Download On the Carrier of Inertia

On the Carrier of Inertia
Patrick Grahn1, Arto Annila2* and Erkki Kolehmainen3
1COMSOL,
FI-00560 Helsinki, Finland
2Department
of Physics, University of Helsinki, FI-00014 Helsinki, Finland
3Department
of Chemistry, University of Jyväskylä, FI-40014 Jyväskylä, Finland
*email: [email protected]
Inertia is described as a reaction taken by vacuum to an action. The vacuum is perceived as a physical substance that
embodies photons in pairs without net electromagnetic field. In this form the free space houses mere energy density in
balance with average energy density of matter in the whole Universe. Therefore any local change in momentum will
invariably perturb the all-embracing vacuum, whose reaction manifests itself as inertia. Accordingly, the vacuum energy density is also in a local balance with energy that is bound in a body. This manifests itself as a local gravitational
potential energy. In this way gravity can be understood as an energy difference between the local and universal potential
energy, and hence gravitational and inertial masses are identical. By the same token, gravity and electromagnetism
share the similar form of force, since both are carried by the photons.
Keywords: free energy, gravity, mass, quantum, photon, the principle of least action, vacuum
1. Introduction
How does mass out there influence motions here? The
question concerns the carrier of inertia whereas the cause
of inertia itself has been understood to be the gravitational
action due to the total mass of the Universe [1,2,3,4]. The
universal gravitational potential experienced here builds up
with distance r from the bodies out there, since their number increases as r2 and gravitational potential falls as 1/r.
Thus, the most distant matter in the Universe contributes
most to the inertial reaction.
It is puzzling only how the inertial reaction due to the
bodies out there acts at once here. Yet, despite being instantaneous, the inertial reaction has all the hallmarks of a
radiative interaction that propagates at the speed of light.
In other words, gravity and electromagnetism share the
same functional form of force [5]. Thus, it is perplexing
how the inertial reaction can on one hand be an action at a
distance and on the other hand display the same characteristics as light? Put differently, how inertia can on one hand
result from the most distant bodies out there and on the
other hand manifest itself instantaneously here, just like a
local field? Pieces of the puzzle do not fit to each other, or
do they?
Mathematically it is possible to combine waves that
propagate forward in time with those that propagate backward in time to make up an instantaneous effect [6]. However, this solution by symmetry appears in a logical contradiction with time’s asymmetry, that is, with the universal
arrow of time resulting from the Universe’s diluting expansion [7,8]. In other words, future does not match the past,
and hence it is hard to imagine how the postulated pairing
of gravitational waves for instantaneous effects could possibly be universally perfect.
The problem is not only irreversibility but also pathdependence. The Universe displays history that accrues
along its evolutionary course from all the past states in a
non-determinate manner, not solely from the initial state
along a deterministic course. Already the most distant observation of universal evolution, namely cosmic microwave background CMB radiation [9,10] reveals that low
multipoles of its angular decomposition are not independent but anomalously correlated [11,12,13]. In general, subsequent states are correlated along the path of a non-holonomic process [8,14]. When history matters, the timeand path-dependent trajectories are at variance with constant-energy equations of motions that can, at least in principle, be transformed to a time-independent frame [15].
Then again, the postulated local field, as a means for
the immediate inertial reaction, ought to be physical and
have its sources, just like any other field. This implies a
substance that embodies the universal gravitational potential in balance with its sources, that is, with all bodies in the
Universe. Such a postulated physical vacuum seems to invite a return of the aether, which, in turn, has been abandoned since Michelson-Morley experiment [16,17]. To
avoid this conflict, various transient or virtual fields have
been suggested [18,19,20,21], thereby picturing the vacuum as an exceptional medium that possesses energy density about nJ/m3 without any substance [22].
Thus, the prevailing perception of vacuum appears to
be inconsistent in one way or the other. To find a way out
of the deadlock we bring forward the recently reconsidered
possibility that the vacuum is after all a physical medium,
not sustaining photon propagation, but embodied by the
photons themselves [23,24,25].
1
2. The photon-embodied physical vacuum
According to the proposed percept the photons do not propagate exclusively in the form of single quanta of light, but
in pairs so that electromagnetic fields of the two photons
sum up to zero, and hence cancel each other exactly (Fig.
1). This phenomenon is also familiar from an anti-reflection coating that does not actually prevent the photons from
reflecting but combines reflected rays to destructive interference, and hence a coated lens appears perfectly transparent. In the out-of-phase configuration the paired photons
display no electromagnetic fields, but carry only energy
density. Therefore, the natural free energy minimum state
is dark and inert as observed.
action as an integral part of matter will become a free quantum as an integral part of immaterial surrounding space
[24,33,34].
