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

 

 

We move on. Today, two things: autonomy and the PSI.

We begin with autonomy.

 

AUTONOMOUS BODIES ARE PHYSICAL BODIES ABLE TO MANAGE THEIR INTERNAL RESSOURCES AND THEIR MOTION ON THEIR OWN.

 

That’s what differentiate them from inert bodies, which cannot move on their own, except a mere rotation around their axis under the influence of their own interaction field(s). Otherwise, one has to apply an external force to such bodies to make them move and they are unable to manage their internal resources.

This shows there is a complexity level to reach before becoming autonomous. But, once a physical system has reached this level, autonomy becomes an entire characteristic of the system, just like mass or charge.

We could roughly classify systems into two big categories: inert systems, for which autonomy is zero and autonomous systems, for which autonomy is positive.

For the time being, I can see no negative autonomy, since you cannot be “more inert than the inert”. Just like for temperature: you cannot be colder than the absolute zero.

 

“LIVING” BODIES ARE AUTONOMOUS BODIES.

 

A bacteria is a living body, since it can move on their own, manage its own resources and exchange with its surrounding environment.

This last ability is not a characteristic of autonomous systems, since any inert system can exchange heat with its external environment (except, by convention, the entire universe, considered as the only closed thermodynamical system).

This definition of the living is very general: nowhere does it precise the need for any material substance. Therefore, as we saw it in the former bidouille, complex yet non-substantial matter can be autonomous and thus living as well. I’d like to emphasize the fact there’s absolutely no physical objection to this. Only could it hurt our familiar (and well-established) conception of “the living”.

To go further, we need to introduce a new conservation law, that will remain a postulate until it’s confirmed or not:

 

IN AUTONOMOUS SYSTEMS, AUTONOMY IS A CONSERVED QUANTITY.

 

This is already obvious for the “substantial living”: as long as an autonomous substantial system lives, it keeps its full autonomy. This covers all biology.

It becomes much less obvious in the transition from “living” to “death”. Let us schematize the process like this:

 

(1)               (living body 1) -> (inert body 1) + (living body 2)

 

In such a kind of “reaction”, we assume autonomy has to be conserved. The “living body 1” has autonomy A₁ > 0. It is supposed to give an “inert body 1” the autonomy of which has become A’₁ = 0 together with a “living body 2”, whose autonomy can be nothing else than A₂ = A₁ > 0. In other words, we had an autonomy transfert from a first body to a second one.

To understand where this “second body” could emerge from, just remind the hypothesis according to which all physical bodies are made “double”, in the sense that an extension of the wave-corpuscle duality to complex macroscopic systems leads to a “substantial / non-substantial” duality. According to this (still purely) theoretical result, we’d better rewrite (1) under the more precise form:

 

(2)               (SB; A > 0 / NSB; A = 0) -> (SB; A = 0 / NSB; A > 0)

 

We see much more clearly the autonomy transfert during the process: Substantial Body (SB) is the biological body. When “living”, its autonomy is > 0. Meanwhile, we assume its wavy counterpart NSB (Non Substantial Body) to remain inert (A = 0). After the transfert, SB turns inert (A = 0) and its previous autonomy has been fully transferred to NSB, who becomes “living”.

So, before the “living to death” transition, SB is “living” and NSB “dead” (inert); after the transition, SB is “dead” and NSB “alive”.

Let’s now go a bit further, introducing the blood pressure p.

For p > p_c » 15 pulses / mn, we have SB “alive”, NSB “dead”, that is, A_SB(p) > 0 and A_NSB(p) = 0.

For p = 0, we have SB “dead”, NSB “alive”, that is A_SB(0) = 0 and A_NSB(0) = A_SB(p>p_c) > 0.

In between, i.e. for 0 < p < p_c, the transition is partial, concerning only subsystems of SB involved in the process (i.e. “dying”). Each of these subsystems then transfers its autonomy to its non-substantial equivalent, while the rest of SB remains autonomous.

Let’s apply this to stade 2 coma. All the areas of the central nervous system involved, whether are damaged or are “down” (silencious). We have inert areas: their autonomy, as cells or assemblies of cells, have fallen down to zero. If autonomy has to be conserved, then it must be transferred “in some other structures”. These “some other structures” being nothing else than the non-substantial counterparts, which become active. The rest of SB being still biologically active, the rest of NSB remains inactive.

