Matter

The confusion began when we refer to singularity as an ultra dense mass. Mass is a property of space-time universe. According to John Earman, mass cannot exist in singularity. If we define singularity as the origin of our universe but out of our space-time structure, we have to take it as a no-mass entity. We may hypothesize this because space and time originated at the time of big bang.

The Einstein formula (Larantz transformation) for a mass in motion is;

m = m0 / sqrt (1 - v2/c2)

The formula for time is

t = t0 / sqrt (1 - v2/c2 )

If we take m as mass inside space-time after big bang (the time that space started and motion could be possible) and m0 as mass which was present at the beginning of time(t0) we come to following conclusion;

m/m0 = t/t0

m0 = mt0/t

m0 = 0/t = 0

So we can conclude that the mass at time equal zero (time of the big bang) had to be zero. Or we may say that singularity had to be mass less.

Alternatively, Nahid S. Gozin Is showing how singularity can not contain mass by following equations.

t = t0 / sqrt (1-v2/c2 )

Or, sqrt (1-v2/c2 ) = to /t , Where to is beginning of time and t is the time of appearance of mass in universe.

If to = 0, then sqr(1-v2 / c2) = 0/t = 0, or sqr(1-v2/c2 ) = 0, therefore (1-v2/c2 ) = 0

So, v2/c2 = 1, or v2 = c2 therefore v = c is speed of mass at the time when it appeared in space-time.

The mass at time 0 comparing to the mass after appearance inside space-time can be calculated from ;

m = m o / sqr(1-v2/c2 ), and

m o = m* sqr(1-v2/c2 )

If the speed of particle at time 0 was equal to speed of light then,

m o = m* sqr(1-1) = 0

According to above singularity could not contain mass. If we believe that singularity was a compressed mass then gravity would stop the infaltion and creation of the universe. Paul Davies argues that in state of maximum compression of matter, we need "some sort of outward force to overcome the enormous gravity, otherwise gravity would win, and the material would be still more compressed." 7-p48-49. He then conclude that under condition of extreme compression such as occurred during the big bang, there is no force in the universe capable of beating off the crushing power of the gravity. 

Elsewhere John Earman suggests "Perhaps. In entailing singular behavior General Theory of Relativity is committed to empirically false predictions" Ref. 4-p224

According to Big Bang Theory quarks first appeared after cosmic inflation. The vacuum energy transforms itself to particles and anti-particles of matter in equal number. So at the beginning of time there was no mass present. Unless we assume that the ultra dense matter turned to pure energy before reformation to matter particles. We can as well assume that universe started with a burst of energy. With this assumption singularity does not have to contain mass.

In this case we will not have positive gravity force and/or event horizon for singularity. Even we may assume a kind of negative gravity force (Repulsive) to initiate space-time.

If we remove mass from singularity, it turns benign.

Dimension

Einstein mentions that singularity cannot contain topological space. So Singularity does not have space. It means there is no spatial dimension in it. In other words, singularity is a mathematical point. Space is a property of space-time. According to Big Bang theory space started at time0 and expanding since. Heizenberg uncertainty principle suggests that, in small-scale location gets blurred. We will discuss this in further detail later.

If we denied mass as origin of universe we have to consider its energy equivalent as the initiator. The formula for the venomous energy which built our space-time universe is as follows;

ψ (E) = E max e i ( κr^n -ωt ) = E max e i ( κnr -ωt )

Where ψ (E) is energy function, i is imaginary number , κ is wave number, nr is number of dimensions, ω is angular velocity and t is time.

ψ(E) = E max e iκnr e -i ωt

in singularity t = 0, then e -i^ω t = e 0 =1

ψ(E) =E max eiκnr

We told that energy is maximum in singularity then ψ(E) =E max therefore e i κnr = 1

If iκrn = 0 we may conclude that n = 0 which means there are no dimension in singularity. or we can claim singularity does not contain space.

The physical reality of imaginary numbers are not defined in space-time. For the time being let us attribute it to virtual functions in singularity. Remember dimensions of superspace in supersymmetry model have zero size.

Time

"As Einstein said, physical laws break down at space- time singularities, and for the big bang and big crunch they break down so strongly that it is physically meaningless to talk about before and after" (Reference 4-p20)

According to theory of big bang, notion of time does not exists in singularity. Time is a property of space-time universe. If we extend the uncertainty principle to energy and time in small-scale time gets blurry.

Energy

If we deny the ultra dense matter, of being the origin of our universe, we have to find another source to substitute it. Big bang model states that our universe started with burst of tremendous amount of energy. This initiated the primary inflation.

Not comfortable with it? this is another evidence; The Heisenberg Uncertainty principle can be extended to time and energy. The second Feynman Diagram for Compton Scattering leads us to such an uncertainty. its formula can be written as;

ΔE * ΔT = or greater than h/2π

Where h is (Planck Constant), ΔE is the uncertainty in energy and ΔT is the uncertainty in time.

ΔE = or greater than h/2πΔT. If the product of ΔTΔE is minimum, then we can write ΔE = h/2πΔT
If ΔT approaches 0, ΔE approaches infinity.

While in larger intervals of time the change of energy of particles are related and proportional, in ultra short intervals the amount of energy increases exponentially. In zero time zone, the changes of time will be zero. Therefore the changes of energy amounts infinity. -later on we conclude that we are exposed to singularity in each Planck distance.

If the changes of energy in singularity is infinity we may conclude that the amount of energy itself is also infinity.

But what kind of benign singularity this can be if it contains infinite amount of energy?

On the above formula when time intervals are 10-43 The amount of energy is huge but as time intervals get bigger energy reduces very fast to harmless levels. Later on we see that if the blast of energy last for ultra short time and disappears, it will not have any effect in our material world.

Energy, through the creation of matter and anti-matter, can initiate our space-time universe, as it is today.