# Thread: Dark energy, Dark matter, Fine tuning problem,Negative mass!

1. Proof of that value of observed dark energy(10^(-47)GeV^4)

I’m sorry, I can’t English well.
The value of observed dark energy has been proved in accordance with theoretical computation.

ρ_de = (0.558 ~ 5.02) X 10^(-47)GeV^4 : Theoretical computation
ρ_obs = 10^(-47)GeV^4 : Observed value

Please have a look the attached proof and inspect the findings.
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U_+ :Plus potential , U_ - :Minus potential , U_T :Total potential

*Potential energy between positive mass and positive mass has - value:
*Potential energy between negative mass and positive mass has + value:
*Potential energy between negative mass and negative mass has - value:

When the number of negative mass is n_- , and the number of positive mass is n_+ , total potential energy is given as follows.

V-2-1)Proof from the definition equation of dark energy

[ Proof Start! ]
In equation (79), Dark energy is corresponding to that plus potential term in total potential energy.

If radius of the universe is 60Gyr, ordinary matter density is about proton 1ea/. So, ,

(because that dark matter has about (23.3/4.6) times ordinary matter in WMAP)

From equation (95)

From analysis of V-5,
If , , Therefore, Define,

( is about total proton number of our universe).

Planck Unit transformation(1cm =0.5063 x )

Observation value is

If R=90Gyr, (refer to fig11).

[Proof End]

In Quantum Field Theory, the energy density of the vacuum is estimated as , which is about orders of magnitude large than the observation value .

Therefore,
You can see that negative mass hypothesis how to close to the observation and the universe.

From equation (80),
Origin of dark energy is particle not pressure or constant energy, because that and are number of particle.

Also, because that gravity is repulsive, it is strongly suggested that negative mass is exist.

is right. It means that is also right.
Thus, from the analysis of , it means that analysis of the inflation, fine tuning problem, decelerating and accelerating expansion, future of our universe are right.

You will know the mean which magnitude of dark energy is proved.
It is saying that cosmological constant has not existed and dark energy has not come from vacuum energy.

Definitely, it is against to the ΛCDM model.

For all that, why did the ΛCDM model show a similar result?
We can find out if we look at the total potential energy section, but if we look at the total potential energy (78 ) equation, (79 ) equation, it is in a form of :

U =(positive potential term) + (negative potential term)= Λ + (ordinary gravitation potential)

Which the positive term played an independent potential role as Λ.

- Negative mass has observed, but it was trashed away -
From the observance of the HSS team(The High-z Supernova Search team) in 1998, they gained the mass density of the negative(), using field equations which do not have the cosmological constant.

HSS team : http://arxiv.org/abs/astro-ph/9805201 :14P 26, 29 lines

- Negative mass is stable at the maximum point!(Refer to II-3) -
As examined in the question of Harmonic oscillation, in case of positive mass, a point of minimum value which energy is the lowest is stable. However, in case of negative mass(minus mass), stable equilibrium is a point of maximum value, not a point of minimum value. So negative mass is toward a point of maximum value to be stable.

In the world of positive mass, ground state is a point that energy is low, but in case of negative mass, ground state is a point that energy is the highest. Accordingly, in the world of negative mass, energy level is filled from the highest to the lowest, and stable state means the highest energy state, so the catastrophe to energy level of minus infinity never happens even if negative mass spontaneously emits energy.

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If the proof above is right, please read another section of the article.

Hypothesis of Dark Matter and Dark Energy with Negative Mass :
http://vixra.org/abs/0907.0015

---Icarus2

2.

3. V-5. Fine tuning problem and inflation mechanism

Pair creation of negative mass and positive mass seems to provide the proper explanation of homogeneity, local non-homogeneity, and flatness of our universe without separate assumption with basic characteristics of Newton dynamics.

With reference to the flatness of universe, the calculation of cosmic critical density with previous positive mass leads to the problem that present density should be close to critical density, the cosmic density at the beginning should be close to critical density, and initial condition should be set delicately.

However, according to the hypothesis of negative mass, potential energy of universe is not single potential when there is only positive mass(potential that has both + and -), and the density of universe close to critical density was from basic mechanism of pair creation, namely 1:1 correspondence of negative mass to positive mass, and form of potential energy.

5-2) Inflation mechanism

- Inflation start -
If we consider that inflation started at the point of time that there were large-scale pair creations of negative mass and positive mass after Big Bang, not at the point of time that the gravity was separated, the number of positive mass and negative mass might be born together at this time, so here also the term of positive potential energy by equation (72)(nU_+(if pair creations are , survives), and this can provide the start power of inflation.

- Inflation finish -
If positive mass is converted to radiant energy(pair annihilation of matter and antimatter, radiation) or energy when strong interaction(Some mass changed to the bond energy. Therefore, positive mass defect has come.), weak interaction, and electromagnetic force are separated after the start of inflation, the number of positive mass falls down below critical ratio which total potential energy is 0 in (V-1.), so at this time, inflation also is naturally finished.