Stade 3 extends this to a larger part of the two bodies. Stade 4 covers the whole bodies.

 

What does this mean? It means the patient in real (= non artificial) coma is indeed “partially unconscious and inert” on the biological viewpoint. But, meanwhile and during all his coma, the corresponding activities are transferred into the associated areas of his non-substantial body. The patient can apparently keep, or not, a memory of his “non-substantial activities” when he awakes. It’s now a question of information transfert, back to his biological body, this time. As the transition from consciousness to coma is far from being reversible (except for stade 1), so is the transfert of informations from the non-substantial body back to the substantial one.

 

Consider now a patient having a heart attack. His blood pressure falls down to zero. You connect him to an artificial heart. His blood pressure goes back up to normal.

Why doesn’t he get back from stade 4, then?

Because his substantial body is still not autonomous again. It’s only fed by external means.

 

AS LONG AS AUTONOMY IS NOT TRANSFERRED BACK FROM THE NON SUBSTANTIAL BODY TO THE SUBSTANTIAL ONE, IF POSSIBLE, THE SUBSTANTIAL BODY REMAINS INERT, WHATEVER YOU TRY TO BRING IT BACK TO NORMAL ACTIVITY.

 

And this remains valid for comas, replacing global inertia with partial one.

You don’t deal with inert matter anymore, you deal with autonomous matter. To “stay biologically alive” therefore becomes a voluntary process. If the (non-substantial) patient is not willing to “get back to life”, he won’t wake up again.

Now, NDEs tell us something more: that the patient could be forced to “get back to biological life”. This is highly metaphysical for the time being (and may even remain). I’m dealing with what (bio)physics can do and cannot. Which laws of Nature can be allowed or not. I hardly can go further.

What we can assert, because we see it, it’s a clinical fact, is that, amongst all the clinical death registered very day, very few “go back to life”. So, on a theoretical viewpoint, we can “almost surely” consider the “dying” process as being non-reversible.

Fortunately enough.

Because, if it was not the case, then we would live in a world of “living deads”.

 

WHAT WE CALL “LIFE” SHOULD BE RENAMED “SUBSTANTIAL” OR “MATERIAL LIFE”. IT COVERS ONLY A SHORT LIFETIME.

AND WHAT WE CALL “DEATH” SHOULD REALLY BE RENAMED “NON SUBSTANTIAL” OR “NON MATERIAL” LIFE.

OUR SECOND LIFE.

 

I know this is very commercial, but we should really end with this negative vision of “death” we’ve been carrying since the emergence of “modern” humanity. I’m talking about the “modern human”, industrial era, who rejected everything “spiritual” and “non material” from his global fate. This credo goes against the principles of physics.

We have evidences of the existence of matter having nothing substantial at all. We just cannot reject this in bulk, only because we have a problem of understanding.

Quantum physics applied to complex systems shows without ambiguity that physical bodies are double, with the consequence that we have two lives and not only a single one.

And the first one is far the shortest one. So?

 

Here’s for the first point of today. The second one now, the PSI.

 

It’s actually very easy to go from the “material dynamics” of macroscopic bodies to the “wavy dynamics” involving wave parameters (wavelengths, periods, group velocity and phase velocity): it suffices to place ourselves in the proper functional spaces and perform an integral transform with a smooth kernel. I will restrict myself to the familiar Laplace transform, since it transforms real quantities into real ones.

The transformation of “material time” t into “wavy time” T (i.e. period) is simply:

 

(3)               T = ò₀^+¥ texp(-t/T)dt/T

 

and that of “material distance” x into “wavy distance” (i.e. wavelength vector) l:

 

(4)   l = òòò_|x|³0 xexp(-å_a=1³ x^a/l^a)d³x/l¹l²l³

 

Going from a “classical trajectory” x(t) to a “wave trajectory” l(T) requires to work in the functional 3-space of classical trajectories:

 

(5)   l(T) = òòò_|x(t)|³0 x(t)exp[-å_a=1³ x^a(t)/l^a(T)]d³x(t)/l¹(T)l²(T)l³(T)

                                                                                                         

To transform an instantanous velocity v(t) = dx(t)/dt into a group velocity n(T) = dl(T)/dT, we need to work in the functional space of 3-velocities (tangent bundle):

 

(6)   n(T) = òòò_|v(t)|³0 v(t)exp[-å_a=1³ v^a(t)/n^a(T)]d³x(t)/n¹(T)n²(T)n³(T)

