Call me stupid… I’ve been talking about « quantum » kernels for many articles and i didn’t even remember that l was a scale… L

The spectral approach seems to be the right one… if i perform it right.

First, I made a mistake that I want to correct right now. In the 1D Laplace kernel r(x,l) = exp(-x/l)/l, l is obviously independent from the position variable x, since the integral equality:

 

(1)               l = ò₀^+¥ xr(x,l)dx = L(x) = Laplace transform of x

 

is a continuous summation over all distances x from zero to infinity. So, the result does not depend on any particular value x in this interval.

Second, x is “local”, while l is “global”. This, again, is obvious in (1), as integration is a global operation.

Third, x and l definitely have different roles. There can be no kind of “inverse kernel” that could be obtained permutating x and l. The inverse Laplace transform L^-1(l) giving back x reverses the kernel r(x,l) and integrates over l (Cauchy’s formula).

All this holds for more sophisticated kernels. Besides, (1) is equivalent to an integration over the differential of the kernel:

 

(2)               r(x,l)dx = -ldr(x,l)  =>  l = -l ò₀^+¥ dr(x,l) = -l[r(x,l)]_x=0^x=+¥

 

This property of the kernel also implies that:

 

(3)               dr(x,l)/dx = instantaneous variation of r in space at scale l =

= -r(x,l)/l = -(mean scale variation of r at the same point x)

 

which means that, going from differential calculus and thus geometry to algebraic calculus, integral geometry and thus topology, is only due to the property of the kernel. It’s only because this kernel verifies (3), which is a bridge between differential geometry and discrete geometry, that the instantaneous variations of any continuous function f of the distance variable x is Laplace-transformed into a discrete derivative of the Laplace spectrum of f with respect to the Laplace spectrum of x, that is, l.

We have here full confirmation, if necessary, that all properties of the Laplace transform are contained in its kernel. More complicated algebraic expressions are obtained with other transforms, but the result is the same: all the properties obtained are contained in kernels.

 

So: 1) x and l are independent quantities; so good; 2) x and l have same physical units (here, meters).

As I said previously, the wrong interpretation would be to deduce from that an extended 6D space or 8D space-time: l is a length, as is x and they both belong to the same space or space-time. The pair (x,l) does not double the number of physical dimensions.

I asked myself why. Why couldn’t l be used as an additional space dimension?

I simply lacked a geometrical representation.

Fix a coordinate system and an origin O. x is the distance of any point in space from O. The distance between the origin and itself is x = 0. x varies from point to point.

l is different. It’s a scale of distances. Say l = 1m, for instance. This choice will mean we include all distances x from x = 0 to x = 1m. So, l is actually not a space variable. It’s a length. The length of a segment [0,l]. It’s the boundary value of a distance interval. When l varies, the length of this interval varies.

 

Geometrically speaking, the introduction of a scale means the ordinary point in space is replaced with a segment of given length l.

 

The substitution is similar to the one in string theory, where a point-like body is “extended” into a small string. However, the geometrical interpretation in spectral analysis is different:

On the one hand, we have point-like bodies located at points x in space; these bodies remain point-like. And, on the other hand, we have distances scales l, representing segments of space. The spectral image of a point x in “original space” is a segment of length l in “spectral space”. Conversely, the original image of a segment of length l in spectral space is a point x in original space.

There’s no “spatial extensions” of point-like bodies. There’s a correspondence between an “original space (or space-time)” with “original (point-like) bodies” and a “spectral space (or space-time)” with “spectral bodies”. These “spectral bodies” are point-like only when l = 0. Otherwise, they have “characteristic size l”.

 

What does that mean?

On the geometrical point of view, this first mean points have to be replaced with segments [0,l] of variable sizes. Consequently, curves have to be replaced with surfaces, surfaces with volumes, volumes with 4D hypervolumes and so on.

On the material viewpoint, only non-deformable solid bodies can be represented as “point-like” (the “hard sphere” model), since all their points move with their centre of gravity at the same time, so that their motions in space(-time) can be brought back to their cog alone.

If a material body shows a spanning in space, it cannot be so. Whether it’s deformable or it cannot be considered as solid.

This last point is very important, since it has important consequences on the internal structure of bodies: if an “original” body can always be considered “point-like” as soon as it’s in a solid and non deformable state, a “spectral” body can be considered as such only for l = 0, that is, when its size is zero. As no substantial body with zero size exists in Nature, we deduce that:

 

NO SPECTRAL BODY CAN BE VIEWED AS A SOLID, NON DEFORMABLE SUBSTANTIAL BODY: WHETHER IT’S SUBJECT TO DEFORMATIONS OR IT CANNOT BE CONSIDERED AS BEING IN A SOLID STATE AS WE CONCEIVE IT.

 

For an “original” (biological) observer, it looks like something “ethered”.

Anyway, as we saw it in B94, on “our” side of light, spectral bodies are unobservable (since l² = lⁱl_i < 0). On “the other side” of light, they are and biological bodies aren’t anymore (k² = kⁱk_i < 0). When we have to deal with 4 scales lⁱ, a point xⁱ in original space-time has to be replaced with a 4D hypervolume in spectral space-time. Hence the easy confusion with a 8D “superspace”, since to any geometrical structure, we add 4 dimensions… J

Actually, it’s all fictuous. The physical frame remains 4D, but the structure of bodies is directly impacted, as the consequence of the change in the nature of space (and time).