Reference-1
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Potential energy when there are generally n pairs of negative mass and positive mass :

If n pairs of negative mass and positive mass are created, generally the number of term of positive potential energy is n^2, the number of term of negative potential energy is n(n-1), so the number of term of positive potential energy is greater than that of term of negative potential energy by n. Accordingly, even if the absolute value of negative mass is the same as that of positive mass at the beginning of universe, the universe has the value of positive potential energy, and expands.
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Reference-2
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Calculate the value of , with equation (79 ) when there is a difference in the number between negative mass and positive mass to examine changes,

We can see the change in total potential energy in accordance with the difference in the number of negative mass and positive mass from 10 samples above.

fig09
caption : Potential energy from ratio of negative mass and positive mass

- The tendency of total potential energy in accordance with the number of negative mass and positive mass -
i)In Critical ratio of the number of negative mass to the number of positive mass, the total potential energy has 0. --> When the universe is flat. (ex. Here, we note that total potential energy does not have 0 when general matter comes under 60% of dark matter. 60% is the proportion by assuming that all terms of potential energy are identical, and prescribing that the number of is 10.

ii)If number of positive mass less than critical number, total potential energy has negative value. --> Cosmic decelerating expansion

iii)If number of positive mass over than criticle number, total potential energy has positive value. --> Cosmic accelerating expansion

iv)The value of total potential energy increases as the number of positive mass approaches to the number of negative mass.

v)If the number of pair of negative mass and positive mass is n, n terms of positive potential remains as shown in equation (72)(). --> Final state of universe.
===========

5-3) Fine tuning problem of mass density and cosmological constant

Universe mass density is same critical mass density, that is correspond with total potential energy=0

I can't seek exactly solution for total potential energy equation.
So I consider that these three potential can be the same U, and I will seek to the whole tendency.

Maybe, consider of uniformly distribution, it is near to stable state when three value of potential energy are almost in same level.

Define, ,
if

Equation(79) is

If x=y=n,

If, =

y , at most the section,
Total potential energy is proportion square term of negative mass number(similar positive mass number)

Divide by equation(105 ),

Ratio of potential size

- Cosmological constant problem -
The reason of that cosmological constant has a small and non-zero value.

is total number of negative mass. If is , we can know how the present potential values are smaller than the absolute value of minimum potential values of universe, how this present potential value is close to zero.

It is means that present dark energy(cosmological constant) has a small positive value. Because that dark energy is gravitational potential energy(eq.(80)) of universe and then total potential energy has positive value at now.

Reference-3
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=========

Other process, total potential energy term by 2n general particles, has a U. The other side, U_max(positive maximum potential energy by negative mass and positive mass) has a nU.

So, if n = 10^80

It is correspond with the ratio of flatness.
is that the upper limit of total potential energy.

fig16
caption : Changes in universe's potential energy over time

- Fine tuning problem of mass density -
The reason of that mass density of universe close to critical mass density.

About the fine tuning of mass density in the early universe, even though the mass density of present universe is equally same with the value of critical mass density, when negative mass and positive mass coexist, it doesn't mean that the density of early universe must be very close with the value of critical density.

And also because negative and positive mass's rate is going close to 1, that present universe is almost at the same with critical density values.

The mass density of universe close to critical mass density
was from basic mechanism of pair creation, namely 1:1 correspondence of negative mass to positive mass, and form of potential energy.

In fig.16, negative and positive mass created n pairs, and in this period that potential energy values in . That cause accelerates expansion of universe(Bigbang or Inflation).

Strong interaction, weak interaction and electromagnetic force are separate(some mass change to the bond energy) and also antimatter and matter generate pair annihilation in during inflation. So most of positive matter became radiation. Then total potential energy become negative value(result of V-1, fig.9). Therefore we call this time (inflation finish time)

As the universe is getting cooler, the radiation is getting lower and that radiation changed the matter with positive mass. And after values of positive mass became the critical ratio of negative mass, that potential energy becomes zero. We call this time by .

According to hypothesis with negative mass, The last state of universe is when positive mass and negative mass almost the same and potential energy has the value of at this time.

- Phase transition problem of dark energy -
The reason of that dark energy have a very big positive value(Inflation Energy) in early universe and very small positive value(Cosmological Constant) at now.

This value is strong power that can generate inflation in early universe. But roll of this value is very smaller than inflation period in the growth universe(mean distance r is very bigger than initial mean distance and because of our universe have positive potential energy, so it's doing expansion now.

If = 1.61624 X ,
= m
, also

It is very important. Because that explain dark energy that very big positive value(Inflation Energy) in early universe and very small positive value(Cosmological Constant) at now.

- The future of universe -

=================
Hypothesis of Dark Matter and Dark Energy with Negative Mass :
http://vixra.org/abs/0907.0015

4. Dark matter and dark energy come from one origin

3-1) Negative mass has observed, but it was trashed away

In 1998 year, observation by HSS(The High-z Supernova Search team) team and SCP team(Supernova Cosmology Project team), I have seen a calculation that if the cosmological constant is 0,

It means that they got a negative mass density from inspected field equation during 70years.
HSS team paper: http://arxiv.org/abs/astro-ph/9805201 :14P 26, 29 lines

However, HSS team and SCP team have asserted that cosmological constant must be revival. Because must not be negative value in they thought.

They did not know that negative mass is stable at the maximum point!
In case of negative mass, ground state is a point that energy is the highest. Accordingly, in the world of negative mass, energy level is filled from the highest to the lowest, and stable state means the highest energy state, so the catastrophe to energy level of minus infinity never happens even if negative mass spontaneously emits energy.(Refer to II-3)

We must to know that not the equation(Einstein's Field Equation) has disposed the value, but our thought disposed that value.
Einstein said that cosmological constant was my biggest mistake, because it was inserted artificially.

In hypothesis with negative mass,
= positive mass( x ) + negative mass( (1~5.1) x ) +
(negative mass positive mass, cosmological constant Λ = 0 )
We assume over 50% of the dark matter as negative mass.

