3 Spacetime Model of a Fundamental Particle
To help explain the proposed model of a spacetime particle, we will first make an
analogy to a superfluid which contains a small amount of angular momentum. For
example, a Bose-Einstein condensate is a superfluid. When angular momentum is
introduced into this condensate, the bulk of the superfluid does not rotate. Instead,
the angular momentum is broken into small rapidly rotating vortices which each
contain h of quantized angular momentum. These are surrounded by the vast
majority of the superfluid which is not rotating. References [9–11] show pictures of
these rapidly rotating vortices and give a more detailed explanation.
The analogy to a vortex in a superfluid is that a fundamental fermion such as an
electron is proposed to be a rapidly rotating Planck amplitude wave in spacetime
with h=2 of quantized angular momentum. It is confined and isolated by the surrounding sea of superfluid-like Planck amplitude waves which lack angular
momentum. More specifically, a fundamental fermion with internal energy E i is
proposed to be a Planck amplitude wave propagating at the speed of light but
circulating within a spherical volume one Compton wavelength k c in circumference. The rotating wave does not have a sharp boundary, but for mathematical
analysis, it can be considered to have a radius equal to the reduced Compton
wavelength
k c . Its rotational rate is equal to the Compton angular frequency x c and
its strain amplitude will be designated as A s . Equations (7–9) quantify these terms.
x c ¼ E i = h ¼ c= k c
ð7Þ
k c ¼ hc=E i ¼ c=x c ¼ h=mc
ð8Þ
A s ¼ L p
k c ¼ T p x c
ð9Þ
The sea of Planck amplitude waves in spacetime are proposed to be the most
perfect superfluid possible. Angular momentum that originated at the Big Bang is
isolated into 1=2 h and h quantized units. While angular momentum cannot be
destroyed, only specific combinations of wave amplitude and rotational frequency
achieve stability through the interaction with the surrounding spacetime field. These
few amplitudes and frequencies that are stable or semi-stable are the fermions and
bosons of the standard model. They can propagate through the superfluid spacetime
field without energy loss. The previously mentioned 10
120 discrepancy in the
energy density of the universe between GR and QM is proposed to be the difference
between the average energy density of fermions and bosons which possess quantized angular momentum and the energy density of the Planck amplitude waves
which lack angular momentum and form the spacetime field.
There is no conflict between these two energy densities. The homogeneous
waves in spacetime which lack angular momentum are responsible for giving
flat spacetime its properties (its physical constants) such as Z s , c, G, h, e o , etc.
Spacetime-Based Foundation of Quantum Mechanics …
225
To help explain the proposed model of a spacetime particle, we will first make an
analogy to a superfluid which contains a small amount of angular momentum. For
example, a Bose-Einstein condensate is a superfluid. When angular momentum is
introduced into this condensate, the bulk of the superfluid does not rotate. Instead,
the angular momentum is broken into small rapidly rotating vortices which each
contain h of quantized angular momentum. These are surrounded by the vast
majority of the superfluid which is not rotating. References [9–11] show pictures of
these rapidly rotating vortices and give a more detailed explanation.
The analogy to a vortex in a superfluid is that a fundamental fermion such as an
electron is proposed to be a rapidly rotating Planck amplitude wave in spacetime
with h=2 of quantized angular momentum. It is confined and isolated by the surrounding sea of superfluid-like Planck amplitude waves which lack angular
momentum. More specifically, a fundamental fermion with internal energy E i is
proposed to be a Planck amplitude wave propagating at the speed of light but
circulating within a spherical volume one Compton wavelength k c in circumference. The rotating wave does not have a sharp boundary, but for mathematical
analysis, it can be considered to have a radius equal to the reduced Compton
wavelength
k c . Its rotational rate is equal to the Compton angular frequency x c and
its strain amplitude will be designated as A s . Equations (7–9) quantify these terms.
x c ¼ E i = h ¼ c= k c
ð7Þ
k c ¼ hc=E i ¼ c=x c ¼ h=mc
ð8Þ
A s ¼ L p
k c ¼ T p x c
ð9Þ
The sea of Planck amplitude waves in spacetime are proposed to be the most
perfect superfluid possible. Angular momentum that originated at the Big Bang is
isolated into 1=2 h and h quantized units. While angular momentum cannot be
destroyed, only specific combinations of wave amplitude and rotational frequency
achieve stability through the interaction with the surrounding spacetime field. These
few amplitudes and frequencies that are stable or semi-stable are the fermions and
bosons of the standard model. They can propagate through the superfluid spacetime
field without energy loss. The previously mentioned 10
120 discrepancy in the
energy density of the universe between GR and QM is proposed to be the difference
between the average energy density of fermions and bosons which possess quantized angular momentum and the energy density of the Planck amplitude waves
which lack angular momentum and form the spacetime field.
There is no conflict between these two energy densities. The homogeneous
waves in spacetime which lack angular momentum are responsible for giving
flat spacetime its properties (its physical constants) such as Z s , c, G, h, e o , etc.
Spacetime-Based Foundation of Quantum Mechanics …
225