Hence too, the confusion with wavepackets: we’re not dealing with wavepackets, but with spectra. Sure, associating x and l can help build wavepackets. But oscillating motions as well!

 

A wave can never be substantial. A spectral body can. Technical subtleties making huge differences in the end…

For substances, we find “originals” and “spectra”.

For links between the “original” state of space-time and the “spectral one”, we can use quantum objects. Because they play on both sets of variables.

 

To sum up, I would say that, in parapsychology, everything that relates to physical substances is not what we call “quantum”. Possible communications between the two sides of light, i.e. between “livings” and “deads” are “quantum”. Rather “wavy”.

 

For all these reasons, I’ll no longer be too severe with technicians seeing in “superstrings”, “extra-dimensions” or other sophisticated quantum devices possible “doors” or “gates” to the “paranormal”. I may be repeating, but confusions are very easy and subtleties much harder to distinguish! And it’s always much easier to add dimensions and “see what it’s gonna give” than to stay in good old 4D space-time.

 

I’d like to bring a final correction to B94:

 

WHEN GOING FROM ONE SIDE OF LIGHT TO THE OTHER, IT’S NOT A QUESTION OF GETTING SUBSTANTIAL, THE SPECTRAL BODY IS SUBSTANTIAL ON BOTH SIDES, IT’S A QUESTION OF BECOMING OBSERVABLE.

 

It all turns around questions of observation and scales…

If you’re spectral, you can be fully substantial and consistent, while seeming unconsistent and therefore unsubstantial to an « original » observer’s conception, because your matter looks like « dispatched into space » (and even time) to him.

You no longer appear as a geometrical object, but as a topological one.

 

Everything but simple, all this stuff…

 

Yep! There’s unfortunately still something that doesn’t fit…

We find exactly the same relations in the corpuscular as for waves. Nothing original? Not sure. For I found no clear explanation about this in my references.

Look.

Take a point-like body B with instantaneous velocity vector v(t) = v(t)n. His energy and momentum in motion are respectively:

 

(1)               E(t) = E₀/[1 – v²(t)/c²]^1/2  ,  p(t) = E₀v(t)/c²[1 – v²(t)/c²]^1/2 = E(t)v(t)/c²

 

From what we deduce that:

 

(2)               E(t)/p(t) = c²/v(t)

 

whereas:

 

(3)               dE(t)/dp(t) = v(t)

 

If the second relation is well understood, my question is:

 

WHAT REPRESENTS THIS SECOND VELOCITY IN (2)?

 

Stupid as usual, isn’t it? We cannot argue c²/v(t) is a phase velocity, since we’re not dealing with waves, but with corpuscles. Hence my (stupid) question. E(t)/p(t) looks like a mean value. Just like Canada Dry, (2) “looks like” a mean velocity, but is not. For letting c²/v(t) = v_moy(t) = x(t)/t would lead to d[x²(t)] = d(c²t²), that is, to c²t² - x²(t) = c²t₀² in the causal region or c²t² - x²(t) = -c²t₀² in the tachyonic one. A quadratic relation analogue to E²(t)/c² - p²(t) = E₀²/c². I turned to the Laplace transform, obviously with no result, since the algebraic quotient of two Laplace spectra sends back to a convolution formula for the originals. Nothing I tried satisfied me. The only relations I found were:

 

(4)               v(t) = original of v_ph(T) = l(T)/T by e^-t/Tdt/T with x(0) = 0;

(5)               c²/v(t) = original of v_gr(T) = dl(T)/dT by e^-x/ldx/l with t(0) = 0;

 

since v(t) = dx(t)/dt <=> 1/v(t) = dt(x)/dx, and:

 

(6)               v_gr(T) = ò₀^+¥ v(t)exp[-v(t)/v_gr(T)]dv(t)/v_gr(T)

(7)               v_ph(T) = ò₀^+¥ v_moy(t)exp[-v_moy(t)/v_ph(T)]dv_moy(t)/v_ph(T)

 

in galilean relativity, while:

 

(8)               V_gr(T) = ò₀^+¥ V(t)exp[-V(t)/V_gr(T)]dV(t)/V_gr(T)

(9)               V_ph(T) = ò₀^+¥ V_moy(t)exp[-V_moy(t)/V_ph(T)]dV_moy(t)/V_ph(T)

(10)           V(t) = v(t)/[1 – v²(t)/c²]^1/2  ,  V_gr(T) = v_gr(T)/[1 – v_gr²(T)/c²]^1/2

(11)           V_moy(t) = v_moy(t)/[1 – v_moy²(t)/c²]^1/2  ,  V_ph(T) = v_ph(T)/[1 – v_ph²(T)/c²]^1/2

 

in einsteinian relativity. That’s all. Besides, for variable velocities, when performing the wave-corpuscle duality, we let aside one more “tiny detail”:

 

(12)           v = v_gr

 

Great. But, formally, this only holds for constant velocities. For variable ones, v depends on t (the “original time”), while v_gr depends on the period T (the “spectral time”)! We can make no mistake between them, since T is the Laplace spectral image of t. So, we’re definitely not dealing with the same time variables. The only thing we can say is, that, in numerical values, v and v_gr are of the same magnitude.

