# Thread: Solution of the Singularity Problem of Black Hole!

1. ## Solution of the Singularity Problem of Black Hole!

I'm sorry! I can't speak English well.

[ Solution of the Singularity Problem of Black Hole ]

1. Understanding of the problem : Generation of singularity

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We assume that the solution for this singularity consists in quantum mechanics. Though exact explanation is not available because quantum gravity theory in integration of quantum mechanics and gravity has not been completed yet.

This writing will prove that an object of positive energy has the minimum size for its existence and that since this size is in proportion to that of energy, there is no singularity with infinite density.

2. Solution of the problem

2-1. Gravitational potential energy with negative values.

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2-1-2. All energies are a gravitational source.

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2-1-3. (except r=0) is considered to provide consequently the right explanation for all points.

Teachers and professors have explained that it is alright to set the randomly reference point for gravitational potential energy because, since the variation of gravitational potential energy has caused kinetic change in the problem under review, there was no problem in dealing with only the variation of gravitational potential energy.

From the equation K + U = const. we obtain such equation as , which can explain motion with variation, but this neither means that all observers in the same inertial system may set randomly reference point at random nor confirms that U is an object with an optional value.

Let's consider the following case that the value of gravitational potential energy has been fixed for the distance of 0 to infinity from gravitational source.

Even though, as above, gravitational potential energy has the value of energy defined for r= 0 to r= infinity from gravitational source, we can obtain the right result in a problem in which its variation matters.

2-1-4. Effect of mass defect in atomic scale caused by binding energy

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2-2. Gravitational self-energy or Gravitational binding energy

The concept of gravitational self-energy is the total of gravitational potential energy possessed by a certain object M itself. Since a certain object M itself is a binding state of infinitesimal mass dM, it involves the existence of gravitational potential energy among these dMs and is the value of adding up these.

Fig06. Since all mass M is a set of infinitesimal mass dMs and each dM is gravitational source, too, there exists gravitational potential energy among each of dMs. Generally, gravitational potential energy by infinitesimal mass that consists of an object itself is reflected on the mass of the object itself. Mass of an object measured from its outside corresponds to the value of dividing the total of all energy into .

Gravitational self-energy or Gravitational binding energy() in case of uniform density is given by:

( : gravitational self-energy)

2-3. For black hole or singularity, never fail to consider gravitational self-energy

In the generality of cases, the value of gravitational self-energy is small enough to be negligible, compared to mass energy . So generally, there was no need to consider gravitational self-energy. However the smaller R becomes, the higher the absolute value of . For this reason, we can see that is likely to offset the mass energy in a certain radius.

Thus, looking for the size in which gravitational self-energy becomes equal to rest mass energy by comparing both,

This equation means that if mass is uniformly distributed within the radius , gravitational self-energy for such an object equals mass energy in size. So, in case of such an object, mass energy and gravitational self-energy can be completely offset while total energy is zero. Since total energy of such an object is 0, gravity exercised on another object outside is also 0.

Comparing with , the radius of Schwarzschild black hole,

This means that there exists the point where gravitational self-energy becomes equal to mass energy within the radius of black hole, and that, supposing a uniform distribution, the value exists at the point , a 30% level of the black hole radius. Even with kinetic energy and virial theorem applied only the radius diminishes as negative energy counterbalances positive energy, but no effects at all on this point: "there is a zone which cannot be compressed anymore due to the negative gravitational potential energy (a sort of the binding energy)")

Since this value is on a level not negligible against the size of black hole, we should never fail to consider "gravitational self-energy'' for case of black hole.
Last edited by icarus2; 2017-Jul-21 at 07:07 AM.

2. ## Black hole does not have a singularity and there exists a uniform energy density zone

2-4. Black hole does not have a singularity and there exists a zone that has a uniform energy density or that cannot be compressed anymore within the black hole.

From the equation above, even if some particle comes into the radius of black hole, it is not a fact that it contracts itself infinitely to the point R=0. From the point , gravity is 0, and when it enters into the area of , total energy within region corresponds to negative values enabling antigravity to exist.

This region comes to exert repulsive effects of gravity on the particles outside of it, therefore it interrupting the formation of singularity at the near the area R=0.

Fig.07. (a)Existing Model. (b)New Model. The area of within has gravitational self-energy of negative value, which is larger than mass energy of positive value. This area (within ) exercises anti-gravity on all particles entering this area, and accordingly prevents all masses from gathering to r=0. Therefore the distribution of mass (energy) can't be reduced to at least radius .

However, it still can perform the function as black hole because is only 30% of with a large difference in volume and, comparing total mass, it still can correspond to a very large quantity of mass. Therefore, it still can perform the function as black hole on the objects outside of .

2-5. The minimal size of existence

[ Existence = the sum of infinitesimal existences composing an existence ]

A single mass M for some object means that it can be expressed as and, for energy, . The same goes for elementary particles, which can be considered a set of dMs, the infinitesimal mass.