3-2) Age of universe

If cosmological constant Λ=0 and mass density of universe is negative value Ω_M = -0.38, to get the age of the universe.
From Friedmann equation,

, ,

Use to =1.38 , km/s/Mpc, h=0.701

define to ,

This value is approach to the t=13.73 Gyr calculated in a WMAP.(+3.6% large) considering the very large changes(Λ=0 and ; Λ is a coefficient of ), it seems to increase existence probability of negative mass.

if ,
we get the =14.927 Gyr

Universe' age by other method
Radioactive decay method : 15.2 2.1Gyr,
HR diagram(Hertzsprung-Russel diagram):13.2 2Gyr,
The arithmetic mean of two methods is 14.2 2.05

So, it(14.225Gyr from negative mass density) is in the range estimated by other observations.

==============
Let’s arrange!
HSS team and SCP team had observed our universe, however they got a negative mass density from field equation.
They are very confused. But, they thought Einstein’s cosmological term(Λ). Wow!

But…,
Although they can be explained that universe is accelerating expansion by insert Λ, they make two new problems at least. Finally, problem has not solved but increased.

What is the origin of cosmological constant? And, what is the reason of that cosmological constant has a special value? Physicist tried to explain with vacuum energy but it was failed.

Also, they have must explained dark matter. But they have not been observed dark matter during 30years at predicted place.

However,
if negative mass density is exist, accelerating expansion is explained rightly.
And I have assert that minus mass can be explained for the dark matter, decelerating expansion and accelerating expansion, fine tuning problem, inflation mechanism, the reason of that dark energy seems to has a small and constant value(like cosmological constant Λ), collision of Bullet cluster.

A certain view :
**************************************************
one person(Icarus2) vs ΛCDM physists after 1998year.(about 50~60%? : relation branch) : No

(Einstein, Direc, Hubble,...Icarus2; Inspected field eq. during 70 years.) vs ( New field eq. supported by 50~60% of relation branch physists during 10 years.) : Yes
**************************************************
Therefore please don’t judge by preconception that this hypothesis wrote by someone. Please has an earnest mind to those posts.

Cosmological constant and plus dark matter are not observed as yet.
Accelerating expansion and gravitational effect(centripetal force effect) are only observed.

I will show that decelerating expansion and accelerating expansion of universe, dark matter, at next post.

=================
Hypothesis of Dark Matter and Dark Energy with Negative Mass :
http://vixra.org/abs/0907.0015[/url]

5. II. Property of negative mass

1-1)The law of motion of positive mass and positive mass

----------
+m1 ------ +m2
Fig01. Positive mass +m1 and positive mass +m2 (initial velocity =0, m1 >0, m2 >0)

Positive mass and positive mass : The force worked between positive mass is attraction, and two objects move toward the center of mass. The force is attraction, thus their potential energy has negative value. The direction of acceleration is in the direction of - r, so the distance between two objects are reduced gradually.

6. 1-2)The law of motion of negative mass and positive mass

----------

-m1 ------- +m2
fig02. Negative mass - m1 and positive mass +m2 (initial velocity =0, m1 >0, m_2 >0)

Negative mass and positive mass : Negative mass is accelerated in the direction of positive mass, and positive mass is accelerated in the direction to be far away from negative mass.

The direction of acceleration a1 worked on negative mass – m1 is - r, so - m1 moves in the direction of reducing distance r, and the direction of acceleration a2 worked on positive mass +m2 is +r, so positive mass +m2 is accelerated in the direction that distance r increases, namely the direction of being far away from negative mass.

If the absolute value of positive mass is bigger than that of negative mass, they will meet within finite time(attractive effect), and if the absolute value of positive mass is smaller than that of negative mass, the distance between them will be bigger, and they cannot meet(repulsive effect). The type of force is repulsion, so the potential energy has positive value.

==> Uniformly distributed negative mass receives attractive effect from massive positive mass(Galaxy and Galaxy cluster), so dark matter which has negative mass is clustered around galaxy because of attraction of galaxy.

---------

is same direction.(In eq.,viewpoint is the spherical coordinate : )

In the spherical coordinate

is, In the rectangular coordinate

for the simple analysis, if m1=m2
Acceleration a1=a2, therefore v1=v2, Momentum conservation is valid.

========
Hypothesis of Dark Matter and Dark Energy with Negative Mass :
http://vixra.org/abs/0907.0015

7. 1-3)The law of motion of negative mass and negative mass

----------

- m1 ------ - m2
fig03. Ngative mass - m1 and negative mass - m2 (initial velocity =0, m1>0, m2> 0)

Negative mass and negative mass: Both two objects are accelerated in the direction of + r which extends distance r, so as time passes, the distance between them is greater than initially given condition, and the force between them is attraction, but the effect is repulsive.

The force is attraction(-Gm1m2/r^2), thus the potential energy between them has negative value.

If negative mass and positive mass were born together at the beginning of universe, positive mass has attractive effect each other, so it forms star and galaxy structure now, but negative mass has repulsive effect each other, so they cannot make massive mass structure like star or galaxy.

----------

View to the acceleration term. , is opposite direction(spherical coordinate +r direction).
So, velocity direction is opposite direction.

In the spherical coordinate

is, In the rectangular coordinate

Momentum conservation is valid.

=========
Hypothesis of Dark Matter and Dark Energy with Negative Mass :
http://vixra.org/abs/0907.0015

8. Dark matter and dark energy come from one origin

[ Dark matter ]

Calculating centripetal force in galaxy from negative mass distributed out of galaxy

fig11
caption : Revolution velocity of galaxy. The revolution velocity through the total quantity of matter that can be observed is A, while the actual observed value is B.

We observed not positive mass but gravitation effect.
That is, universe has not said that dark matter is positive mass.