In one sense, this reinforces what I support in favour of the existence of two bodies, a double nature of things: on one “side” of light, what is described by a dynamics based on x(t), v(t), E(t), p(t) and so forth and on “the other side”, what is described by a dynamics based on l(T), v_gr(T), E^(T) and p^(T), spectral transforms of E(t) and p(t).

So, why shouldn’t I be fully satisfied?

Because if we really were in presence of spectral transforms, the original motion x(t) and the spectral motion l(T) would never be independent… As an example, l(T) can simply be realized two ways:

 

(13)           l(T) = ò₀^+¥ x(t)e^-t/Tdt/T = L_t[x(t)]

 

Laplace transform of x(t) with respect to time(s), or:

 

(14)           l(T) = ò₀^+¥ x(t)exp[-x(t)/l(T)]dx(t)/l(T) = L_x(t)[x(t)]

 

the same transform, but with respect to x(t), i.e. in a functional space of corpuscular trajectories spanning from 0 to the infinity.

In any case, x(t) = x(0) for all t, that is, a fixed position in original space(-time) implies l(T) = cte = l(0) for all T, that is, a corresponding fixed position in spectral space(-time), due to the normalization of the Laplace kernel: ò₀^+¥ e^-t/Tdt/T = 1 and ò₀^+¥ exp[-x(t)/l(T)]dx(t)/l(T) = 1.

In civilized language, this means that, when the biological body is fixed in space, the spectral body should remain fixed in spectral space… and conversely.

I suggested, that’s right, to go beyond spectral transforms but, this time, it demands two completely independent set of dynamical variables and parameters: the set {x,t,x(t),f(x,t),…} and the set {l,T,l(T),F(l,T)…} on each side of light. Setting up a duality between them would lead to waves, wavepackets and finally the quantum.

But what about oscillating motions?...

We can have a substantial pendulum moving according to x(t) = x(0)cos(t/T) for instance… such a motion makes use of both set of variables and still represents a “corpuscular” motion (the motion of a corpuscle)… When oscillating, the pendulum behaves like a wave. More precisely, its motion in space resembles a wave.

 

I’m a bit lost for we haven’t been rigorous enough in the mathematical description of our contemporary physics. We neglected too many things. Let me just recall that the quantization procedure is still not completely proven. I’d be very annoyed to be forced to leave the quantum frame, not only because it would demand to develop a brand new physics “based on nobody knows what”, but also because many aspects of parapsychology are in sound adequation with quantum behaviours. For instance, this feeling of “heat” in NDEs: the superfluid motion is very sensitive to heat. There are numerous details such as this one going in favour of quantum theory.

Yet, there remains a lot of technical points that do not satisfy me: not all oscillating motions are quantum; spectral dualities involve dependent motions; corpuscular dynamics having the very same relations as wave dynamics;…

As I said above, we haven’t built a mathematical frame solid enough to be able to move on “quietly” in parapsychology. Too many aspects of “well-established” physics are actually more than shallow…

“it works” for it’s “in agreement with experiments” so far.

Now, in biophysics, it doesn’t work. Or it does, but not properly.

I don’t want “hypothesis” nor “postulates”. I want proves. I want things, reasonings, to be proven.

Now, the only kind of solid proves we have in quantum physics is… experiments.

And as we still don’t have solid protocols in parapsychology, we can only base ourselves on theoretical work.

The snake bites its toe…

I had some successes, found some explanations, but there remains too many open questions that should have found an answer if our theoretical basis in physics were tough.

This is the most frustrating in all and I cannot move on mainly because of that.

I cannot be sure of what I propose for, each time, there’s some “tiny correction” or “completion” to bring…

Instead of moving on, I spend my time trying to correct existing physics!!! 8((((

 

What’s really unbelievable… is this.

 

As promised, let’s now turn to technical details and see the consequence for NDEs.

We’ve already reviewed spectral analysis several times on this blog, so I won’t write all the calculations down again. For our present purpose, anyway, the Laplace transform is sufficient. More sophisticated transforms would only complicate things, but wouldn’t change anything to the principles.

In bidouille 37, eq. (7), is given the equation for rather general kernels r(x/l). According to (1), bidouille 93, the equation for the 3-volume of a body B’ is the equation for r(x/l) in 3 dimensions with only a change of sign before the identity, that is: -3Id in place of +3Id (nId in n dimensions). Moreover, for any smooth kernel r(x/l) = Kexp[-a(x/l)]/l¹l²l³, where x/l is short writing for (x¹/l¹,x²/l²,x³/l³) and a(x/l) = 0 at x = 0, one finds V(0) = K^-1l¹l²l³ to be the volume of B’ around B, when B is located at the origin of a chosen reference frame. This alone shows that V(0) is spectral.

To deduce from this result that the physical space in which parapsychological phenomena have to be studied would be 6D, 3 xⁱ for “ordinary” space + 3 lⁱ for “spectral” space would be a mistake. Indeed, I’ve already pointed out the fact that, in more than 3 space dimensions, physical bodies should keep a 3D basis. This is not what NDEs tell us and to say that would be a wrong interpretation of them.