 

Finally, going from the contact space [x(t),v(t),t] to the contact space [l(T),n(T),T] combines all three transforms. The “contact elementary 7-volume” is d³x(t)d³v(t)dt. Then, we can transform a Lagrange function L[x(t),v(t),t] into a L^[l(T),n(T),T] and do “spectral dynamics”:

 

(7)   L^[l(T),n(T),T] = ò₀^+¥òòò_|x(t)|³0òòò_|v(t)|³0 L[x(t),v(t),t]exp(-t/T)exp(-å_a=1³ x^a/l^a)exp[-å_a=1³ x^a(t)/l^a(T)]dtd³x(t)d³v(t)/Tl¹(T)l²(T)l³(T)n¹(T)n²(T)n³(T)

 

In space relativity, both x(t) and v(t) are unlimited. So, we can set x(0) = 0, v(0) = 0 and x(+¥) = +¥, v(+¥) = +¥. In space-time relativity, the xⁱ(t)s replace the x(t)s and the cuⁱ(t)s the v(t)s. There, both xⁱ(t) and uⁱ(t) are unlimited, while 3-velocity v(t) must have modulus between 0 and c.

The rest consists in applying the known formulas of “material dynamics”, using the wave parameters and variables. Simple. For instance, the 3-momentum will be:

 

(8)   p(T) = ¶L^[l(T),n(T),T]/¶n(T)

 

and so on.

 

WHAT WE WILL CALL A “MACROSCOPIC PSI BODY” WILL SIMPLY BE A NON SUBSTANTIAL, ELECTRICALLY NEUTRAL BODY WITH FINITE “SPECTRAL 3-VOLUME” l¹l²l³, ALL l^a BOUNDED (a = 1,2,3), I.E. A COMPACT WAVE OR “WAVEPACKET”.

 

Again, we find inert PSI bodies and autonomous ones, elementary PSI bodies and complex ones. Again, in “spectral 3-space”, I can neglect the shape of the body to bring everything back to its centre of gravity.

A PSI body has “wavy mass”:

 

(9)   M(T) = ò₀^+¥ m(t)exp(-t/T)dt/T

 

m(t) is the mass of its substantial counterpart. The wavy mass of the substantial body is zero, the substantial mass of the PSI body is zero. Formula (9) above transforms a substantial mass into a wavy one. A kinetic contribution like ½ m(t)v²(t) can be directly transformed into ½ M(T)n²(T) because the integration domains are different: m(t) -> M(T) sums up over t, v(t) -> n(T) sums up over v(T).

If we had limited ourselves to substantial masses, we would have never been able to properly define nor describe any “PSI interaction” between PSI bodies. With wavy masses, it’s straightforward. The gravitational potentials G_i(x) become:

 

(10)           G^_i(l,T) = òòò_|x|³0ò₀^+¥ G_i(x,t)exp(-t/T)exp(-å_a=1³ x^a/l^a)d³xdt/Tl¹l²l³

 

Derivatives are upon the l^a and l⁰ = cT. G^_i(l,T) is a « spectral » or « PSI » (whatever) gravity field for it is produced by a PSI body with wavy mass M’(T). This source mass produces a 4-current [M’(T)c , M’(T)n(T)]. The spectral gravity field acts upon wavy masses but has no effect on substantial masses. Conversely, the usual gravity field G_i(x,t) acts upon substantial masses but has no effect on wavy masses.

Always the same “duality”.

To see a gravity field having effects on both types of masses would require the field to span over both groups of variables: G_i(x,t,l,T). Formula (10) would then have to be changed into a convolution formula:

 

(11)           G^_i(x,t,l,T) = òòò_|x’|³0ò₀^+¥ G_i(x’,t’)exp(-|t-t’|/T)exp[-å_a=1³ |x^a – x’^a|/l^a]d³x’dt’/Tl¹l²l³

 

I have to introduce absolute values |.| in the exponential arguments, since integration over t’ and x’ still have to cover the domains |x’| ³ 0 and t’ ³ 0 and some of these values can appear to be greater than given x or t, respectively. This, for instance, would not happen for a Gaussian kernel. An initial G_i(x,t), acting on mere substantial masses, would then be extended into a G^_i(x,t,l,T) acting on both types of masses.

This can obviously be done for any field.