We remind right away that this view of the photon as
the elementary constituent was abandoned shortly after being introduced [31], because it was thought to be at variance with radiative decay via two or more alternative paths.
Namely, the conservation of quanta seems to be violated
when an initial state decays to the same ground state either
directly by a single photon emission or via two intermediate states yielding three photons in succession. However,
to reject the conservation of quanta by this reasoning does
not appear to us full proof, because the quanta in the form
of paired photons are not considered and counted. Therefore, it is of interest to see what can be explained and understood by the photon-embodied vacuum.
3. Comprehension by the physical vacuum
(a)
(b)
Figure 1. When two photons, whose electromagnetic fields are
shown in blue and red, co-propagate exactly out-of-phase, there
is no net electromagnetic field, and hence the photon pair carries
mere energy density (a). When the phase configuration departs
from the complete destructive interference, e.g., near a charge,
electromagnetic fields will manifest (b).
This portrayal of vacuum in terms of the paired photons
explains both radiative and seemingly instantaneous attributes of inertia. The vacuum’s radiative character is formalized in the equality c2oo = 1 that relates the speed of light
to the free space properties of permittivity o and permeability o. Although the photon as the force carrier has its
characteristic finite speed, the inertial reaction appears as
instantaneous, because the vacuum is all-around. Then
again, balance between the vacuum’s energy and the universal gravitational potential energy is given by the renowned zero-energy principle Mc2 – GM2/R = 0 [26,27]
which can be written also as the unitary condition GM/c2R
= 4Gt2 = 1 where the universal mass M is within radius
R = ct of the Universe at its current age t = 13.8 billion
years and G is the gravitational constant and  is the average density of matter [22]. In the evolving Universe c and
G cannot be constants but functions of the decreasing universal energy density [28,29]. In the other words, the properties of the diluting vacuum are changing, just as those of
any other evolving substance.
The idea of photon-embodied vacuum entails that the
photon is an indestructible entity [30,31]. This means, for
instance, that the total number of quanta is a constant in an
isolated system [32]. Conversely, when the system opens
up for radiative emission, at least one bound quantum of
3.1. Inertia’s radiative and instantaneous character
There is no dilemma with inertial reaction appearing as if
instantaneous despite the finite speed of light, because the
photon-carried energy density is already present everywhere, and hence it will react to any action. In other words,
the inertial reaction in fact propagates at the finite speed of
light, but the universal gravitational potential here is highly
invariant by summing up gravitational potentials of all bodies out there. Only a massive dematerialization out at a distant galaxy could momentarily perturb inertia here. Such a
perturbation would arrive here at the speed of light, and
hence could, at least in principle, be detected also by a
measurement of the inertial reaction, not only by means of
an interference detector. The perturbation on inertia would
be minute, since the power of this propagating vector potential [4] will decrease inversely to the squared optical distance and directly to the frequency that shifts down due to
expansion of the Universe [35,36].
Likewise, when the action perturbs the photon-embodied vacuum here, the energy density perturbation will start
to propagate the Universe over and eventually it will reach
distant bodies out there. By the same token, when the Universe is regaining its balance after the perturbation here,
any one of its bodies out there will be tossed hardly at all.
Any change in momentum dtp will inevitably couple to
some dissipation. The change will manifest itself also relative to the universal vacuum. For instance, our motion
along with the Milky Way is inescapably somewhat asymmetric, i.e., non-inertial relative to bodies in the rest of the
Universe, and hence dtp displays itself in the cosmic microwave background radiation as a dipolar temperature
gradient across the sky. Likewise, acceleration relative to
the physical vacuum will manifest itself as Unruh effect
[37]. In fact no motion along a piece of an open trajectory
is truly non-dissipative, because the moving body will in-
2
variably keep changing its state relative to some other bodies whose distribution is asymmetric, albeit uniform on the
largest scale.
3.2. Rotational inertia
By the same token, rotational inertia is understood as the
reaction taken by the universal vacuum to balance the action due to the body moving along the orbit. Only over a
complete period absorption and emission relative to the
whole Universe will sum up to zero. The quadratic dependence r2 of rotational inertia on the distance r from the axis
of rotation follows from the same reasoning that the larger
the radius of rotation, the larger realm of surrounding energy density is perturbed. Thus, the gravitational effect of
distant bodies via the physical vacuum manifests itself as
Coriolis and centrifugal forces, e.g., as a spinning body being oblate and as a meniscus of water spinning along with
a bucket being curved [38].
