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THE TECHNICAL PAGE
By Philippe VIOLA
Self-trained mathematical physicist
Scientific writer
This technical page is dedicated to the proof of three crucial physical theorems : the non-existence of
physical time as an inherent property of the universe independent of the human being, the
disincarnation theorem that shows that a non-trivial spirit survive to the so-called “clinical death
condition” (also called the “flat E.E.G. condition”) and the formal equivalence between the
metaphysical concept of God and the physical concept of the Universal Vacuum.
The prophecy of prophecies asserts that “at the end of times, deads will be resurrected”. Here is a
physical (that is, finite) realization of it, which is not opposite to the metaphysical one (time infinity),
but complementary.
All questions and comments, technical or not : [email protected].
1
TIME IS VACUUM
Let E3 be 3-dimensional real euclidian flat space, x² = xixi the square of vector x (i = 1,2,3) and :
(1)
s = exp(-V²/2).x , s² = exp(-V²).x²,
where V is a real-valued parameter. Equation (1) defines a local conformal structure over E3 as well
as a regular group action on vectors of E3 with s = x for V = 0. The first-order development of (1b)
near V = 0 gives :
(2)
s² = x²[1 – V² + O(V4)],
where O(V4) contains all powers of V² greater than or equal to 2. These additional terms are all
negligible near V = 0. Expression (2) shows that the isometry group of E3, SO(3), infinitesimally
deforms into the Lorentz group SO(3,1) near V = 0. As this last group is the isometry group of 4dimensional Minkowski space-time E3,1, the infinitesimal deformation is propagated to the euclidian
structure of E3. In other words, E3 infinitesimally deforms into E3,1 near V = 0. This enables us to
identify the time-like direction x0 = ct on E3,1 formally with the length of V.x (up to the sign) or :
(3)
t² = V²x²/c².
Taking the square root of this last expression gives a redefinition of time :
(4)
t = ±Vx/c , x = xiei,
the ei (i = 1,2,3) being the constant vierbeins on E3. Notice that :
(5)
R sdV =R exp(-V²/2).xdV = x.(2)1/2 , R s²dV =R exp(-V²).x²dV = x².()1/2.
Physically speaking, what all this amounts to is that time clearly appears as a natural deformation of
euclidian 3-space near the deterministic value V = 0, where V stands for the universal vacuum.
Consequently, it is not an inherent property of the universe independent from the human observer, as
space-time relativity assumed it. This explains why space and time are only grouped together but not
unified in Einstein’s “classical” (= deterministic) vision of the world. Here, we straightforwardly see
in eq. (4) that the universal vacuum actually generates time. This is impossible to deduce from the
classical vision of a “rigid” vacuum everywhere zero in all space. Nonetheless, the vacuum in the
present proof is not to be identified with the famous ether, as ether was assumed to be an absolute
concept (rigid medium), whereas the vacuum is actually a relative concept (deformable medium). One
cannot see it in the elementary proof above, but it clearly appears in the general proof. So let us now
generalize all this in the physical frame of the new bioquantum synthesis.
Let QW be the Quantum World, that is, a 9-dimensional complex manifold endowed with the mirror
symmetry S that exchanges points z of QW with their complex conjugate z*:
(6)
S.z = z* , S.z* = z , S² = 1.
In a local coordinates system, the line element of QW writes :
(7)
dL = EI(z,z*)dzI
(I = 1,…,9).
The invariance group of QW is the special unitary group SU(9), a 80-parameters group, so QW has a
hermitian structure locally given by :
(8)
dL² = GIJ(z,z*)dzIdz*J , GIJ(z,z*) = Tr[EI(z,z*)E*J(z,z*)],
where the trace Tr(.) is that of SU(9) and dl² is real-valued. As before, we let :
(9)
dS = exp(-¦V¦²/2).dL , dS² = exp(-¦V¦²).dL²
where V = V(z,z*) is now a complex-valued scalar field on QW and¦V¦² = V.V* as usual. Again, near
the deterministic value V = 0, the first-order development of (8b) leads to the local formulas for time
(synchronous coordinates system) :
(10)
dz0 = V(z,z*)dL , (dz0)* = V*(z,z*)dL.