This study mentioned the effect of centripetal force described previously, and the effect of centripetal force of negative mass with the description of dark matter. The researcher suggests that it is possible to prove the existence of negative mass with the comparison between observed value and revolution velocity of star according to the distance in galaxy which is calculated from negative mass distributed out of galaxy.

fig12
caption : Negative mass effect on arms of galaxy. The actual observed spiral galaxy is on the left. Since repulsive effects occur between negative masses in Newton’s dynamics, 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.

When negative mass is distributed uniformly, if we examine the area of galaxy diameter working the gravity on the basis of mass m for the analysis, there is no negative mass in the space of spiral space on the left, so negative mass can exist as much as the size of black and white on the right. negative mass on the right works the force on positive mass m on the origin to the left(positive mass moves after receiving the force that becomes farther from negative mass), and this direction will be in keeping with the central direction of gravity of real galaxy.

From the calculation of centripetal force in Newton dynamics, the important matters to calculate gravity effect of negative mass are the size and model of empty space of negative mass by real galaxy on the left, in case of spiral galaxy or oval galaxy, it may be close to oval if we consider the fact that most of mass is placed on galaxy core, the rotation of galaxy, and the gravitational radius of galaxy core, thus we regard empty space of negative mass as spherical or oval, and perform calculation to compare with observed value.

fig13
caption : Effective negative mass.
The negative mass distribution, where gravity is applied without cancellation of the oblique field located on the right side.

()

Adding the term of centripetal force by negative mass to the term of centripetal force by positive mass as described above, we compare revolution velocity of star and the density of negative mass, then expand this to apply to other galaxies, and we can inspect if the interpretation of dark matter distributed out of galaxy is proper or not.

The distribution of negative mass that remains without being offset in Fig. 13 is crescent-shaped, so it seems to be difficult to calculate, but if we assume that the white empty space on the left is full with negative mass and positive mass at the same density, here negative mass is uniformly distributed over the whole area, so the effect of negative mass on mass m is 0. Remaining positive mass is distributed over the white area on the left at the density of negative mass, and the gravity that uniformly distributed positive mass works on positive mass m place on radius r is worked only by the distribution of mass within radius r.

fig14
caption : Equal to the degree of gravity that is applied on the equally distributed positive mass within the radius r of the left side.
The gravitational effect from negative mass, which functions at mass m is equal to the gravitational effect from positive mass within radius r.

Therefore, the effect of negative mass that remains out of galaxy without being offset can make it approximate to the gravity generated by the distribution of positive mass within the radius R in galaxy

In equation(93)

The mass density of collisionless isothermal sphere is given as in galaxy dynamics. is velocity dispersion.

Equation (97) is applied to arbitrary spherical or oval galaxy, and in case of normal shaped spiral galaxy, the distance which spherical approximation can be applied from the center of galaxy will be effective.

So if we consider that the distribution of negative mass out of galaxy comes under isothermal, the effect of mass in galaxy by the distribution of negative mass out of galaxy is proportional to r as shown in equation (98 ), and this is in keeping with observed dark matter.

Positive mass dark matter distributed in galaxy does not form the spherical distribution, and it is broken owing to the gravity of galaxy core, gravitational action with stars, and rotation of galaxy, if its shape is not very intentionally assumed. Furthermore, there are various heat sources in galaxy according to position, so it cannot be regarded as collisionless Isothermal.

However, the effect of centripetal force that negative mass works from the exterior of galaxy can keep the spherical distribution of mass, and make the mass effect that increases linearly in accordance with distance r as seen above because it receives less influence from elements such as the gravity of galaxy core, or rotation of galaxy. Also ideal state of collisionless can be achieved by negative mass, because negative mass has repulsive effect each other.

At the solar system, non-observation of dark matter is explained. In negative mass hypothesis, dark matter exists at the exterior of galaxy, so dark matter is not observed at the solar system.

It described that the quantity of negative mass decided at the beginning of universe can explain the effect of centripetal force in galaxy(V-4), repulsion effect on cosmic expansion(V-3), decelerating expansion at the first half, and accelerating expansion(V-1) of universe at the second half(7 billion years ago) at the same time.

Therefore, it is necessary to try to calculate and observe negative mass more strictly, laying aside the abstract aversion of negative mass.

Please review to the fig12, fig13, fig14.
And then, please understand that the gravitational effect from negative mass is equal to the gravitational effect from positive mass within radius r.

========
Hypothesis of Dark Matter and Dark Energy with Negative Mass :
http://vixra.org/abs/0907.0015

9. A nice lot of maths there but does it actually translate into the real world? A few observations from skimming over your rather long posts:

How can you have negative mass? That would negate gravity.

Minus infinity is a nonsense term.

Pair creation is positive and negative charges.

Inflation is usually said to be faster than light, so wrong by all we know. If any matter is created from a great energy density, then you are quickly going to form a black hole, so end of inflation.

Is (positive) mass is converted to radiant energy? Isn't it supposed to be the opposite with matter forming at 10^-32 of a second after the BB?

Dark Energy seems to have come about around several billion years ago (so increased the speed of expansion), so several billion years after the big bang.

Our galaxy core has (the super massive black hole) has less than 1% of 1% of the galaxy's mass contained there so is irrelevant in a sense to the rest of the galaxy. The spiral arms rotate at maybe 150 miles per second so are spread out due to centripetal force (from original momentum) over eons.

10. Originally Posted by Cyberia
A nice lot of maths there but does it actually translate into the real world? A few observations from skimming over your rather long posts:

How can you have negative mass? That would negate gravity.

Minus infinity is a nonsense term.

Pair creation is positive and negative charges.

Inflation is usually said to be faster than light, so wrong by all we know. If any matter is created from a great energy density, then you are quickly going to form a black hole, so end of inflation.