3.3. Equivalence principle
When both the universal vacuum and the local gravitational
potential are understood to embody the paired photons that
can be regarded as gravitons, equivalence between the inertial and gravitational mass is inescapable. In other words,
the equivalence principle is inevitable. The equivalence
can be comprehended by considering mass as a measure of
the total geodesic curvature of a quantized action. This
measure, defined by Euler for curves, expresses how much
a photon, bound in matter as an inter-action, or a particle,
as a quantized action, is more curved than the freely propagating photons that constitute the reference vacuum.
[39,40,41,42]. Of course, it will be only after eons of expansions that the tiny reference curvature 1/R will be flattened markedly from that it is today. Therefore mass appears as an invariant attribute of a body rather than being
the measure relative to the whole Universe. By the same
token, also charge and magnetic moment are understood as
manifestations of the particle’s quantized geometry.
When everything is understood in terms of the quantized actions, then the quanta of light propagating in the
vicinity of a body will increase in energy density, i.e., blueshift by assuming paths of increased curvature to attain
thermodynamic balance with the body’s mass, i.e., to adapt
to the body’s curvature. According to this physical portrayal of everything in terms of actions the curved
spacetime is an excellent mathematical model for the photon-embodied vacuum [43].
3.4. Gravity
When the local and universal energy densities are not in
balance, the energy difference, i.e., the force manifest itself
as gravity. When the surrounding energy density is sparser
than the gravitational potential energy density within the
system of bodies, then quanta will escape along the energy
gradient from the system to its surroundings, and hence the
bodies will move toward each other. Conversely, when the
surrounding energy density is higher than that within the
system of bodies, then quanta will enter the system from
the rich surroundings, and hence the bodies will move
apart. Most notably, distant galaxies move away from us,
because the Universe shines quanta, albeit mostly in the invisible pairs of photons, between us and the distant bodies.
Thus, gravity is not exclusively an attractive force but
repulsive when the surroundings is rich energy. This character of gravity is no different from that of the electrostatic
force. Neither two charges of opposite sign are exclusively
attracted to each other, but move apart when the surrounding medium increases with energy. This repulsion of ions
is obvious when a salt crystal dissolves in water.
3.5. Manifestations of universal gravity
On cosmological scale the quantized physical vacuum
when emerging from quanta that are emitted from matter,
spans an energy density gradient across the Universe. The
contemporary surroundings is sparse whereas the distant
nascent environ is dense in energy. This gradient manifests
itself as the universal gravitational force. The resulting acceleration, ao = c/t = cH in terms of Hubble constant H, is
on the order of 10-10 ms-2. It is balanced by motions that
display themselves in galaxy rotation and velocity dispersion of galaxies [25,44,45].
In general, the arrow of time relates to consumption of
energy gradients [7]. The expansion of the Universe is by
the physical portrayal of vacuum understood to result from
the incessant combustion of matter-bound high-energy
quanta to those free quanta of low-energy embodying the
vacuum [46,47]. The current rate of expansion, i.e., on-going vacuum genesis, depends on mechanisms of combustion, most notably on contemporary stars of various kinds
including black holes. Likewise, the nascent rate is understood to have depended on primordial mechanisms that
produced ingredients for baryogenesis along with the dissipated quanta that constitute space.
3.6. Appearance of electromagnetic force carriers
According to the textbook physics it seems a bit of a puzzle
from where the photons of electromagnetic field appear instantaneously when an atom ionizes. In contrast there is no
mystery, when the photons are understood to have been
around all the time but paired in the out-of-phase configuration. Electromagnetic fields will appear instantaneously
when an atom ionizes and induces a phase shift away from
the paired-photon minimum-energy configuration (Fig. 1).
Clearly, the photon can be detected easily when it is no
longer exactly at the opposite phase to its co-propagating
partner. Also the textbook’s virtual photon comes to existence only when it is detected. Thus, consequences of considering the vacuum as being physically embodied by the
paired photons is not formally that different from picturing
the vacuum comprising of virtual particles.
3
3.7. Casimir effect
The photon-embodied vacuum can account for Casimir effect [48] as well. Instead of imagining virtual photons making up a field, the real but paired photons of vacuum generate a net force, attractive just as repulsive depending on
the energy density difference between adjacent plates and
their surroundings. In other words, the formalism remains
the same, but the tangible interpretation substitutes the abstract construct of virtual photons.
Furthermore, the dynamical Casimir effect [49] can be
understood so that when the vacuum is subject to high-frequency perturbation, the photons in pairs will shift away
from the perfect out-of-phase balance, and hence the single
photons will emerge for detection at microwave band that
covers most of the vacuum’s spectrum.
