So far the electrostatic force equations have assumed Planck charge as implied
by the symbol F E . Since q
2
p ¼ e
2
a, the conversion to the force exerted between
two elementary charges e is: F E ¼ F e =a. For example, Eq. (22) becomes Eq. (23)
below.
F G
F e
¼
F e
F p
N
2
a 2
ð23Þ
Equation (23) applies not only to charged leptons such as electrons or muons,
but it can also be used to express the ratio of forces between two of the same
hadrons, each with charge ±e. For hadrons, the reduced Compton wavelength of the
entire hadron is used. For example, the force ratio between two protons at any
distance is F G =F e % 8:1 Â 10
À37 . The right side of the Eq. (23) is also independent
of separation because of offsetting effects of F e and N
2 .
Until now the forces have only been between two fundamental particles.
However these forces are additive. Every particle in body A interacts with every
particle in body B. The total of all these individual forces add up to the total
gravitational and electrostatic forces between bodies A and B (still assuming weak
gravity). A goal for the future will be to see if incorporating additional nonlinear
effects achieves the exact equations of GR.
It is often said that gravity was united with the other forces at the start of the Big
Bang when all the particles had Planck energy. Figure 1 shows that indeed the electrostatic and gravitational force graphs intersect (the same magnitude of force) when
particle energy equals Planck energy E ¼ E p
E p ¼ 1. However, the point of this
graph and analysis is that even today when E 6 ¼ E p there is still a unification between
the gravitational and electrostatic forces. For example, the electrostatic force graph
line in Fig. 1 is the square root of the gravitational force graph line. The vast difference
in the magnitudes of these forces comes from a simple difference in exponents. This
relationship was previously unnoticed until the missing assumption (the universe is
only spacetime) was adopted. The existence of these simple relationships provides
support for this assumption and the proposed spacetime particle model.
The previous explanation was simplified. It contained correct components, but
the model implied the continuous emission of waves and a repulsive force. The
more complete explanation takes two chapters in the online companion book [14]
and therefore is beyond the scope of this paper. However, a brief explanation of the
key conceptual points will be given here. The proposed particle model has energy
density which can be calculated using Eq. (4). Energy density U and pressure P
both have units of kg/m
2 s. Since the spacetime particle model has energy propagating at the speed of light in a confined volume, the energy density is directly
equated to pressure. For example, an electron has a pressure of about 10
24 N/m
2
which produces a force of about 0.2 N over the area of
k
2
c for an electron. An
electron is stable because its amplitude, frequency etc. interact with the surrounding
spacetime field and achieve an offsetting pressure which stabilizes the structure.
234
J.A. Macken
by the symbol F E . Since q
2
p ¼ e
2
a, the conversion to the force exerted between
two elementary charges e is: F E ¼ F e =a. For example, Eq. (22) becomes Eq. (23)
below.
F G
F e
¼
F e
F p
N
2
a 2
ð23Þ
Equation (23) applies not only to charged leptons such as electrons or muons,
but it can also be used to express the ratio of forces between two of the same
hadrons, each with charge ±e. For hadrons, the reduced Compton wavelength of the
entire hadron is used. For example, the force ratio between two protons at any
distance is F G =F e % 8:1 Â 10
À37 . The right side of the Eq. (23) is also independent
of separation because of offsetting effects of F e and N
2 .
Until now the forces have only been between two fundamental particles.
However these forces are additive. Every particle in body A interacts with every
particle in body B. The total of all these individual forces add up to the total
gravitational and electrostatic forces between bodies A and B (still assuming weak
gravity). A goal for the future will be to see if incorporating additional nonlinear
effects achieves the exact equations of GR.
It is often said that gravity was united with the other forces at the start of the Big
Bang when all the particles had Planck energy. Figure 1 shows that indeed the electrostatic and gravitational force graphs intersect (the same magnitude of force) when
particle energy equals Planck energy E ¼ E p
E p ¼ 1. However, the point of this
graph and analysis is that even today when E 6 ¼ E p there is still a unification between
the gravitational and electrostatic forces. For example, the electrostatic force graph
line in Fig. 1 is the square root of the gravitational force graph line. The vast difference
in the magnitudes of these forces comes from a simple difference in exponents. This
relationship was previously unnoticed until the missing assumption (the universe is
only spacetime) was adopted. The existence of these simple relationships provides
support for this assumption and the proposed spacetime particle model.
The previous explanation was simplified. It contained correct components, but
the model implied the continuous emission of waves and a repulsive force. The
more complete explanation takes two chapters in the online companion book [14]
and therefore is beyond the scope of this paper. However, a brief explanation of the
key conceptual points will be given here. The proposed particle model has energy
density which can be calculated using Eq. (4). Energy density U and pressure P
both have units of kg/m
2 s. Since the spacetime particle model has energy propagating at the speed of light in a confined volume, the energy density is directly
equated to pressure. For example, an electron has a pressure of about 10
24 N/m
2
which produces a force of about 0.2 N over the area of
k
2
c for an electron. An
electron is stable because its amplitude, frequency etc. interact with the surrounding
spacetime field and achieve an offsetting pressure which stabilizes the structure.
234
J.A. Macken