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**Jayakar Joseph**: *on* 10/31/12 at 5:05am UTC, wrote Dear Ernst Fischer, Potential energy described in Coherently-cyclic...

**Sridattadev**: *on* 10/29/12 at 19:40pm UTC, wrote Dear Ernst, You are right about the point that gravitational collapse...

**Sergey Fedosin**: *on* 10/4/12 at 8:41am UTC, wrote If you do not understand why your rating dropped down. As I found ratings...

**Georgina Woodward**: *on* 10/3/12 at 8:31am UTC, wrote Your essay seems well appreciated by the community- congratulations : )...

**Sergey Fedosin**: *on* 10/2/12 at 18:07pm UTC, wrote After studying about 250 essays in this contest, I realize now, how can I...

**James Dwyer**: *on* 9/29/12 at 21:46pm UTC, wrote Dear Ernst, Yes, I was merely presuming the common general conception of...

**Ernst Fischer**: *on* 9/29/12 at 20:25pm UTC, wrote Dear Jim, You correctly state that no finite amount of matter can fit into...

**Ernst Fischer**: *on* 9/29/12 at 11:41am UTC, wrote Dear Sergey, Thank you for the hint to the misprint in eq.(7). There is a...

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CATEGORY:
Questioning the Foundations Essay Contest (2012)
[back]

TOPIC: Does Gravitational Collapse Lead to Singularities? by Ernst Fischer [refresh]

TOPIC: Does Gravitational Collapse Lead to Singularities? by Ernst Fischer [refresh]

According to conventional modelling by general relativity the collapse of radially symmetric gravitating objects may end in a singular state. But by inclusion of potential energy into the energy tensor, which is required to guarantee global energy conservation, the occurrence of singularities is avoided. Instead the final states of the collapse of mass concentrations of arbitrary size are nuclear matter objects, from which jets of matter can be recycled into space. The mysterious dark energy, supposed as the main constituent of the universe, may even be the potential energy of matter itself.

Ernst Fischer, born 1938 in Stolberg, Germany. I have studied physics with the main topic plasma physics. My main professional activity was research on light sources. But in my spare time I was active also in astrophysics and cosmology and have published some papers in this field.

Dear Ernst Fischer,

Many thanks for a well written essay. I've read and reread it several times. There is much to consider.

Could these concepts also be applied towards the structure of an individual particle? Or worded differently, if a singularity is avoided, is the maximum allowable matter density equal to that of a neutron?

Best Regards and Good Luck with the contest.

Gary Simpson

Houston, Tx

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Many thanks for a well written essay. I've read and reread it several times. There is much to consider.

Could these concepts also be applied towards the structure of an individual particle? Or worded differently, if a singularity is avoided, is the maximum allowable matter density equal to that of a neutron?

Best Regards and Good Luck with the contest.

Gary Simpson

Houston, Tx

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Dear Gary,

I do not think that a density in the classical sense can be attributed to individual elementary particles. Of course, by defining a characteristic dimension by the Compton length l=h/mc you can define a density by m/(4/3 pi l^3), but this can only be regarded as an order of magnitude estimation for the density, at which degeneracy pressure can play a role in the stabilisation of objects against gravitational collapse. Only when the mean distance between individual fermionic particles is of the order of their Compton length, this pressure occurs, as no two fermionic particles can be in the same quantum state. You are right that in the supposed final state of the collapsed objects, which we denote as neutron stars, the density should be in the order of the value mentioned above (>10^14 g/cm^3). But even if with increasing mass of the collapsed object this density increases, as more and more energy states of the fermions must be occupied, there will never be a limit, where a balance between gravitational attraction and degeneracy pressure is impossible.

Best regards,

Ernst

I do not think that a density in the classical sense can be attributed to individual elementary particles. Of course, by defining a characteristic dimension by the Compton length l=h/mc you can define a density by m/(4/3 pi l^3), but this can only be regarded as an order of magnitude estimation for the density, at which degeneracy pressure can play a role in the stabilisation of objects against gravitational collapse. Only when the mean distance between individual fermionic particles is of the order of their Compton length, this pressure occurs, as no two fermionic particles can be in the same quantum state. You are right that in the supposed final state of the collapsed objects, which we denote as neutron stars, the density should be in the order of the value mentioned above (>10^14 g/cm^3). But even if with increasing mass of the collapsed object this density increases, as more and more energy states of the fermions must be occupied, there will never be a limit, where a balance between gravitational attraction and degeneracy pressure is impossible.

Best regards,

Ernst

Dear Ernst Fisher,

your essay addresses a very interesting conundrum.I found it well structured, argued and illustrated. I have only read it quickly so far but can already agree that taking potential energy into account could give a far better picture of what is occurring.

I too intend to read it again, to learn what I can. Good luck in the competition.

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your essay addresses a very interesting conundrum.I found it well structured, argued and illustrated. I have only read it quickly so far but can already agree that taking potential energy into account could give a far better picture of what is occurring.

I too intend to read it again, to learn what I can. Good luck in the competition.

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Dear Ernst Fischer,

A superbly written essay which very accessible to the layperson. I need to reread it too. I totally agree with you at first impression. Only one thing stuck out i you say "nuclear matter objects, from which jets of matter can be recycled into space". Surely this matter can also be distributed into space aswell during stellar supernovae events?! This is the same as my own model, but I assume that the matter is high energy density exotic matter, being highly anisotropic and non-baryonic, i.e. dark matter. I would very much appreciate it if you would consider my own essay entry Newtons Isotropy and Equivalence..

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A superbly written essay which very accessible to the layperson. I need to reread it too. I totally agree with you at first impression. Only one thing stuck out i you say "nuclear matter objects, from which jets of matter can be recycled into space". Surely this matter can also be distributed into space aswell during stellar supernovae events?! This is the same as my own model, but I assume that the matter is high energy density exotic matter, being highly anisotropic and non-baryonic, i.e. dark matter. I would very much appreciate it if you would consider my own essay entry Newtons Isotropy and Equivalence..

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Dear Alan,

You say that to your opinion supernova explosions can recycle matter into space. But as far as we know from observations, all the matter which is expelled in this case is processed matter, consisting of heavier elements. The temperature in the interior of the exploding stars is determined by nuclear fusion, which is not sufficient to produce new hydrogen or helium. On contrary for jets emanating from neutron stars the energy of the particles in the interior of the star is so high that individual atoms can no longer exist and only during ejection new atomic nuclei are formed, preferably hydrogen and helium. Only under these conditions a process is possible, which recycles matter of primordial composition into space. From the existence of this process we must conclude that the present element composition of the universe must not necessarily be the consequence of element synthesis in a hot initial Big Bang.

Best regards,

Ernst

You say that to your opinion supernova explosions can recycle matter into space. But as far as we know from observations, all the matter which is expelled in this case is processed matter, consisting of heavier elements. The temperature in the interior of the exploding stars is determined by nuclear fusion, which is not sufficient to produce new hydrogen or helium. On contrary for jets emanating from neutron stars the energy of the particles in the interior of the star is so high that individual atoms can no longer exist and only during ejection new atomic nuclei are formed, preferably hydrogen and helium. Only under these conditions a process is possible, which recycles matter of primordial composition into space. From the existence of this process we must conclude that the present element composition of the universe must not necessarily be the consequence of element synthesis in a hot initial Big Bang.

Best regards,

Ernst

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.

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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.

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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.

attachments: 2_Exotic_Cores.jpg

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attachments: 2_Exotic_Cores.jpg

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It is one year that I search to obtain the mass spectrum of the elementary particles using the Landau-Lifsitz pseudotensor like density energy measure; I don’t consider the spin effect, to simplify the theory.

I use two curvature spherical region (I shall try with three curvature region), that represent the particles, and I use 5 parameters to adapt the energy spectrum to the energy function (I assume that the particles are a sequence of integer power of the metric density).

Until now I obtain only 145 right masses for 190 data masses (Particle Data Group).

I must read with more attention your essay, that contain interesting observations

I see a very high level of the essays this year; there are some that merit a magazine publication.

Saluti

Domenico

post approved

I use two curvature spherical region (I shall try with three curvature region), that represent the particles, and I use 5 parameters to adapt the energy spectrum to the energy function (I assume that the particles are a sequence of integer power of the metric density).

Until now I obtain only 145 right masses for 190 data masses (Particle Data Group).

I must read with more attention your essay, that contain interesting observations

I see a very high level of the essays this year; there are some that merit a magazine publication.

Saluti

Domenico

post approved

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

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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

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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

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

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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

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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

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 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

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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

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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

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

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

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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

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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

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

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

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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

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"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

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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

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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

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

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

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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

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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

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

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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

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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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'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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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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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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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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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

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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

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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

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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

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Dear Ernst Fischer

Your work is similar to my work in my paper http://gsjournal.net/Science-Journals/Research%20Papers-Rela

tivity%20Theory/Download/2310

But the difference you depending on the GRT. In my modified relativity (special and General) theory according to quantum theory concepts and principles, the Lorentz factor is equivalent to something like refractive index. and thus when Einstein proposed the light moving through the gravitational field in a geodesic path that is because to illustrate why the light is taking during his trip more time separation according according to a clock faraway from this field, and thus he proposed according to an observer faraway from the field the light will take more distance (Geodesic path) and thus it takes more time separation according to a clock faraway. This increasing in the distance and time will lead to measuring the light speed to equal c light speed in vacuum for an observer faraway. I don't say Einstein's interpretation is wrong, but what I say the two interpretations as the light bending by gravity or diffracted is the same meaning.The Geodesic path is coming from the refractive index around the mass M is changing according to the distance r from the center of mass M. But in the case of inertial frame, the refractive index (Lorentz factor) is constant depending on the speed of the moving frame which is constant. If you review my paper http://fqxi.org/community/forum/topic/1272 you will see how the contradiction between quantum and relativity can be solved and everything in physics can be solved

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Your work is similar to my work in my paper http://gsjournal.net/Science-Journals/Research%20Papers-Rela

tivity%20Theory/Download/2310

But the difference you depending on the GRT. In my modified relativity (special and General) theory according to quantum theory concepts and principles, the Lorentz factor is equivalent to something like refractive index. and thus when Einstein proposed the light moving through the gravitational field in a geodesic path that is because to illustrate why the light is taking during his trip more time separation according according to a clock faraway from this field, and thus he proposed according to an observer faraway from the field the light will take more distance (Geodesic path) and thus it takes more time separation according to a clock faraway. This increasing in the distance and time will lead to measuring the light speed to equal c light speed in vacuum for an observer faraway. I don't say Einstein's interpretation is wrong, but what I say the two interpretations as the light bending by gravity or diffracted is the same meaning.The Geodesic path is coming from the refractive index around the mass M is changing according to the distance r from the center of mass M. But in the case of inertial frame, the refractive index (Lorentz factor) is constant depending on the speed of the moving frame which is constant. If you review my paper http://fqxi.org/community/forum/topic/1272 you will see how the contradiction between quantum and relativity can be solved and everything in physics can be solved

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Dear Ernst

Very nicely argued essay on an important foundational question. As an astronomer my work has paralleled this and identified the source of re-ionization as toroidal EM 'twin vortex' AGN activity, the 'neutron star' crab nebula core showing the process as scale invariant. This then points to evidence of the anisotropic CMB 'flow' on the 'axis of evil' and computer derived 'spiral' resolution of the CMB quadrupolar asymmetry, suggesting pre big bang conditions and a variant of the Dicke/Peebles model cyclic universe. Your work looks very important in terms of a consistent mathematical model for the ontology to support. I am by the way now no mathematician since finding a number of areas where mathematical abstraction has mislead us.

You may be interested to know that there was a peak of AGN quasar activity which has been hidden by a stellar locus, and indicates a recycling period, (discussed in detail a current paper, yet unpublished). There is much other misinterpreted evidence in astronomy and I've derived a full new galactic recycling model. I did post a short preprint on viXra a while ago, but this is purely a 'popular' explanation of an extended version consistent with your far more professional and quantitative approach. I hope and believe our work may inform each others.

I discussed this briefly in last year's (finalist) essay '2020 vision' http://fqxi.org/community/forum/topic/803 but only refer to it obliquely and mainly in the end notes this year. My essay is on the rest of the consistent ontological basis at which cosmic recycling and re-ionization forms the core, which can unify QM and Classical Physics, even consistently with the SR postulates.