Instead, NDEs show us we’re in front of two complementary states of the same 4D Universe: an “ordinary” state with coordinates xⁱ and a “spectral” state with coordinates lⁱ (i = 0,1,2,3). When taking these two states into account, we get a mechanical description of a quantum Universe: giving us coordinates (xⁱ,lⁱ) is actually equivalent to giving us coordinates xⁱ alone and wavepackets y(xⁱ,lⁱ) with squared amplitude r(xⁱ,lⁱ), as these wavepackets connect physical objects depending on the xⁱs (and called “originals” in the language of spectral analysis) to physical objects depending on the lⁱs (and called “spectral images” or simply “spectra”), through a global, integral, transform. As a practical example, we have the Laplace transform of a space trajectory x(t):

 

(1)               l(T) = L[x(t)] = ò₀^+¥ x(t)e^-t/Tdt/T

 

which gives a spectral trajectory l(T) in spectral space. Simple calculation then shows that the instantaneous velocity v(t) = dx(t)/dt of a substantial body B moving into “original” 3-space is transformed into v_ph(T) = l(T)/T, the phase velocity of a signal “associated with B”, according to the initial formulation of De Broglie’s wave-corpuscle duality. We now see that v_ph(T) is actually the mean velocity of a “spectral” body B’ complementing B in the quantum picture. It’s merely the equivalent of the mean velocity v_moy(t) = x(t)/t in “spectral” space, i.e. in the spectral state of (quantum) 3-space.

Let’s now go back one more time to the spectral relation k² = kⁱk_i, with kⁱ = 2p/lⁱ the components of the 4-wave vector. We know that:

 

(2)               k² > 0 => kⁱ time-like => v_ph > c <=> v_gr < c

(3)               k² = 0 => kⁱ light-like => v_ph = c <=> v_gr = c

(4)               k² < 0 => kⁱ space-like => v_ph < c <=> v_gr > c

 

since

 

(5)               v_ph(T).v_gr(T) = c²

 

for a group velocity v_gr(T) = dl(T)/dT, whatever the original motion in original 3-space, uniform or not. Now, v_ph(T) = l(T)/T implies:

 

(6)               k² > 0 => v_ph > c => l² = lⁱl_i < 0

(7)               k² = 0 => v_ph = c => l² = 0

(8)               k² < 0 => v_ph < c => l² > 0

 

Truly, there’s absolutely nothing new in what we’re talking at the moment. These are all elementary and well-known results of spectral analysis in space-time.

We’re used to say a signal is “causal” when k² > 0. It therefore means l² < 0, i.e. lⁱ is space-like or “tachyonic”, meaning it stands “on the other side of the light cone”.

We consider a signal to be “tachyonic” when k² < 0, meaning l² > 0, i.e. standing “on ‘our’ side of the light cone”.

And we consider a signal to be light-like when k² = 0, meaning l² = 0, i.e. standing exactly on the light cone.

Are you beginning to see what I’m undermeaning in all that?

In our reclassified interpretation of the wave-corpuscle duality, we find a body B’ in place of the signal.

 

LET B BE A “SUBSTANTIAL” BODY IN ORIGINAL 4-SPACE-TIME AND B’ ITS “SPECTRAL EXTENSION” IN QUANTUM 4-SPACE-TIME.

WHEN k² > 0, l² < 0 AND B’ IS “NON SUBSTANTIAL” IN ORIGINAL 4-SPACE-TIME.

WHEN k² = 0, l² = 0 AND B’, AS B, IS “IN BETWEEN”.

WHEN k² < 0, l² > 0 AND B’ IS “SUBSTANTIAL” IN SPECTRAL 4-SPACE-TIME.

 

What do we have at the precise moment when the patient’s blood pressure p falls down to zero? An “OBE”. Well, that’s not really what spectral physics tells us: nothing needs to “get out” of the biological body. Instead, we have a double “quantum” body, from the beginning, with a “substantial” part B and a “spectral extension” B’. Both are “alive”. But, when B is thermodynamically active, we have no direct perception of our B’, for a simple reason: B’ alone is thermodynamically reversible. And just like in superfluids, there exist exchanges between B and B’, but implying no mass transfert, i.e. no energy-momentum transfert. If there’s no perceptible changes in such exchanges, we perceive nothing. Or only a “single” body.

Things begin to change when p = 0, for B becomes inert. Surprisingly enough, the patient then “becomes conscious he/she gets a ‘second’ body, ‘of a different nature’”.

He/she just becomes conscious his/her “spectral extension” B’ is alive… because p = 0 does not concern it… J Or, much better, autonomy is transferred from B to B’. Whatever really happens, B’ is now autonomous and conscious.

 

So, what’s the need for a “Tunnel” with a “Great White Light” at the end?

 

This is where things become really extraordinary. Look at (6) to (8): what does spectral physics tells us?

 

THE SPECTRAL BODY NEEDS TO GO THROUGH LIGHT TO GET SUBSTANCE.

TO BECOME FULLY CONSISTENT.

 

Incredible, isn’t it?

When this “fake OBE” happens, B’ is “wavy”, “unsubstantial”, for it stands in the same “causal” region of the Universe, on “our” side of the light cone, where it appears to us as a signal. But this is the region of pretended “substantial matter”. He’s not in his region! His region is “on the other side of the light cone”. This is where it appears “substantial”, where he gets “consistence”, whereas previous “substantial matter” there becomes “unsubstantial”! J

It’s all about the choice of observers: to an observer in the “causal” region k² > 0 of space-time, l² being < 0, everything with l² < 0 looks non substantial, as matter “cannot move faster than light” and waves “move at the speed of light”… J. To an observer in the “tachyonic” region k² < 0, l² > 0 and everything inside the previous “causal” region looses all substance, for the very same reasons, as this “tachyonic” region is actually “spectral causal”.