From the viewpoint of physics, V now identifies with the gravitational nothingness. In Dirac’s
notations :
(11)
¦V¦² = <0¦Tr(EIE*I)¦0> = Tr(<0¦EIE*I¦0>).
If we were fully deterministic, as in general relativity, we would have Tr(EIE*I) = 9 which would
imply ¦V¦² = 9 too, as <0¦0> = 1 and so, V would be a universal constant of amplitude 3 that could be
brought back to zero only shifting the reference level. However, the real physical situation is
stochastic and the vector gravitational potential EI has a fluctuating component over QW that can
never be eliminated. Hence the purely fluctuating complex-valued field V, called the Universal
Nothingness.
As nothingness was a purely metaphysical concept in deterministic physics, it could definitely not be
used to link time to space. But a realistic vacuum is made of a “classical” component, constant over
all space, and of a purely fluctuating component, randomly variable from point to point. This last
component stands for the physical nothingness in vacuum physics.
2
THE DISINCARNATION THEOREM
Let [z(e),z*(e)] be a complex PSI field on the Structured Quantum World QW(e), where e is a realvalued parameter called the complexity scale (0 < emin  e  emax < +8) and let z(e) = [zI(e)]I=1,…,9 =
[zi(e)]i=1,2,3;=-,0,+ be a structured object on QW(e). We assume e = emax, the maximal complexity scale
(order 1 m). In the frame of the present proof, objects z(e) (and c.c.) will then represent brains : the
latin indices being “external”, latin-indexed components will represent biological supports, whereas
the greek indices being “internal”, greek-indexed components will represent minds. So, for each state
of mind  = -,0,+, the 3 families of objects [zi(e)]i=1,2,3 will represent “material” brains (the biological
organs), while for each direction i = 1,2,3 of space, the 3 families of objects [zi(e)]=-,0,+ will
represent “virtual” brains (the psychological organs or minds). States z(e) and c.c. are stochastic.
However, as the elementary description level is that of probabilities (the Prigogine approach), PSI
fields obey deterministic laws with respect to the stochastic variables z(e), z*(e).
All these starting considerations being made, the clinical death condition, also named the flat E.E.G.
condition writes :
(12)
< z(e)> = 0 , < z*(e)> = 0,
<.> standing for the mean value with respect to the probability law used. Clinical observations show
that there always remain fluctuations of cerebral signals :
(13)
< zi(e)z*i(e)> = ¦V(e)¦².  0.
(isotropy of fluctuations). The system (12)-(13) describes the cerebral nothingness : it is a topcomplexity structured vacuum. Therefore, V(e) is made of all structured nothingnesses of complexity
emin  e’ e = emax, ordered according to an increasing inclusion law, V(emin) being the elementary
nothingness, which corresponds, in the present context, to the cellular nothingness (mesoscopic
observation scale, order 1 m).
CLINICAL DEATH = CEREBRAL NOTHINGNESS STATE
A definition in full agreement with the common assumption.
Structured nothingnesses are self-similar (conservation law of the vacuum):
(14)
dV(e)/de = 0 , dV*(e)/de = 0,
which means their structure is fractal. Writing z(e) and c.c. under the canonical forms :
(15)
z(e) = <z(e)> + V(e).n(e) , z*(e) = <z*(e)> + V*(e).n*(e),
where n(e) and c.c. are the normal vectors on QW(e) and applying (12) only leaves the fluctuating
parts of z(e) and c.c. As these parts are non-zero, it follows that the PSI field [z(e),z*(e)] reduces to
[V(e).n(e), V*(e).n*(e)], which is everything but trivial, as it still depends on the cerebral
nothingness V(e) and c.c., a purely fluctuating structured object of maximal complexity on QW(e).