I hope you'll find the time to read my essay, which has easy read theatrical metaphores but goes to the heart of kinetics and SR, and I feel will test anyone's intellect and visualization skills to the full. I look forward to discussing more and will send a link. I hope I may cite you in the current draft. Do you have any recent published papers on this theme?

Well done and best of luck.

Peter

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Very nicely argued essay on an important foundational question. As an astronomer my work has paralleled this and identified the source of re-ionization as toroidal EM 'twin vortex' AGN activity, the 'neutron star' crab nebula core showing the process as scale invariant. This then points to evidence of the anisotropic CMB 'flow' on the 'axis of evil' and computer derived 'spiral' resolution of the CMB quadrupolar asymmetry, suggesting pre big bang conditions and a variant of the Dicke/Peebles model cyclic universe. Your work looks very important in terms of a consistent mathematical model for the ontology to support. I am by the way now no mathematician since finding a number of areas where mathematical abstraction has mislead us.

You may be interested to know that there was a peak of AGN quasar activity which has been hidden by a stellar locus, and indicates a recycling period, (discussed in detail a current paper, yet unpublished). There is much other misinterpreted evidence in astronomy and I've derived a full new galactic recycling model. I did post a short preprint on viXra a while ago, but this is purely a 'popular' explanation of an extended version consistent with your far more professional and quantitative approach. I hope and believe our work may inform each others.

I discussed this briefly in last year's (finalist) essay '2020 vision' http://fqxi.org/community/forum/topic/803 but only refer to it obliquely and mainly in the end notes this year. My essay is on the rest of the consistent ontological basis at which cosmic recycling and re-ionization forms the core, which can unify QM and Classical Physics, even consistently with the SR postulates.

I hope you'll find the time to read my essay, which has easy read theatrical metaphores but goes to the heart of kinetics and SR, and I feel will test anyone's intellect and visualization skills to the full. I look forward to discussing more and will send a link. I hope I may cite you in the current draft. Do you have any recent published papers on this theme?

Well done and best of luck.

Peter

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Dear Peter,

Thank you for reading and commenting on my essay. I have read your essay, too. But for me it is difficult to find out, what the basic idea behind your view of the universe is and why it can unify QM and classical physics consistently with SR. I would have preferred a more mathematical form. But I assume that this is a problem of my way of thinking.

You ask for recently published papers on this theme. Some years ago I have written an extensive paper, in which I have tried to set up an equilibrium model of the universe without a Big Bang singularity, looking for alternative explanations of red shift, microwave background, chemical element composition and cosmic structure formation. (arXiv:0708.3577)

Discussion of red shift, which should be present also in a static universe, can be found at (arXiv:0805.1638).

The properties of homogeneous static solutions of the Einstein equation under the assumption that time is not absolute, but may dependon distance, can also be found in a published paper (ApSS 325, 69-74 (2010)).

Best regards,

Ernst

Thank you for reading and commenting on my essay. I have read your essay, too. But for me it is difficult to find out, what the basic idea behind your view of the universe is and why it can unify QM and classical physics consistently with SR. I would have preferred a more mathematical form. But I assume that this is a problem of my way of thinking.

You ask for recently published papers on this theme. Some years ago I have written an extensive paper, in which I have tried to set up an equilibrium model of the universe without a Big Bang singularity, looking for alternative explanations of red shift, microwave background, chemical element composition and cosmic structure formation. (arXiv:0708.3577)

Discussion of red shift, which should be present also in a static universe, can be found at (arXiv:0805.1638).

The properties of homogeneous static solutions of the Einstein equation under the assumption that time is not absolute, but may dependon distance, can also be found in a published paper (ApSS 325, 69-74 (2010)).

Best regards,

Ernst

Ernst.

Your past papers are exceptionally close to mine. One is in review but I'll send privately if you wish (send you address to mine on my essay) A full galactic cycle is described, which you already had more than half of, but no jet accretion back to the old disc is found. The other touching on the ontology webarchived here; http://vixra.org/abs/1102.0016 Your red shift findings are also agreed with.

You said: "for me it is difficult to find out, what the basic idea behind your view of the universe is and why it can unify QM and classical physics consistently with SR."

What is does is derive all the classical effects of SR and 'curved space time' in a similar way to you, with just matter, with a complete consistent quantum mechanism but overcoming all the previous obstacles. It only takes SR to be derived from QM to complete unification. Gravity emerges consistently with your own far better quantified construction if not described in the same way.

i.e. Take 'Stellar Aberration', the main reason SR was formulated in the first place (photon particles not waves were needed to explain it), and CSL. Both emerge direct from scattering at c by all absorbing particles (= Local c, always, at all detectors). Asymmetry of charge with lateral motion during wave particle interaction then rotates the optical axis of re-emission. This IS diffraction, which matter in space (plasma) is precisely able to produce.

I believe our work is very compatible and could be valuably co-joined to be far greater than the sum of the parts (but you'd have to collect the Nobel). I hope you may agree.

Best wishes

Peter

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Your past papers are exceptionally close to mine. One is in review but I'll send privately if you wish (send you address to mine on my essay) A full galactic cycle is described, which you already had more than half of, but no jet accretion back to the old disc is found. The other touching on the ontology webarchived here; http://vixra.org/abs/1102.0016 Your red shift findings are also agreed with.

You said: "for me it is difficult to find out, what the basic idea behind your view of the universe is and why it can unify QM and classical physics consistently with SR."

What is does is derive all the classical effects of SR and 'curved space time' in a similar way to you, with just matter, with a complete consistent quantum mechanism but overcoming all the previous obstacles. It only takes SR to be derived from QM to complete unification. Gravity emerges consistently with your own far better quantified construction if not described in the same way.

i.e. Take 'Stellar Aberration', the main reason SR was formulated in the first place (photon particles not waves were needed to explain it), and CSL. Both emerge direct from scattering at c by all absorbing particles (= Local c, always, at all detectors). Asymmetry of charge with lateral motion during wave particle interaction then rotates the optical axis of re-emission. This IS diffraction, which matter in space (plasma) is precisely able to produce.

I believe our work is very compatible and could be valuably co-joined to be far greater than the sum of the parts (but you'd have to collect the Nobel). I hope you may agree.

Best wishes

Peter

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The TOV equations describe a static distribution of matter. The det(-g) leading to sqrt(h) and the potential is a reflection of this fact. The result that

m= 4π∫ρr^2dr + 4πG∫ρdr/rc^2

is then due to nongeodesic motion, say at some point or radial distance in the interior. As a result your conclusion there is no singularity or horizon is built into the initial assumptions.

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m= 4π∫ρr^2dr + 4πG∫ρdr/rc^2

is then due to nongeodesic motion, say at some point or radial distance in the interior. As a result your conclusion there is no singularity or horizon is built into the initial assumptions.

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Dear Lawrence,

You correctly mention that the TOV equations describe a static distribution of matter. But there is no motion at all, be it geodesic or not, and no initial condition involved in this equilibrium. That there exists the second term in your equation results from the deviation of the spatial geometry from Euclidean space. It reflects the fact that the relation between local parameters and integral data differs from Euclidean geometry. The volume enclosed between surfaces with two values of the radial parameter differs from the corresponding value in Euclidean space.

With every volume integration in curved space we have to take into account this change of the volume elements by curvature, if we apply it to quantities defined locally in Euclidean tangent space.

If we want to transfer the local definition of density from Euclidean space into curved space, we have to add a correction term to account for the change of the volume element by curvature. The identification of this correction term with the potential energy, as we know it from Newtonian theory, comes in with the basic idea of GR, to relate curvature to the gravitational action of mass or energy.

The introduction of the potential energy term in my essay is nothing more than demanding the correct application of volume integration in curved space. With this correction the problem of singularities and horizons vanishes automatically.

Best regards

Ernst Fischer

You correctly mention that the TOV equations describe a static distribution of matter. But there is no motion at all, be it geodesic or not, and no initial condition involved in this equilibrium. That there exists the second term in your equation results from the deviation of the spatial geometry from Euclidean space. It reflects the fact that the relation between local parameters and integral data differs from Euclidean geometry. The volume enclosed between surfaces with two values of the radial parameter differs from the corresponding value in Euclidean space.

With every volume integration in curved space we have to take into account this change of the volume elements by curvature, if we apply it to quantities defined locally in Euclidean tangent space.

If we want to transfer the local definition of density from Euclidean space into curved space, we have to add a correction term to account for the change of the volume element by curvature. The identification of this correction term with the potential energy, as we know it from Newtonian theory, comes in with the basic idea of GR, to relate curvature to the gravitational action of mass or energy.

The introduction of the potential energy term in my essay is nothing more than demanding the correct application of volume integration in curved space. With this correction the problem of singularities and horizons vanishes automatically.

Best regards

Ernst Fischer

The correction due to sqrt{g} ~ 1 + GM/rc^2 with this potential does reflect curvature as interpreted in a Euclidean format as the inclusion of a gravity potential. This gravity potential occurs this way because there are spacetime paths for units of matter, but they are not geodesic. The whole mass is moving forwards in time with no spatial motion relative to a coordinate system tied to the center of the mass. It is for this reason I think the nonexistence of the horizons occurs because the set up has a static mass to begin with.

Cheers LC

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Cheers LC

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Dear Ernst

JETS

Thank you for this paper. Could you elaborate on the proposed jet formation mechanics:

"Inflow of matter near the rotational plane will cause an outflow along the axis of rotation."

Thank you

Dirk

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JETS

Thank you for this paper. Could you elaborate on the proposed jet formation mechanics:

"Inflow of matter near the rotational plane will cause an outflow along the axis of rotation."

Thank you

Dirk

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Dear Dirk,

By now I have no detailed model of the jet formation process. Formation of jets is a highly dynamical process, while the model described in my essay is only on static equilibrium conditions. But the physics, which governs the equilibrium, must, of course, be valid also in dynamical situations.

There is observational evidence that the jets, which emanate from the collapsed cores of galaxies consist of highly relativistic matter consisting mainly of protons and electrons, which must have been processed at extreme energy densities, which only occur inside nuclear matter concentrations. In the accretion flows around these concentrations on contrary we expect processed matter from stars, that means matter enriched with heavier elements. Thus the source of the jets must be inside the core. This core cannot be a black hole, from which an escape of matter is impossible.

Gravity may become repulsive, when the contribution of potential energy exceeds the matter equivalent, just as it is discussed with the so called dark energy. This situation can occur in the dynamical processes of accretion onto a nuclear matter concentration, but not in an exactly spherically symmetric case. In a rotating core, where the collapse is slowed down by centrifugal forces in the plane of rotation, the repulsive situation will occur preferably in direction of the rotational axis, so that ejection of matter will be preferred in this direction. An additional collimation of the jets will normally occur by the strong magnetic fields, which exist in the accretion region of the 'black hole'. As the ejected particles are electrically charged, matter can escape only in the polar direction of the field, while in other directions the ejected matter is led back into the core along the field lines.

This qualitative picture is all I can offer to you at the moment. I hope that other experts in the field will take up this idea to develop quantitative models, which lead to a complete understanding of the mysterious cosmic jets.

Best regards,

Ernst

By now I have no detailed model of the jet formation process. Formation of jets is a highly dynamical process, while the model described in my essay is only on static equilibrium conditions. But the physics, which governs the equilibrium, must, of course, be valid also in dynamical situations.

There is observational evidence that the jets, which emanate from the collapsed cores of galaxies consist of highly relativistic matter consisting mainly of protons and electrons, which must have been processed at extreme energy densities, which only occur inside nuclear matter concentrations. In the accretion flows around these concentrations on contrary we expect processed matter from stars, that means matter enriched with heavier elements. Thus the source of the jets must be inside the core. This core cannot be a black hole, from which an escape of matter is impossible.

Gravity may become repulsive, when the contribution of potential energy exceeds the matter equivalent, just as it is discussed with the so called dark energy. This situation can occur in the dynamical processes of accretion onto a nuclear matter concentration, but not in an exactly spherically symmetric case. In a rotating core, where the collapse is slowed down by centrifugal forces in the plane of rotation, the repulsive situation will occur preferably in direction of the rotational axis, so that ejection of matter will be preferred in this direction. An additional collimation of the jets will normally occur by the strong magnetic fields, which exist in the accretion region of the 'black hole'. As the ejected particles are electrically charged, matter can escape only in the polar direction of the field, while in other directions the ejected matter is led back into the core along the field lines.