The equation above means that if masses are uniformly distributed within the radius , the size of negative binding energy becomes equal to that of mass energy. This can be the same that the rest mass, which used to be free for the mass defect effect caused by binding energy, has all disappeared. This means the total energy value representing “some existence” coming to 0 and “extinction of the existence”. Therefore, is considered to act as “the minimal radius” or “a bottom line” of existence with some positive energy.

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2-6. Expansion of the general relativity

2-6-1. We can solve the problem of singularity by separating the term() of gravitational self-energy from mass and including it in the solutions of field equation.

M -->

In the Schwarzschild solution,

For the sphere with uniform density,

In general, , so we get the Schwarzschild solution. But we should never fail to consider "gravitational self-energy'' for case of black hole.

1)If , we get the Schwarzschild solution.
2)If ,

i) , By eq.(47)

ii)
The area of within has gravitational self-energy of negative value, which is larger than mass energy of positive value. This area(within ) exercises antigravity on all particles entering this area anew, and accordingly prevents all masses from gathering to r=0.

Besides, negative mass has gravitation effect which is repulsive to each other. Therefore, we can assume that is almost evenly distributed. Therefore is constant. And we must consider the Shell Theorem.

If ,

There is no singularity.

In practice, gravitational contraction(collapse) must be stopped at the point where .

For Schwarzschild black hole, the Kretschmann scalar is,

In the preexisting model, if , it does diverse.

However, this model is

If ,

It does not diverge. Therefore,
Black hole doesn't have singularity.
Last edited by icarus2; 2017-Jul-21 at 12:14 PM.

3. ## The distribution of energy can't be reduced to at least radius R_gs.

Waiting for quantum gravity theory to be completed to solve the singularity issue in a black hole is wrong as it was made by our stereotypes.

When there occurred a problem in singular "point", one dimensional idea that problems should be solved from , wavelength that has a little bigger than "point" was partially acted. Of course, we should try to establish a quantum gravity theory for other reasons.

We can think of a black hole of big size and approach this problem by reducing the mass of this black hole. In other words, we should form a certain internal structure of usual size and apply the experience that we had applied the limit.

If you are still uncomfortable with , think about a black hole with the size 10 billion times bigger than the solar mass. Schwarzschild radius of this black hole is and of this black hole . Average density of this black hole is about . However average density of the Earth is about .

Is it a size that requires quantum mechanics?
Is it a high density state that requires quantum mechanics?
Black hole of this size is Newtonian mechanics’ object and therefore, gravitational potential energy must be considered.

Let's reduce the mass of this black hole gradually and approach three times the solar mass, the smallest size of black hole where stars can be formed!

In case of the smallest black hole with three times the solar mass, about . of this object is as far as 3km. In other words, even in a black hole with smallest size that is made by the contraction of a star, the distribution of internal mass can't be reduced to at least radius 3km().

Gravitational self-energy can provide the concept of minimal size, one of the reasons for introducing string theory.
In quantum mechanics we could think of De Broglie’s matter wave theory about length of some objects.

However this formula does restrict the upper limit of velocity to c, but does not have the upper limit for mass. In other words this implies there is no lower limit of wavelength. It's the same with Heisenberg’s Uncertainty Principle.

Furthermore, 0.02 milligram of Planck mass() they introduced is not even the size for the role of upper or lower limit among "". Since Planck mass cannot perform a role as the upper limit, Planck length, inversely related to the Planck mass, cannot do a role of lower limit either.

Planck mass and length means that "within such a size we should consider the quantum mechanical effects." but does not indicate "no more or no less can exist."

To remove singularity, considering gravitational self-energy is only enough without need to assume some minimal unit like a string. Thus, the existing relations need to be transformed so that they may include the minimal length by dint of gravitational self-energy.

Black hole does not have a singularity and there exists a zone that has a uniform energy density within the black hole. The distribution of mass (energy) can't be reduced to at least radius . Gravitational self-energy can solve singularity problem and rescue general relativity that collapses itself. Also it can be grounds for the expansion in the early universe and the uniform universe.

==========
#Paper
On Problems and Solutions of General Relativity. (Commemoration of the 100th Anniversary of General Relativity)
https://www.researchgate.net/publication/287217009
https://www.researchgate.net/publication/313314666
Last edited by icarus2; 2017-Jul-21 at 07:19 AM.

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Originally Posted by icarus2
I'm sorry! I can't speak English well.
Hi icarus2. A tiny suggestion - there is no need to color your text. There is also no need to repeat what is easily available elsewhere, e.g. Wikipedia has an article on Gravitational potential energy.

Originally Posted by icarus2
Solution of the Singularity Problem of Black Hole
The big problem with your ATM idea is that a collapsing body does not stop collapsing when gravitational self-energy = rest mass as energy. The collapse stops when the force of the pressure within the body matches the gravitational force of the mass. A well known example of this is the formation of stars. They collapse until their pressure balances gravitation.

Do your calculation for the Earth. What is the predicted size of the Earth? What is the actual size of the Earth?

This makes your next two posts unneeded - your solution is wrong.

A small point: Planck mass and Planck length are not anything physically special. They are the mass and length in the Planck units which are one of many units of measurement, e.g. the SI units of kilogram, meter, etc.
Last edited by Reality Check; 2017-Jul-25 at 01:49 AM.