Here, we have used the unified representation (triplet of isomorphic 3-spaces). But we can
equivalently change representation letting zi(e) = zi0(e) (i = 1,2,3) and a(e) = [zi-(e), zi+(e)] (a =
1,…,6) so that we will have 1 = z1-, 2 = z2-, 3 = z1-, 4 = z1+, 5 = z2+ and 6 = z3+. In such a
representation, the a(e)s will be considered as functions of the zi(e)s. on the physical viewpoint, this
situation corresponds to the familiar non-quantum field theory, where the structured 6-components
vector fields (e) are dynamical variables (“internal” variables – “virtual” world), while the structured
3-vectors z(e) are dynamical space parameters (“external” variables – “material” world). As can be
seen, time is nowhere present in both representations. The PSI field [(e), *(e) ; z(e), z*(e)] is then
a true quantum field in the sense of de Broglie’s quantum duality. In the context of the disincarnation
theorem, parameters z(e) and c.c. represent the material brain, while variables (e) and c.c. represent
the virtual brain or mind. Therefore, in this representation, the cerebral organ is a 3-dimensional
object, while mind is a 6-dimensional object or equivalently, a 3-dimensional object in two possible
base states (+ and -, positive and negative). As for , it represents the spirit (if it is source-dependent)
or the soul (if it is free, that is, source-independent). This means that, in bioquantum theory, the spirit
or the soul (the free form of a spirit) is not mind, but a function of mind. Finally, notice that it is a
purely virtual medium : the material world is set at the background, meaning there can be no material
support at all, as long as there is a virtual support, it is sufficient for a spirit to exist (the existence of a
virtual support is also a necessary condition).
Assuming all this, we can now only focus on -variables (and c.c.) to write down the clinical death
condition, as we do not need to describe the state of the material brain to make sure that the spirit does
not degenerate under a trivial form (this is already present in a implicit way in eq. (13)). In this second
and more explicit representation, eqs (12) then become :
(16)
<(e)> = 0 , <*(e)> = 0,
while the isotropic relations (13) become :
(17)
<a(e)*b(e)> = ¦V(e)¦².ab  0.
Decomposing (e) and c.c. as in (15) and applying (16) again leads to the non-trivial PSI field
[V(e).n(e), V*(e).n*(e)], where V(e) now stands for the non-quantum structured nothingness field
(mind only) and n(e) is now a 6-dimensional normal vector, with na(e)na(e) = 1 for all e.
3
GOD
Taking (11) as the definition of the gravitational nothingness, we are going to give the physical proves
enabling us to formally identify the metaphysical concept of God with the physical concept of
Universal Nothingness.
Lemma 1: The gravitational nothingness is a vector PSI-field on QW.
Indeed, the gravitational field E on QW is a function of z and z*, both points of QW. Therefore, it is a
vector PSI field on QW and so is its fundamental state V.
Lemma 2: (the fairness of God)
The gravitational nothingness is universal.
Indeed, according to the Newton Equivalence Principle, the gravitational field E acts on everything
the same way, whatever the physical properties : gravitation is mass-independent.
Definition 1: The Universal Nothingness is the gravitational nothingness on QW.
Lemma 3: (God is a pure spirit)
The Universal Nothingness is a free PSI field.
Indeed, the fundamental state of the gravitational field is the state in which no vector particle is
produced. Such a state is therefore necessarily source-independent, for a source would emit gravitons
(particles of gravitation). It follows that the gravitational nothingness is a PSI wave, that is, a free (or
pure) PSI field.
Lemma 4: (unicity of God)
The Universal Nothingness is unique.
Indeed, there is a single fundamental state of the gravitational field on QW. Moreover, it is a scalar
PSI field, as it has a single component.
Lemma 5: (God has no beginning and no end)
The Universal Nothingness is self-sufficient.
By definition, a nothingness has no creator, it exists prior to everything and it is a self-sufficient
physical medium : vacuum physics shows that it self-stabilizes and self-regenerates.
Self-stabilizing is a purely autonomous process, a spontaneous search for natural equilibrium, as the
deterministic value V = 0 is unstable (self-interaction and the Higgs process). It needs nothing
“external” to realize. Notice in passing that the instability of V = 0 means that Einstein’s purely
deterministic vision of the world leads to fundamentally unstable universes, which vanish as soon as
they are created. It is therefore an unreal representation of things.