This qualitative picture is all I can offer to you at the moment. I hope that other experts in the field will take up this idea to develop quantitative models, which lead to a complete understanding of the mysterious cosmic jets.

Best regards,

Ernst

A very interesting and well written essay, which conclusions I find myself in agreement with.

The notion of a balance or state of equilibrium, is central, not only for cosmic scale objects but also for objects at the fundamental scale. I believe that the laws the impose certain size limit on atomic nuclei, for example, play a role in determining the maximum density and size of, for instance, black holes.

I hope the essay gets all the attention it deserves.

DLB

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The notion of a balance or state of equilibrium, is central, not only for cosmic scale objects but also for objects at the fundamental scale. I believe that the laws the impose certain size limit on atomic nuclei, for example, play a role in determining the maximum density and size of, for instance, black holes.

I hope the essay gets all the attention it deserves.

DLB

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Mr Ernst Fischer,

It is a pleasure to read your essay on gravitational collapse and resulting singularities. I removed myself from mainstream physics to develop my own understanding of nature long time back. This gave me an opportunity to develop an alternative thought processes. It is Pico-Physics. In this thought process we have one founding statement as 'Space contains Energy' and all other axioms describing different aspects of nature are related to this statement called unary law .

In PicoPhysics thought process, we begin with attempts to understand energy and space. This projects nature as Five- dimensional universe . The relevance of PicoPhysics is unification of phenomenon of gravitation, expanding universe and space singularities with unary law.

The thought processes begins with separating neutralization from conservation, to evolve Konservation concept and hypothesising a reality Knergy as host to this concept. Space is considered as host reality of anti-Konservation that makes it consumable. It is created in space and consumed by matter (Knergy). The Hubble's constant represents the process of creation of space and Energy represents consumption of space by Knergy. The two processes together explain;

1. Gravitation

2. Expanding Universe (apparent motion of astronomical objects to observer proportional to the distance from observer) - No big-Bang singularity.

3. Limitation on atomic mass of nuclei (absence of high atomic number elements)

4. A higher limit to energy density - no singularities on gravitational collapse

Thus, in PicoPhysics we do not encounter singularities and view universe in dynamic equilibrium (sort of).

I request and appreciate your time to review and comments on this approach.

Thanks and best regards,

Vijay Gupta

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It is a pleasure to read your essay on gravitational collapse and resulting singularities. I removed myself from mainstream physics to develop my own understanding of nature long time back. This gave me an opportunity to develop an alternative thought processes. It is Pico-Physics. In this thought process we have one founding statement as 'Space contains Energy' and all other axioms describing different aspects of nature are related to this statement called unary law .

In PicoPhysics thought process, we begin with attempts to understand energy and space. This projects nature as Five- dimensional universe . The relevance of PicoPhysics is unification of phenomenon of gravitation, expanding universe and space singularities with unary law.

The thought processes begins with separating neutralization from conservation, to evolve Konservation concept and hypothesising a reality Knergy as host to this concept. Space is considered as host reality of anti-Konservation that makes it consumable. It is created in space and consumed by matter (Knergy). The Hubble's constant represents the process of creation of space and Energy represents consumption of space by Knergy. The two processes together explain;

1. Gravitation

2. Expanding Universe (apparent motion of astronomical objects to observer proportional to the distance from observer) - No big-Bang singularity.

3. Limitation on atomic mass of nuclei (absence of high atomic number elements)

4. A higher limit to energy density - no singularities on gravitational collapse

Thus, in PicoPhysics we do not encounter singularities and view universe in dynamic equilibrium (sort of).

I request and appreciate your time to review and comments on this approach.

Thanks and best regards,

Vijay Gupta

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Mr Ernst Fischer,

I read some comments about dark energy. PicoPhysics has a view on Dark-Energy. It is the low density distribution of Knergy in space, such that rate of consumption of space (Energy density) balances with rate of generation of space, over large extent of space. It is distinguished from cosmic background radiation based on Knergy per occurence being unity in CBR in contrast to dark energy where significant amount of knergy is glued together.

Picophysics has an equilibrium view of universe that cycles through Knergy/Dark-Energy->elementary particles->Matter->Astronomical objects->Cosmic Background radiation->Dark-Energy/Knergy.

I thought I shall mention the same. as my previous message got recorded as Anonymous. To be Anonymous was not the intention, but a mistake.

Thanks and Regards,

Vijay Gupta

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I read some comments about dark energy. PicoPhysics has a view on Dark-Energy. It is the low density distribution of Knergy in space, such that rate of consumption of space (Energy density) balances with rate of generation of space, over large extent of space. It is distinguished from cosmic background radiation based on Knergy per occurence being unity in CBR in contrast to dark energy where significant amount of knergy is glued together.

Picophysics has an equilibrium view of universe that cycles through Knergy/Dark-Energy->elementary particles->Matter->Astronomical objects->Cosmic Background radiation->Dark-Energy/Knergy.

I thought I shall mention the same. as my previous message got recorded as Anonymous. To be Anonymous was not the intention, but a mistake.

Thanks and Regards,

Vijay Gupta

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Hi Ernst. Some important clarification regarding gravity. Gravity is both seen AND felt, and it fundamentally requires/involves visible and invisible space in fundamental balance/equilibrium.

GRAVITY (SEEN AND FELT) IS KEY TO DISTANCE IN/OF SPACE.

ULTIMATELY, GRAVITY, INERTIA, AND ELECTROMAGNETISM together INVOLVE BALANCED ATTRACTION AND REPULSION. OPPOSITES ARE REQUIRED FOR EXTENSIVENESS. THIS IS NECESSARY FOR STABILIZED DISTANCE IN/OF SPACE, AND BECAUSE GRAVITY CANNOT BE SHIELDED.

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GRAVITY (SEEN AND FELT) IS KEY TO DISTANCE IN/OF SPACE.

ULTIMATELY, GRAVITY, INERTIA, AND ELECTROMAGNETISM together INVOLVE BALANCED ATTRACTION AND REPULSION. OPPOSITES ARE REQUIRED FOR EXTENSIVENESS. THIS IS NECESSARY FOR STABILIZED DISTANCE IN/OF SPACE, AND BECAUSE GRAVITY CANNOT BE SHIELDED.

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Dear Earnst:

Beautiful… I was astonished to see the following conclusions in your paper that are strongly vindicated by the predictions of the GNMUE model and comparison against universal observations described in my paper -“ From Absurd to Elegant Universe” :

“Neglecting potential energy in the balance equations appears as a general problem in the conventional methods of general relativistic modeling. In the description of the global dynamics of the universe, in addition to the search for dark matter, people are looking for the so called dark energy, which is necessary to bring the theoretical model into agreement with observations. This dark energy should be present throughout the universe and exhibit a negative pressure and an energy density comparable in order of magnitude to that of matter. Potential energy of matter itself just fulfills all these requirements. In a homogeneous solution of the Einstein equation it would look just like a cosmological constant, with the only difference that it is not a true constant, but varies with the matter density. No mysterious dark energy is necessary to fulfill the balance. Potential energy of matter itself can do the job.”

I would greatly appreciate if you read my paper and offer your comments on the similarities ( as well as differences) between them.

Regards

Avtar

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Beautiful… I was astonished to see the following conclusions in your paper that are strongly vindicated by the predictions of the GNMUE model and comparison against universal observations described in my paper -“ From Absurd to Elegant Universe” :

“Neglecting potential energy in the balance equations appears as a general problem in the conventional methods of general relativistic modeling. In the description of the global dynamics of the universe, in addition to the search for dark matter, people are looking for the so called dark energy, which is necessary to bring the theoretical model into agreement with observations. This dark energy should be present throughout the universe and exhibit a negative pressure and an energy density comparable in order of magnitude to that of matter. Potential energy of matter itself just fulfills all these requirements. In a homogeneous solution of the Einstein equation it would look just like a cosmological constant, with the only difference that it is not a true constant, but varies with the matter density. No mysterious dark energy is necessary to fulfill the balance. Potential energy of matter itself can do the job.”

I would greatly appreciate if you read my paper and offer your comments on the similarities ( as well as differences) between them.

Regards

Avtar

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Dear Avtar,

You cite the paragraph of my essay, in which I mention that potential energy may play the role of the so called dark energy in an expanding universe. But also with this interpretation the problem remains that there must be some unknown physical effect, which drives the expansion, and that the expansion must have started in a singular state. The same problem occurs in your model, too. What is the mechanism, which transforms matter into expansion energy?

The other possibility, which I mentioned at the end of my essay, appears to me more sensible: a stable static universe. The only thing we must abandon is the belief that red shift is a consequence of expansion. Other explanations are possible. In a paper, which I have submitted to arXiv (arXiv:0805.1638), I have shown that curvature of space together with the consequent application of Lorentz invariance must inevitably lead to red shift also in a static universe.

A further comment on your GNMUE model I will post on your blog.

Regards,

Ernst

You cite the paragraph of my essay, in which I mention that potential energy may play the role of the so called dark energy in an expanding universe. But also with this interpretation the problem remains that there must be some unknown physical effect, which drives the expansion, and that the expansion must have started in a singular state. The same problem occurs in your model, too. What is the mechanism, which transforms matter into expansion energy?

The other possibility, which I mentioned at the end of my essay, appears to me more sensible: a stable static universe. The only thing we must abandon is the belief that red shift is a consequence of expansion. Other explanations are possible. In a paper, which I have submitted to arXiv (arXiv:0805.1638), I have shown that curvature of space together with the consequent application of Lorentz invariance must inevitably lead to red shift also in a static universe.

A further comment on your GNMUE model I will post on your blog.

Regards,

Ernst

Dear Ernst:

Thanks for reading my paper and offering thoughtful comments. I have provided response to your comments under my posted blog.

Below is a response to your comments above:

You cite in your essay that potential energy may play the role of the so called dark energy in an expanding universe. In my GNMUE model, the so-called dark energy is not potential energy but kinetic energy (see equation 7 in my paper) generated via evaporation of mass via the well-known phenomenon of spontaneous decay. All masses, from small particles to large structures are seen to decay sooner or later via converting mass to energy. This mechanism is modeled via the GNMUE model presented in my paper. The physics of this mechanism has been missing from current theories including general relativity that leads to their failure to predict the observed accelerated expansion of the universe.

Hence, your comment above regarding the unknown mechanism is adequately addressed by the GNMUE model in my paper.

Regards

Avtar

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Thanks for reading my paper and offering thoughtful comments. I have provided response to your comments under my posted blog.

Below is a response to your comments above:

You cite in your essay that potential energy may play the role of the so called dark energy in an expanding universe. In my GNMUE model, the so-called dark energy is not potential energy but kinetic energy (see equation 7 in my paper) generated via evaporation of mass via the well-known phenomenon of spontaneous decay. All masses, from small particles to large structures are seen to decay sooner or later via converting mass to energy. This mechanism is modeled via the GNMUE model presented in my paper. The physics of this mechanism has been missing from current theories including general relativity that leads to their failure to predict the observed accelerated expansion of the universe.

Hence, your comment above regarding the unknown mechanism is adequately addressed by the GNMUE model in my paper.

Regards

Avtar

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Hi Ernst. Our ability to understand outer space is inherently limited. I am positive of this. Outer space is a larger space that is not expanding. It is quite simply, expanded. The detachment of this space from our [natural] touch and thought makes it less sensible and comprehensible. The red shift relates to the space being larger/magnified and smaller/visible on balance, to stabilize/balance distance in/of space. Don't forget where visible light is in the electromagnetic spectrum.

The body and body/eye is what ultimately and fully balances inertia and gravity or there would be no stabilized distance in/of space. Where do you think the conceptual/theoretical equivalency comes from? We exist between larger and smaller space. Balance and completeness.

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The body and body/eye is what ultimately and fully balances inertia and gravity or there would be no stabilized distance in/of space. Where do you think the conceptual/theoretical equivalency comes from? We exist between larger and smaller space. Balance and completeness.

