# Dark Energy in the Zero Energy Universe

1. Dec 7, 2011

### 7icarus7

Hello~ I’m sorry. I can’t English well.

1. Assuming that total energy of universe is zero.
It looks more natural when an initial energy value of universe is 0. Therefore, negative energy is needed to offset positive energy of matters.
$$E_T = 0 = ( + E) + ( - E) = 0$$
2. Mass-energy equivalence
$$E = \sum {m_ + c^2 } ; - E = \sum { - m_ - c^2 }$$
$$(m_ + ,m_ - > 0)$$
3. Positive energy(mass) and negative energy(mass) can exist in the same space-time.
http://4.bp.blogspot.com/_udXTGLmmdK4/Su-xBLdm3PI/AAAAAAAAAAM/ByaVtThbj_E/s320/Fig4-02-380.jpg

The acceleration of negative mass is opposite of the direction of force, and in case of negative mass, it does harmonic oscillation at the maximum point and is stable at the maximum point.

In case of a positive mass, it is stable at the low state, whereas, in case of negative mass, it is stable at the high state. Due to this, “the problem of the transition of the energy level of minus infinity” does not occur, and therefore, in our universe, positive mass and negative mass can exist in the same space-time.

4. Gravitational potential energy of zero energy universe
If negative energy(mass) and positive energy(mass) coexist, GPE consists of the below three items.
$$U_T = U_{ - + } + U_{ - - } + U_{ + + }$$
$$U_T = \sum\limits_{i,j}^{i = j = n} {( - \frac{{G( - m_{ - i} )m_{ + j} }}{{r_{ - + ij} }})} + \sum\limits_{i,j,j > i}^{i = j = n} {( - \frac{{G( - m_{ - i} )( - m_{ - j} )}}{{r_{ - - ij} }})} + \sum\limits_{i,j,j > i}^{i = j = n} {( - \frac{{Gm_{ + i} m_{ + j} }}{{r_{ + + ij} }})}$$
$$U_T = \sum\limits_{i,j}^{i = j = n} {( + \frac{{Gm_{ - i} m_{ + j} }}{{r_{ - + ij} }})} + \sum\limits_{i,j,j > i}^{i = j = n} {( - \frac{{Gm_{ - i} m_{ - j} }}{{r_{ - - ij} }})} + \sum\limits_{i,j,j > i}^{i = j = n} {( - \frac{{Gm_{ + i} m_{ + j} }}{{r_{ + + ij} }})}$$
*GPE between positive masses are negative value.
*GPE between negative masses are negative value.
*GPE between positive mass and negative mass are positive value.

When the number of negative mass is n-, and the number of positive mass is n+, total potential energy is given as follows.
$$U_T = (n_ - \times n_ + )U_{ - + } + (\frac{{n_ - (n_ - - 1)}}{2}U_{ - - } + \frac{{n_ + (n_ + - 1)}}{2}U_{ + + } )$$
For example, two pairs exist.
$$U_T = (U_1 + U_2 + U_3 + U_4 ) + (U_5) + (U_6 )= 4U_{ - + } + 1U_{ - - } + 1U_{ + + }$$
Gravitational potential shows significant characteristic when negative mass and positive mass both exist. While n2 positive gravitational potential is produced above, n2-n negative gravitational potential are produced. Therefore, total GPE can have various values.(<0, 0, >0)

5. Simulation setting
a)Definition of parameter
A few parameters were needed to be defined for simulation.
Distance between pair creation negative energy and positive energy(distance of 1 pair) : d0
Minimum distance between particle pairs for density modification during pair creation : dm
Radius of pair creation range : R0 =500
Particle number of pair creation : N0 =2000ea (1000 pair)

b)Finding mean value
Through Gravitation3D program, 1000 particle pairs (total 2000ea particles) were produced by random and one mean value (GPE) of each distance value was found 5 times each.

c)Verification on program
To check if the calculated results of the program were correct, we calculated the GPE when 1, 2, and 3 pairs (consist of 15ea potentials) of particles existed by hand and confirmed that this value corresponded to the calculated results of the program.