Moreover, fluctuations in the photon-embodied vacuum can be understood to result in the Lamb Shift in the
same way as quantum electrodynamics attributes fluctuations to field-theoretic vacuum [50,51]. The paired quanta
fluctuate about the free energy minimum state, and hence
their phases shift transiently away from the perfect cancelation. This perturbative potential gives rise to a small but
detectable effect on electron orbits.
The interdependency between electromagnetism and
gravity due to their common force carrier is inevitable. The
inseparable paired-photon phase and density can be qualitatively understood to manifest, for instance, as a difference in the measured proton charged radius depending on
whether an electron or a much heavier muon is circulating
the nucleus [52,53,54].
3.8. Double-slit experiment
Conceptual conundrums of the double-slit experiment resolve with ease when photons and other projectiles on their
way to detector are understood to perturb and interfere with
the paired photons that embody the vacuum. Put differently, when the physical vacuum is ignored, the projectiles
are erroneously assumed to propagate in an imaginary
emptiness, and hence the troublesome conceptual constructs.
The Aharonov–Bohm effect [55], in turn, demonstrates
that the surrounding energy density is a sum of an added
vector potential and the omnipresent vacuum potential.
The increase in energy density along the particle’s path of
propagation, as usual, displays itself as a phase shift.
3.9. Field exclusion and phase-locking
The Meissner effect [56] can be understood to display the
physical character of vacuum so that a superconductor, as
a closed system without coupling to its surroundings, cannot accept quanta from the applied field, but excludes
them. Conversely, the Tajmar effect [57] can be interpreted
so that when a ring cools down to the superconductive
state, it will enclose the surrounding quanta as an integral
part of its stationary state. Thus, when the superconductive
ring is set to rotation, the phase-locked quanta in the immediate surroundings will follow. Nearby optical gyroscopes sense that the quanta that are next to the ring, will
track the superconductor put in rotation. Conversely, when
the ring is in a normal state, the quanta of vacuum are not
locked but free, and hence the adjacent gyroscopes do not
register such a marked inertial reaction when the ring is put
in rotation.
4. Formalism of the physical vacuum
Physics communicates by equations of motion its quantitative comprehension about nature. Specifically, when energy is conserved, the equation of motion accounts for the
system in a steady-state thermodynamic balance in its surroundings or eventually decoupled from its surroundings
altogether. In general, when energy is not conserved, the
equation of motion describes the system in evolution from
one state to another by either absorbing or emitting quanta
with energy to gain balance with its surroundings in least
time. We apply the same reasoning for the vacuum.
4.1. Vacuum at stationary-state dynamic balance
When the vacuum’s photons are shifted away from the perfect out-of-phase configuration, typically due to presence
of charges, and hence are readily detectable as electromagnetic fields, the familiar Lorenz gauge [58]
Α 
1
 t  0
c2
(1)
that links mathematically the electric potential  and magnetic vector potential A, can be recognized as the physical
equation of motion for the photon-embodied vacuum. For
example,  will decrease with time when the photons move
away from a dense locus to sparser surrounding down
along the spatial gradient of A, and vice versa, to maintain
the thermodynamic balance. An energy density gradient
due to a charge will manifest itself as the electric field E =
– – ∂tA embodied by the vacuum’s photons. Accordingly a steady-state circulation due to an electric current
will manifest itself as the magnetic field B =   A. When
the vacuum’s photons are in the perfect out-of-phase configuration, and hence hard to detect merely as gravitational
fields, the same equation (Eq. 1) applies describing mere
changes in energy density.
The motion of vacuum at thermodynamic balance,
where net dissipation vanishes, is no different from the
changes in momentum p that keep leveling off sporadic
gradients of potential energy U
U  t p  0
(2)
to maintain the system in its thermodynamic balance. It is
straightforward to show that Eq. 2 transcribes to Eq. 1 via
4
c∙ = ∂t and  = U/ and |A| = |p|/ when the scalar potential U and the momentum p are divided by charge density
.
The to-and-fro flows of energy at thermodynamic balance are obtained explicitly when Eq. 2 is multiplied with
velocity v to give
v U  t 2K  0 .
(3)
where changes in kinetic energy 2K = p∙v direct down
along the gradients of potential energy U. The equation 3
applies equally to the stationary-state vacuum whose density perturbations level off at the speed of c, and hence Eq,.
3 reduces to Eq. 1. The steady-state circulation of vacuum
about a body that is spinning with angular momentum L, is
similar to magnetism, and hence it will manifest itself as
gravito-magnetism due to the divergence-free part of the
gravitational potential, i.e., vector potential A = GL ×
r/c2r3 [59,60].