5. OMG! I can't see! I have been thoroughly blinded by science!

OMG! I can't see! I have been thoroughly blinded by science!

7. Originally Posted by Reality Check
The big problem with your ATM idea is that a collapsing body does not stop collapsing when gravitational self-energy = rest mass as energy. The collapse stops when the force of the pressure within the body matches the gravitational force of the mass. A well known example of this is the formation of stars. They collapse until their pressure balances gravitation.

Do your calculation for the Earth. What is the predicted size of the Earth? What is the actual size of the Earth?
The singularity problem is a problem that occurs inside the black hole.

The general black hole is the object that the gravitational collapse overcomes electron degeneracy pressure and other pressure. And gravitational collapse continues to exist in the black hole, too. Thus, in the central part of black hole exists a point with infinite density of mass (or total mass), which point we call singularity.

In the general relativity that has been acknowledged to date, there is no mechanism to prevent this gravitational collapse inside the black hole. Therefore, it is claimed that a black hole necessarily forms a singularity inside.

In my paper,
In the process of collecting all the masses inside the black hole at the singular point, it must pass the point where R = R_gs.
And when R < R_gs is reached, there is a repulsive force due to gravitational self-energy, so that it does not form a singularity.
Last edited by icarus2; 2017-Jul-27 at 01:46 PM.

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Originally Posted by icarus2
The singularity problem is a problem that occurs inside the black hole.

The general black hole is the object that the gravitational collapse overcomes electron degeneracy pressure and other pressure. And gravitational collapse continues to exist in the black hole, too. Thus, in the central part of black hole exists a point with infinite density of mass (or total mass), which point we call singularity.
Correct - that is the known and working laws of physics that form a black hole.

Originally Posted by icarus2
In the general relativity that has been acknowledged to date, there is no mechanism to prevent this gravitational collapse inside the black hole.
It is the other known and working laws of physics (not GR) that state there is no mechanism to stop the gravitational. That mechanism must be a pressure.

Gravitational self-energy is not a pressure or a force! So time for formal questions.
IF01: What do you think gravitational self-energy is, icarus2?
N.B self-energy is also called binding energy since it is the amount of energy needed to disassemble a object.

IF02: How does gravitational self-energy provide a pressure between quarks to stop them getting closer together, icarus2?
Quarks because when the neutron degeneracy pressure is overcome, the neutrons are squeezed together to form quark matter.

IF03: Apply your theory to the Earth - what does it predict for the radius of the Earth, icarus2?
This question is to emphasize that it is not only gravity that needs to be considered. It is the pressure resisting gravity that is missing from your idea.

9. Originally Posted by Reality Check
IF01: What do you think gravitational self-energy is, icarus2?
N.B self-energy is also called binding energy since it is the amount of energy needed to disassemble a object.
The concept of gravitational self-energy is the total of gravitational potential energy possessed by a certain object M itself. Since a certain object M itself is a binding state of infinitesimal mass dM, it involves the existence of gravitational potential energy among these dMs and is the value of adding up these. Refer to the fig.06.

In general, gravitational binding energy is defined as a value to which gravitational self-energy is affixed with a minus sign.
This is because the binding energy is defined as the energy required to free an object from gravitational constraint.

So, is the gravitational self-energy exactly the same as the concept of binding energy?
In my thought, strictly speaking, it seems that a little modification is needed in the definition of binding energy.

We are accustomed to the world of positive energy, and so our concepts are mostly defined in the state of total energy as positive energy. So ……

Originally Posted by Reality Check
IF02: How does gravitational self-energy provide a pressure between quarks to stop them getting closer together, icarus2?
Quarks because when the neutron degeneracy pressure is overcome, the neutrons are squeezed together to form quark matter
If we formalize the situation where the mass m is in some potential energy ~

By the mass energy equivalence law, we can make the following equation.

In the usual case, when the positive mass has a negative potential energy level, the total energy of the system is still positive energy.

Thus, they acted as objects with a positive inertial mass.

But, if U has a negative value and

If the total energy itself has a negative value, it must act as an object with a negative inertial mass.

In the classical mechanics,
If the total energy becomes negative due to the negative potential energy, we introduce and explain the phenomenon with the negative effective mass.

Recently~
Of course, this is not the case for classical mechanics.
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http://www.telegraph.co.uk/science/2...tes-backwards/

"Washington State University physicists explained that this mass, unlike every physical object in the world we know, accelerates backwards when pushed."

~~~~~~~~

Our everyday world sees only the positive effect of the law: if you push an object, it moves away from you.

"That's what most things that we're used to do," said Michael Forbes, a WSU assistant professor of physics and astronomy and an affiliate assistant professor at the University of Washington. "With negative mass, if you push something, it accelerates toward you."

~~~~~~~~

The heightened control gives researchers a new tool to engineer experiments to study similar behaviours in astrophysics, such as neutron stars, and cosmological phenomena like black holes and dark energy, where experiments are impossible.

========

The important point above is that the inertial mass can shows a motion with a negative value.