There’s a complementarity between the two dynamical regions of space-time.

Statically, now, we find three states of the same Universe: the “original” state (k² > 0 , l² < 0), the “spectral state” (k² < 0 , l² > 0) and the “quantum” state, gluing together these two states.

 

So, B’ has to move from “this” side of the light cone to “the other” to get consistence. And this can only be done with the help of a wormhole (Bidouille 89) and the velocity (!) condition G_iGⁱ = c² on the gravitational potentials.

It all goes around velocities…

 

ONCE B’ IS “ON THE OTHER SIDE OF THE LIGHT CONE”,

HE CANNOT COME BACK.

 

There can be no “return from the Deads”. This is not what happens. Again, it’s a feeling.

B’ cannot come back, for he’s now substantial and no substance can go through the light cone. Now, to “come back” in the “biological region” he left, he would need to go back through the light cone. Impossible for substantial matter.

 

BESIDES, NO “TUNNEL BACK” IS REPORTED IN NDEs.

 

The Tunnel was possible for B’ was not substantial yet. Now he is, it’s no longer possible…

 

BUT THIS APPARENT CONSTRAINT ACTUALLY EXPLAINS THE RADICAL CHANGE IN THE PATIENT’S BEHAVIOUR WHEN HE WAKES UP:

BECAUSE WHAT HE WAS BEFORE p = 0, I.E. A BIOLOGICAL BODY WITH A SPIRITUAL INCONSISTENT EXTENSION, HAS BECOME A DOUBLE CONSISTENT BODY, WITH A CONSISTENT BIOLOGICAL PART “ON ONE SIDE OF THE LIGHT CONE” AND A CONSISTENT SPIRITUAL PART “ON THE OTHER SIDE OF THE LIGHT CONE”

HIS “SOUL” TOOK CONSISTENCE.

 

And that makes the system completely different from what he was before…

Because the two bodies can communicate through the light cone.

How?

 

THERE’S A VERY INTERESTING SPECIFICITY OF NEURON CELLS, THAT IS TO PRODUCE AN ELECTROMAGNETIC ACTIVITY. AND THIS ACTIVITY PRECISELY PROPAGATES AT THE SPEED OF LIGHT.

AS A CONSEQUENCE, THE BIOLOGICAL BODY AND THE SPECTRAL ONE (HIS “SOUL”) STAY IN CONNEXION AND CAN COMMUNICATE THROUGH THESE ELECTROMAGNETIC FIELDS.

AND THIS CAN EXPLAIN WHY A NDE CAN BE INTERPRETED AS A “CONSCIOUSNESS EXPERIMENT”: BECAUSE THE “LINK” BETWEEN THE BIO AND THE PSI, IN ANIMALS, CAN ONLY BE THEIR NERVOUS SYSTEM AND THEREFORE THEIR CONSCIOUSNESS.

 

I’m particularly satisfied with these results, as they first reconciliate all points of view, the biologists’, the spiritualists’ and the physicists’ and because they gratify a hard work done throughout these last two years, showing all I developed so far was kind of founded and that the blame was actually on the incompleteness of quantum physics. It was these incompleteness that led me into dead ends or to unadapted scenario like phase transitions.

 

I’m glad I managed to understand a tiny, but central, part of what’s susceptible to happen “when we die” and to bring a physically consistent scenario to NDEs.

 

I have a very nice story to tell today. And what physics tells me, through the interpretation of its equations is rather extraordinary.

First of all, I have now acquired the certainty that

 

QUANTUM PHYSICS IS INCOMPLETE.

 

Which surely explains why everyone agrees in recognizing actual quantum physics still lacks coherence.

For weeks, not to say months, as I was progressing in the investigation of NDEs, something deeper and deeper inside of me was telling me something was missing in our general frame of description. According to the wave-corpuscle duality, a substantial corpuscle was to be associated with a wavepacket. But such an association just can’t be. Because we then associate two physical objects of different nature and belonging to two different categories: a body is a static object, a wave is a dynamical object.

A wave, and in particular a wavepacket, is a motion, not an object: what we model through y(x,t), or only y(x), is not a body, but a trajectory. It’s a generalization of x(t). So, associating a corpuscle with a wavepacket would amount to associating a body with a trajectory. This is clearly unadapted. What actually happens is that, when going from “classical” physics to “quantum” physics, trajectories are double: while the “classical” corpuscle continues following a “classical” trajectory x(t) through space, a second trajectory appears, modelled by y(x,t) or y(x), depending on the context. So, where the wave-corpuscle is correctly adapted is when it tells us this:

 

ACCORDING TO THE WAVE-CORPUSCLE DUALITY, EVERY PHYSICAL BODY IS ALLOWED TO HAVE TWO MOTIONS THROUGH SPACE AND EVEN TIME: THE SO-CALLED “CLASSICAL” MOTION x(t), AS OFTEN AS THIS BODY BEHAVES LIKE A CORPUSCLE, AND THE WAVY MOTION y(x) OR y(x,t), AS OFTEN AS IT BEHAVES LIKE A WAVE, I.E. LEADS TO INTERFERENCE PICTURES ON SCREENS.