Self-regeneration is due to the fact that, when matter or radiation of opposite signs interact, the energy
set free returns to nothingness.
The symmetry group of gravitation being SU(9) in the frame of the bioquantum synthesis, there is a
Yang-Mills gauge theory for the vector gravitational field E and a SU(9)-Higgs model for the
Universal Nothingness V. As V is universal, its associated Higgs model must be coefficientindependent. Consequently, both the mass and the coupling constant of V are unity. This situation is
fully consistent with older models of quantum gravity where the coupling constant was written by
means of the Planck radius. Here, the value 1 for the coupling constant of supersymmetric gravitation
actually corresponds to taking the Planck radius as the universal reference (minimal length). The
corresponding lagrangian now writes :
(18)
L = (DIV)(DIV)* - VV* + (VV*)²/2 , DI = I - EI , D*I = *I - E*I.
The minimum of the potential energy W = VV* - (VV*)²/2 is given by W/V* = 0 and so is located
at VoVo* = 1 (read “V naught”), from which we deduce that Vo = ei, where  is any constant phase
angle.
Definition 2: The Universal Vacuum is the PSI field U = ei + V, sum of the Classical Universal
Vacuum ei and of the Universal Nothingness V.
We are now ready to prove the formal identity between the metaphysical concept of God and the
physical concept of the Universal Vacuum.
UNIVERSAL THEOREM: The Universal Vacuum is the original source of both matter and
radiation in the Elementary Quantum World QW.
Proof: Let C, Â and |0> be respectively the creation operator, the annihilation operator and the
vacuum state of the gravitational field in Dirac’s notation. According to one of the definitions of a
vacuum, we first have :
(19)
Â.|0> = 0,
meaning the vacuum state can never be annihilated, even by itself (no action of Â). Then, applying the
creation operator on that state and iterating, we successively get :
(20)
C.|0> = |1> , C².|0> = C.|1> = |2> , … , Cn.|0> = |n>
for n integer > 0,
where |n> is the state in which n particles of gravitation are created. Conversely :
(21)
Â.|1> = |0> , ².|2> = Â.|1> = |0> , … , Ân.|n> = |0>
for n integer > 0.
Because the physical frame QW has the mirror symmetry, it is automatically supersymmetric. This
means that, each time a supergraviton is created or annihilated, both a spin-1 graviton and a spin-1/2
gravitino are simultaneously created or annihilated. Indeed, take the expression (8) for the
deterministic surface element on QW. Separating the metrical tensor GIJ into a symmetric part gIJ and
a skew-symmetric one IJ , GIJ = gIJ + iIJ and decomposing dzI into its real part dxI and its imaginary
part dyI, dzI = dxI + idyI, (8) writes :
(22)
dL² = (gIJ + iIJ)( dxI + idyI)( dxJ - idyJ) = gIJ(dxIdxJ + dyIdyJ) + IJ(dxIdyJ – dxJdyI)
The 2-form  = IJ(dxIdyJ – dxJdyI)/2 defines a natural symplectic structure on QW. As this 2-form
equivalently writes  = ij(dxidyj – dxjdyi)/2, it naturally projects onto a 3-dimensional “external”
symplectic structure involving only latin indices (fixed greek indices) and onto a dual 3-dimensional
“internal” symplectic structure involving only greek indices (fixed latin indices). Both projections
realize an irreducible representation of SO(3)  SU(2)/Z² and so, correspond to a spin-1/2 structure.
The “external” projection is relative to the “material” gravitino (fermionic corpuscule), while the
“internal” projection is relative to the dual “virtual” gravitino (fermionic wave).
The creation and the annihilation operators are complementary parts of the gravitational field, as they
appear in its canonical decomposition into modes. In flat space, the plane waves are now ep.z and c.c
so a new situation occur, that had already been pointed out by Prigogine in the 1980s (in the context
of dynamical systems) : when the real part Re(p.z) > 0, there is an exponential increase of the
fundamental mode, synonymous of inflation and, when Re(p.z) < 0, there is an exponential decrease
of that mode, synonymous of damping or even collapsing if the damping rate is quick enough. Such a
situation could not occur in conventional quantum field theory, as the phase factors were ip.x and –
ip.x, with both p (momentum vector) and x (space vector) real-valued.