In some system, if , the experiment say that they act m_T(negative mass), not m(positive mass).

We emphasize the effective mass because we have a sense of rejection of the negative mass and also because the initial mass is positive.
However, the important point here is that it acts as a negative inertial mass.

Back to the question,
Negative masses generate antigravity. Thus, in this case, we can say that the source of pressure is anti-gravity.

"From the point R_gs, gravity is 0, and when it enters into the area of R_gs, total energy within R_gs region corresponds to negative values enabling anti-gravity to exist. This 0.3R_S region comes to exert repulsive effects of gravity on the particles outside of it, therefore it interrupting the formation of singularity at the R=0."

Originally Posted by Reality Check
IF03: Apply your theory to the Earth - what does it predict for the radius of the Earth, icarus2?
This question is to emphasize that it is not only gravity that needs to be considered. It is the pressure resisting gravity that is missing from your idea.
The earth's gravitational self-energy is roughly 4.2x10^-10 times as large as the earth’s rest mass energy. The moon's gravitational self-energy is roughly 0.2x10^-10 times as large as the moon's rest mass energy.

In usual cases, |U_gs| << mc^2, so generally, there was no need to consider gravitational self-energy.

According to this model, the earth cannot shrink to less than a radius of R_gs(about 2.6mm). Therefore a singularity cannot be formed.

Conventional objects stop gravitational contraction at the point where the gravitational force and the electromagnetic repulsive force are in equilibrium. So what?
It's a universal phenomenon that if the scale changes, things can change and the importance can change.

It is only because the size of the object has not contracted to such a size that gravitational self-energy becomes important. However, in the singularity problem, it is necessary to consider the gravitational self-energy because it reaches that size.
Last edited by icarus2; 2017-Jul-31 at 05:36 PM.

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Originally Posted by icarus2
The concept of gravitational self-energy is the total of gravitational potential energy possessed by a certain object M itself.
Almost right and then irrelevance about dM, a fig.06, etc. Read the definition of gravitational self-energy (also gravitational called binding energy). It is the amount of energy that is need to remove all of the parts of a system of particles to infinity against gravity. Alternately it is the work needed to assemble the system using particles from infinity. The gravitational self energy of the solid sphere is the same as its binding energy.

A waste of math and our time (not one mention of quarks!) is not an answer to
IF02: How does gravitational self-energy provide a pressure between quarks to stop them getting closer together, icarus2?

The mass in gravitational self energy is positive, not negative. The negative sign in front of is a result of setting the potential to be 0 at infinity. It is a convention.
This is negative masses which a speculative concept that is never been observed and would have very strange properties if it did. There is no known way to create negative mass.

IF03a: What is the measured radius of the Earth and why has your model got it totally wrong, icarus2?

Originally Posted by icarus2
Conventional objects stop gravitational contraction at the point where the gravitational force and the electromagnetic repulsive force are in equilibrium. So what?
Conventional objects include the Earth, stars, neutron stars and the mass inside a black hole ! The full picture is
1. Ordinary pressure stops stars from collapsing. Add mass and:
2. Electron degeneracy pressure stops dwarf stars from collapsing. Add mass and:
3. Neutron degeneracy pressure stops neutron stars from collapsing. Add mass and:
4. There is nothing known (no fantasies about positive mass changing to negative mass) to stop neutron stars from collapsing to a singularity.

ETA: There is a tiny suggestion of about a century of ignorance by scientists. Gravitational self energy (a first year undergraduate concept) was taught to all of the people who worked out that black holes have a central singularity. There has been a century of people who know about gravitational self energy trying to remove that singularity. None of them have underestimated the "importance" of gravitational self energy. They have all considered gravitational self energy. The science is that gravitational self energy has no influence on a body collapsing to form a black hole. It is just a measure of how much energy it would take to disassemble the body.
Last edited by Reality Check; 2017-Jul-31 at 09:43 PM.

11. ## Gravitational potential energy is also a source of gravity!

I already explained about it. By the way, you just cannot catch.

Originally Posted by Reality Check
IF03a: What is the measured radius of the Earth and why has your model got it totally wrong, icarus2?
Originally Posted by Reality Check
Conventional objects include the Earth, stars, neutron stars and the mass inside a black hole ! The full picture is
1. Ordinary pressure stops stars from collapsing. Add mass and:
2. Electron degeneracy pressure stops dwarf stars from collapsing. Add mass and:
3. Neutron degeneracy pressure stops neutron stars from collapsing. Add mass and:
4. There is nothing known (no fantasies about positive mass changing to negative mass) to stop neutron stars from collapsing to a singularity.
I know the above process (1,2,3). However, in the singularity problem, 1, 2, and 3 are not important at all. In the mainstream physics, gravitational collapse has already overcome process 1, 2, and 3 and has reached the fourth step. I am claiming a new hypothesis about the 4th course, and You are still obsessed with steps 1, 2, and 3.

Originally Posted by Reality Check
The mass in gravitational self energy is positive, not negative. The negative sign in front of is a result of setting the potential to be 0 at infinity. It is a convention.
Many students think so. But there are physicists who think differently from their thoughts.