 

This is a first reclassification of physical events that is in agreement with the classification of objects in physics: both x(t) and y(x) or y(x,t) are now dynamical and both belong to the category of trajectories. With a straightforward consequence: properties like the kinetic momentum, for instance, are not properties of bodies, but of their motions. The position x(t) of a body in space at time t has never been considered as a property of this body so far. Nor its momentum p(t). Both are features of its motion. Consequently, M(t) = x(t) x p(t), the vector product of them, is a feature of the body’s motion. It characterizes its rotation around its own axis. Well, the very same hold for waves. The “position” of a wavepacket in space is given by X^.y(x) = xy(x), where X^ = xId is now the “position operator” acting on the functional space of wavepackets. The corresponding “momentum” is P^.y(x) = -iħÑy(x), where P^ = -iħÑ is th “momentum operator” acting on the same space. Both “quantum” operators are now (non commutative) features of the wavy motion. Not of the body! We could say that the “quantum numbers” induced by these operators solving for eigenvalues equations are “carried by the wavepacket”: they aren’t properties of the body itself, like mass or electrical charge, for instance. It goes out of this that the kinetic momentum operator M^ = X^ x P^, where X^ and P^ no longer commute, is a feature of the wavy motion y(x), and the spin number, which is proportional to this “quantum” or “intrinsic” kinetic momentum, is not carried by the corpuscle, but by its wavepacket. When we say a (quantum) particle has “spin s” in its reference frame, we actually refer to the property of its wavepacket. A spin s means this wavepacket can be separated into 2s+1 polarized wavepackets. Or that the wavy trajectory of this “particle” can be separated into 2s+1 polarized trajectories. Hence a spin-1/2 describes a 2-component wavepacket, that is, a 2-component wavy motion, one polarized “up” (s = + ½) and one polarized “down” (s = -½). These “branches” are the “pure states” (i.e. completely polarized states) of the wavy motion of the quantum corpuscle (the “particle”). Otherwise, there’s a statistical mixing of these pure states, indicating the wavepacket, whether is only partially polarized, or is not polarized at all. Obviously, we can always associate the spin with an “intrinsic” rotation of the particle around its axis, just like for the classical kinetic momentum, but deducing it’s some “internal property” of the particle itself, the “quantum body”, is incorrect. It’s a feature of its wavy trajectory.

So, the wave-corpuscle duality postulates any “quantum body” is allowed to move into space or space-time two different ways, according to the results of experiments. Again, deducing “it behaves sometimes as a corpuscle, sometimes as a wave” is incorrect: the body is one thing, its motions are another.

Besides, we retrieve this double nature of the motion at the macroscopic level in superfluids and superconductivity: in superfluids, we find the “normal” component of the motion, which concerns uncorrelated “fluid particles”, together with the “superfluid” component of the motion, which concerns quantum-correlated fluid particles. In superconductivity, uncorrelated electrons (“conduction electrons”) move a “normal” way, while quantum-correlated electrons move a “superconducting” way, i.e. resistance-free.

Yet, something still seemed to miss in this description of Nature. The argument brought by pretended “OBEs” in NDEs was in clear contradistinction with the uniqueness of physical bodies. My argumentation went toward a double nature of physical bodies as well. It appeared to me as the only way to explain OBEs. The phase transition scenario was not appropriated, even the semi-classical ones, for they transform the dynamics of a single body and, as I said earlier, this is not what NDEs report us. All NDEs are crystal-clear on this point: a second body “appears”, of a different nature, and this additional body had no place in today’s physics, not even quantum physics.

So, I went to the “almost-certainty” that quantum physics not only doubles trajectories, but doubles bodies as well.

Anyway, whether a brand new physics was to build and quantum physics had no role to play in parapsychology at all, whether quantum physics was incomplete.

I first tried the simplest solution, the second one, as usual. And we would see, as usual.

Okay, then, let’s now try to extend the wave-corpuscle duality a bit more.

 

ACCORDING TO THE EXTENDED WAVE-CORPUSCLE DUALITY, QUANTUM PHYSICS DOUBLES PHYSICAL BODIES AND TRAJECTORIES.

 

The new quantum frame looks now like this: starting from a single body, say B, with a motion x(t), we find two bodies B and B’ and two motions, x(t) and y(x) or y(x,t). Since B has motion x(t), B’ must have motion y(x) or y(x,t). B and B’ constitute one “quantum” body. [x(t),y(x)] or [x(t),y(x,t)] one “quantum” trajectory. Physical bodies are with physical bodies, trajectories are with trajectories. The classification of things is correct.

If this is so, then B’ can be nothing else than some kind of a “non-substantial body”. However, put this way, it hardly means anything. The adapted physical picture is a “substantial body” B, brought back to point-like, the famous “corpuscle”, surrounded by a “non-substantial” body B’ expanding inside a volume V of space around B.

What can be this volume? Quantum physics immediately answers us:

 

(1)               r(x) = |y(x)|²  in m^-3  =>  V(x) = 1/r(x)  in m³

 

The squared of the amplitude of the wavepacket being in m^-3, its inverse gives the searched volume around the point x of space where the corpuscle B is located. Should B moves along x(t), then (1) transforms into:

 

(2)               r[x(t)] = |y[x(t)]|²  in m^-3  =>  V[x(t)] = 1/r[x(t)]  in m³

 

so that the volume surrounding B can vary from V₀ = V[x(t₀)] = V(x₀) to V₁ = V[x(t₁)] = V(x₁). We can even have:

 

(3)               r[x(t),t] = |y[x(t),t]|²  in m^-3  =>  V[x(t),t] = 1/r[x(t),t]  in m³

 

and our volume is even allowed to change shape in time at each fixed point of space.