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Dear Researcher Fischer,

I found your essay absorbingly interesting, although because of my not having had the benefit of a formal education, I did not understand any of the mathematics it contained. As I tried to clumsily explain in my essay Sequence Consequence, I doubt that the seeming perverse irrationality of mathematics can be at all useful for understanding how the Universe continues working. For instance, the physicist’s insistence that originally abstract nothing was a possible real singularity is rather like the Orwellian contention “war is peace.” Only a real one can have a real eternal singularity once. While it is true that a natural object has to have three differing observable aspects once, each of these real differing observable aspects is also subject to three true differing rational explanations once. One could go on interminably asserting that each true rational explanation of an object’s existence also is subject to three real differing experimental methodologies once and so on. Nothing actually equates. Although as I understand it, Albert Einstein tried to prove that abstract energy equaled two of the differing aspects of abstract mass and the so-called constant speed of abstract light, he failed to take into account that real energy has three real incalculable differing potentials; real light has three real differing appearances, and squares are completely unnatural because they do not have three differing aspects.

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I found your essay absorbingly interesting, although because of my not having had the benefit of a formal education, I did not understand any of the mathematics it contained. As I tried to clumsily explain in my essay Sequence Consequence, I doubt that the seeming perverse irrationality of mathematics can be at all useful for understanding how the Universe continues working. For instance, the physicist’s insistence that originally abstract nothing was a possible real singularity is rather like the Orwellian contention “war is peace.” Only a real one can have a real eternal singularity once. While it is true that a natural object has to have three differing observable aspects once, each of these real differing observable aspects is also subject to three true differing rational explanations once. One could go on interminably asserting that each true rational explanation of an object’s existence also is subject to three real differing experimental methodologies once and so on. Nothing actually equates. Although as I understand it, Albert Einstein tried to prove that abstract energy equaled two of the differing aspects of abstract mass and the so-called constant speed of abstract light, he failed to take into account that real energy has three real incalculable differing potentials; real light has three real differing appearances, and squares are completely unnatural because they do not have three differing aspects.

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Dear Joe

I do not know why every thing should have three observable aspects. But if it helps you:

According to general relativity energy has three aspects: rest energy, kinetic energy and potential energy. The best way to understand, how a universe can be created from nothing is to assume that, averaged over the whole universe, these three aspects add to zero.

Best regards,

Ernst Fischer

I do not know why every thing should have three observable aspects. But if it helps you:

According to general relativity energy has three aspects: rest energy, kinetic energy and potential energy. The best way to understand, how a universe can be created from nothing is to assume that, averaged over the whole universe, these three aspects add to zero.

Best regards,

Ernst Fischer

When I assume it only makes an ass of u and me. Real objects can never be at reat. What is the real base unit of "potential energy?" Is "potential energy" greater or lesser than real energy? It has to be one or the other because it cannot be identical to real energy can it?

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Dear Ernst Fischer,

I see a good chance for you to win the contest with a surprising and perhaps mathematically correct alternative to some counter-intuitive tenets. If you already tried in vain to publish it elsewhere, this would demonstrate how valuable the open-minded exchange of ideas at fqxi is.

You wrote: "To my opinion the only things that count are spatial and causal distances which set up a relative space-time continuum, in which the spatial distance (the shortest spatial connection) is related to the shortest causal connection by the constant c and thus defines the notion of time."

I notice, you did not mention Einstein's observer. In that I agree with you to presumably disagree with the mandatory special theory of relativity and the usual notion of time.

While I do not expect you dealing in public with my related more comprehensive criticism, may I hope for a phone call from Stolberg to Magdeburg 0391 2516557?

Best regards,

Eckard Blumschein

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I see a good chance for you to win the contest with a surprising and perhaps mathematically correct alternative to some counter-intuitive tenets. If you already tried in vain to publish it elsewhere, this would demonstrate how valuable the open-minded exchange of ideas at fqxi is.

You wrote: "To my opinion the only things that count are spatial and causal distances which set up a relative space-time continuum, in which the spatial distance (the shortest spatial connection) is related to the shortest causal connection by the constant c and thus defines the notion of time."

I notice, you did not mention Einstein's observer. In that I agree with you to presumably disagree with the mandatory special theory of relativity and the usual notion of time.

While I do not expect you dealing in public with my related more comprehensive criticism, may I hope for a phone call from Stolberg to Magdeburg 0391 2516557?

Best regards,

Eckard Blumschein

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Dear Ernst Fischer,

It is important to read my essay http://fqxi.org/community/forum/topic/1272

In my theory there is no length contraction as Einstein proposed in his SRT. The length of the moving train will not be contracted in the direction of the velocity. In my theory the interpretation of the length contraction is different from Einstein interpretation. My interpretation is agreed with the predicted experimental results of quantum field theory, and thus interpreting faster than light without violation of Lorentz transformation or causality. read my another paper also http://vixra.org/abs/1208.0018

What I predicted is agreed what your proposed also.

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It is important to read my essay http://fqxi.org/community/forum/topic/1272

In my theory there is no length contraction as Einstein proposed in his SRT. The length of the moving train will not be contracted in the direction of the velocity. In my theory the interpretation of the length contraction is different from Einstein interpretation. My interpretation is agreed with the predicted experimental results of quantum field theory, and thus interpreting faster than light without violation of Lorentz transformation or causality. read my another paper also http://vixra.org/abs/1208.0018

What I predicted is agreed what your proposed also.

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Dear Ernst Fischer,

You have stated, "Without inclusion of potential energy into the balance, gravitational collapse would be accompanied by a continuous gain of energy from the gravitational field. But in the geometrical concept of general relativity there exists no gravitational field which might possess energy. Gravitation is only a consequence of curvature. So this energy is created...

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You have stated, "Without inclusion of potential energy into the balance, gravitational collapse would be accompanied by a continuous gain of energy from the gravitational field. But in the geometrical concept of general relativity there exists no gravitational field which might possess energy. Gravitation is only a consequence of curvature. So this energy is created...

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Dear G S Sandhu,

I think that is was Einstein's brilliant idea that all forms of energy contribute to interactions, be it gravitational or electromagnetic and that causality of these interactions is limited to the speed of light. It is the equivalence of mass and energy, expressed by E=mc², which suggests this assumption, which has been confirmed by many observations.

In your example of two moving masses it makes no difference, if you take the rest masses as a source of gravitational attraction or the sum of rest energy, kinetic energy and potential energy. The balance will remain the same.

Now to your questions:

1. You ask: Do you really believe that GR does not admit of any gravitational field which might possess energy?

A gravitational field does not possess energy. This is the case also in Newtonian theory. If there is no matter in the neighbourhood of some central mass, there is no energy. Only if there is some matter, there is energy in the form of potential energy additional to the rest energy of this matter.

2. You ask: Could it be that matter actually produces a gravitational field that contains field energy, but GR represents this phenomenon through curvature of spacetime?

As said before, potential energy is no extra field which contains energy, but must be regarded as a change of the properties of matter caused by the existence of other surrounding matter. This change can be expressed through the mathematical description that the matter is contained in curved space.

3. You ask: Do you believe that 4D spacetime manifold of GR is a physical entity which could actually get curved or deformed in the presence of matter?

Yes, there is no absolute space or time, but what exists are spatial and causal distances between events in a manifold. The spatial and causal connections and thus the effective distances depend on the distribution of matter.

4. You ask: Where do you think the potential energy of a matter particle is actually stored, within the physical volume of the particle or within its associated field?

As said before, potential energy is no additional localized field, but must be regarded as a change of properties of matter induced by the existence of other matter.

I hope that my answers will contribute to a better understanding.

Best regards,

Ernst Fischer

I think that is was Einstein's brilliant idea that all forms of energy contribute to interactions, be it gravitational or electromagnetic and that causality of these interactions is limited to the speed of light. It is the equivalence of mass and energy, expressed by E=mc², which suggests this assumption, which has been confirmed by many observations.

In your example of two moving masses it makes no difference, if you take the rest masses as a source of gravitational attraction or the sum of rest energy, kinetic energy and potential energy. The balance will remain the same.

Now to your questions:

1. You ask: Do you really believe that GR does not admit of any gravitational field which might possess energy?

A gravitational field does not possess energy. This is the case also in Newtonian theory. If there is no matter in the neighbourhood of some central mass, there is no energy. Only if there is some matter, there is energy in the form of potential energy additional to the rest energy of this matter.

2. You ask: Could it be that matter actually produces a gravitational field that contains field energy, but GR represents this phenomenon through curvature of spacetime?

As said before, potential energy is no extra field which contains energy, but must be regarded as a change of the properties of matter caused by the existence of other surrounding matter. This change can be expressed through the mathematical description that the matter is contained in curved space.

3. You ask: Do you believe that 4D spacetime manifold of GR is a physical entity which could actually get curved or deformed in the presence of matter?

Yes, there is no absolute space or time, but what exists are spatial and causal distances between events in a manifold. The spatial and causal connections and thus the effective distances depend on the distribution of matter.

4. You ask: Where do you think the potential energy of a matter particle is actually stored, within the physical volume of the particle or within its associated field?

As said before, potential energy is no additional localized field, but must be regarded as a change of properties of matter induced by the existence of other matter.

I hope that my answers will contribute to a better understanding.

Best regards,

Ernst Fischer

Dear G S Sandhu

It is worth mentioning that the notion of an energetically isolated gravitational system might be inherently incompatible with a Machian theory of gravitation. Mach's principle supposes that the rest energy of an object is gravitational potential energy due to distant matter. If we are to accept this viewpoint, it is not unreasonable to anticipate some as yet unknown energetic relation between the particles and distant matter.

Let me put forward a simple idea that seems to fit. This is necessarily speculative. If changes in potential energy are mutual and presumably equal, it is conceivable that the change in potential energy of the two particles is (somehow) mirrored in the potential energy of distant matter - they all rise or they all fall.

If we let U be the potential energy of distant matter, then U will vary with the change in potential energies V1 and V2 resulting in a balance if U is included in the accounting of energy.

This particular proposal may be half-baked, and perhaps not convincing, but it must be realized that the notion of an isolated gravitational system is in conflict with Mach's concept of energy.

Colin

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It is worth mentioning that the notion of an energetically isolated gravitational system might be inherently incompatible with a Machian theory of gravitation. Mach's principle supposes that the rest energy of an object is gravitational potential energy due to distant matter. If we are to accept this viewpoint, it is not unreasonable to anticipate some as yet unknown energetic relation between the particles and distant matter.

Let me put forward a simple idea that seems to fit. This is necessarily speculative. If changes in potential energy are mutual and presumably equal, it is conceivable that the change in potential energy of the two particles is (somehow) mirrored in the potential energy of distant matter - they all rise or they all fall.

If we let U be the potential energy of distant matter, then U will vary with the change in potential energies V1 and V2 resulting in a balance if U is included in the accounting of energy.

This particular proposal may be half-baked, and perhaps not convincing, but it must be realized that the notion of an isolated gravitational system is in conflict with Mach's concept of energy.

Colin

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Dear Colin,

I cannot accept the Machian theory of gravitation for want of any physical mechanism for the same. In my opinion, the electrostatic field of charged particles (electrons, positrons) and the gravitational field of neutral particles, both contain energy which is actually accounted in the mass energy of these particles. That is, the gravitational field of matter particles is...

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I cannot accept the Machian theory of gravitation for want of any physical mechanism for the same. In my opinion, the electrostatic field of charged particles (electrons, positrons) and the gravitational field of neutral particles, both contain energy which is actually accounted in the mass energy of these particles. That is, the gravitational field of matter particles is...

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dear Ernst Fischer

I'm very interested with your conclusion "Instead every spherically symmetric gravitational collapse can find a

final equilibrium state of finite density. No matter is inevitably lost from the

surrounding space."

Please will you read my paper "The Exact Solution of the Pioneer Anomaly According to the General Theory of Relativity and the Hubble's Law" http://vixra.org/abs/1109.0058

I interpreted the Hubble law same as what you proposed in your paper. Pioneer anomaly can be solved by that. My solution to the Pioneer anomaly is more accurate than the thermal origin of the Pioneer anomaly, see http://vixra.org/abs/1205.0006

I hope to discuss by this point, specially solving the Pioneer anomaly and the Hubble law is good proof that I and you are moving in the right side relative to reinterpreting the GRT by quantum concepts and principles.