Edward Tryon, Stephen Hawking, Alan Guth, Alexander Vilenkin, Alexei V.filippenko, Jay M. Pasachoff, and Lawrence Krauss etc. are argued that positive mass energy could be offset by the gravitational potential energy.

Stephen Hawking’s book "A Brief History of Time"
==========
~~~~~
In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.

Now twice zero is also zero. Thus the universe can double the amount of positive matter energy and also double the negative gravitational energy without violation of the conservation of energy. This does not happen in the normal expansion of the universe in which the matter energy density goes down as the universe gets bigger. It does happen, however, in the inflationary expansion because the energy density of the supercooled state remains constant while the universe expands: when the universe doubles in size, the positive matter energy and the negative gravitational energy both double, so the total energy remains zero.
~~~~~
==========

Alan Guth’s lecture: Inflationary Cosmology 4:50s~
https://youtu.be/vG0_Y0MtjCM?t=289

=========

The energy of a gravitational field is negative!
The positive energy of the false vacuum was compensated by the negative energy of gravity. The total energy of the universe may very well be zero.

Gravitational fields has negative energy density.
~~~~
=========

They treat negative gravitational potential energy as real energy that can offset positive mass energy.

In the general relativity and strong equivalence principle, all energies are a gravitational source. Therefore, gravitational potential energy and gravitational self-energy are also a source of gravity, so it should not have random value at any particular location.

Originally Posted by Reality Check
This is negative masses which a speculative concept that is never been observed and would have very strange properties if it did.
From the discovery of the accelerating expansion of the universe, people generally claim the existence of cosmological constants or vacuum energy. However, by borrowing their logic, the accelerating expansion of the universe can be interpreted as evidence for the existence of negative mass.

1)Negative mass and negative energy were the first result of the field equation.
However, since those who received the first result had the wrong stereotype of negative mass and negative energy, so they rather modified the field equation to their taste. They resurrected the cosmological constant and modified the equation.

But what if they had a problem because they had the wrong knowledge of negative mass or negative energy levels?

The standard explanation of negative mass is that the state of low energy is stable when a negative energy level exists and that the lowest state of energy is minus infinity. Thus, this means that all positive mass emits energy and it will transit to the energy level of minus infinity and the universe will collapse.

However, at the present, our universe exists without collapsing, so the explanation for this has become strong proof of the nonexistence of the negative mass and negative energy level of.

P.A.M. Dirac also had a false concept of negative energy levels. He avoided this problem by introducing the false assumption that "all negative energy levels are filled by electrons with negative energies" to prevent transitions to negative infinity energy levels.

Whenever professors and physicists explain antiparticles, they teach their students a misinformation about negative energy levels.

Let's take a look at the experiments at the University of Washington.
Objects with negative energies behave with a negative inertial mass.

Fig.02
F = ( - m_ )a (m_ >0)
a = - (F/m_ )

The acceleration of negative mass is opposite to the direction of force. Therefore, the negative mass has harmonic oscillation at the maximum point and it is also stable at the high energy state.
In the case of positive mass, it was stable at the minimum point at which energy is the low. However, in case of negative mass, stable equilibrium is a point of maximum value, not a point of minimum value.

Therefore, "The problem of transition to minus infinite energy level" does not occur. This is a very important result because it means that negative mass and negative energy can exist stably in our universe. If there is a negative mass or a negative energy level (the total energy is negative), it is wrong to say that this universe will collapse.

2)Physically, negative mass is no worse than vacuum energy and cosmological constant. Vacuum energy and cosmological constant are a concept that violates the law of conservation of energy.

The monster they produce act as negative pressure with a positive energy density, and in the case of relativistic particles with the largest momentum compared to the mass energy, the pressure is only 1/3 of the energy density, but the monster they produce is three times more pressure than the pressure of relativistic particles. Negative pressure is also a problem, but its size is also a problem. Physically, negative mass is no worse concept than vacuum energy and cosmological constant.
Last edited by icarus2; 2017-Aug-13 at 09:25 AM.

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Originally Posted by icarus2
The concept of gravitational self-energy ...
It looks like we know what gravitational self-energy is.

Originally Posted by icarus2
In my thought, strictly speaking, it seems that a little modification is needed in the definition of binding energy.
Binding energy has a definition. People cannot just change it because they want to change it because it is then no longer binding energy.

Originally Posted by icarus2
We are accustomed to the world of positive energy...
That is not correct for physicists. They are also accustomed to the world of negative energy. For example during learning quantum field theory they encounter the Dirac sea.

Originally Posted by icarus2
By the mass energy equivalence law, we can make the following equation...
In E=mc2 m is rest mass. That rest mass is positive. Add a potential field, e.g. gravity, and the rest mass does not change and is still positive.
You do not answer the question:
IF02: How does gravitational self-energy provide a pressure between quarks to stop them getting closer together, icarus2?

You ignored: "4.There is nothing known (no fantasies about positive mass changing to negative mass) to stop neutron stars from collapsing to a singularity." If your ATM idea is that positive mass changes to negative mass then it is wrong.
Last edited by Reality Check; 2017-Aug-14 at 01:14 AM.

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## Gravitational potential energy is not also a source of gravity!

Gravitational potential energy is not also a source of gravity!
The source of gravity is the stress–energy tensor "that describes the density and flux of energy and momentum in spacetime". The energy is the E=mc2 energy.

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Hi icarus2,

From the discovery of the accelerating expansion of the universe, people generally claim the existence of cosmological constants or vacuum energy. However, by borrowing their logic, the accelerating expansion of the universe can be interpreted as evidence for the existence of negative mass.
The idea of negative mass is worth pursuing to see where it leads. So long as it does not have need for the arbitrary introduction of additional theoretical supports to maintain itself, it can be evaluated fairly by empirical evidence.

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Originally Posted by icarus2
But there are physicists who think differently from their thoughts.
For example read what you quoted from Hawking:
In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.
Black holes do not have a total energy of zero. Black holes are not inflationary cosmology.

Originally Posted by icarus2
From the discovery of the accelerating expansion of the universe, people generally claim the existence of cosmological constants or vacuum energy. However, by borrowing their logic, the accelerating expansion of the universe can be interpreted as evidence for the existence of negative mass.
No distortion of logic or physics makes dark energy into negative mass.
