國立台灣師範大學物理系 物理教學示範實驗教室(網站) 物理問題討論區 (黃福坤)
我們也針對科學教學建立開課系統:科學園,讓老師更方便運用網路科技輔助教學,歡迎教師多加利用! 中學物理(維基)
(學習物理不只是know HOW 更重要的是 know WHY, 歡迎參考聞名全球的物理動畫, 英文網頁NTNUJAVA以動畫為主) 白話物理
關鍵詞 最近 物理名詞中英檢索 無法登入或系統功能不正常回報
討論區首頁 >>物理課程相關問題(分成國中/高中/大學等區) >>大學物理相關內容討論>>Final Grand Unified Field Equation
本區 註冊登入 者方可留言
近代物理 標題:Final Grand Unified Field Equation
1:wanchung榮譽點數17點(大學(院))張貼:2010-10-07 18:30:44:

Title: Charge Relativity and Theory of Everything

Wan-Jiung Hu

Abstract

General relativity deals with mass and its cause on space-time curvature. The other fundamental force-electromagnetism and its effect on space-time geometry are being neglected. Here, we propose that electromagnetism causes space-time to become a spiral shape structure. Coulomb’s electricity causes open spiral with non-zero divergence, and magnetism causes close spiral with zero divergence. The author calls this new relation between electric charges and space-time “charge relativity”. The original general relativity should be called “mass relativity”. Electromagnetic Faraday tensor is actually the torsion tensor of space-time structure. Charge relativity can explain sun’s magnetic field shape-parker spiral. The charge relativity can explain why the spiral galaxies are spiral shaped. Because there is electromagnetism in spiral galaxies mediating attraction, dark matter is not needed any more to explain the discrepancy between Virial mass and mass from light-to-mass ratio. The spiral shaped space-time structure can also explain the repulsive characteristics as well as attractive characteristics between two charges. According to the new charge relativity, general relativity, and universal lightity, forces mediated by space-time can be summarized in one equation. I call this equation “A Grand-unified Field Theory”. The equation is Guv+Fuv-Tuv=Ruv; T is temperature-stess tensor caused by radiation pressure P=(KT^4)/c. This equation is like Einstein’s field equation and is to explain the universe space-time structure. The new theory is very exciting and it can bring us some important breakthrough in physics research.

Standard model is a very successful field unification theory. However, current standard model only deals with electromagnetism, weak force, and strong force( U(1)xSU(2)xSU(3)). Standard model doesn’t deal with gravity and is not considering dark energy. Since I proposed that radiation pressure is dark energy and QED is wrong, I think that U(1) should be radiation pressure mediated by photons transfer. Thus, the structure and symmetry of standard model are not changed. Here, I also propose that gravity and electromagnetism is derived from radiation pressure. Thus, all the fundamental forces can be united to form a grand unification fields theory(GUTS) or theory of everyting(TOE).

Main Text

It is well known that Einstein’s general relativity says that mass causes space-time curvature to produce gravity. However, the relationship between electromagnetism and space-time is neglected. Here, we propose that electromagnetism is also mediated by space-time structure change. This new theory-charge relativity is going to replace current quantum electrodynamic theory (QED). QED says that electromagnetism is mediated by photo transfer and change. This description cannot explain the field (strength line of force) characteristics of electromagnetism. If electromagnetism is mediated by photo change, there will be no difference when test charge is near the central charge or the test charge is far away from central charge. According to Faraday’s force line theory, test charge will receive more field force when it is approaching the central charge. Second, I propose a new atom model saying that all electrons are orbiting in the same plane around the atomic nucleus. For example: Neon has full 8 electrons in its outer orbit, so two electrons must be in the opposite position in the orbit. It means that when one electron is in the right side of atomic nucleus, there must be the other electrons in the left side of atomic nucleus. QED says when attractive electromagnetism is mediated when two charges are releasing photos back to back. Thus, when proton and the first electron are releasing photos back to back for electromagnetism attraction, there must be the other electron receiving the photos released by protons and the second electron will be expelled out due to repulsive electromagnetism explained by QED. Third, QED is based on Schrodinger and Dirac’s quantum mechanics formula, and quantum mechanics is proved to be wrong according to my new atom model. Fourth, radiation pressure is due to heat, and electromagnetism is due to charge. Heat is not equal to charge. Thus, QED claimed that electromagnetism is mediated by radiation pressure is wrong. Fifth, the most important, QED needs to use virtual photons to explain electromagnetic attraction and repulsion. It need to claim that virtual particles move backward in time to explain repulsion and attraction. However, virtual photons are never observed. In addition, particles should not move backward in time that disobeys the principle of causality. In addition, current Lamb shift experiment gets exact results which are very different from QED’s prediction. Based on the above reasons, I will need to propose a new theory to replace QED.