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I'm very interested with your conclusion "Instead every spherically symmetric gravitational collapse can find a

final equilibrium state of finite density. No matter is inevitably lost from the

surrounding space."

Please will you read my paper "The Exact Solution of the Pioneer Anomaly According to the General Theory of Relativity and the Hubble's Law" http://vixra.org/abs/1109.0058

I interpreted the Hubble law same as what you proposed in your paper. Pioneer anomaly can be solved by that. My solution to the Pioneer anomaly is more accurate than the thermal origin of the Pioneer anomaly, see http://vixra.org/abs/1205.0006

I hope to discuss by this point, specially solving the Pioneer anomaly and the Hubble law is good proof that I and you are moving in the right side relative to reinterpreting the GRT by quantum concepts and principles.

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Dear Ernst Fischer,

I do agree your concept that energy density has limitation and it provides the mass energy conversions at the heated center of astronomical objects. Nearly 8 years ago, so when Bush ex-us-president won the second term election, I posted a comment to a physics forum that if you are tired hearing or saying "four more years", next you should say is "no more holes". Well, I didn't have any followed at that time ;)

So, I as well built up my idea based density limitation entry here, the part is section 2 and 3 would be related. I would be glad if we can exchange thoughts.

I am wondering if your description of GRT can be connected to my graviton and wave function model as both stands on the same principle newly introduced.

Regards,

Ryoji Furui

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I do agree your concept that energy density has limitation and it provides the mass energy conversions at the heated center of astronomical objects. Nearly 8 years ago, so when Bush ex-us-president won the second term election, I posted a comment to a physics forum that if you are tired hearing or saying "four more years", next you should say is "no more holes". Well, I didn't have any followed at that time ;)

So, I as well built up my idea based density limitation entry here, the part is section 2 and 3 would be related. I would be glad if we can exchange thoughts.

I am wondering if your description of GRT can be connected to my graviton and wave function model as both stands on the same principle newly introduced.

Regards,

Ryoji Furui

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Dear Ernst Fischer,

After reading your paper several times, I cannot say I can fully understand yours yet but I pick up what I can understand and applied to my graviton's energy definition and it became beautiful math in result.

Please see my latest post at my essay page.

My previous solution to infinite problem was to set a finite value for mass, -1

post approved

After reading your paper several times, I cannot say I can fully understand yours yet but I pick up what I can understand and applied to my graviton's energy definition and it became beautiful math in result.

Please see my latest post at my essay page.

My previous solution to infinite problem was to set a finite value for mass, -1

post approved

I found an error of this posting system. Both above post ends before "less than sign" automatically so I repost the message without it below.

Sorry for many posts, I found my previous post was cut off in the description of my solution for infinite energy. My mass term comes from contraction of time axis so the infinite energy comes when $\eta=-1$ in equation (7) in my paper. So if we can set $-1 "less than" \eta "less than" 0$ for the origin of mass and let it the max density of energy, we can avoid infinite, I think. And I wondered if we could connect it to the lhc newly discovered mass term.

Thanks,

Ryoji

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Sorry for many posts, I found my previous post was cut off in the description of my solution for infinite energy. My mass term comes from contraction of time axis so the infinite energy comes when $\eta=-1$ in equation (7) in my paper. So if we can set $-1 "less than" \eta "less than" 0$ for the origin of mass and let it the max density of energy, we can avoid infinite, I think. And I wondered if we could connect it to the lhc newly discovered mass term.

Thanks,

Ryoji

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Dear Ernst Fischer

The Schwarzschild solution is a vacuum solution: rho(r) = 0 exactly. If you add in a density, “even if the density is arbitrarily small but not exactly zero at r = rs, this yields an infinite value, in contradiction to the assumption that the mass is negligibly small.” This is because of the non-linearity of the Einstein equations: no matter how small the density, it...

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The Schwarzschild solution is a vacuum solution: rho(r) = 0 exactly. If you add in a density, “even if the density is arbitrarily small but not exactly zero at r = rs, this yields an infinite value, in contradiction to the assumption that the mass is negligibly small.” This is because of the non-linearity of the Einstein equations: no matter how small the density, it...

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Dear Professor Ellis,

Thank you for reading my essay and for your critical comments. But I cannot agree with your arguments. Of course, you are right that "no matter how small the density, it is no longer a Schwarzschild solution", but the exact Schwarzschild solution is only a theoretical approximation.

If there were really no matter and nothing else outside some value of the radial...

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Thank you for reading my essay and for your critical comments. But I cannot agree with your arguments. Of course, you are right that "no matter how small the density, it is no longer a Schwarzschild solution", but the exact Schwarzschild solution is only a theoretical approximation.

If there were really no matter and nothing else outside some value of the radial...

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Hi Ernst,

An interesting essay. You as many others recognise that a singularity in nature cannot exist. You also recognise that a universe as a whole cannot change its energy content.

Here I fully agree with you, but your solution to avoid the singularity is to fix a theory that is faulty in the first place. New theories have to be found, a possible ansatz you will find in my essay.

Regards

Anton @ ( /topic/1458 )

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An interesting essay. You as many others recognise that a singularity in nature cannot exist. You also recognise that a universe as a whole cannot change its energy content.

Here I fully agree with you, but your solution to avoid the singularity is to fix a theory that is faulty in the first place. New theories have to be found, a possible ansatz you will find in my essay.

Regards

Anton @ ( /topic/1458 )

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Ernst,

We have essays with similar themes concerning potentials within the EFE running through them.

My essay is based also on a simple premise. If the function F_{1} is the Newtonian gravitational field strength, then F_{1}' is the gravitational force. How do we know we have been anti-differentiating the Newtonian field correctly since we could have just been mistaking F1' for (C-F2)' following the rules concerning arbitrary constants of integration. This should lead back to a substitution in the Einstein field equation of . If the constant term is equated to the potential energy of the vacuum, then the L_{uv} term is just equated to the dynamic residual energy tensor. This would seem to solve the cosmological constant magnitude problem, make it look like gravity is attractive but also allow for a repulsion after a certain radius.

Reading more through your essay. Comments on mine appreciated.

Regards,

Jeff

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We have essays with similar themes concerning potentials within the EFE running through them.

My essay is based also on a simple premise. If the function F

Reading more through your essay. Comments on mine appreciated.

Regards,

Jeff

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Dear Ernst,

I enjoyed reading your essay! One question that comes to mind is how dark matter fits into this picture. As you point out, potential energy of the form you describe might account for the negative pressure and energy density associated with dark energy, but it seems that dark matter exhibits roughly the "opposite" effect, albeit at a smaller scale, in the sense that it seems to involve an increased attractive effect.

Do you agree with the conventional dark matter hypothesis that dark matter is "real matter," then, or do you think it is an unexplained dynamical effect? The reason I ask is because I am interested in scale-dependence of phenomena; I discuss this more in my essay

On the Foundational Assumptions of Modern Physics

Let me be clear that I'm not suggesting you're under any obligation to explain both dark matter and dark energy with your ideas; after all, conventional GR explains neither! I'm just interested to know your thoughts on the subject. Take care,

Ben Dribus

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I enjoyed reading your essay! One question that comes to mind is how dark matter fits into this picture. As you point out, potential energy of the form you describe might account for the negative pressure and energy density associated with dark energy, but it seems that dark matter exhibits roughly the "opposite" effect, albeit at a smaller scale, in the sense that it seems to involve an increased attractive effect.

Do you agree with the conventional dark matter hypothesis that dark matter is "real matter," then, or do you think it is an unexplained dynamical effect? The reason I ask is because I am interested in scale-dependence of phenomena; I discuss this more in my essay

On the Foundational Assumptions of Modern Physics

Let me be clear that I'm not suggesting you're under any obligation to explain both dark matter and dark energy with your ideas; after all, conventional GR explains neither! I'm just interested to know your thoughts on the subject. Take care,

Ben Dribus

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Dear Ben,

To my opinion dark matter consists of real particles which react only by gravitation. But observations show that it must be rather low mass particles, which are stable and cannot annihilate with their antiparticles into photon pairs (they do not even know what electromagnetism is). I have recently written a paper on this topic: "The properties of dark matter" which you can find in arXiv (arXiv:1104.2525).

This dark matter together with the intergalactic plasma, which is observed by the x-ray continuum from thermal bremsstrahlung, fulfils the global matter balance, even if the visible matter in galaxies amounts only to a few percent. That the balance can be fulfilled without further ingredients I have shown in the paper "An Equilibrium Balance of the Universe" (arXiv:0708.3577).

I am sceptical that, to understand the universe, we really have to reject so many fundamental assumptions as you propose in your essay. The concepts of special and general relativity are a suitable basis. We only have to apply them in a better way.

Regards,

Ernst

To my opinion dark matter consists of real particles which react only by gravitation. But observations show that it must be rather low mass particles, which are stable and cannot annihilate with their antiparticles into photon pairs (they do not even know what electromagnetism is). I have recently written a paper on this topic: "The properties of dark matter" which you can find in arXiv (arXiv:1104.2525).

This dark matter together with the intergalactic plasma, which is observed by the x-ray continuum from thermal bremsstrahlung, fulfils the global matter balance, even if the visible matter in galaxies amounts only to a few percent. That the balance can be fulfilled without further ingredients I have shown in the paper "An Equilibrium Balance of the Universe" (arXiv:0708.3577).

I am sceptical that, to understand the universe, we really have to reject so many fundamental assumptions as you propose in your essay. The concepts of special and general relativity are a suitable basis. We only have to apply them in a better way.

Regards,

Ernst

Rethink...

All The Mass Of The Universe Formed At The Pre-Big-Bang Singularity

The universe is a two-poles entity, an all-mass and an all-energy poles.

The elementary particle of the universe is the graviton. The gravitons are compacted into the universal inert singularity mass only for the smallest fraction of a second, when all the gravitons of the universe are compacted together, with zero distance between all of them. This state is mandated by their small size and by their hence weak force.

The big bang is the shattering of the short-lived singularity mass into fragments that later became galactic clusters. This is inflation. The shattering is the start of movement of the shatters i.e. the start of reconversion of mass into energy, which is mass in motion. This reconversion proceeds at a constant rate since the big bang since the resolution of gravitons, their release from their shatters-clusters, proceeds at constant rate due to their weak specific force due to their small size.

Dov Henis (comments from 22nd century)

http://universe-life.com/

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All The Mass Of The Universe Formed At The Pre-Big-Bang Singularity

The universe is a two-poles entity, an all-mass and an all-energy poles.

The elementary particle of the universe is the graviton. The gravitons are compacted into the universal inert singularity mass only for the smallest fraction of a second, when all the gravitons of the universe are compacted together, with zero distance between all of them. This state is mandated by their small size and by their hence weak force.

The big bang is the shattering of the short-lived singularity mass into fragments that later became galactic clusters. This is inflation. The shattering is the start of movement of the shatters i.e. the start of reconversion of mass into energy, which is mass in motion. This reconversion proceeds at a constant rate since the big bang since the resolution of gravitons, their release from their shatters-clusters, proceeds at constant rate due to their weak specific force due to their small size.

Dov Henis (comments from 22nd century)

http://universe-life.com/

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Dear Ernst,

Your well written and well argued essay (which I have read between the equations)is most interesting. Even though I don't understand all of it, I feel that I have learnt something new and also found some possible answers to the questions i ask in my own essay.

Thank you and best wishes in the contest!

Inger

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Your well written and well argued essay (which I have read between the equations)is most interesting. Even though I don't understand all of it, I feel that I have learnt something new and also found some possible answers to the questions i ask in my own essay.

Thank you and best wishes in the contest!

Inger

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Dear Inger,

I am glad that my essay has pleased you. I did enjoy your essay, too. Hoping that you will give me a high rating,

best regards,

Ernst

I am glad that my essay has pleased you. I did enjoy your essay, too. Hoping that you will give me a high rating,

best regards,

Ernst

Dear Ernst,

The present top rating of your essay is exactly where I like it to be. Not only your peers have given it high ratings, but as a lay(wo)man I too feel that you have something of great importance to say (eventhough I cannot follow your eqations but briefly). Keep the top ranking is my best wish to you!

Inger

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The present top rating of your essay is exactly where I like it to be. Not only your peers have given it high ratings, but as a lay(wo)man I too feel that you have something of great importance to say (eventhough I cannot follow your eqations but briefly). Keep the top ranking is my best wish to you!