1) "Negative mass and negative energy were the first result of the field equation" is wrong about the history of GR.
The cosmological constant was added to allow the universe to be static. Too little mass and it expands. Too much mass and it contracts. Add the cosmological constant and its value can stop the expansion or contraction.

P.A.M. Dirac had a valid concept of negative energy levels that predicted the existence of positrons.

What that team has done have is take normal matter (really cold rubidium atoms) and put it into a state that the atoms act like we think negative matter would act according to Newton's 3 laws.
Negative-Mass Hydrodynamics in a Spin-Orbit–Coupled Bose-Einstein Condensate

Back to the real world: There is no evidence that negative masses generate antigravity.

2) Physically, negative mass is massively worse than vacuum energy and cosmological constant. This is negative mass.
GR locally obeys the conservation of energy, e.g. for black holes. Globally it is a different matter - the general answer is "it depends"!
Vacuum energy as in the creation of virtual particles is totally the conservation of energy! Virtual particle + antiparticle creation is energy being conserved.

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Originally Posted by James Putnam
The idea of negative mass is worth pursuing to see where it leads.
Not correct James Putnam. A star collapsing to form a black hole is made of normal matter. So the ATM idea needs some kind of magic to convert positive mass into negative mass.
But even then: The overwhelming consensus among physicists is that antimatter has positive mass and should be affected by gravity just like normal matter.

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Originally Posted by Reality Check
Not correct James Putnam. A star collapsing to form a black hole is made of normal matter. So the ATM idea needs some kind of magic to convert positive mass into negative mass.
But even then: The overwhelming consensus among physicists is that antimatter has positive mass and should be affected by gravity just like normal matter.
Reliance upon Relativity Theory, consensus in the absence of empirical evidence, and Wikipedia is not what guides the content of my messages. I wrote in response to icarus2's comments and the value that I find in them. I await icarus2 telling me their reasoning.

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Originally Posted by James Putnam
I wrote in response to icarus2's comments and the value that I find in them.
I wrote that there is little value to find in icarus2's comments because they are currently invalid. Black holes form from positive mass.
Negative mass and Gravitational interaction of antimatter give the current status of negative matter which is irrelevant to black holes. In short
• No effects of negative mass has ever been observed.
• There is no empirical evidence that anti-matter has negative mass (yet).
• The consensus is that there will be no difference.
Last edited by Reality Check; 2017-Aug-14 at 03:51 AM.

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I have Wikipedia available also. It does not tell me that I should not find this or find that of value in icarus2's comments. Your "currently invalid" claim is sufficiently too weak for telling me I should not find value in icarus2's comments in the ATM forum. Has current theory finished theoretical physics?

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Originally Posted by James Putnam
I have Wikipedia available also...
You need to read Black holes, Negative mass and Gravitational interaction of antimatter which show that icarus2's comments are currently invalid. Also read and understand icarus2's comments which show little knowledge of what negative mass is or that there is no evidence for it or that black holes are created from collapsing positive mass (stars). The ATM section of the forum needs more than a wish that stars are made of negative mass (they are not!) or a hope that negative mass appears because the proposer wants it to appear.

Encouragement of invalid physics will not help icarus2 to understand where he went wrong.
Last edited by Reality Check; 2017-Aug-14 at 04:27 AM.

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I have Wikipedia also! I know about black holes! I see purpose in introducing negative mass!
Gravitational interaction of antimatter which show that icarus2's comments are currently invalid.
I already asked you if current theory has finished theoretical physics? As a general finding of your complaints, this is the ATM forum. If it is the case that current theory has not finished theoretical physics then, I await icarus2's reasoning.

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Encouragement of invalid physics will not help icarus2 to understand where he went wrong.
Encouragement of furthering physics thought, at times, has released us from the unwarranted restraints of unfinished theoretical physics. I understand where you think, for your reasons, where icarus2 has gone wrong. I await icarus2's reasoning for offering to introduce their view of why mass can be negative. I put the limitations that I find to be unavoidable into my message to them.

23. Originally Posted by James Putnam
<snip> I await icarus2's reasoning.

And yes, that is where this discussion stops.
This is icarus's thread, and not a fighting place for James and Reality.
thread closed, until icarus decides if they want to continue.

24. icarus2 has requested the thread to be reopened, and so we have done so. And even though icarus2 has expressed he is fine with the off-topic /side discussion, the Moderation Team is not. One ATM thread, one topic. Comments and questions are to icarus2, on the original topic, no side conversations.

25. ## Gravitational self-energy is also a source of gravity!

Originally Posted by Reality Check
Gravitational potential energy is not also a source of gravity!
No. That was wrong!
Gravitational potential energy is also a source of gravity!

Gravitation and Spacetime – by Hans C. Ohanian and Remo Ruffini
https://www.amazon.com/Gravitation-S...+and+spacetime

I do not want to rely on the authors' authority~

Hans Ohanian : studied physics at Berkeley and at Princeton, where he worked on relativity with John A. Wheeler. He has taught at Rensselaer Polytechnic Institute, Union College, the University of Rome, and the University of Vermont. He is the author of several physics textbooks and dozens of articles dealing with relativity, gravitation, and quantum theory, including many articles on fundamental physics published in the American Journal of Physics, where he served as associate editor for several years.

Remo Ruffini : He is Director of ICRANet, International Centre for Relativistic Astrophysics Network. Moreover, he is President of the International Centre for Relativistic Astrophysics (ICRA); he initiated the International Relativistic Astrophysics PhD (IRAP PhD), a common graduate school program of several universities and research institutes for the education of theoretical astrophysicists. He is Director of the Erasmus Mundus IRAP PhD program (IRAP Ph D Erasmus Mundus). He has been Professor of Theoretical Physics at the University of Rome "Sapienza" from 1978 to 2012.

==========

P25~

Table 1.3 lists different kinds of energy and their contribution to the gravitational mass as calculated from the experimental result of Braginsky and Panov (the slightly higher sensitivity of the experiment of Adelberger et al. does not improve the limits listed in this table, because the slightly higher measurement sensitivity is nullified by a reduced energy-sensitivity of the test samples, aluminum and beryllium for Adelberger, and aluminum and platinum for Braginsky).

Table 1.3 Different forms of energy as sources of gravity*
Form of Energy |mG − mI|/mI
Rest mass, protons + electrons 0 (by definition)
Rest mass, neutrons <8 × 10^−12
Strong fields in nucleus <3 × 10^−10
Electric fields in nucleus <4 × 10^−10
Magnetic fields in nucleus <2 × 10^−7
Weak fields in nucleus <5 × 10^−3
Kinetic energy of nucleons <10^−9
Gravitational energy in Earth <5 × 10^−4
* Adapted from Will (1993), with corrections.

