Grand Unified Field Theory

Curvature and Torsion are two major basic components of differential geometry which stands for gravitospinnism and electromagnetism, respectively. In fact, physic is geometry.

Torsion tensor is：

T(X,Y)=xY-yX-[X,Y]

And torsion satisfies

=d+

Curvature tensor is:

R(X,Y)Z=x yZ-yxZ-[x,y]Z

And curvature satisfies

=d+

We can use curvature form and torsion form to restore curvature and torsion. If there is a point u in FxM, then

T(x,y)=u[2(-1(x),-1(y))]

R(x,y)z=u[2(-1(x),-1(y) )][u-1(z)]

And, Bianchi identities link torsion and curvature in geometry. If cyclic sum is G, then

G(R(x,y)z):=R(x,y)z+R(y,z)x+R(z.x)y

The First Bianchi identity：

G(R(x,y)z)=G[T(T(x,y),z)+(xT)(y,z)]

The Second Bianchi identity：

G[(xR)(y,z)+R(T(x,y),z)]=0

Thus, torsion tensor and curvature tensor can be linked together.

In my previous article, I proposed that radiation pressure (universal lightity) is the best candidate of dark energy which causes universe expansion. Because gravity, electromagnetism, and lightity are all mediated by space-time, the three fundamental forces can be united in one equation. I call this a Grand-unified Field Theory.

In electroweak theory, electromagnetic radiation is a U(1) group. The electromagnetic radiation can also be expressed by a rank-2 tensor:

Tuv=δAu/δXv-δAv/δXu (Au and Av are electro-vector potentials)

We can see that radiation emitted from the galaxy or charge center are moving out via a spiral (vortex) shape. Then, the radiation will reach the peripheral of universe and circulate the universe. The net effect of electromagnetism is to be spirally convergent in a certain point in space-time. However, the net effect of electromagnetic radiation is to be spirally divergent in the peripheral space-time. Thus, these two fundamental fields cancel each other. There are two possibilities about the cancellation of these two fundamental forces. First, when the charge is annihilated in galaxy, the common sequel is neutron production from proton due to nuclear fusion. The net product is a photon and the spacetime vortex from the original charge such as proton is vanished. The generated photon can produce energy-momentum tensor via radiation pressure. It means that net effect of electromagnetism and lightity is equal to zero. Second, when the charge is present in galaxy, the charge will suffer from gravity field acceleration. Thus, this charge will still have thermal radiation due to this acceleration. This thermal radiation can radiate out along with the 4D spacetime vortex line due to electromagnetism. This explains why every charge can radiate as it is above absolute zero temperature. The electromagnetic potential of the electromagnetic field and the radiation-lightity field is the same-retarded potential. According to the field tensor formula, these two tensors still cancel each other out. The net effect is still zero.

In summary, we can list the three major tensors by definition:

Gravitospinnity tensor by Einstein: -Guv=-kEuv=Ruv-1/2g_uvR

Faraday(electromagnetic) tensor Fuv=∂Au/∂Xv-∂Av/∂Xu

Temperature-lightity tensor Tuv==∂Au/∂Xv-∂Av/∂Xu

by U(1) Abelian group

Because lightity is out-expanding force and electromagnetism is inward force. The two forces should cancel each other. Because both F^k_uv and T^k_uv can cancel each other in the 4D space-time, the total net effect of these two in the new field equation is zero.

Similar to Einstein’s universe field equation (-Guv=Ruv-1/2g_uvR), I propose:

Guv+Fuv-Tuv=-(Ruv-1/2g_uvR),

It is worth nothing that the original Einstein field equation is derived from Bianchi identity with vanishing torsion. Since the Fuv and Tuv cancel each other, the net effect of torsion is vanished. Einstein provided the relativity of Energy, INertia and SpaceTime. Thus, Einstein’s deduction is reliable and correct.

Due to Einstein’s deduction in his book: the meaning of general relativity:

R=g^uvRuv and g_uv*g^uv=4 in four dimensional space-time

Introduce this, we can get:

Ruv=Guv+Fuv-Tuv

(Ruv=Ricci-Riemann curvature tensor; means sphere surface)

Guv is “G”ravitospinnity tensor, Fuv is “U”(1) “F”araday electromagnetic tensor, Tuv is u(1) “T”emperature-lightity tensor. It is worth noting that Einstein originally introduced a cosmological constant in his Einstein field equation because he assumed that our universe is a static universe. However, Hubble observed that our universe is actually accelerated expansion. Thus, the item of cosmological constant should be omitted. Professor Friedmann omitted this cosmological constant in Einstein field equation, and he found the solutions of this equation means our universe is either expanding or contracting. This fits the observation of our expanding universe.

Ricci flow is a concept used by Grigori Perelman to prove Poincare conjecture. In fact, the formula of Ricci flow is identical to Einstein field equation:

Ricci flow=Ruv-1/2g_uvR

By the characteristics of Ricci flow, positive Ricci curvature can contract to a point and negative Ricci curvature can expand in terms of Einstein manifold (Ricci=constant*metric g_uv).

Since Ruv-1/2g_uvR=-KEuv

Energy-momentum tensor Euv=ρUuUv-pg_uv

(ρ=mass density, Uu or Uv=velocity, p=pressure=radiation pressure, g_uv=metric tensor)

Since radiation has both characteristics of mass(E=mc2) and charge(EM radiation), it should has one tensor included in mass-like energy-momentum tensor and the other tensor included in charge-like temperature-lightity tensor.

Thus,

Ricci flow=Ruv=Guv=kEuv=k(ρUuUv-pg_uv)

When mass is dominant than radiation, ρUuUv is greater(>>) than pg_uv. Then, the positive Ricci curvature will contract due to Ricci flow. When radiation is dominant than mass, ρUuUv is less(<<) than pg_uv. Then, the negative Ricci curvature will expand to its maximum. This formula can prove our universe is radiation dominant expanding universe.

Thus, Ricci flow=Ruv=-k(pg_uv)

Radiation pressure P is σT4/c which is in proportion to the fourth power of acceleration. Our universe is accelerated expanding!

G mediates space-time curvature, F mediates space-time spiral shape (spiral convergence), and T mediates space-time spiral expansion. G and F cause matter to gather together. It is a new universe field equation. The initials of G, F, T stand for “G’rand-“U”nified, ‘F’ields, ‘T’heory.