Is (positive) mass is converted to radiant energy? Isn't it supposed to be the opposite with matter forming at 10^-32 of a second after the BB?

Dark Energy seems to have come about around several billion years ago (so increased the speed of expansion), so several billion years after the big bang.

Our galaxy core has (the super massive black hole) has less than 1% of 1% of the galaxy's mass contained there so is irrelevant in a sense to the rest of the galaxy. The spiral arms rotate at maybe 150 miles per second so are spread out due to centripetal force (from original momentum) over eons.
==========
Thanks Cyberia.
I’m sorry! I can’t English well.

A nice lot of maths there but does it actually translate into the real world? A few observations from skimming over your rather long posts:
==> Explain of dark matter of Bullet Cluster and MACS J0025.4-1222 Cluster will be posting.

Also, I had write to method to prove the existence of negative mass.
(V. Method to prove the existence of negative mass)

Minus infinity is a nonsense term.
==> Please read to “II-3. Negative mass is stable at the maximum point!”. I will posting.

Inflation is usually said to be faster than light, so wrong by all we know. If any matter is created from a great energy density, then you are quickly going to form a black hole, so end of inflation.
==> If positive mass was only created, universe is black hole as your say,
But if negative mass and positive mass were born together at the beginning of universe, universe is not black hole. Also total potential energy has a plus value at that time. So expansion is not problems.

Is (positive) mass is converted to radiant energy? Isn't it supposed to be the opposite with matter forming at 10^-32 of a second after the BB?
==> Refer to the V-5 at the paper.

Dark Energy seems to have come about around several billion years ago (so increased the speed of expansion), so several billion years after the big bang.
==> No. Dark Energy is existed at the beginning of universe. Also Inflation has come from the dark energy. It is mainstream argument. That problem is called “CC Problem or Phase transition problem of dark energy”

Our galaxy core has (the super massive black hole) has less than 1% of 1% of the galaxy's mass contained there so is irrelevant in a sense to the rest of the galaxy. The spiral arms rotate at maybe 150 miles per second so are spread out due to centripetal force (from original momentum) over eons.
==> It is a bad understanding of the below sentence.

so it seems to be difficult to calculate, but if we assume that the white empty space on the left is full with negative mass and positive mass at the same density, here negative mass is uniformly distributed over the whole area, so the effect of negative mass on mass m is 0. Remaining positive mass is distributed over the white area on the left at the density of negative mass, and the gravity that uniformly distributed positive mass works on positive mass m place on radius r is worked only by the distribution of mass within radius r.

Remaining positive mass density is equal to the negative mass density(Out of galaxy). It has not means to galaxy density.

11. II-3. Negative mass is stable at the maximum point!
therefore the catastrophe to energy level of minus infinity never happens

Nature prefers stable state, and has the tendency to go to stable state. Additionally, this can be expressed in another way that nature prefers low energy state, and has the tendency to go to low energy state.

Such an idea is frequently used as a logic which denies the existence of negative mass. That is, if there is negative mass and negative energy level, negative mass spontaneously emits energy to be stable, and goes to energy state of minus infinity, so finally it is confronted by catastrophe. Is it right?

In case of positive mass, stable state means low energy state, therefore it is not necessary to divide which one nature prefers among two states(stable state and low energy state).
By the way, does stable state mean low energy state also in case of negative mass?

We can get an answer, if we examine Harmonic oscillation.

fig04
caption : When there is negative mass in potential which has a point of maximum value and a point of minimum value.

We begin by considering the oscillatory motion of a particle that is constrained to move in one dimension. We assume that there exists a position of unstable equilibrium for the particle and we designate this point as the origin. Restoring force is in general some complicated function of the displacement and perhaps of the particle's velocity or even of some higher time derivative of the position coordinate.

We consider here only case in which the restoring force F is a function only of the displacement

F(x) can be expanded in a Taylor series,

Since the origin is defined to be the equilibrium point, F(0) must vanish, Then, if we confine our attention to displacements of the particle that are sufficiently small, we can neglect all terms involving and higher powers of x. We have, therefore, the approximate relation

The force is always the opposite directed toward the unstable equilibrium position(the origin), the derivative F'(0) is positive and therefore k is a positive constant.

This form of differential equation is the same as that of particle which has positive mass. But we have to notice that positive mass carries out harmonic oscillation on a point of minimum value, whereas negative mass carries out harmonic oscillation on a point of maximum value. Additionally, restoring force is +kx at this time.

In phase space

This equation is ellipses equation, because total energy

As examined in the question of Harmonic oscillation, in case of positive mass, a point of minimum value which energy is the lowest is stable. However, in case of negative mass, stable equilibrium is a point of maximum value, not a point of minimum value. So negative mass is toward a point of maximum value to be stable, not a point of minimum value which energy is low.

In the world of positive mass, ground state is a point that energy is low, but in case of negative mass, ground state is a point that energy is the highest.

Accordingly, in the world of negative mass, energy level is filled from the highest to the lowest, and stable state means the highest energy state, so the catastrophe to energy level of minus infinity never happens even if negative mass spontaneously emits energy.

