313v1, 2006.

        Majernik starts from the beginning by including an unknown gravitational potential energy in rest energy as an explicit expression of Mach's principle. He ends up with an exponential metric as I do in my essay using a completely unrelated method involving Mach's principle.

        I completely agree with your conclusion proposing the inclusion of potential energy on page 4 of your essay, where the need for it is clearly shown. Majernik's paper seems to start off where yours ends, and always seemed a bit 'ad hoc' in its premise. It seems to me that your essay provides the rationale for Majernik's work.

        Can you comment on how your proposal might relate to Majernik's paper?

        By the way, that is a nice result at the end of the essay about the stability of a static universe.

        Colin

          Dear Tom,

          Thank you for the hint to my misunderstanding of Edwins question on one-dimensional black holes. But if his remark is related to the Bekenstein-Mayo problem of entropy flux through the space-time discontinuity at the supposed surface of a black hole, it is of no practical relevance, as such discontinuities do not exist in nature according to the arguments given in my essay.

          Ernst

          Dear Vladimir

          Things are easier than you think. To understand gravity you should look at a swinging pendulum on earth. In Newtonian theory gravitation is described by motion of an object in a field, which is caused by the mass of the earth. During each swinging period the object takes up kinetic energy by changing its position in the gravity field. The gravity field itself has no energy. If there is no pendulum, there is no energy. It is only the fact that the swinging object changes its position relative to the mass of the earth that changes its energy state. That is, what we call potential energy.

          The difference in GR is that the dependence of the state of an object on the position relative to other objects is encoded in a deviation of geometry from Euclidean space so that motion under the influence of gravitation can be regarded as geodesic motion in the distorted geometry. But with this introduction of a distorted geometry we must keep in mind that the relation between coordinates and the size of areas or volume elements is changed. Thus our accustomed definitions of densities and their relation to the integral properties of objects change.

          It is only this correction of the energy balance due to the change of geometry, which I have discussed in my essay. There is no "energy of the gravitational field immediately outside the star" which carries potential energy. The gravitational field itself or some equivalent in GR does not carry any energy. It is only the state of matter within this field, which contributes to the energy balance.

          Ernst

          Dear Jim,

          I think that the matter jets emanating from black holes result from internal instabilities of rotating black holes and occur when additional matter is accreted from the surrounding galaxy. I suppose that the jet activity is coupled to the accretion rate and will come to an end, when all surrounding matter is consumed. The final dead black hole can be destroyed only in collisions with other celestial bodies. Maybe that such collisions are the cause of the mysterious gamma-ray bursts.

          Ernst

          Dear Colin,

          Thank you for the valuable hint to the work of Vladimir Majernik. I think that the basic concept of his paper agrees with mine. Mach's idea that the energy of matter at some point contains a contribution from its relation to all the other matter in the universe is just the justification of the introduction of potential energy into the energy tensor, in this case expressed by the change of the volume element by the curvature of space. Together with the equivalence of mass and energy this constitutes the basis of GR. That means: all forms of energy, be it the energy equivalent of rest mass, field energy of massless fields like radiation or the potential energy of these fields, contribute to gravitation. I have not yet studied Majernik's paper in detail, but I think he is on the right track.

          With respect to the stability of a static universe: Some years ago, based on the assumption that energy conservation is valid also in the case of the entire universe, I have tried to develop an equilibrium model of the universe, similar to Einstein's static solution. I have shown that it is possible to find alternative explanations for all the observations, which are usually considered as confirmations of the Big Bang model. The cosmological red shift, the microwave background, the chemical element composition and the formation of cosmic structures can all find an alternative interpretation without invoking such mysterious things like dark energy or an inflationary expansion. If you are interested in this stuff you can find it under arXiv:0708.3577.

          Ernst Fischer

          Hi Ernst

          I am glad you are interested in Majernik's work, and hope you have time to examine the details and evaluate his conclusion about an exponential metric.

          Thank you very much for your arXiv paper. A static universe is a subject which has interested me ever since I heard of, and doubted, Hubble's law as recession. Countering the Big Bang is a challenge because the evidence is so indirect and varied - it is a multi-headed monster. Black holes from general relativity can at least in principle be falsified by experiment.

          I am very pleased to have met you online. Good luck in the contest!

          Colin

          5 days later

          Thanks Ernst you explained it well one may call it a variation of GR? In GR mass warps spacetime around it and I will take your word that there is no energy out there.

          The rather simple-minded ether-based approach I have proposed sees things quite differently, and hopefully should explain Newtonian and GR theories each within its area of validity. In my approach action-at-a-distance is explained as a linkage of dielectric forces of twisting ether nodes acting somewhat like a spring. Bending of light is because of local density changes in space (i.e. gravitational potential energy).

          Of course GR has the weight of Einsten's genius and authority. I have nothing like that to offer, but I hope that my simple new approach or something similar will one day be found to cover a lot of what is now puzzling, too complicated, anti-intuitive or incomplete in physics.

          Cheers. Vladimir

          Ernst,

          'No mysterious dark energy is necessary to fulfill the balance'

          Big bang cosmology, in the concept of cosmic time states that the universe lives in a time continuum not of its own making: big bang cosmologists look at the universe from an imaginary vantage point outside of it.

          In contrast, a universe which creates itself out of nothing, without any outside intervention does NOT live in a time realm of its own making, but contains and produces all time within, so here we should see clocks showing an earlier time as they are more distant, and, as I argue in my essay (Einstein's Error) NOT because of a finite light velocity.

          As clocks can only show an earlier time if they (are observed to) run slower as they are more distant, even if they are at rest with respect to us, here the redshift of galaxies should vary linearly with their distance, as is observed, so here we don't need any mysterious dark energy to explain observations.

          Anton

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          • Post #24

          The existence of potential energy implies that the motion of test masses is NOT geodesic in the theory discussed in this Essay. This generates macroscopic violations of Equivalence Principle. As Equivalence Principle is today tested at a level 10^-13, such observations rule out the theory developed in this Essay in a definitive way.

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          • Post #25

          The existence of potential energy implies that the motion of test masses is NOT geodesic in the theory discussed in this Essay. This generates macroscopic violations of Equivalence Principle. As Equivalence Principle is today tested at a level 10^-13, such observations rule out the theory developed in this Essay in a definitive way.

            Hi Darth

            I think you are wrong in stating that observations rule out the theory. The strength of the gravitational field of the earth is about GM/rc^2 = 10^-9. The entire planet reduces the equivalent mass of an object by that factor. Near the surface, raising an object by a distance h increases its equivalent mass by a factor of about (h/r)(GM/rc^2), which is 10^-14 for h = 60 meter. I doubt if any earthbound experiment could be considered decisive.

            Colin

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            • Post #27

            Dear Colin,

            I regret but who is wrong is you. You have to computate the gravitational mass in a free falling reference frame and the inertial mass in a inertial reference frame which is very far from every source of gravitational field. The Equivalence is between such reference frames. A reference frame in which you measures the strength of the gravitational field CANNOT be used to test Equivalence Principle.

            Best regards,

            Darth