Basic Principles and Laws of
Nature’s Four Fundamental Forces/Interactions
Tian Ma, Shouhong Wang
Supported in part by NSF, ONR and Chinese NSF
http://www.indiana.edu/˜fluid
I. Four fundamental forces/interactions
II. Unified Field Theory
1
I. Four Fundamental Forces/Interactions
Physical laws of nature are based on a few simple and universal first first principles,
and are often described by equations.
2
Gravity
GM m
• Galilei, Newton: F = −m∇φ(r) = − 2 ,
r
GM
φ(r) = −
r
8πG
1
• Einstein: Rµν − gµν R = − 4 Tµν
2
c
• Ma-Wang, 2012:
1
8πG
Rµν − gµν R = − 4 Tµν − ∇µΦν
2
c
k0
1
F = −m∇g00 = −mM G 2 +
− k1 r ,
r
r
where k0 = 4 × 10−18km−1, k1 = 10−57km−3. Gravity can display both
attractive and repulsive behaviors, and the new gravitational field equations give
rise to a new unified theory for dark energy and dark matter.
3
Strong interaction
• Quantum Chromodynamics based on an SU (3) gauge theory (Yukawa, YangMills, Gell-Mann, O. Greenberg, ...)
• Layered strong interactions potentials (Ma-Wang, 2012 & 13): based on two new
principles: principle of interaction dynamics (PID), and principle of representation
invariance (PRI):
1 As
r −r/R
S0 = gs(ρ)
1+
e
,
−
r
ρ
R
gs(ρ) = gs
ρw
ρ
3
,
where As is a constant depending on the particle type, and R is the attracting
radius of strong interactions given by
( −16
10 cm for w∗ and quarks,
R=
10−13cm for hadrons.
4
Φ
r̄
r
These potentials match very well with experimental data.
Again, strong interaction demonstrates both attraction and repelling behaviors.
5
Quark confinement: With these potentials, the binding energy of quarks can be
estimated as
(1)
Eq ∼
ρn
ρ0
6
En ∼ 1024En ∼ 1022GeV,
where En ∼ 10−2GeV is the binding energy of nucleons.
This clearly explains the quark confinement.
6
Short-range nature of strong interaction:
With the strong interaction potentials, at the atom/molecule scales, the ratio
between strong force and electromagnetic attraction force is
Fa
ρ0
= 9gs2
Fe
ρa
6 .
(
e2 ∼
10−38 at the atomic level,
10−44 at the molecular level.
This demonstrates the short-range nature of strong interaction.
7
Weak interactions
• An SU (2) gauge theory
• Ma-Wang, 2012 & 2013: Layered gauge weak interaction potentials:
W0 = gw (ρ)e
−r/r0
1 Aw
2r −r/r0
−
1+
e
,
r
ρ
r0
gw (ρ) = gw
ρw
ρ
3
where ρw and ρ are the radii of the constituent weakton and the particle, Aw is
a constant depending on the types of particles, and r0 ' 10−16cm is the radius
of weak interaction.
• The potentials show that the weak interaction is also short-ranged
• The weak interaction/force demonstrates both attraction and repelling behaviors.
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Stability of matters
The attraction and repelling nature of all four forces leads to the stability of the
matter in the universe.
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II. Unified Field Theory
The unified field model is determined by the following first principles:
• principles of general relativity and Lorentz invariance, postulated by Einstein
(1905, 1915)
• principle of gauge invariance, postulated by J. C. Maxwell (1861), H. Weyl
(1919), O. Klein (1938), C. N. Yang & R. L. Mills (1954).
• spontaneous symmetry breaking, by Y. Nambu 1960, Y. Nambu & G. JonaLasinio 1961
• principle of interaction dynamics (PID), postulated by Ma-Wang, 2012
• principle of representation invariance (PRI), postulated by Ma-Wang, 2012
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Unified field model (Ma-Wang, 2012):
(2)
(3)
(4)
(5)
(6)
eαE
8πG
gw αaw a gsαks k
1
Aµ −
Wµ −
S Φν ,
Rµν − gµν R + 4 Tµν = ∇µ −
2
c
~c
~c
~c µ
w
s
E
gw αa a gsαk k E
eα
Aµ −
Wµ −
Sµ φ ,
∂ ν Fνµ − eψ̄γµψ = ∇µ −
~c
~c
~c
h
i
g
w
ν
b
c
Gw
λbcdg αβ Wαµ
Wβd − gw L̄γµσaL
ab ∂ Wνµ −
~c
eαE
gw αbw b gsαks k w
1 mH c 2
= ∇µ +
xµ −
Aµ −
Wµ −
Sµ φa ,
4
~
~c
~c
~c
h
gs j αβ c d i
s
ν j
Gkj ∂ Sνµ − Λcdg SαµSβ − gsq̄γµτk q
~c
s
E
w
2
1 mπ c
eα
gw αa a gsαj j s
= ∇µ +
xµ −
Aµ −
Wµ −
S φ ,
4
~
~c
~c
~c µ k
(iγ µD̃µ − m̃)Ψ = 0.
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