 

All this to say quantum physics already brings us solid arguments proving the existence of a second “non substantial” body B’ in direct connexion with the “wave extension” of a point-like “classical” body. This is everything but sci-fi. It only required a suitable reclassification of objects according to their physical categories. The rest is already included in quantum physics.

 

The addition of complexity leads us to the quantum picture of a biological body B surrounded by a “non substantial” body B’, precisely the one we’ve been searching for since the beginning… B and B’ are quantum-correlated, as any quantum object. Where B can be the biological location of a psychological activity, B’ is rather the location of a spiritual activity. B’ is a kind of “spiritual aura” around B, to give a (very) rough idea of it. It’s something “living”, as B, but with “no substance”, despite it remains material.

 

Tomorrow, I’ll give all the technical details about B’, as I have no time left to develop this.

I’ll also explain what the “Tunnel” and the “Great White Light” are for.

It’s not personal interpretation, only physical results.

And it’s just extraordinary.

When practicians report their patients show “a different behaviour” after an NDEs, that’s the least to say. A radical change does happen and we’ll see how and why.

 

Some precisions now about the results obtained.

We first used the proof of the existence of massless particles of matter such as neutrinos to build our own proof of the existence of much more general non-substantial matter.

Then, we used the Laplace transform to show how to go from substantial objects and motions to non-substantial ones. This is surely not the only possible transform, it’s only one of the simplest ones. It should give a first idea of how the whole process works.

Formulas (3) to (12) are useful for massive and/or charged substantial bodies. However, the existence of massless material objects forces us to go beyond the concept of integral transform, as purely non-substantial matter will have no substantial “original”. This means that a physical quantity like the wavy mass M(T), for instance, may exist despite its substantial “original function” m(t) is identically zero. Again, neutrinos are typical examples of this situation. Hence again, their interest to remain massless. On the opposite, the existence of a substantial mass m(t) non zero that would lead to a non-substantial M(T) identically zero would contradict the wave-corpuscle duality: if a substance is present, there’s automatically a wave associated with it. Once more, the physical evidence for this comes from particle physics. The rest is a mere question of assembling and complexification. Purely substantial objects like those encountered in classical physics are “mind simplifications”, “idealizations” of Nature. It only means the wave properties are not taken into account.

To sum up, to a m(t) non identically zero must correspond a M(T) non identically zero, but to a m(t) identically zero can correspond a M(T) non identically zero.

And the same holds for any other charge.

Mathematically speaking, we would say that, in this case, the integral kernel of the transform is no longer injective, as to a zero original may correspond non zero images. It isn’t of course reversible, since these non zero images would set back to zero originals.

From this mathematical viewpoint, the situation of so-called “massless substance” shows “singular” (with respect to the regularity of integral transforms for non zero originals).

There so exist an entire class of constructible objects and motions that are purely non-substantial and that correspond to no substantial objects and motions, but the converse is false.

 

Another important point I’d like to talk about today is on the general physical properties of waves and their fundamental differences with substantial matter.

As I recalled many times, the first of these essential difference is separation. Substantial matter is separable (unless it shows to be very fundamental): if you cut a solid in two parts, you’ll get two solids. Waves aren’t: if you “cut” a wave in two, you double it. The two “copies”, identical, can then always “glue back again”, without interference, since it’s the very same wave on both parts [interferences appear between two interacting waves of different shapes, for instance, a sin(wt) and a cos(w’t)].

Another crucial feature: substantial matter is subject to both internal and external friction, waves aren’t. The reason for this is: substance is stiff, because of its molecular structure, waves aren’t. To get convinced of it, just remind the properties of superconducting and superfluids motions: all purely wavy properties of matter show a complete absence of friction. Superconducting electronic Cooper-Bose pairs induce no resistance. Superfluid motion induces no viscosity.

Everything purely wavy automatically implies no dissipation processes at all. This is because, when combining altogether, waves give a “smooth” assembling.

So, where the decrease of substantial mass m(t) with respect to time is mostly due to friction (in inert substance), a similar decrease of a non substantial (inert) mass M(T) with respect to the period has a different origin. For particles and atoms, we have the simple formula M(T) = h/c²T, which immediately shows the wavy mass can only decrease with |T| (T < 0 for antimatter). In B87, we showed that any non substantial object, however complex, keeps the same phase numbers as its most elementary components. The difference lays in the combinations of Fourier coefficients at each complexification level. So, we would be tempted to say a wave(packet) is “lighter” at low frequency and “heavier” at high frequency, albeit I’d prefer to keep the more general dependence M(T), in case more complex laws appear.

After all, we still don’t know where mass originates from.

 

NO FRICTION = NO DOWNGRADING = NO DISSIPATION

= SELF-REGENERATION = THERMODYNAMICAL REVERSIBILITY

 

A purely wavy structure cannot “get old”, it can only be absorbed or destroyed by interferences with other wavy structures.

