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

      • [deleted]

      • 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.

      • [deleted]

      • 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

        • [deleted]

        • 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

        Dear Vladimir,

        I agree with you that action-at-a-distance is a conceptual problem in most physical theories. In quantum physics the existence of carrier particles is assumed, which are transferred between distant objects, while other models propose the existence of some ubiquitous ether, which has the only job to transport information. But as long as the outcome of an interaction is independent of the method of transfer, the answer to this question is rather academic.

        But an important question is, if the transfer to distant points is simultaneous or limited to some maximum velocity. In GR it is generally assumed that every interaction is limited to the speed of light. Causality requires that action-at-a-distance is a chain of information transport processes, which cannot exceed this speed. You may describe it as a propagating twist of ether nodes or any other transfer process. The important fact is that any action is limited to the speed of light. The chain of causalities and its relation to the distance of interacting objects defines the notion of time. Just as there is a shortest spatial connection of objects, which we call their distance, there is a shortest causal connection of distant events, which we call the temporal distance.

        Best regards,

        Ernst

        Inclusion of potential energy in the energy tensor does in no way violate the Equivalence Principle as it affects acceleration and gravity in exactly the same way, even at a level of 10^-13. That the motion of test masses is not exactly geodesic is true. Geodesic motion must always be regarded as an approximation, which is valid as long as the contribution of the test mass to the metric is negligible. This is just the main aspect in the definition of "test mass". But by principle every motion of a test mass changes the geometry of space and thus it produces a back reaction. There is one essential difference between force free motion in Newtonian physics and geodesic motion in General Relativity: In curved space motion along a geodesic line does not imply conservation of kinetic energy of the moving mass.

        Ernst Fischer

        Dear Anton,

        I agree with you that the existence of a global cosmic time, as it is assumed in Big Bang cosmology, is not justified. Time is a parameter imposed to changes and interactions by the finite speed of causality. Time depends on distance and not, as assumed in Big Bang theory, distance depends on time (on a clock outside the universe). I must confess that I have not understood all the thoughts in your essay, but the basic fact that the universe must be a self consistent entity without any rules imposed from outside appears to me very reasonable.

        Ernst

        Hi Darth

        I wonder if you are overlooking an important point in the paper. The equivalence principle essentially becomes:

        inertial mass = gravitational mass plus change in potential

        For example, the author states on page 4: "Thus it appears logical to consider the summed density of [gravitational] mass energy and potential energy as the equivalent to [inertial] mass energy in Euclidean space." (I added 'gravitational' and 'inertial' to make the context clear, to the best of my understanding.) This is also the theme of Majernik's paper.

        Colin

        • [deleted]

        • Post #32

        Dear Colin,

        in general relativity not only the potential depends from the coordinates, but also its changing. For example, in the two references frames that I cited the gravitational field is null. Hence, its potential is null and also its changing.

        I suggest you to carefully read Misner, Wheeler, Thorne, "Gravitation", Freeman and Company (1973) pages 466-468. The stress energy tensor of the gravitational field does not exist. It is a pseudo-tensor, i.e. a coordinate-dependent quantity.

        Best regards,

        Darth