One important reason for Einstein’s proposing general relativity is Newton’s gravity formula (F=GMm/r^2) implies that gravity is a force with action in distance and gravity can be mediated faster than lightspeed. This disobeys the basis principle of special relativity. However, Coulomb’s electrostatic force formula (F=KQq/r^2) also implies that electromagnetism is also a force with action in distance and electromagnetism can be mediated faster than lightspeed. Thus, we need to propose a new theory to let electromagnetism obeys the fundamental principle of special relativity. I propose here that electromagnetism is also mediated by space-time structure change. We know mass can cause a dent (curvature) of space-time due to Einstein’s general relativity. I propose that charge can cause spiral formation of space-time structure. Because dent (curvature) can cause inertia, spiral formation by charge is not causing a central dent or curvature. However, positive charge and negative charge should have different spiral orientation in a given space-time. It means charges know that orientation of space-time 4D structure and produce two kinds of spiral formation. If two negative charges or two positive charges are approaching, the space-time spiral structure in-between the two charges are differently oriented and there will be repulsion. If one positive charge and one negative charge are approaching, the space-time spiral structure in-between the two charges are same oriented and there will be attraction. Thus, it well explains that attractive and repulsive characteristics of electromagnetism. It is worth noting that electricity is mediated by rest charge and magnetism is mediated by spinning charge. Coulomb’s electricity causes open spiral with non-zero divergence, and magnetism causes close spiral with zero divergence. Due to the non-zero divergence, spiral structure caused by rest charge should be open spiral. It means that vortex lines originate from the central object and they curve and extend to reach the peripheral boundary. The spiral structure is a three dimensional structure. It means that charge can recognize space-time orientation and causes spiral shape structure in three horizontal planes. If the space-time is defined by x,y,z axis, then the spiral structure can be found in xy plane, yz plane, and xz plane. Spiral structure itself is a plane with vortex shape. When a charge is spinning(magnetism), the direction of spiral formation will be changed to align the charge’s spinning direction. Thus, it can explain why two charges with different spin direction will attract each other and two charges with same spin direction will repulse each other.

The relation between charge and space-time is called “charge relativity”. The formula is F=(Ue/c^2)*Te

(F is Faraday tensor, Ue is (electro)magnetic permeability in free space, c is lighspeed, Te is electromagnetic tensor)

General relativity’s formula is:

R=(8 pi G/c^4)*Tg

(Tg is stess-energy tensor, G=gravity constant=(1/2)S*c^2, S=spinity constant)

Since gravity and spinity are closely related, I think Tg should represent gravitospinity tensor.

Thus,

R=(4 pi S/c^2)*Tg

Let S=Ug/4 pi(Ug is gravitospinity permeability in free space), the formula becomes:

R=(Ug/c^2)*Tg

When Tg=diag(T00,0,0,0), Tg=diag(cp^4,0,0,0). Thus, we can see similarity between general relativity and charge relativity. Gravity(spinity) is symmetric curvature tensor, and electromagnetism is anti-symmetric torsion tensor.

Why is torsion tensor equal to electromagnetic tensor(Faraday tensor)? We can also derive it from the definition of torsion tensor and Faraday tensor.[1] By definition, torsion tensor is:

T^k_uv=A^k_uv-A^k_vu-R^k_uv

If the basis is holonomic, then the Lie bracket vanishes. It means that R^k_uv=0. Because Coulomb electromagnetic force is conservative force, the force is path independent and is only associated with the beginning state and end state of a charge. Thus, Coulomb electromagnetic force is holonomic. Then, the torsion tensor becomes:

T^k_uv=A^k_uv-A^k_vu

By differentiation, form covariant terms of second rank:

Auv=δAu/δXv-{uv,t}At

Auv is extension(covariant derivative) of the tensor Au

The second term in the above equation is symmetrical in the indices u and v. Thus,

Tuv=Auv-Avu=δAu/δXv-δAv/δXu

By the definition of Faraday tensor, electromagnetic tensor F is equal to:

Fuv=δAu/δXv-δAv/δXu

Thus, Fuv=Tuv. Faraday tensor is torsion tensor.