Last edited: Dec 7, 2011
2. Dec 7, 2011

### 7icarus7

6. Results of simulation

http://4.bp.blogspot.com/-VzDZh_NziBA/TpFDFdz_8DI/AAAAAAAAANQ/jwksQTnrrFw/s320/fig04.jpg

It was found out that U-+ value having positive value could be much higher than |U++ | + |U--|. Thus, even though the size of positive mass and negative mass was equal, it could be known that repulsive GPE could be much higher than attractive GPE.

We will describe that an unknown repulsive energy U-+ higher that attraction of visible matter exists for the energy value of above.

According to the observance result of WMAP, it is predicted that current dark energy, dark matter, and matter is approximately 72.1%, 23.3%, and 4.6%, respectively.
Dark matter and matter correspond to negative gravitational potential because they have attractive gravitational potential and dark energy correspond to positive gravitational potential because it produces repulsive effect.
Therefore, observation ratio of current universe is 72.1/27.9 = 2.584.

http://2.bp.blogspot.com/-02LUy-R3gy4/TpFDHLBNc7I/AAAAAAAAANU/-MOImVYvwWo/s320/fig05.jpg

Is shows similar condition to 2.63 which was found above.
If conditions are changes, ratio of negative gravitational potential and positive gravitational potential can have various conditions close to 2.58.

7. Accelerating expansion of the universe
Expansion of the universe means increase of the distance between cluster of galaxies or the galaxy while the sizes of individual galaxies are the same.

d0, which is the distance between negative and positive mass, is maintained as a constant in this simulation, or the radius value of the size of the universe increases when d0 decreases.

http://3.bp.blogspot.com/-CDaYtsWxljs/TpFCwbmifnI/AAAAAAAAANE/fmp3TXkCL5U/s400/fig12.jpg
Change of potential energy by change of radius R

Pay attention on the change of negative gravitational potential energy and positive gravitational potential energy ratio!

Ratio of positive gravitational potential and negative gravitational potential increases as the universe expands and this is seen to mean that percentage of repulsive effect (Dark Energy) increases compared to the attractive effect of ordinary matter.

8. Centripetal force effect in the galaxy from dark matter(negative mass) halo out of the galaxy

If the negative mass is disposed at the outline, the test mass vibrates, and a kind of restoring force (This corresponds to the centripetal force when considering rotation of the galaxy) exists.

This suggests that the halo, dark matter (negative mass) of the external Galaxy could get additional effects of centripetal force to the inner Galaxy.

9. Results of simulation
1) Even though negative and positive mass have the same size, total GPE can have +, 0, - values depending on the placement of each.

2) U-+value is higher as d0 is smaller and the total GPE also have a high positive value.

3) Looking into the numerical calculation of 6, it can be seen that positive gravitational potential value U-+ can have much higher values than negative gravitational potential values (138% - 3,201%).
From the observation result of WMAP, we know that dark energy value, which generates repulsion, is 2.58 times the total of matter and dark matter. Until now, it is predicted that dark matter produces attraction. Closely look into numbers 6.
http://4.bp.blogspot.com/-tB_Btl59wEY/TpFDeX7_9vI/AAAAAAAAANo/ARwsI8t92N8/s1600/fig05-00.jpg

4) Because we judge components of the universe by gravity or GPE, it can be assumed that there is dark energy of 2.63 times or inner energy of 2.63 times regarding the situation of U-+ value having approximately 2.63 times U++ and U-- values in number 5. There are several situations satisfying 2.58 times.

5) The above results show that 72.1% of dark energy doesn't exist independently, but implies that there is possibility that negative energy having the same size of positive energy can emerge.