~~~~~~~~

Table 1.3 also includes a result for gravitational energy, which was obtained by different means. The Eotvos experiments do not permit a direct test of the hypothesis that gravitational energy contributes to the gravitational mass, because the ostensible macroscopic amounts of gravitational self-energy in masses of laboratory size are much too small to affect these experiments.

Theoretical considerations suggest that the rest masses of electrons, protons, and neutrons include large amounts of gravitational self-energy, but we do not know how to calculate these self-energies (for the implications of this, see the later discussion). If we want to discover whether gravity gravitates, we must examine the behavior of large masses, of planetary size, with significant and calculable amounts of gravitational self-energy. Treating the Earth as a continuous, classical mass distribution (with no gravitational self-energy in the elementary, subatomic particles), we find that its gravitational self-energy is about 4.6 × 10^−10 times its rest-mass energy. The gravitational self-energy of the Moon is smaller, only about 0.2 × 10^−10 times its rest-mass energy.

If gravitational self-energy does not contribute in the normal way to the gravitational mass, then the Earth and the Moon would fall at different rates in the gravitational field of the Sun. The difference in the rates of fall is effectively equivalent to a uniform extra force field pulling the Moon toward the Sun (if gravitational energy gravitates less than normal) or away from the Sun (if gravitational energy gravitates more than normal). Such an extra force leads to a distortion of the orbit of the Moon relative to the Earth, a distortion called the Nordvedt effect. As Fig. 1.12 shows, the orbit is elongated, or polarized, in the direction of the Sun. Although the distortion effect is small, very precise measurements of the Earth-Moon distance have been performed by the laser-ranging technique already mentioned in Section 1.2, with a pulse of laser light sent from the Earth to the Moon and reflected back to the Earth by the corner reflectors installed on the Moon during the Apollo mission. Measurements of the travel time of the pulse determine the distance to within an uncertainty of a centimeter, and recent improvements are reducing this to a millimeter. If the uncertainty is taken as 1 cm, the analysis of the orbital data places a direct limit of 5 × 10^−4 on the fractional difference between the contributions of gravitational energy to the inertial and the gravitational mass. Thus, these experiments indicate that gravitational energy gravitates in the normal way.