========
Hypothesis of Dark Matter and Dark Energy with Negative Mass :
http://vixra.org/abs/0907.0015

12. II-2. Negative mass cannot form the structure greater than atom

As examined the equation of motion for negative mass, it is marked in form of F= - ma (m>0), when attraction is applied together with nuclear force(when usually nuclear force is attraction, but has the form of repulsive core, and assuming nuclear force has the form of , Q(r) is the positive function of distance r, thus nuclear force is in the form of attraction worked in the direction of -. Here, for the force worked on negative mass –m,

The term of acceleration is positive, so the effect of increasing distance r, namely repulsive effect appears. This means that negative mass cannot form the structure like atom(massive nucleon, baryon, particle consists of multi elementary particle), because nuclear force has not binding negative mass when it is applied to negative mass. Also, gravity has not binding negative mass(repulsive)

Additionally, for the problem of mesons that mediates nuclear force or weak interaction, if there is no meson that delivers strong interaction or weak interaction, it is doubtful if strong interaction or weak interaction can be worked or not.

For example, nucleon must have internal structure including meson or quark, but in case of negative mass, nuclear force is repulsive, so it cannot have the internal structure of nucleon from the beginning. That is, there is a great possibility that negative mass cannot include meson or quark which has negative mass in nucleus.

The fact that it cannot make nucleon means that it is impossible to form massive mass structure like a star in addition to atomic structure. This provides proper explanation of the fact that negative mass is not seen as it has visible massive mass structure. Also generally it satisfies the nonbaryonic matters required for dark matter.

If negative mass was born at the beginning of universe, there is higher possibility that it exists until now as a certain basic state born at the beginning of universe, and that it does not have strong interaction like nuclear force, weak interaction, and electromagnetic interaction(neutral or has not internal structure(positive mass elementary particle has a ±1/2, ±1/3, 2/3 charge)). This point is keeping with current characteristics required for dark matter.

If negative mass and positive mass were born together at the beginning of universe, positive mass has attractive effect each other, so it forms star and galaxy structure now, but negative mass has repulsive effect each other and nuclear force cannot form nucleons by binding negative mass, so they cannot make massive mass structure like star or galaxy.

If dark matter is negative mass, non-observation of dark matter star and galaxy can be explained.

========
Hypothesis of Dark Matter and Dark Energy with Negative Mass :
http://vixra.org/abs/0907.0015

13. V-6. Colliding with Bullet Cluster

As shown in the recent observation of dark matter, dark matter seems not to interact with each other when colliding with galaxy clusters, and it can be predicted with essential characteristics of negative mass.

Uniformly distributed negative mass receives attractive effect from massive positive mass, so dark matter which has negative mass is clustered around galaxy because of attraction of galaxy. If the type of force worked between negative mass when colliding with galaxy clusters is repulsive, and negative mass is distributed almost uniformly without forming massive mass structure, the shape of dark matter is not distorted or transformed even if dark matter(negative mass) and dark matter(negative mass) pass through similar area, that is, they will seem not to interact each other. Also there is repulsive effect between dark matters that are made up with negative mass, thus there will be almost no direct collision as well.

Repulsive effect that is the nature between negative mass as described above provides the proper description that existing dark matters do not interact each other, although they interact gravitationally with positive mass.

As the factor that breaks the uniform distribution of negative mass,

First, negative mass receives the attractive effect from massive positive mass, thus for the distribution of negative mass near massive positive mass such as galaxy or galaxy cluster, the density of negative mass is higher as it is closer to galaxy or galaxy cluster, and is lower as it is farther.

Second, If positive mass(like galaxy cluster) that has strong gravity or interstellar cloud that has positive mass pass through existing area that negative mass is distributed, negative mass can be disappeared when meeting positive mass or it can be drawn owing to attractive effect of massive positive mass at this moment, so there can be the area that negative mass, namely, dark matter is not uniformly distributed

Fig20. Collision of Bullet Cluster.
We can see that general matters(red color) are close to each other, and dark matters(blue color) are on the far side.

(http://arxiv.org/abs/astro-ph/0608407v1)

Fig23. MACS J0025.4-1222 Cluster.
We can see that general matters(yellow line) are close to each other(center), and dark matters(red line) are on the far side.
(http://arxiv.org/abs/0806.2320v2)

==========
i)Positive mass, positive mass : attractive

ii)Negative mass(dark matter), negative mass(dark matter) : repulsive

iii)Massive positive mass, negative mass : attractive

iv)Result : At least, from 3 characteristics above, we can predict that positive mass and positive mass are arranged on the close side, and negative mass(dark matter) and negative mass(dark matter) are arranged on the far side.

Can we explain the phenomenon that dark matter is arranged on the far side and visible positive matter is arranged on the close side in Fig.20 with other dark matters?

Negative mass shows the result matched with the phenomena, and it means that it is necessary to perform more strict simulation with negative mass.

========
Hypothesis of Dark Matter and Dark Energy with Negative Mass :
http://vixra.org/abs/0907.0015

14. [ Abstract ]

From the observance of the HSS team in 1998, they gained the mass density of the negative( Ω_M = -0.38( ± 0.22)), using field equations which do not have the cosmological constant.

The quantity of the mass couldn't be negative value in they thought, the value is trashed away.
We have to know that not the field equation has disposed the value, but our thought disposed that value.

In the world of positive mass, ground state is a point that energy is low, but in case of negative mass, ground state is a point that energy is the highest.

Accordingly, in the world of negative mass, energy level is filled from the highest to the lowest, and stable state means the highest energy state, so the catastrophe to energy level of minus infinity never happens even if negative mass spontaneously emits energy.

Assuming that negative mass exists, Newton's Law of motion was derived in between negative and positive masses and also between negative and negative masses.

As a method for proving the existence of negative mass, an explanation on the revolution velocity of the galaxy through negative mass has been presented. In this process, the existence of spherical mass distribution was given; furthermore, explanation was done using this, to show observation results where dark matter effect through negative mass is proportional to distance r.

If Ω_M is -0.38, universe's age is 14.225 Gyr. It is in the range estimated by other observations.