6) This "increase of dark energy" doesn't come from a newly generated space, but shows feature of GPE which is made by negative mass and positive mass.

No one has seen dark energy or dark matter. We must remember that we only recognize it through gravitational effect.

When we judge the components of the universe, we judge the components by gravitational effect rather than mass energy.

Therefore, when GPE U-+ exists larger than GPE U which is generated by materials, we will be confused to think that some mass energy bigger than the mass energy of materials exists.

Simulation Video

Last edited by a moderator: Sep 25, 2014
3. Dec 8, 2011

### Chalnoth

1. Negative mass objects do not exist, as near as we can tell.
2. Gravitational potential energy itself is negative, and if we live in a closed universe that gravitational potential energy exactly balances the energy in matter fields no matter what the matter content of the universe.

4. Dec 8, 2011

### 7icarus7

1)Most of people have strong aversion of negative energy(mass), but there is no physical law that says such a particle cannot exist.

All the while, the field of physics did not seriously consider the possibility of existence of negative energy(mass) at the general state.
The standard explanation about negative mass is, if energy level of negative exists, that the state of low energy is stable, and the lowest state of energy is minus infinity, so the positive mass of all 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 became the strong proof for the nonexistence of the negative mass and the energy level of negative. We have taken this as the natural common sense and teach it to students.

At the center of this background, there is the fundamental proposition that "State of low energy is stable". But, we show that the "State of low energy is stable" proposition is an incomplete one, and in case of a positive mass, it is stable at the low state, whereas, in case of negative mass, it is stable at the high state. Due to this, the problem of the transition of the energy level of minus infinity does not occur, and therefore, in our universe, the existence of negative energy(mass) is possible.

At least, negative mass observes energy conservation and momentum conservation. This means negative mass is not severe target more than cosmological constant or vacuum energy in physics.

2) The reason why we have not found negative mass on the earth
As examined with Newton dynamics of negative mass, attraction works between positive mass, and they have attractive effect, so they gradually clusters each other, and then make massive mass like star or galaxy. On the other hand, attraction works between negative mass, but they have repulsive effect, so they cannot make massive mass structure like star or galaxy.

Since repulsive effects occur between negative masses, negative masses will be distributed all over space because it cannot form large mass structures like stars. Negative mass within the galaxy is cancelled out by attraction from large positive mass during the galaxy formation process. Furthermore, the space, other that the galaxy, will maintain the distribution state of negative mass.

In case of only positive mass or negative mass, It’s ok.
However, GPE between positive mass and negative mass are positive value.

In my opinion : Our universe is not black hole

Gravitational self-energy or Gravitational binding energy in case of uniformly density:
$$U_S = \sum U = - \frac{3}{5}\frac{{GM^2 }}{R}$$
$$\frac{3}{5}\frac{{GM^2 }}{R} = Mc^2$$
$$R = \frac{3}{5}\frac{{GM}}{{c^2 }}$$

Black hole’s radius : $$R_c = \frac{{2GM}}{{c^2 }}$$
If gravitational potential energy exactly balances the energy in matter, our universe must be almost black hole. But ~

At present, the gravitational potential energy doesn't completely offset mass energy. So, "negative mass", which corresponds to "negative energy", is needed.

Last edited: Dec 9, 2011
5. Dec 9, 2011

### Chalnoth

Yes, but there's no experimental evidence that they do exist either. That was my point: so far as we know there is no such thing. There is, furthermore, no theoretical reason to even suspect that they may exist.

If we have negative mass objects, this gravitational force is exactly the same. So negative mass objects would show the exact same clumping behavior as positive-mass objects. But if we compare the force between a negative-mass object and a positive-mass object, the two would repel one another. So we'd end up with clumps of negative-mass matter and positive-mass matter that tend to separate from one another.

While it is always possible that there may be a tiny amount of this negative-mass stuff, there is no conceivable way that it could balance positive-mass matter equally, because we would have noticed it by now.