Inger

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Dear Ernst,

You have written a well-argued essay and I am very sympathetic to your point of view. What I would like to know is, surely redefining the Energy-Momentum Tensor in the way you suggest should have observable consequences testable by direct experiment? For instance, would the application of your idea to a Pound-Rebka Experiment (possibly over a much larger distance than the original one) not give a prediction that deviates from that of standard GR? If so, I think it should be tested.

All the best,

Armin

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You have written a well-argued essay and I am very sympathetic to your point of view. What I would like to know is, surely redefining the Energy-Momentum Tensor in the way you suggest should have observable consequences testable by direct experiment? For instance, would the application of your idea to a Pound-Rebka Experiment (possibly over a much larger distance than the original one) not give a prediction that deviates from that of standard GR? If so, I think it should be tested.

All the best,

Armin

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Dear Armin,

Thank you for reading my essay. To my opinion what I have discussed in my essay is standard GR, where the action of gravity is encoded in a change of geometry by the presence of matter. The main difference to Newtonian gravity is that not only the rest energy of mass but all forms of energy contribute to gravitation. The Pound-Rebka experiment just shows that also massless particles underlie gravitation and nobody doubts that the change of frequency in these experiments is caused by take-up of potential energy. The problem in the conventional treatment of gravitational collapse by GR is that this potential energy is only taken into account to describe the behaviour of test particles in a given metric field, but not in the determination of the source term itself, expressed by the metric.

No additional effect is to be expected by the correction, introduced in my essay, for Pound-Rebka-like experiments. The contribution of the potential to the earth rest energy is negligibly small and it would show up only as a minimal change of the effective mass of the earth. Sorry that the influence of potential energy cannot be tested on earth. We must be content with the observations from the collapsed systems in space.

Best regards,

Ernst

Thank you for reading my essay. To my opinion what I have discussed in my essay is standard GR, where the action of gravity is encoded in a change of geometry by the presence of matter. The main difference to Newtonian gravity is that not only the rest energy of mass but all forms of energy contribute to gravitation. The Pound-Rebka experiment just shows that also massless particles underlie gravitation and nobody doubts that the change of frequency in these experiments is caused by take-up of potential energy. The problem in the conventional treatment of gravitational collapse by GR is that this potential energy is only taken into account to describe the behaviour of test particles in a given metric field, but not in the determination of the source term itself, expressed by the metric.

No additional effect is to be expected by the correction, introduced in my essay, for Pound-Rebka-like experiments. The contribution of the potential to the earth rest energy is negligibly small and it would show up only as a minimal change of the effective mass of the earth. Sorry that the influence of potential energy cannot be tested on earth. We must be content with the observations from the collapsed systems in space.

Best regards,

Ernst

Dear Dr. Fisher,

Thank you for clarifying the point. My original questions was motivated by the fact that already in classical physics potential energy is in a sense a shared property between the test particle and the source mass, but you are correct, the fact that the earth is much more massive does not allow your idea to be tested in this way.

However, what do you think of this possible experiment: Place two objects that are as much as possible equal in mass (and shape) at a Lagrangian point, where the earth and Sun's gravity fields cancel. Then measure their relative acceleration towards each other. It seems to me that under your idea, the relative acceleration should be very slightly higher than under standard GR. Of course, the idea needs to be quantitatively fleshed out to see whether the effect is even realistically measurable, but for now, let us just consider this in principle. Is my statement of the prediction of your idea correct?

Armin

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Thank you for clarifying the point. My original questions was motivated by the fact that already in classical physics potential energy is in a sense a shared property between the test particle and the source mass, but you are correct, the fact that the earth is much more massive does not allow your idea to be tested in this way.

However, what do you think of this possible experiment: Place two objects that are as much as possible equal in mass (and shape) at a Lagrangian point, where the earth and Sun's gravity fields cancel. Then measure their relative acceleration towards each other. It seems to me that under your idea, the relative acceleration should be very slightly higher than under standard GR. Of course, the idea needs to be quantitatively fleshed out to see whether the effect is even realistically measurable, but for now, let us just consider this in principle. Is my statement of the prediction of your idea correct?

Armin

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Dear Armin,

The experiment you propose is a nice idea, but I fear it would not work. The effect is simply too small. There is an influence of potential energy on acceleration (a reduction of acceleration, as potential energy is negative). But it is such a tiny effect that it would scarcely be measurable. For two masses of 1000 kg at a distance of 1m the quantity GM/Rc^2, which denotes the ratio between mass energy and potential energy, is in the order of 10^-24. The effect is relevant only under the extreme conditions in collapsed systems, where the matter densities are supposed to reach values in the order of 10^14 g/cm^3. Your statement is correct (apart from the wrong sign), but unfortunately it cannot help us to verify the correct treatment of GR.

Best regards,

Ernst

The experiment you propose is a nice idea, but I fear it would not work. The effect is simply too small. There is an influence of potential energy on acceleration (a reduction of acceleration, as potential energy is negative). But it is such a tiny effect that it would scarcely be measurable. For two masses of 1000 kg at a distance of 1m the quantity GM/Rc^2, which denotes the ratio between mass energy and potential energy, is in the order of 10^-24. The effect is relevant only under the extreme conditions in collapsed systems, where the matter densities are supposed to reach values in the order of 10^14 g/cm^3. Your statement is correct (apart from the wrong sign), but unfortunately it cannot help us to verify the correct treatment of GR.

Best regards,

Ernst

Ernst, what is not actual, true/real, and natural may be held to be potential; as we cannot experience outer space. The sensiblity and comprehensibility of outer space is, and will remain, lacking. Telescopic observations GENERALLY make matters even less sensible. Outer space is, in an important sense, less real. Truth and reality go together -- WITH NATURAL EXPERIENCE TOO.

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Dear Fischer,

Your introduction states that GRT is the best description of gravitational interaction. But the Newtonian concept is more simple. The perihelion shift is the only thing that cannot be explained by that classical concept.

The problem of singularity appears in Newtonian gravity also.The reason is we take the mathematical equation as a 'physical law'. If we put a physical limit to gravity, and include that in the equation, the equation can be made finite, and the singularity can thus be avoided.For example,in the case of two moving bodies, their motion physically opposes the attraction which tries to bring them together in a resultant direction.So the force components that oppose this can be represented in terms of one of the masses as (-mv^2)/d.

So in the case of a body orbiting another, gravitational energy used becomes equal to kinetic energy.That is, gravity need be balanced by kinetic energy and there need not be any static orbit. This removes the perihelion anomaly also.

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Your introduction states that GRT is the best description of gravitational interaction. But the Newtonian concept is more simple. The perihelion shift is the only thing that cannot be explained by that classical concept.

The problem of singularity appears in Newtonian gravity also.The reason is we take the mathematical equation as a 'physical law'. If we put a physical limit to gravity, and include that in the equation, the equation can be made finite, and the singularity can thus be avoided.For example,in the case of two moving bodies, their motion physically opposes the attraction which tries to bring them together in a resultant direction.So the force components that oppose this can be represented in terms of one of the masses as (-mv^2)/d.

So in the case of a body orbiting another, gravitational energy used becomes equal to kinetic energy.That is, gravity need be balanced by kinetic energy and there need not be any static orbit. This removes the perihelion anomaly also.

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1/2mv² =mgh=.........they turn so they are :)and the finite number is ....

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Ernst,

While my math skills are poor, I fully agree with your explanation of curvature on physical terms and that current theory is a simplistic abstraction of part of the process. I am concerned that in the last few lines you seems to assume a finite universe. ? As I see it, Big Bang theory is based on the same conceptual simplifications being reconstituted in physically illogical and...

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While my math skills are poor, I fully agree with your explanation of curvature on physical terms and that current theory is a simplistic abstraction of part of the process. I am concerned that in the last few lines you seems to assume a finite universe. ? As I see it, Big Bang theory is based on the same conceptual simplifications being reconstituted in physically illogical and...

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Heaven Breasts and Heaven Calculus

http://vixra.org/abs/1209.0072

Since the birth of mankind, human beings have been looking for the origin of life. The fact that human history is the history of warfare and cannibalism proves that humans have not identified their origin. Humanity is still in the dark phase of lower animals. Humans can see the phenomenon of life only on Earth, and humans' vision does not exceed the one of lower animals. However, it is a fact that human beings have inherited the most advanced gene of life. Humans should be able to answer the following questions: Is the Universe hierarchical? What is Heaven? Is Heaven the origin of life? Is Heaven a higher order of life? For more than a decade, I have done an in-depth study on barred galaxy structure. Today (September 17, 2012) I suddenly discovered that the characteristic structure of barred spiral galaxies resembles the breasts of human female essentially. If the rational structure conjecture presented in the article is proved then Sun must be a mirror of the universe, and mankind is exactly the image on earth of the Heaven.

http://galaxyanatomy.com

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http://vixra.org/abs/1209.0072

Since the birth of mankind, human beings have been looking for the origin of life. The fact that human history is the history of warfare and cannibalism proves that humans have not identified their origin. Humanity is still in the dark phase of lower animals. Humans can see the phenomenon of life only on Earth, and humans' vision does not exceed the one of lower animals. However, it is a fact that human beings have inherited the most advanced gene of life. Humans should be able to answer the following questions: Is the Universe hierarchical? What is Heaven? Is Heaven the origin of life? Is Heaven a higher order of life? For more than a decade, I have done an in-depth study on barred galaxy structure. Today (September 17, 2012) I suddenly discovered that the characteristic structure of barred spiral galaxies resembles the breasts of human female essentially. If the rational structure conjecture presented in the article is proved then Sun must be a mirror of the universe, and mankind is exactly the image on earth of the Heaven.

http://galaxyanatomy.com

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Dear Ernst Fisher,

You are right about collapse, singularities, and dark energy.

As explained in the section 7 of my essay, general relativity relies on approximating the total stress-energy tensor by the tensor for matter alone, ignoring the interaction T_{int}^{\mu\nu} and gravitational T_{grav}^{\mu\nu} components. Effectively, when one considers those components the black holes and its singularities cannot form. You consider only the potential correction, but it is easy to show that a positive 'pressure' from the gravitational component T_{grav}^{\mu\nu} impedes the collapse of massive stars and other objects. One of the traditional problems of general relativity --that of singularities-- is absent in the improved theory. You are right on that the singular states occurring in GR should be regarded as "a purely mathematical approximation".

You are also right on that adding the potential component is needed to recover conservation of energy. But we need to consider also the gravitational component T_{grav}^{\mu\nu} in the general law of conservation --eq. 26 in the reference [9] in my essay--. Your law of conservation is an approximation valid when there is not interchange between the material system and the graviton field.

In the last part of your essay you speculate that the potential energy of matter would play the role of dark energy in a cosmological context. Again this is right! When we consider the missing terms in general relativity we arrive to the general equation (27) in the reference [9] in my Essay. I already computed the 'dark energy' term T_{DE}^{\mu\nu} in equation (27) and I got that it predicts a cosmological constant \Lambda in excellent agreement with last observations. Of course, the physical interpretation is different, it is not a true constant such as h or c but a parameter of our universe such as density.

Regards.

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You are right about collapse, singularities, and dark energy.

As explained in the section 7 of my essay, general relativity relies on approximating the total stress-energy tensor by the tensor for matter alone, ignoring the interaction T_{int}^{\mu\nu} and gravitational T_{grav}^{\mu\nu} components. Effectively, when one considers those components the black holes and its singularities cannot form. You consider only the potential correction, but it is easy to show that a positive 'pressure' from the gravitational component T_{grav}^{\mu\nu} impedes the collapse of massive stars and other objects. One of the traditional problems of general relativity --that of singularities-- is absent in the improved theory. You are right on that the singular states occurring in GR should be regarded as "a purely mathematical approximation".

You are also right on that adding the potential component is needed to recover conservation of energy. But we need to consider also the gravitational component T_{grav}^{\mu\nu} in the general law of conservation --eq. 26 in the reference [9] in my essay--. Your law of conservation is an approximation valid when there is not interchange between the material system and the graviton field.