Assuming that negative mass and positive mass were born together at the beginning of universe, it satisfies the various problems that previous dark matter and dark energy possess, such as,

[ Dark matter ]
- Centripetal force effects of galaxy and galaxy clusters from previous dark matters,
- Mass effects that is proportional to the distance r,
- Low interaction between dark matter when collision occurs between dark matter.

[ Dark energy ]
: Repulsive force needed for expansion, dark energy that has positive values,

[ Fine tuning problem of mass density ]
: The reason of that mass density close to the critical mass density.

[ Cosmological Constant Problem ]
- The reason of that dark energy seems to has a small and non-zero value.
- Phase transition problem of dark energy

[ Others ]
- Collision of Bullet cluster,
- Deceleration expansion and acceleration expansion of universe,
- Age of the universe with negative mass density
- Size of the universe

[ Proof of that observed dark energy value ]
: Dark energy observation value ()

As a result, the necessity of observation focusing on exact computation and detection of negative mass is stated.

========
Hypothesis of Dark Matter and Dark Energy with Negative Mass :
http://vixra.org/abs/0907.0015

15. Size of the universe

fig11. Relations between radius of the universe and dark energy density

* mass density of ordinary matter = 1 proton/5m3
* Proton mass= 1.67264 X 10-27kg
* G =6.6726 X 10-11 m3/s2kg
* 1J = 6.242 x 1018 eV
*
*
* If , dark energy density has a 1/3 smaller than .

In a WMAP, observed value

Dark energy density :

Radius of the universe : 96.7 Billion light years!

In the hypothesis of dark matter and dark energy with negative mass
Size of the universe(diameter) : about 193.5 Billion light years!
Circumference of the universe : about 607.65 Billion light years!
Volume of the universe : about 3.792 X 10^15 (light years)^3

From Neil J. Cornish, the universe' radius is at least 24Gpc(78Gly).
(2003, Neil J. Cornish, "Constraining the Topology of the Universe", http://arxiv.org/abs/astro-ph/0310233v1 )

=========
Hypothesis of Dark Matter and Dark Energy with Negative Mass :
http://vixra.org/abs/0907.0015

16. no one is going to read this. it is far too long.

17. Originally Posted by gravityguru
no one is going to read this. it is far too long.
What I find refreshing is the presence of actual equations and predictions. Given that so many posters with new ideas would rather write terse posts and link us to their websites, I really don't think it is fair or productive to criticise the people actually willing to put in some detailed content.

Please restrict further discussion to questions or criticism about the actual topic.

18. I can propose some ways to prove validity of hypothesis of negative mass.

1) Dark matter and dark energy come from one origin
According to hypothesis of negative mass, most of dark matters have negative mass and it proves that dark energy is a gravitational potential energy(with positive value) between negative mass and positive mass.

Currently, there are Ω_m = - 0.38(±0.22) and Ω_m = - 0.4(±0.1) values what HSS team and SCP team calculated in relation to size of negative mass corresponding with size of dark energy and another one what I calculated in V-2.

What we have to do now, is to induce rotation curve or the quantity of dark matters within the galaxy, referring to the method what I proved in V-4.(Calculating centripetal force in galaxy from Negative Mass(Dark Matter) distributed out of galaxy.)

Therefore, when centripetal force effect by density of this negative mass can explain rotation curve within the galaxy after setting density of negative mass outside of the galaxy as Ω=-0.38 or to be five ~ X times bigger than positive mass’s, it would explain dark energy and dark matters at once through negative mass, thus proves that hypothesis is right.

2) Verification of equation of dark energy suggested in V-2.
Since there are some equations of dark energy and they are explaining that they are the same forms. Therefore, by analyzing characteristics of this equation, we can know whether hypothesis is right or wrong.

3) Simulation of the Bullet Cluster
It is expected that hot gas exists in the middle, from attractive gravitational interaction, while negative mass still surrounds two galaxy clusters when carrying out a simulation in the structure what negative mass surrounds two galaxy clusters before the crash.

i)Positive mass(hot gas), positive mass(hot gas) : attractive
ii)Negative mass(dark matter), negative mass(dark matter) : repulsive
iii)Massive positive mass(Galaxy), negative mass(dark matter) : attractive
: View to the simulation video-1
(Motion of the negative mass and dark matter -1

4) Some details are additionally described to verify other hypotheses of negative mass.

Have a nice day!
--- Icarus2

==========
1) Hypothesis of dark matter and dark energy with negative mass :
http://vixra.org/abs/0907.0015
2) Video of the motion of negative mass, dark matter, dark energy :

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

[ Dark matter and dark energy come from one origin ]

According to hypothesis of negative mass, most of dark matters have negative mass and it proves that dark energy is a gravitational potential energy(with positive value) between negative mass and positive mass.

Currently, there are Ω_m = - 0.38(±0.22) and Ω_m = - 0.4(±0.1) values what HSS team and SCP team calculated in relation to size of negative mass corresponding with size of dark energy and another one what I calculated in V-2.

What we have to do now, is to induce rotation curve or the quantity of dark matters within the galaxy, referring to the method what I proved in V-4.(Calculating centripetal force in galaxy from Negative Mass(Dark Matter) distributed out of galaxy.)

Therefore, when centripetal force effect by density of this negative mass can explain rotation curve within the galaxy after setting density of negative mass outside of the galaxy as Ω=-0.38 or to be five ~ X times bigger than positive mass’s, it would explain dark energy and dark matters at once through negative mass, thus proves that hypothesis is right.