The flows of energy density without electromagnetic
fields are difficult, but not impossible to detect. Recently
density waves originating from black hole mergers were
picked up by sensitive interferometers [36]. Those huge
collisions out there did not rock much anything here. It is
worth emphasizing that according to the physical percept
of vacuum, the gravitational wave is not a temporal distortion of an abstract metric, but a tangible density wave
whose passage will amount to an increased index along the
optical path of a diffractometer.
4.2. Vacuum in evolution
When the vacuum is perturbed away from the free energy
minimum state by accelerating charges, the familiar Poynting’s theorem [8,61]
e v  E   e v    0c2  E  B 
(4)
describes the charge density e in acceleration down along
the electric field E, and thereby consuming the potential
energy , that couples to dissipation of photons along
Poynting vector S = E  B to the surrounding vacuum. This
is to say that the universal vacuum acquires quanta from
the local potential that keeps diminishing due to the decreasing separation of charges. When all material densities
in energy have transformed to mere radiation, i.e.  → 0
and v → c, Eq. 4 will reduce to Eq. 1 of equilibrium [8].
When the electromagnetic fields are not apparent for
detection, but a net neutral body with mass m is falling
down along the gradient of gravitational potential energy
U = GmM/r due to mass M, the general equation of motion
is
dt 2K   v U  idt Q
(5)
where dtQ = c2dtm is annotated with i to denote that dissipation is orthogonal to U just as S in Eq. 4 is orthogonal
to . When recalling that the change in kinetic energy
dt2K = dt(p∙v), the integral form of Eq. 5 is recognized as
the principle of least action in its original dissipative form
by Maupertuis [62,63]. Thus, emergence and evolution of
the vacuum is no different from other natural processes
[8,64,65,66]. Accordingly, dispersion of vacuum energy,
just like that of any other system, is skewed about the average energy kBT given by the Planck’s radiation law.
4.3. State equations of a single quantum
In addition to the equation of motion for the vacuum as a
physical substance there is the equation for the single quantum itself. The quantum of action in propagation carries
energy E within its (period of) time t, and hence measures
up to Planck’s constant h = Et. Likewise, ħ = E applies,
when the quantum’s circulates within period  = 2t. The
vacuum’s photon-embodiment displays itself also in the invariant measure h = 2eΦ0 that relates the magnetic flux
quantum Φ0 of a current loop, whose circulation amounts
to 2e in units of the elementary charge e.
These forms of Planck’s constants are, of course, mathematically identical to those in the textbooks where h appears only as a proportionality factor rather than being the
measure of the indivisible basic constituent of nature.
All in all, the familiar equations describe the physical
vacuum without revision but with re-vision. The proposed
photon-embodied vacuum provides merely a tangible account on various phenomena that inevitably involve the
vacuum, most notably the inertial reaction.
5. Discussion
The physical vacuum in the form of paired photons without
net electromagnetic fields is such a trivial thought that one
would expect it to have appeared already a long time ago
to account for the universal gravity that manifests itself as
inertia. It might well have surfaced, but presumably when
luminiferous aether as a medium for the propagation of
light was abandoned, also the idea of a photon-embodied
vacuum submerged. Still today, the photons may seem like
innumerable when appearing from the vacuum as if from
nowhere and disappearing to the vacuum as if to nothingness. This superficially non-conserved character of photons is solidified by theory that introduces creation and annihilation operators without bookkeeping of quantized actions.
The field-theoretic vacuum of quantum electrodynamics, albeit compliant with data, appears to us as a contrived
abstraction. Virtual photons or other ephemeral embodiments of gravity and electromagnetism strike a contrast
with the tangible thought that fields require sources. Therefore, we reason that the actual photons embodying the
physical vacuum are precisely the field quanta of both electromagnetic and gravitational fields whose sources are the
5
charged and neutral bodies. Thus, the proposition of photon-embodied vacuum to explain gravity and electromagnetism in general and inertia specifically does not necessitate revision in the mathematical forms of modern physics,
and hence matches measurements alike, but still provides a
tangible interpretation of observations.
The physical vacuum makes no categorical distinction
between local and universal, because the quantized energy
density permeates everything. For instance, the photons
embody gravitational and Coulomb potential within an
atom, and the photons embody likewise the surrounding
vacuum. Thus, the quanta that are material as inter-actions,
are not fundamentally distinct from the quanta that are radiative, i.e., immaterial. This revelation sheds light on
Newton’s thinking [67]. Gravity must be caused by an
agent, acting constantly according to certain laws; but
whether this agent be material or immaterial, I have left to
the consideration of my readers.
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