In setting these limits on how the strong, electromagnetic, weak, and gravitational energies gravitate, we have ignored the self-energies locked up within the rest masses of electrons, protons, and neutrons. This is a rather questionable attitude, since quantum theory suggests that all these particles contain large amounts of strong, electromagnetic, weak, and gravitational self-energies. These particles would therefore not be expected to gravitate in the normal way, unless all these forms of energy gravitate in the normal way. However, from the equal rates of fall of electrons, protons, and neutrons we cannot extract quantitative conclusions for the rates of fall of the self-energies locked up in the rest masses, because we have no way of calculating the magnitudes of these self-energies. A naive calculation of the, say, gravitational self-energy of the electron gives an infinite value; this, of course, proves only that the calculation is wrong and that our understanding of the quantum dynamics is faulty.

==========

Gravitational potential energy is also a source of gravity!

In the general relativity and equivalence principle, all energies are a gravitational source. Therefore, gravitational potential energy and gravitational self-energy are also a source of gravity, so it should not have random value at any particular location. It is not just a convention, but a right convention.

While not important to this debate, in my opinion,
The author appears to be struggling with the infinite problems caused by treating the particles as point particles(maybe). Maybe, this infinity problem can be solved through chapter 2-5(The minimal size of existence) of my paper.

This diverges.

2-5. The minimal size of existence

[ Existence = the sum of infinitesimal existences composing an existence ]

A single mass M for some object means that it can be expressed as and, for energy, . The same goes for elementary particles, which can be considered a set of dMs, the infinitesimal mass.

The equation above means that if masses are uniformly distributed within the radius , the size of negative binding energy becomes equal to that of mass energy. This can be the same that the rest mass, which used to be free for the mass defect effect caused by binding energy, has all disappeared. This means the total energy value representing "some existence" coming to 0 and "extinction of the existence". Therefore, is considered to act as “the minimal radius(size)” or “a bottom line” of existence with some positive energy.

This does not diverge.
Last edited by icarus2; 2017-Aug-15 at 10:31 PM.

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Originally Posted by icarus2
Gravitational potential energy is also a source of gravity!
A link to an entire book is not support for an assertion. But that table and text is support: The gravitational [potential] energy of the Earth is part of the source of gravity of the Earth. Ditto for other bodies.

IF02: How does gravitational self-energy provide a pressure between quarks to stop them getting closer together, icarus2?

ETA: As part of your answer, can you can tell us at what point in the collapse the positive mass of the quarks turns into negative mass? And how that happens?
Last edited by Reality Check; 2017-Aug-15 at 10:58 PM.

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Originally Posted by icarus2
2-5. The minimal size of existence
The text after this does not show that there is a minimal size, icarus2.
Assuming a uniform distribution of masses and then applying invalid reasoning does not give a minimal size. That equation in "The equation above" is just the sum of energies of each particle in a hypothetical system of particles.

The statement "The same goes for elementary particles" is wrong. Elementary particles by definition are single particles, not collections of particles. The physical evidence is that elementary particles do not have internal structure, e.g. we scatter electrons and the scattering is that from a point particle. Quantum field theory works and uses point particles.

28. Originally Posted by Reality Check
For example read what you quoted from Hawking:

Black holes do not have a total energy of zero. Black holes are not inflationary cosmology.
Stephen Hawking say that
"one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter."

What you need to think of from the claims of physicists is not "total energy is zero”, but “the negative gravitational energy can cancels the positive energy represented by the matter.”

one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter.

What you need to understand is that this is a (a + b) structure. And
What you need to think about is "can cancels".
The situations are available in all three cases.

It depends on the energy density.

The smaller R becomes, the higher the absolute value of . For this reason, we can see that is likely to offset the mass energy in a certain radius R_gs. And in the region of R< R_gs, we are faced with situations where the negative gravitational potential energy is greater than the positive mass energy.

That point is R_gs, and it exists in the event horizon of the black hole.

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Originally Posted by icarus2
Stephen Hawking say that
Once again - cosmology, not black holes. It is the entire universe that has an energy of zero because we observe that it is very probably flat.
Last edited by Reality Check; Yesterday at 01:07 AM.

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Originally Posted by icarus2
one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter.
One has not shown that because black holes have a positive total energy (we do not measure their masses to be zero or negative) so only the first of your equation applies. Or maybe you can answer:
IF03: What is your evidence that black holes can gave an energy of zero, e.g. how does the energy equivalent to their mass vanish?
IF04: What is your evidence that black holes can gave an energy of less than zero, e.g. how does the energy equivalent to their mass vanish and more energy be removed?

Your equations do not include kinetic energy. Think about the stars that collapse to form black holes. Their total energy is E=mc^2 + kinetic energy + gravitational potential energy. During the collapse gravitational potential energy is converted to kinetic energy. The sum of gravitational potential energy and kinetic energy is constant.
P.S. Kinetic energy is a source of gravitation (see the Table 1.3 that you quoted which lists "Kinetic energy of nucleons").
Last edited by Reality Check; Yesterday at 01:21 AM.