[ Simulation Video ]

In the simulation,
When negative mass's shells exist at outline, collision time is shorter compared to existing only with positive mass's shells. This implies that there exist additional effects of centripetal force by the dark matter halo at the galaxy's outside in case of the galaxy having the axial symmetry(rotating galaxy).

1. Observation evidence for dark matter
1) Galactic rotation curves
2) Galaxy clusters and gravitational lensing
3) WMAP
4) Bullet cluster
5) Structure formation

2. In the Galaxy, No evidence for dark matter
1) At the Earth : non-observation(Xenon100, CDMS-II...)

2) At the solar system : non-observation

3) At the center of galaxies : no evidence
Greedy Supermassive Black Holes Dislike Dark Matter
http://www.universetoday.com/13091
Astronomers Find Black Holes Do Not Absorb Dark Matter
http://www.universetoday.com/60422

4) At the galactic plane : no evidence
"No evidence for a dark matter disk within 4 kpc from the galactic plane"
http://arxiv.org/abs/1011.1289v1.pdf

5) At the galactic halo : no evidence
Globular Cluster problem
"Evidence Against Dark Matter Halos Surrounding the Globular Clusters MGC1 and NGC 2419"
http://arxiv.org/abs/1010.5783

3. Negative mass hypothesis
It is simply explained.
Dark matter which has negative mass is clustered around galaxy. And centripetal force effect exist in the galaxy from dark matter halo out of the galaxy.
===========

Additional effects of centripetal force exist from the previous simulation.
Unfortunately, evidencing the effects of centripetal force in the negative mass has not been succeeded yet owing to my knowledge shortage.

However, this simulation program was designed by other persons, and thus more trustworthy than me.-_-;;

If there is a person among readers of this report who can treat with classical mechanics(or general relativity) skillfully, please attempt evidences on the centripetal force’s effects having been made by the negative mass’s shell (having the axial symmetry or sphere one).

Refer to video :

=============
Hypothesis of dark matter and dark energy with negative mass :
http://vixra.org/abs/0907.0015

20. Why dark matter does not emit photon? My answer!

We are now living in the era of new revolution.

Are we again treading on the process of huge revolution that occurred in the late 19th century and the early 20th century?

The current observation of dark matter requires explanation on two important situations as the following.

Situation 1: Denial of the gravitational (attractive) phenomenon
Dark matter is five times more than the general matter, but it does not show macro-structure like the structure of galaxy or galaxy cluster, or micro-structure like fixed star or planet. The result of the current observation is that dark matter has attractive interaction with the general matter, but does not interact with the other dark matter. In other words, the observation or interpretation is that dark matters do not exert gravity(attraction) on each other.

Situation 2: Denial of the fundamental phenomenon of physics that absorbs or emits photons
It is not the level that dark matter has not interacts electromagnetically because it is electrically neutral, but the observation result is the level that dark matter does not emits or absorbs photons.

From the several explanations above(refer to my old thread or my paper), Situation 1 shows that the essence of dark matter is negative mass, and that consequently they have the repulsive gravitational effect, so it can be explained.

In regard to Situation 2, without giving that kind of characteristics of “the observation result that seems to be that it does not emit or absorb photons” from the first, can this kind of result be induced from other basic principle?

A. Negative mass is stable at the state of high energy.

Fig1. ,
,(). 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.

B. The problem of transition from positive energy level to negative energy level
Since we do not know clearly about the characteristics of negative mass yet, we do not know whether transition of positive mass at the positive energy level to negative energy level is possible or not.

Fig2. Transition to the negative energy level

However, for positive mass to enter the area of negative energy level, energy should have the negative value, and this means that it should have the characteristics of the negative mass.
When considering the process of entering the domain of negative energy level from positive energy level, it must pass through the domain between 0 and . In case it follows the laws of negative mass because it's in the domain of negative energy, it cannot reach ,which is the first energy level of negative, because it is stable at the state of high energy, and it tries to have higher value of energy. It is because the energy level is much higher than the energy level . That is to say that it shows possibility that the law of negative mass itself does not allow the situation where positive mass at the positive energy level succeed to the negative energy level.

Even if it reaches , the first energy level, at the negative energy level, it must follow the law of negative mass, it is stable at the state of high energy, and thus “the problem of the transition of the energy level of minus infinity” does not occur.

As we have examined above, “the problem of the transition of the energy level of minus infinity” does not occur, and thus positive mass and negative mass can exist in the same spacetime. This is a very important result because it means that negative mass and negative energy can exist stably in our universe.

(This finding suggests that “the problem of the transition of the energy level of minus infinity”, which we have had for eighty years regardless of whether negative mass exists or not, does not occur, and it itself has important meaning. Thus, it needs to be reflected in the teachings that are being performed when explaining the solution to negative energy, which the relativistic energy eq. suggests.)

In regard to Situation 2, without giving that kind of characteristics of “the observation result that seems to be that it does not emit or absorb photons” from the first, can this kind of result be induced from other basic principle?

C. Why dark matter does not emit photon?
1) The process of negative mass emitting photon

: Initial energy of negative mass,
: Energy of photon

The relational expression above means that if negative mass emits photon(with positive energy), then the energy after emitting gets lower than the energy before emitting.

Negative mass is stable at the state of high energy, so the voluntary transition that negative mass emits photon and succeeds to the lower energy level does not exist. Therefore, negative mass explains the result of the current observation that dark matter does not emit photon from the fundamental principle.

* The explanation on why dark matter does not emit photon is enough with this. In my paper, more various situations are set-up.

---Icarus2

Negative Mass is Stable at the State of High Energy
viXra.org e-Print archive, viXra:1107.0052, Negative Mass is Stable at the State of High Energy

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