In the last part of your essay you speculate that the potential energy of matter would play the role of dark energy in a cosmological context. Again this is right! When we consider the missing terms in general relativity we arrive to the general equation (27) in the reference [9] in my Essay. I already computed the 'dark energy' term T_{DE}^{\mu\nu} in equation (27) and I got that it predicts a cosmological constant \Lambda in excellent agreement with last observations. Of course, the physical interpretation is different, it is not a true constant such as h or c but a parameter of our universe such as density.

Regards.

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Dear Juan R. González-Álvarez

You are right that the approximation of the stress-energy tensor by the tensor for matter alone is not correct. But it is the basic concept of general relativity that there is no gravitational field which contains energy or momentum. Instead the effect of gravitation is encoded in the geometry of space-time. So there is no component T_{grav}^{\mu\nu} in the energy tensor. But this does not imply that the interaction part T_{int}^{\mu\nu} is zero, too. While field energy of the gravitational field should depend on the square of the deviation from Minkowskian geometry, the interaction term depends linearly on the matter distribution and on the deviation parameter of the geometry. What I have done is just to include this interaction term into the balance.

It is this interaction term, which is sufficient to avoid the formation of singularities not only in the so called black holes, but also the Big Bang singularity as a starting point of the universe. It can replace the dark energy, but the fact remains that there must be some kind of dark matter, which influences the dynamics of galaxies and clusters. After all I think that general relativity is not so bad. We only have to apply the mathematics of curved space-time in the correct way. In my essay I mentioned that with inclusion of the interaction term (or potential energy term) a stable static solution of the Einstein equation is possible. The attempt to explain all cosmological observations within such a model, you can find in an article which I sent to arXiv some years ago (An equilibrium balance of the universe, arXiv:0708.3577 )

I hope that your datermination of the cosmological term leads to the same result, which I have used as derived from the Hubble constant.

Regards,

Ernst

You are right that the approximation of the stress-energy tensor by the tensor for matter alone is not correct. But it is the basic concept of general relativity that there is no gravitational field which contains energy or momentum. Instead the effect of gravitation is encoded in the geometry of space-time. So there is no component T_{grav}^{\mu\nu} in the energy tensor. But this does not imply that the interaction part T_{int}^{\mu\nu} is zero, too. While field energy of the gravitational field should depend on the square of the deviation from Minkowskian geometry, the interaction term depends linearly on the matter distribution and on the deviation parameter of the geometry. What I have done is just to include this interaction term into the balance.

It is this interaction term, which is sufficient to avoid the formation of singularities not only in the so called black holes, but also the Big Bang singularity as a starting point of the universe. It can replace the dark energy, but the fact remains that there must be some kind of dark matter, which influences the dynamics of galaxies and clusters. After all I think that general relativity is not so bad. We only have to apply the mathematics of curved space-time in the correct way. In my essay I mentioned that with inclusion of the interaction term (or potential energy term) a stable static solution of the Einstein equation is possible. The attempt to explain all cosmological observations within such a model, you can find in an article which I sent to arXiv some years ago (An equilibrium balance of the universe, arXiv:0708.3577 )

I hope that your datermination of the cosmological term leads to the same result, which I have used as derived from the Hubble constant.

Regards,

Ernst

Dear Ernst,

Effectively, general relativity is obtained in the limit when both the gravitational field and the interaction part T_{int}^{\mu\nu} are neglected, leaving a purely geometrical description of gravitation.

You say that the "field energy of the gravitational field should depend on the square of the deviation from Minkowskian geometry". The field depends on the gravitational potential h_{\mu\nu}, which in general diverges from the deviation from Minkoskian geometry. Only in a weak field limit both coincide [9]. Moreover, the interaction term depends linearly on the matter distribution only as a first approximation. This term is much more complex because gravitons also interact with the linear interaction term.

Yes, you reintroduce partially the missing interaction part, providing a modification of general relativity. I agree with that modification. Precisely in [9] I wrote the generalized equation (27), with terms that replace dark matter and dark energy. Computation of those new term is in agreement with observations --including observations which are in conflict with dark matter models--. Neither dark matter nor dark energy are needed anymore.

As stated in [9], a modification of GR that includes only a generalization of the ordinary source T^{\mu\nu} is a bit "tricky". Why? Because you cannot arbitrarily modify the right-hand side of the Hilbert-Einstein equations without modifying the left-hand side as well. Fortunately you can still use Einstein tensor for weak fields, but for strong fields this tensor has to be extended as well.

Regards

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Effectively, general relativity is obtained in the limit when both the gravitational field and the interaction part T_{int}^{\mu\nu} are neglected, leaving a purely geometrical description of gravitation.

You say that the "field energy of the gravitational field should depend on the square of the deviation from Minkowskian geometry". The field depends on the gravitational potential h_{\mu\nu}, which in general diverges from the deviation from Minkoskian geometry. Only in a weak field limit both coincide [9]. Moreover, the interaction term depends linearly on the matter distribution only as a first approximation. This term is much more complex because gravitons also interact with the linear interaction term.

Yes, you reintroduce partially the missing interaction part, providing a modification of general relativity. I agree with that modification. Precisely in [9] I wrote the generalized equation (27), with terms that replace dark matter and dark energy. Computation of those new term is in agreement with observations --including observations which are in conflict with dark matter models--. Neither dark matter nor dark energy are needed anymore.

As stated in [9], a modification of GR that includes only a generalization of the ordinary source T^{\mu\nu} is a bit "tricky". Why? Because you cannot arbitrarily modify the right-hand side of the Hilbert-Einstein equations without modifying the left-hand side as well. Fortunately you can still use Einstein tensor for weak fields, but for strong fields this tensor has to be extended as well.

Regards

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Dear Uncle Ernst Fischer

Using measures of the Mathematics subjects to determine : how are "dark" and "mysterious"?

With all due respect and best wishes!

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Using measures of the Mathematics subjects to determine : how are "dark" and "mysterious"?

With all due respect and best wishes!

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Ernst Fischer,

Congratulations, your excellent essay is in the top 35 essays of this contest.

Please answer my final two questions on your essay.

1. As a final conclusion of your essay, which of our 'Basic Physical Assumptions' are wrong in your opinion?

2. As per the main thrust of your essay, you are proposing to include the potential energy term in the EFE of GR. Assuming the existing framework of GR yields the correct (as per current observations) dynamic and kinematic solutions for the motion of earth in our solar system, what changes the inclusion of your 'potential energy' term will introduce in such solutions for the motion of earth in our solar system?

Anonymous

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Congratulations, your excellent essay is in the top 35 essays of this contest.

Please answer my final two questions on your essay.

1. As a final conclusion of your essay, which of our 'Basic Physical Assumptions' are wrong in your opinion?

2. As per the main thrust of your essay, you are proposing to include the potential energy term in the EFE of GR. Assuming the existing framework of GR yields the correct (as per current observations) dynamic and kinematic solutions for the motion of earth in our solar system, what changes the inclusion of your 'potential energy' term will introduce in such solutions for the motion of earth in our solar system?

Anonymous

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Dear Anonymus,

The basic assumption which is wrong in the current description of garavity by general relativiy is that energy conservation should be valid only locally, but not on global scale. The effects of gravitation on the definition of energy density are ommitted in the energy tensor.

Solutions of GR for the motion of the earth in the solar system are only marginally affected by the inclusion of potential energy, as the ratio of potential energy of the earth to its mass energy Mc^2 in the gravitational field of the sun is of the order 10^-8. That means that for the time span for which observations or fossil records of the system earth-sun exist, no significant effects are expected. Only on the scale of the Hubble time changes are expected, as angular momentum may have been changed by transfer of kinetic energy to potential energy. But such effects result only from the Lorentz invariance of GR together with the inclusion of potential energy. In my essay I have only considered equilibrium situations, though, of course, exact static equilibria are not possible, when there is motion of any form. The description of highly dynamical processes like the actual gravitational collapse of stars or galaxies and the formation of matter jets from these systems may be strongly influenced by the inclusion of potential energy.

Regards,

Ernst Fischer

The basic assumption which is wrong in the current description of garavity by general relativiy is that energy conservation should be valid only locally, but not on global scale. The effects of gravitation on the definition of energy density are ommitted in the energy tensor.

Solutions of GR for the motion of the earth in the solar system are only marginally affected by the inclusion of potential energy, as the ratio of potential energy of the earth to its mass energy Mc^2 in the gravitational field of the sun is of the order 10^-8. That means that for the time span for which observations or fossil records of the system earth-sun exist, no significant effects are expected. Only on the scale of the Hubble time changes are expected, as angular momentum may have been changed by transfer of kinetic energy to potential energy. But such effects result only from the Lorentz invariance of GR together with the inclusion of potential energy. In my essay I have only considered equilibrium situations, though, of course, exact static equilibria are not possible, when there is motion of any form. The description of highly dynamical processes like the actual gravitational collapse of stars or galaxies and the formation of matter jets from these systems may be strongly influenced by the inclusion of potential energy.

Regards,

Ernst Fischer

Dear Ernst,

I think that < singular states occurring in GRT should be regarded as a purely mathematical approximation> as in your essay. I agree with you that < There is no horizon, from which no escape of matter or radiation is possible and black holes as singular points of infinite density cannot exist.> It seems there is a misprint in the second part of the formula (7) of your essay. May be it will be interesting for you: Covariant theory of gravitation .

Sergey Fedosin

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I think that < singular states occurring in GRT should be regarded as a purely mathematical approximation> as in your essay. I agree with you that < There is no horizon, from which no escape of matter or radiation is possible and black holes as singular points of infinite density cannot exist.> It seems there is a misprint in the second part of the formula (7) of your essay. May be it will be interesting for you: Covariant theory of gravitation .

Sergey Fedosin

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Dear Ernst,

I must commend you on your excellent responses to so many commentators. As have so many others, I have also found your topic to be stimulating for some time. I must explain though that I'm a simple retired information systems analyst with no education or background in physics and only simple math. I think you can determine much from the descriptive title of my essay, Inappropriate Application of Kepler's Empirical Laws of Planetary Motion to Spiral Galaxies Created the Perceived Galaxy Rotation Problem - Thereby Establishing a Galactic Presence for the Elusive, Inferred Dark Matter. All that said, if you can bear with some improper terminology I'd very much appreciate your brief consideration...

It's obvious that no amount of physical matter could possibly fit within a dimensionless singularity, yet SMBHs have observationally been confirmed to represent at least some exceeding compact enormously massive object.

Considering what form of physical matter might produce such a dense mass, the next densest material object should be evaluated. As I understand, Neutron stars, produced by gravitational collapse, are thought to consist mostly of neutrons, with a core that may contain a hyperdense free quark-gluon plasma. This poses a problem, since these are the densest forms of matter known, yet Neutron stars do not seem to approach the density or compact gravitational characteristics exhibited by SMBHs.

It seems clear then that no form of physical matter could produce the properties required of a black hole singularity, yet the existence of some type of object more dense and compact than a Neutron star has been confirmed.

I suggest that these conditions require the separation of matter's dimensional occupancy requirements from its potential mass-energy capacity for producing gravitational effects (described in GRT as the curvature of spacetime).

Accreted massive objects are decomposed and their constituent atoms seem to be disintegrated by the processing of the extreme conditions of compaction and collision while being accelerated toward the event horizon. If in fact all these material elements are ejected as streams of high energy fundamental particles, x rays and gamma rays, perhaps even the potential mass energy previously configured within the processed materials is separated, analogous to the dispersal of elementary particles and mass produced by high energy particle colliders.

In this case, I suggest that only the potential mass-energy of ejected material is retained within the event horizon, that it collectively distorts spacetime to be exceedingly curved in relation to a single geometric focal point - a singularity. The singularity is simply to focus of retained potential energy while all dimensional matter has been extracted and ejected through the relativistic polar jets.

This scenario is speculative if not even fanciful, of course, but would allow the coexistence of effective singularities without unphysical states of matter and the appearance of relativistic jets.

I'd be very pleased if you can consider these 'wild' ideas briefly and comment freely.

Sincerely, Jim

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I must commend you on your excellent responses to so many commentators. As have so many others, I have also found your topic to be stimulating for some time. I must explain though that I'm a simple retired information systems analyst with no education or background in physics and only simple math. I think you can determine much from the descriptive title of my essay, Inappropriate Application of Kepler's Empirical Laws of Planetary Motion to Spiral Galaxies Created the Perceived Galaxy Rotation Problem - Thereby Establishing a Galactic Presence for the Elusive, Inferred Dark Matter. All that said, if you can bear with some improper terminology I'd very much appreciate your brief consideration...