The creation process of supergravitons is fully autonomous. This is made possible thanks to the nontrivial structure of the gauge group of gravitation in the frame of bioquantum theory, which enables
self-interaction. This self-interacting term is given by the Lie bracket in the SU(9)-Yang-Mills model.
In this model, the intensities of the gravitational field are :
(23)
WIJ = DIEJ - DJEI = IEJ - JEI + [EI , EJ] and WIJ* = DIE*J - D*JEI = IE*J - *JEI + [EI , E*J],
where D =  + E and c.c. are the Yang-Mills covariant derivatives, elements of the tangent bundle
TQW. Consequently, the Universal Vacuum does interact with itself and thus, self-polarize. This selfpolarization separates pairs and leads to the simultaneous creation of a supergraviton of positive
energy and of a supergraviton of negative energy.
Conversely, the annihilation process occurs when two supergravitons of opposite energies interact.
The energy set free is then given back to the Universal Vacuum, which regenerates.
There is as matter and radiation of positive energy produced than there is of negative energy, so that
the energetic balance always remains “zero”, that is, the minimal energy of the Universal Vacuum.
4
FIRST ELEMENTS OF TIMELESS PHYSICS
From (10), we first have, up to the sign :
(24)
cdt = dzo = V(z,z*)dL , cdt* = (dzo)* = V*(z,z*)dL , dL² = dzIdz*I
The velocity vectors u = dz/dt and v = dz/dt* can then now write in terms of the Universal Vacuum V
:
(25)
u = cn/V , v = cn/V* , |u| = |v| = c/|V| , n.n* = 1
As a consequence, the kinetic energy Ec of a point-like body (corpuscule) writes :
(26)
Ec = m(|u|² + |v|²)/4 = mc²/2|V|²,
where m is the mass of the body at rest. We recognize here Einstein’s famous formula for the energy
at rest Eo = mc². Yet, we are no longer in space-time relativity, but back to pure space relativity !
The acceleration vectors a = du/dt , a’ = dv/dt , a” = du/dt* and a’” = dv/dt* write :
(27)
a = -(c²n/V3)dV/dL , a’ = -(c²n/VV*²)dV*/dL , a” = -(c²n/V*V²)dV/dL , a’” = 3
(c²n/V* )dV*/dL.
There is still a conic structure on QW. However, it is no longer an inherent property of the physical
frame, but a direct consequence of the fact that the Universal Vacuum is a deformable physical
medium. Therefore, from (25c), we can still de fine a Mach number, the luminic Mach number :
(28)
ML = |u|/c = |v|/c = 1/|V|.
This means that, in complete opposition with Einstein’s space-time relativity, the speed of light c is no
longer a speed limit unreachable to matter, but only a critical speed that can be crossed which is
completely different ! Thus, for :
- |V| > 1, ML < 1 and we are in the subluminic region, corresponding to the causal zone in space-time
relativity ;
- |V| = 1, ML = 1 and we are in the transluminic region, corresponding to the surface of the light cone
in space-time relativity ;
- |V| < 1, ML > 1 and we are in the superluminic region, corresponding to the tachyonic zone in spacetime relativity.
Only radiations can propagate at exactly the speed of light, as in non-quantum fluids, only sound can
propagate at exactly the speed of sound. However, matter can now “jump over the wall of light”
thanks to a restructuring of the Universal Vacuum. As a consequence, all events and phenomena
become observable, even instantaneous ones, a consistent answer to the famous problem of time in the
Aspect, Gizin and al. experiments on correlated protons (the E.P.R. paradox).
In the superluminic region, physical phenomena qualitatively change and we should wait for
observing superluminic shock waves. Indeed, the Universal Vacuum, as any other vacuum, has
thermodynamical properties (temperature, pressure and density). Because of that, entropy should
increase when passing from the subluminic region to the superluminic one and shock waves should
locally reheat the Universal Vacuum behind them.
More will be said and done later on about timeless physics. I am just beginning to study it.
Philippe VIOLA
28/11/2004