3 The Dirac Electron and Basic Physical Concepts
69
Table 3.2 Some universal constants and electron properties (upper half) and a few physical properties (lower half) with dimensions scaled to ∼ c ∼ 1 (dimensionwise)
Name
Symbol
Formula
Dim.
Newton constant
G
F grav = Gmm /d 2
L 2 ∼ T 2
Coulomb constant
k e
F elec = k e ee /d 2
Q −2
Planck constant
ΔE = ω
1
Light velocity
c
Constant in all frames
1
Elementary charge
e
Negative or positive
Q
Fine-structure constant
α
k e e 2 /c
1
Electron rest mass
m e
Negative for positrons
L −1 ∼ T −1
Gravitational invariant
δ
G m 2
e /c
1
Classical electron radius
r 0
k e e 2 /m e c 2
L
Compton electron radius
r C
/2m e c
L
Hydrogen Bohr radius
a 0
k −1
e 2 /m e e 2
L
Gravitational electron radius
r G
(G/c 2 )m e
L
Force
F
F = mg
L −2 ∼ T −2
Pressure
P
P = F/d 2
L −4 ∼ T −4
Energy
E
E = F d
L −1 ∼ T −1
Power
W
W = E/t
L −2 ∼ T −2
Electric potential
V
V = E/Q
Q −1 T −1
Electric resistance
Ω
Ω = V /A
Q −2
Electric inductance
H
H = V t/A
Q −2 T
Electric capacitance
F
F= Q/V
Q 2 T
Electric field
E
E = V /l
Q −1 T −2
Magnetic flux density
B
B = V t/l 2
Q −1 T −2
Electric moment
d
d = er
QL
Magnetic moment
μ
μ = e/2m e
QL
to which was later added k e = (4πε 0 ) −1 [38]. As they are free of anthropocentric
choices, these units help physicists to reframe fundamental questions such as the
smallness of G relative to k e in SI units. Expressing Universe properties such as
age or temperature in terms of Planck units discloses a regular occurrence of large
dimensionless numbers, which led Weyl, Hoyle, Eddington, Wheeler, Dirac, and
others to speculations which inspired Carter’s Anthropic Principle in 1973 [33, 34].
Table 3.3 gives expressions of some Planck units and their values in the SI system.
Those for E P and F P were used in deriving Eq. (3.25).
In the system we use here (Table 3.2), only c and ∼ 1 (dimensionwise). As
expected, both the fine-structure constant α (pregnant in quantum electrodynamics)
and the similar gravitational invariant δ (introduced in our previous paper) remain
dimensionless. This choice also will help to reframe some basic physical concepts.
69
Table 3.2 Some universal constants and electron properties (upper half) and a few physical properties (lower half) with dimensions scaled to ∼ c ∼ 1 (dimensionwise)
Name
Symbol
Formula
Dim.
Newton constant
G
F grav = Gmm /d 2
L 2 ∼ T 2
Coulomb constant
k e
F elec = k e ee /d 2
Q −2
Planck constant
ΔE = ω
1
Light velocity
c
Constant in all frames
1
Elementary charge
e
Negative or positive
Q
Fine-structure constant
α
k e e 2 /c
1
Electron rest mass
m e
Negative for positrons
L −1 ∼ T −1
Gravitational invariant
δ
G m 2
e /c
1
Classical electron radius
r 0
k e e 2 /m e c 2
L
Compton electron radius
r C
/2m e c
L
Hydrogen Bohr radius
a 0
k −1
e 2 /m e e 2
L
Gravitational electron radius
r G
(G/c 2 )m e
L
Force
F
F = mg
L −2 ∼ T −2
Pressure
P
P = F/d 2
L −4 ∼ T −4
Energy
E
E = F d
L −1 ∼ T −1
Power
W
W = E/t
L −2 ∼ T −2
Electric potential
V
V = E/Q
Q −1 T −1
Electric resistance
Ω
Ω = V /A
Q −2
Electric inductance
H
H = V t/A
Q −2 T
Electric capacitance
F
F= Q/V
Q 2 T
Electric field
E
E = V /l
Q −1 T −2
Magnetic flux density
B
B = V t/l 2
Q −1 T −2
Electric moment
d
d = er
QL
Magnetic moment
μ
μ = e/2m e
QL
to which was later added k e = (4πε 0 ) −1 [38]. As they are free of anthropocentric
choices, these units help physicists to reframe fundamental questions such as the
smallness of G relative to k e in SI units. Expressing Universe properties such as
age or temperature in terms of Planck units discloses a regular occurrence of large
dimensionless numbers, which led Weyl, Hoyle, Eddington, Wheeler, Dirac, and
others to speculations which inspired Carter’s Anthropic Principle in 1973 [33, 34].
Table 3.3 gives expressions of some Planck units and their values in the SI system.
Those for E P and F P were used in deriving Eq. (3.25).
In the system we use here (Table 3.2), only c and ∼ 1 (dimensionwise). As
expected, both the fine-structure constant α (pregnant in quantum electrodynamics)
and the similar gravitational invariant δ (introduced in our previous paper) remain
dimensionless. This choice also will help to reframe some basic physical concepts.