From the above equations, we see that torsion tensor is T^k_uv but the Faraday tensor is Tuv. It means that torsion tensor produces a 4D space-time vortex.

T^k_uv; k,u,v=0,1,2,3 in any reference frame(X0,X1.X2,X3) or (ct,X,Y,Z)

Thus, we can have four Faraday Tensors: T^0_uv for time vortex; T^1_uv along X with axis in YZ plane for space vortex; T^2_uv along with Y axis in XZ plane for space vortex; T^3_uv along with Z axis in XY plane for space vortex. Each T^k_uv has 6 components(T^k_01,T^k_02,T^k_03,T^k_12,T^k_13,T^k_23).

Torsion tensors produce four Faraday tensors to cause space-time vortex or space-time torsion.

From the above equations, we can get electromagnetic field tensor (F). It is also because vector Cu represents the generalized electromagnetic potential. If we say electromagnetism causes space-time structure spiral formation, then it is very reasonable to use torsion tensor to describe electromagnetic tensor since vortex lines are aligned with torsion tensor. We can find similarity because both Faraday tensor and torsion tensor are anti-symmetric tensors. Although one may argue that torsion tensor can have 24 components, I think each torsion tensor(6 components) matches each Faraday tensor(6 components;Ex,Ey,Ez,Bx,By,Bz) since charge can recognize the space-time structure orientation and give one 3D spiral structure in xy, yz, and xz planes.

We need to look at charge relativity in detail, Faraday tensor means it is the number of force lines from an element charge. Thus, it suggests that Faraday’s force lines actually cause the spiral formation of space-time structure. The spiral space-time structure itself is actual Faraday’s force line and Faraday tensor. Thus, I propose the charge relativity formula here to explain the relationship between charge and space-time. Recently, there is a new theory called Einstein-Cartan-Evans theory to unite gravity and electromagnetism. It also assumed that electromagnetic tensor is torsion tensor. However, it thought that electromagnetism is caused by spin. In my opinion, spin doesn’t cause electromagnetism. Mass spin causes spinity which in turns causes space-time rotation. In addition, spinity caused by spin is closely related to gravity since they have the same permeability constant. Electromagnetism should cause space-time spiral structure formation!

In astronomy, dark matter theory was proposed because there is huge discrepancy between Virial mass calculated by dynamic law and mass estimated by light-to-mass ratio. The total amount of mass in spiral galaxies cannot explain why the peripheral galaxies can rotate around the central galactic core in such high speed. If we consider the electromagnetism attraction between galactic core and peripheral stars, we can explain why spiral galaxies can gather together to rotate. Thus, dark matter is not needed any more. In the Milky Way galactic core, there is huge amount of antimatter cloud (positron cloud), so there should be strong electromagnetic attraction between peripheral galaxies with large amount of electrons and central galactic core with large amount of positrons. Charge relativity can also explain why spiral galaxies are spiral shaped. In elliptical galaxies, there are not assumed dark matter existing. It is because there is no electromagnetism in elliptical galaxies. Thus, elliptical galaxies are not spiral shaped. Current density wave theory to explain galaxy’s spiral shape is wrong. Because of charge relativity, the electromagnetism causes spiral galaxies to have open spiral shapes. In elliptical galaxies, the amount of dark matter is estimated fewer. It is because the dominant force of elliptical galaxies is gravity. The effect of electromagnetism is less in elliptical galaxies. However, both gravity and electromagnetism are still important in elliptical galaxies since the energy emission from both elliptical galaxies and spiral galaxies are from pair annihilation due to nuclear fusion.

In addition, this theory can explain why our sun’s magnetic field is spiral shaped. The sun’s magnetic field is called “Parker Spiral” and is a open spiral structure. This shape of magnetic field was thought to be influenced by solar wind release. However, I think the real reason is that our sun has charges that is different from usual planets without charges in solar system. Thus, sun’s electromagnetism causes space-time spiral structure. This new theory can also explain why spiral galactic magnetic fields are aligned to its spiral arms. It is because the galaxy’s electromagnetism causes space-time spiral shape structure to aggregate peripheral stars to rotate. Thus, the galaxy’s magnetic field is perfectly aligned to its spiral arms.