As an example, consider a substantial cell. The wave-corpuscle duality together with complexity associates a non substantial cell with it. As long as the substantial cell is “living”, i.e. autonomous, the non substantial cell remains “dead”, i.e. inert, “silencious”. We now know from biology that “paroptosis”, the “programmed death” of the cell is due to the shorting of its telomeres, the molecules at the end of chromosomes. During its life, the length of these telomeres shortens. They “disappear” one after the other. We cannot say a telomere is autonomous, since autonomy really begins at the complexity level of the cell (even a protein is not autonomous, it only has a function). When chromosomes have lost all their telomeres, the coding of the cell is no longer assured, bugs appear, free radicals begin to attack the mitochondria, responsible for the management of the cell resources and the “death” process starts. It proceeds in three steps: contraction of the cell, inner dismantling and general fragmentation. A mitochondria is itself a bacteria, so it’s complex enough to be autonomous. When it “dies”, its autonomy is transferred to its wavepacket. And when the whole cell “dies”, its autonomy is transferred to its wavepacket. So, we don’t mind if the cell dismantles afterward: it’s merely biological. As a material substance, it follows the rules of thermodynamics. What’s important for us is that, once the biological cell inert, its wavepacket replaces it. The cell “continues to live”, but as a compact wave. This wavepacket contains, as sub-structures, all the wavy components of the biological cell, including the molecular wavepackets of its telomeres. It no longer downgrades, for its dynamics is now thermodynamically reversible.

An assembly of biological cells will make a tissue adhering ones to the others, thanks to the adherence molecules they possess on the external face of their membranes.

An assembly of cellular wavepackets will make a tissue combining altogether through constructive interferences. This will give a new wavepacket (B87).

And so on.

If you tear a biological tissue apart, you’ll destroy it once you’re over its plasticity limit.

If you try to tear a tissue wavepacket apart, all you’ll do will be to extend it. You’ll never manage to destroy it this way, for all the cellular wavepackets composing it are strongly correlated. Basically, you could extend it “from one side of the Universe to the other”, you’ll never get it. The only way to destroy it is to expose it to negative interferences.

If you cut somebody alive in two, you’ll (almost) surely kill him.

If you cut his “soul” in two, you’ll double it…

 

These are only basic examples of the striking differences there are between substantial matter and non substantial one. If you limit yourself to biology or even behavioural sciences, you can’t even approach anything about “parapsychology”. For you, nothing happens, but in peoples’mind. And, indeed, nothing “extra-biological” happens.

You see no “ghosts”.

But, in particle accelerators, physicists see no neutrinos… to “see” them, they have to deduce their presence from the reaction balance.

So, you naturally laugh at “ghosts walking through walls”.

But, wavepackets go through walls… they can change shape against a potential barrier (energy), but they won’t through substantial matter, since they experience no friction at all…

As for neutrinos, they can go through lightyears of matter without interacting…

Now, don’t think I’m trying to say this non substantial matter is made of neutrinos, that’s not what I’m saying, nor what I’m thinking! And it’s not the case at all. I just emphasized the fact that the discovery of neutrinos was the first experimental evidence to the existing on purely non substantial matter. A first step to go much further, far beyond neutrino matter.

 

I’d also like to insist on the fact that, when you’re “alive”, your “soul” stays inert, but it’s completely formed! Just as your biological body.

And that precisely explains why, when your heart suddenly stops, your soul relay straight away and you experience what you interpret as a “OBE”. Within our frame, you don’t need to “get out of your body” anymore. It becomes a mere autonomy transfert from your biological body, now inert, to your soul, now activated.

That would be just impossible if your soul had to form step by step in some mysterious development process. Within 7 mns chrono?...

 

Your memory. Same. Suppose a mental object is stocked in a neuron network somewhere inside your cortex. This mental object is made of electrochemical charges and electromagnetic radiations. It’s an electrochemical information. This network is damaged. The information is transferred into the corresponding wavepacket. For your brain, it’s lost. For your soul, it’s not.

If the information transfert is reversible and if your brain, thanks to its very high plasticity, has recreated a neuron network able to stock this object again, or transferred this ability to another network, than you can recover this information.

Apparently, this is what happens in NDEs. It cannot be “because the experience carries a strong emotional charge”, since your brain is OFF… and a neuron cell can stay silencious within an active brain, while it soon starts to die inside a silencious brain. The difference there is the same as between sleep (an active process) and biological death.

How would you otherwise explain an NDE experiencer remind, not only what happened to him/her, but what he/she saw, hear, everything, in the operation room, in the corridors of the hospital,…?

How could he/she remind what his/her brain was unable to capture?....

The only reasonable answer is that there necessarily is another active process in another body.

Another active process to replace the now inert one.

And another body to take place of the whole inert one.

To be distinguished from its biological counterpart.

 

Otherwise, we always fall into a dead end.

For the time being, it doesn’t work so bad…

 

Ah! And a “last minute”:

 

You no more see no “angels” nor “evils”.

But physicists see positive and negative frequencies, leading to positive and negative wave energies.

 

WHAT WE USE TO CALL “ANGELS” MAY BE REINTERPRETED AS PSI ENTITIES WITH POSITIVE WAVY MASS.

AND WHAT WE USE TO CALL “EVILS” MAY BE REINTERPRETED AS PSI ENTITIES WITH NEGATIVE WAVY MASS.

BOTH SIGNS ARE NOW ALLOWED, INSIDE THE SAME SPACE-TIME.

AS FOR INTERACTIONS, I.E. INTERFERENCES, THEY ARE:

-         CONSTRUCTIVE BETWEEN ANGELS AND BETWEEN EVILS;

-         AND DESTRUCTIVE BETWEEN ANGELS AND EVILS.

 

Choose your side. J