in spacetime which have displacement amplitudes of ÆL p and ÆT p will be called
“Planck amplitude waves”. Unlike virtual particle pairs, Planck amplitude waves in
spacetime can exist indefinitely because these waves are undetectable even with a
long observation time. This is a fundamental property of spacetime that is not only
allowed by the uncertainty principle, but in this model this turbulence causes the
uncertainty principle.
It should be mentioned that the Planck amplitude waves in spacetime are a
completely different concept than the granularity or pixelation proposed by loop
quantum gravity. This granularity (pixelation) of loop quantum gravity is not
sinusoidal wave oscillations. The pixelation model of spacetime is stagnant. It does
not possess the tremendous energy density required to explain the 10
113 J/m
3 of
ZPE. In the remainder of this paper, the term “spacetime field” will be used to
indicate the model of spacetime proposed here which is filled with Planck amplitude waves (ÆL p and ÆT p ) at all frequencies up to Planck angular frequency
x p ¼
ffiffiffiffiffiffiffiffiffiffiffiffi ffi
c 5 = hG
p
% 1:9 Â 10
43 s
À1
:
There is another insight that can be extracted from our starting assumption. Since
an objective is to construct fundamental particles out of waves in spacetime, those
waves must be able to affect proper volume and the rate of time. This is said
because a particle (mass) affects the rate of time and proper volume in the surrounding spacetime (matter curves spacetime). If this model is going to explain this
effect, it is most reasonable to first explore the possibility that particles are made of
waves in spacetime that modulate both the rate of time and proper volume.
Gravitational waves are waves in the medium of spacetime, but they do not
modulate the rate of time or proper volume. For example, a gravitational wave
would convert a spherical volume into an oscillating ellipsoid which has the same
volume and rate of time as the spherical volume. The only type of wave that would
affect time and volume is a dipole wave in spacetime. This is a theoretical concept
that would be the simplest type of wave in spacetime. However, it barely gets
mentioned in standard texts on GR because dipole waves in spacetime are
impossible on the macroscopic scale covered by GR. For example, in the 1,300
page tome titled Gravitation [1], dipole waves in spacetime receive only a three
line mention which can be paraphrased as there can be no mass dipole radiation
because the second time derivative of mass dipole is zero €
d ¼ _
p ¼ 0. If dipole
waves existed in spacetime on the macroscopic scale, they would violate the
conservation of momentum and the conservation of energy. However, QM permits
dipole waves to exist in spacetime provided that the displacement amplitude is
limited to ÆL p and ÆT p . This is no problem because we have already accepted this
limitation for any energetic waves to exist in spacetime. Therefore, the spacetime
field model being developed will assume dipole waves in spacetime with the Planck
amplitude limitation.
To test the contention that ZPE is Planck amplitude dipole waves in spacetime,
we will start with an equation that gives the intensity I of a wave with amplitude
A at angular frequency ω propagating in a medium with impedance Z.
222
J.A. Macken
“Planck amplitude waves”. Unlike virtual particle pairs, Planck amplitude waves in
spacetime can exist indefinitely because these waves are undetectable even with a
long observation time. This is a fundamental property of spacetime that is not only
allowed by the uncertainty principle, but in this model this turbulence causes the
uncertainty principle.
It should be mentioned that the Planck amplitude waves in spacetime are a
completely different concept than the granularity or pixelation proposed by loop
quantum gravity. This granularity (pixelation) of loop quantum gravity is not
sinusoidal wave oscillations. The pixelation model of spacetime is stagnant. It does
not possess the tremendous energy density required to explain the 10
113 J/m
3 of
ZPE. In the remainder of this paper, the term “spacetime field” will be used to
indicate the model of spacetime proposed here which is filled with Planck amplitude waves (ÆL p and ÆT p ) at all frequencies up to Planck angular frequency
x p ¼
ffiffiffiffiffiffiffiffiffiffiffiffi ffi
c 5 = hG
p
% 1:9 Â 10
43 s
À1
:
There is another insight that can be extracted from our starting assumption. Since
an objective is to construct fundamental particles out of waves in spacetime, those
waves must be able to affect proper volume and the rate of time. This is said
because a particle (mass) affects the rate of time and proper volume in the surrounding spacetime (matter curves spacetime). If this model is going to explain this
effect, it is most reasonable to first explore the possibility that particles are made of
waves in spacetime that modulate both the rate of time and proper volume.
Gravitational waves are waves in the medium of spacetime, but they do not
modulate the rate of time or proper volume. For example, a gravitational wave
would convert a spherical volume into an oscillating ellipsoid which has the same
volume and rate of time as the spherical volume. The only type of wave that would
affect time and volume is a dipole wave in spacetime. This is a theoretical concept
that would be the simplest type of wave in spacetime. However, it barely gets
mentioned in standard texts on GR because dipole waves in spacetime are
impossible on the macroscopic scale covered by GR. For example, in the 1,300
page tome titled Gravitation [1], dipole waves in spacetime receive only a three
line mention which can be paraphrased as there can be no mass dipole radiation
because the second time derivative of mass dipole is zero €
d ¼ _
p ¼ 0. If dipole
waves existed in spacetime on the macroscopic scale, they would violate the
conservation of momentum and the conservation of energy. However, QM permits
dipole waves to exist in spacetime provided that the displacement amplitude is
limited to ÆL p and ÆT p . This is no problem because we have already accepted this
limitation for any energetic waves to exist in spacetime. Therefore, the spacetime
field model being developed will assume dipole waves in spacetime with the Planck
amplitude limitation.
To test the contention that ZPE is Planck amplitude dipole waves in spacetime,
we will start with an equation that gives the intensity I of a wave with amplitude
A at angular frequency ω propagating in a medium with impedance Z.
222
J.A. Macken