Currently, there is an experiment which can fully support my “charge relativity”. [2] When light is passing a strong magnetic field in vaccuum, there is optic rotation. Thus, it can be explained that light is passing through a torsion space-time affected by the strong magnetic field. Thus, the path of light is rotated. We can also predict there is optic rotation in vacuum when light is passing through electric field. Charge relativity is correct!

In my last 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. It is a preliminary small building and I hope to hear everybody’s comments. Because the radiation pressure formula is

P=(K/c)T^4 (K=Stefan-Boltzman constant, T=absolute temperature)

The stress tensor should be:

Th=F/A=(K/c)*a*T^4/A (a=surface area of central galactic core, A=peripheral area which includes four dimension A0(time), Ax(space),Ay(space),Az(space))

Thus,

Tuv=(K/c)*Tr (T=temperature-lightity tensor, Tr=radiation pressure stress tensor)

T is rank2 tensor

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.

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

Gravitospinity tensor Guv=Ruv-1/2g_uvR

Faraday(electromagnetic) tensor Fuv=δAu/δXv-δAv/δXu

Temperature-lightity tensor Tuv=δAu/δXv-δAv/δXu 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)+(δAu/δXv-δAv/δXu)-( δAu/δXv-δAv/δXu)

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. 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”ravitospinity 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.

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.

Currently, standard model is a successful theory to describe fundamental forces and related particles. It successfully predicts the masses of Z and W particles. It united electromagnetism, weak force, and strong force in the equation: U(1)xSU(2)xSU(3). Currently, U(1) is quantum electrodynamics(QED) mediated by photon transfer. However, I proposed that QED is wrong and photons are the actual mediators of radiation pressure. Thus, U(1) should be radiation pressure(universal lightity) which can explain the Casamir force. Thus, the new U(1)xSU(2)xSU(3) unites dark energy, weak force, and strong force. The basic structure of the unification is not changed. U(1) is still a gauge theory mediated by one dimensional photon boson. SU(2) is also a gauge theory mediated by W+, W-, and Z bosons(3 dimensional=2^2-1). SU(3) is also a gauge theory mediated by 8 gluon bosons(8 dimensional=3^2-1). Thus, the new standard model equation is given by:

Langragian= ∫ (1/y^2)YuvY^uv+(1/w^2)trWuvW^uv+(1/g^2)trGuvG^uv

  1. With A U(1) gauge field Y with coupling y (weak hypercharge or weak U(1))
  2. An SU(2) gauge field W with coupling w (weak SU(2) or weak isospin )
  3. An SU(3) gauge field G with coupling g (gluons or strong color)

In the above equation, photon is y, W/Z particles are w, and gluons are g. The traces(tr) are over the SU(2) and SU(3) indices hidden in W and G respectively. The two-index objects are the field strengths derived from W and G the vector fields.

I call this equation: New standard model. After this modification, the advantage is preserved and the disadvantage is avoided in the new standard model. W and Z particles’ masses can still be accurately predicted. But, the detailed equations and deductions need further efforts. Fundamental forces mediated by particles can be beautifully presented in one equation: U(1)xSU(2)xSU(3).

From above article, I also united the fundamental forces mediated by space-time. Those are radiation pressure (dark energy), electromagnetism, and gravitospinity. Electromagnetism causes space-time vortex (torsion tensor) and gravitospinity causes space-time curvature(curvature tensor). In addition, radiation pressure(dark energy) is time arrow and causes space spiral expansion. This equation is given by:

G+F-T=R

G mediates space-time curvature (gravitospinity), F mediates space-time spiral shape (electromagnetism), and T mediates space-time expansion (radiation pressure=dark energy). G and F cause matter to gather together. I sincerely hope to get your invaluable comments!

References

1. A. Einstein The Foundation of the General Theory of Relativity Annalen der Physik 49,769; 1916

2. E. Zavattini et al. Experimental observation of optical rotation generated in vacuum by a magnetic field Phy Rev Lett 96,110406;2006