It's obvious that no amount of physical matter could possibly fit within a dimensionless singularity, yet SMBHs have observationally been confirmed to represent at least some exceeding compact enormously massive object.

Considering what form of physical matter might produce such a dense mass, the next densest material object should be evaluated. As I understand, Neutron stars, produced by gravitational collapse, are thought to consist mostly of neutrons, with a core that may contain a hyperdense free quark-gluon plasma. This poses a problem, since these are the densest forms of matter known, yet Neutron stars do not seem to approach the density or compact gravitational characteristics exhibited by SMBHs.

It seems clear then that no form of physical matter could produce the properties required of a black hole singularity, yet the existence of some type of object more dense and compact than a Neutron star has been confirmed.

I suggest that these conditions require the separation of matter's dimensional occupancy requirements from its potential mass-energy capacity for producing gravitational effects (described in GRT as the curvature of spacetime).

Accreted massive objects are decomposed and their constituent atoms seem to be disintegrated by the processing of the extreme conditions of compaction and collision while being accelerated toward the event horizon. If in fact all these material elements are ejected as streams of high energy fundamental particles, x rays and gamma rays, perhaps even the potential mass energy previously configured within the processed materials is separated, analogous to the dispersal of elementary particles and mass produced by high energy particle colliders.

In this case, I suggest that only the potential mass-energy of ejected material is retained within the event horizon, that it collectively distorts spacetime to be exceedingly curved in relation to a single geometric focal point - a singularity. The singularity is simply to focus of retained potential energy while all dimensional matter has been extracted and ejected through the relativistic polar jets.

This scenario is speculative if not even fanciful, of course, but would allow the coexistence of effective singularities without unphysical states of matter and the appearance of relativistic jets.

I'd be very pleased if you can consider these 'wild' ideas briefly and comment freely.

Sincerely, Jim

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Dear Jim,

You correctly state that no finite amount of matter can fit into a dimensionless singularity. But the compact centers of galaxies, the SMBHs are not such singular point masses. It is only that the (wrong) balance equations of the conventional GR treatment lead to the assumption that there exists an upper limit for the mass of collapsed objects, which are stabilized by degeneracy pressure of neutrons (or possibly by a quark gluon plasma).

By the way, there is no observational evidence that the SMBHs in the centers of galaxies must have a density much higher than neutron stars. At present by observations even for the milky way spatial resolution is about two orders of magnitude less than necessary to discriminete objects of the size of an alledged event horizon.

As you have written, in this highly condensed state, be it a pure neutron plasma or some more exotic state consisting of quarks, gluons or other high energy elementary particles, ordinary atomic species cannot exist, but will be formed only in the jets, which emanate from the collapsed cores. But there is no event horizon inside which matter can be included without the possibility to be recycled into space.

The existence of event horizons is only a consequence of the inaccurate application of differential geometry to the problem of gravitation. Physics in curved space differs more from Euclidean geometry than assumed in conventional treatment of gravitational interaction. Quantities like density lose their innate meaning, when volume is no longer a conserved quantity but is subject to dynamical changes.

As I think that there exist no event horizons, I cannot agree with your idea of the existence of a singular focal point of potential energy. To my opinion potential energy must be directly coupled to matter. It is the response of matter to being surrounded by other matter or energy fields.

I hope that my comments will stimulate your thoughts to further ideas on gravity. Your comments were helpful in the discussion.

Regards,

Ernst

You correctly state that no finite amount of matter can fit into a dimensionless singularity. But the compact centers of galaxies, the SMBHs are not such singular point masses. It is only that the (wrong) balance equations of the conventional GR treatment lead to the assumption that there exists an upper limit for the mass of collapsed objects, which are stabilized by degeneracy pressure of neutrons (or possibly by a quark gluon plasma).

By the way, there is no observational evidence that the SMBHs in the centers of galaxies must have a density much higher than neutron stars. At present by observations even for the milky way spatial resolution is about two orders of magnitude less than necessary to discriminete objects of the size of an alledged event horizon.

As you have written, in this highly condensed state, be it a pure neutron plasma or some more exotic state consisting of quarks, gluons or other high energy elementary particles, ordinary atomic species cannot exist, but will be formed only in the jets, which emanate from the collapsed cores. But there is no event horizon inside which matter can be included without the possibility to be recycled into space.

The existence of event horizons is only a consequence of the inaccurate application of differential geometry to the problem of gravitation. Physics in curved space differs more from Euclidean geometry than assumed in conventional treatment of gravitational interaction. Quantities like density lose their innate meaning, when volume is no longer a conserved quantity but is subject to dynamical changes.

As I think that there exist no event horizons, I cannot agree with your idea of the existence of a singular focal point of potential energy. To my opinion potential energy must be directly coupled to matter. It is the response of matter to being surrounded by other matter or energy fields.

I hope that my comments will stimulate your thoughts to further ideas on gravity. Your comments were helpful in the discussion.

Regards,

Ernst

Dear Ernst,

Yes, I was merely presuming the common general conception of black holes and applying them to galactic SMBHs. However, as I understand the most massive pulsar observed is thought to be less than 2 Solar masses, while the total mass of the SMBH at center of the Milky Way has been estimated at more than 4 million Solar masses based on the orbital characteristics of nearby stars. It would seem that even unknown exotic forms of degenerate matter would have finite limits in their degeneracy pressure, limiting the total mass of any physical object. I can't reasonably evaluate, though.

The rational for separation of configured mass energy from quantum particles comes directly from the disintegration of massive particles in collider experiments. It seems that in such cases potential mass energy is thought to be dissipated into the environment through the manifestation of short-lived exotic particles. However, within an exceedingly dense gravitational field (I think only indirectly described in GRT through changing dimensional coordinates of spacetime), the potential energy of particle mass might be imparted directly as gravitational effects (curving spacetime). That particles of matter can disintegrate, including their configured potential mass-energy, seems to have been definitively established by collider experiments...

I do very much appreciate you consideration and realize that I'm only skimming the surface of possibilities, without fully establishing any basis for my interpretation within the context of physical laws. That's so much easier...

Sincerely, Jim

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Yes, I was merely presuming the common general conception of black holes and applying them to galactic SMBHs. However, as I understand the most massive pulsar observed is thought to be less than 2 Solar masses, while the total mass of the SMBH at center of the Milky Way has been estimated at more than 4 million Solar masses based on the orbital characteristics of nearby stars. It would seem that even unknown exotic forms of degenerate matter would have finite limits in their degeneracy pressure, limiting the total mass of any physical object. I can't reasonably evaluate, though.

The rational for separation of configured mass energy from quantum particles comes directly from the disintegration of massive particles in collider experiments. It seems that in such cases potential mass energy is thought to be dissipated into the environment through the manifestation of short-lived exotic particles. However, within an exceedingly dense gravitational field (I think only indirectly described in GRT through changing dimensional coordinates of spacetime), the potential energy of particle mass might be imparted directly as gravitational effects (curving spacetime). That particles of matter can disintegrate, including their configured potential mass-energy, seems to have been definitively established by collider experiments...

I do very much appreciate you consideration and realize that I'm only skimming the surface of possibilities, without fully establishing any basis for my interpretation within the context of physical laws. That's so much easier...

Sincerely, Jim

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Dear Ernst, I hope this finds you well.

Hello. This is group message to you and the writers of some 80 contest essays that I have already read, rated and probably commented on.

This year I feel proud that the following old and new online friends have accepted my suggestion that they submit their ideas to this contest. Please feel free to read, comment on and rate these essays (including mine) if you have not already done so, thanks:

Why We Still Don't Have Quantum Nucleodynamics by Norman D. Cook a summary of his Springer book on the subject.

A Challenge to Quantized Absorption by Experiment and Theory by Eric Stanley Reiter Very important experiments based on Planck's loading theory, proving that Einstein's idea that the photon is a particle is wrong.

An Artist's Modest Proposal by Kenneth Snelson The world-famous inventor of Tensegrity applies his ideas of structure to de Broglie's atom.

Notes on Relativity by Edward Hoerdt Questioning how the Michelson-Morely experiment is analyzed in the context of Special Relativity

Vladimir Tamari's essay Fix Physics! Is Physics like a badly-designed building? A humorous illustrate take. Plus: Seven foundational questions suggest a new beginning.

Thank you and good luck.

Vladimir

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Hello. This is group message to you and the writers of some 80 contest essays that I have already read, rated and probably commented on.

This year I feel proud that the following old and new online friends have accepted my suggestion that they submit their ideas to this contest. Please feel free to read, comment on and rate these essays (including mine) if you have not already done so, thanks:

Why We Still Don't Have Quantum Nucleodynamics by Norman D. Cook a summary of his Springer book on the subject.

A Challenge to Quantized Absorption by Experiment and Theory by Eric Stanley Reiter Very important experiments based on Planck's loading theory, proving that Einstein's idea that the photon is a particle is wrong.

An Artist's Modest Proposal by Kenneth Snelson The world-famous inventor of Tensegrity applies his ideas of structure to de Broglie's atom.

Notes on Relativity by Edward Hoerdt Questioning how the Michelson-Morely experiment is analyzed in the context of Special Relativity

Vladimir Tamari's essay Fix Physics! Is Physics like a badly-designed building? A humorous illustrate take. Plus: Seven foundational questions suggest a new beginning.

Thank you and good luck.

Vladimir

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After studying about 250 essays in this contest, I realize now, how can I assess the level of each submitted work. Accordingly, I rated some essays, including yours.

Cood luck.

Sergey Fedosin

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Cood luck.

Sergey Fedosin

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Your essay seems well appreciated by the community- congratulations : ) Georgina

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If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is and was the quantity of people which gave you ratings. Then you have of points. After it anyone give you of points so you have of points and is the common quantity of the people which gave you ratings. At the same time you will have of points. From here, if you want to be R2 > R1 there must be: or or In other words if you want to increase rating of anyone you must give him more points then the participant`s rating was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

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Sergey Fedosin

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Dear Ernst,

You are right about the point that gravitational collapse does not lead to multiple singularities, as there is only one singularity - the universe itself. The universe is in a "Steady Big Bang State". The question you pose is similar to what happens when one dies? Answer is one just trasnforms in to anothoer being.

who am I? I "am" a variant, i is the constant.

Please see Conscience is the cosmological constant.

Absolute truth is zero = i = infinity.

Theory (divine view) of everything is that there is absolutely nothing but "i".

Love,

Sridattadev.

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You are right about the point that gravitational collapse does not lead to multiple singularities, as there is only one singularity - the universe itself. The universe is in a "Steady Big Bang State". The question you pose is similar to what happens when one dies? Answer is one just trasnforms in to anothoer being.

who am I? I "am" a variant, i is the constant.

Please see Conscience is the cosmological constant.

Absolute truth is zero = i = infinity.

Theory (divine view) of everything is that there is absolutely nothing but "i".

Love,

Sridattadev.

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Dear Ernst Fischer,

Potential energy described in Coherently-cyclic cluster-matter paradigm of universe, is the tensor product on eigen-rotation of a string-segment in that its inertial angular-velocity is causal for that potential energy. Thus the potential energy of an eigen-rotational string-segment is equivalent to the inertial angular kinetic energy of that string-segment. As the angular kinetic energy of an eigen-rotational string-segment is conserved by homeomorphism with other coherent eigen-rotational string-segments, no gravitational collapse of that string-segment and no gravitational singularity are expressional in this paradigm, in that the dark energy is the energy of non-observational eigen-rotational dark matter of strings in the holarchy of universe.

With best wishes

Jayakar

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Potential energy described in Coherently-cyclic cluster-matter paradigm of universe, is the tensor product on eigen-rotation of a string-segment in that its inertial angular-velocity is causal for that potential energy. Thus the potential energy of an eigen-rotational string-segment is equivalent to the inertial angular kinetic energy of that string-segment. As the angular kinetic energy of an eigen-rotational string-segment is conserved by homeomorphism with other coherent eigen-rotational string-segments, no gravitational collapse of that string-segment and no gravitational singularity are expressional in this paradigm, in that the dark energy is the energy of non-observational eigen-rotational dark matter of strings in the holarchy of universe.

With best wishes

Jayakar

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