Not only mass is involved as a possible characteristic of a PSI body. Any wavy charge can be, as long as the substantial counterpart carries an associated charge. Take the example of the nervous cell: there are electrical charges on both sides of the membrane. Let q(t) be an amount of electric charge at time t.

 

(12)           Q(T) = ò₀^+¥ q(t)exp(-t/T)dt/T

 

is the corresponding amount of « wavy charge » at period T. Just like for mass, the neuron cell remains free of wavy charge, while the corresponding “PSI cell” (its associated wavepacket) remains free of electrical charge.

 

That’s all for today, folks. What follows needs “a little survey”…

 

Pfff… To say i encounter problems is simply an euphemism… Basically, the central obstruction is the appearance of a second body at stade 4, in addition to the biological one. But, overall, it is this aptitude of this second body to apparently disconnect from the first one. And this strikingly contradicts all known approaches from quantum theory and intrication. That’s the main reason why I’ve been turning in circles these last days.

There may be a way out, but it requires a reinterpretation of the wave-corpuscle duality.

Let’s try.

 

The node is the question of massless particles. For massive particles, one can define energy and 3-momentum without ambiguity using space-time relativity, for these quantities are corpuscular characteristics of a given physical body. So, for a corpuscle of mass at rest m₀, its energy of motion at velocity v(t) and its 3-momentum are simply:

 

(1)               E_corp(t) = m₀c²/[1 – v²(t)/c²]^1/2  ,  p_corp(t) = m₀v(t)/[1 – v²(t)/c²]^1/2

 

On the other hand, a wave with pulsation w and 3-wave number k will have wavy energy and wavy 3-momentum:

 

(2)               E_wav = ħw  ,  p_wav = ħk

 

When m₀ ¹ 0, on can always find a reference frame where the corpuscle is at rest and E_corp(t) as p_corp(t) are perfectly well defined for 0 £ v(t) < c. Going from classical to quantum, we can then use the De Broglie’s relations:

 

(3)               E_corp(t) = E_wav  ,  p_corp(t) = p_wav

 

and define the « (quantum) particle » as being a physical object with both corpuscular and wavy properties. Some experiments enlight its corpuscular behaviour, some its wavy behaviour. We interpret this saying the particle “is a corpuscle and a wave at the same time” or “sometimes behaves like a corpuscle and sometimes like a wave”. This is known as the “wave-corpuscle duality”.

A difficulty appears for massless particles. Consider first the case of the photon. There has been two decisive works on its quantum nature: that of Planck on the so-called “black body” and that of Einstein, on the photoelectric effect. Planck revealed the discrete nature of the electromagnetic radiation in a closed oven at temperature T: when trapped inside a close finite volume of space, an electromagnetic radiation behaves as an harmonic oscillator and its energy spectrum contains only discrete values, namely integral multiples of ħw₀, the energy of the fundamental state. Einstein then studied the photoelectric effect, i.e. emission of an electromagnetic radiation by atomic electrons. His theoretical work was confirmed 20 years later by Compton: an atomic electron did seem to emit a single quantum of electromagnetic radiation, when the atom interacted with an electromagnetic wave. The Compton wavelength was in perfect agreement with de Broglie’s relations, bringing people to consider the corpuscle known as “photon”, i.e. the quantum of electromagnetic light, a “quantum reality”, satisfying the De Broglie relations.

Still, there remains a problem with the corpuscular properties of the photon. When m₀ = 0, (1) leads to E_corp º 0 and p_corp º 0 all the time for 0 £ v(t) < c, meaning there’s no classical corpuscle at all. When v = c, (1) leads to 0/0, indefinite quantities, since m₀ is not supposed to depend on v and the situation is no better.

I want to point out here the fact that the choice m₀ = 0 ó v = c has nothing formal in space-time relativity. It’s merely a result “suitable for everybody”. But, no mathematics based on this frame shows that (m₀ = 0 ó v = c) guarantees a finite energy and a finite momentum at all times. De Broglie’s relations (3) then become no longer fully adapted in this case and it’s quite easy to understand it: there’s an essential difference between discrete wavy values such as nħw₀, n integer, and associating to them a set of n identical corpuscles.

 

THE PHYSICAL REALITY IS: THE PHOTON HAS NOTHING SUBSTANTIAL AT ALL. IT’S A PURELY WAVY OBJECT. ONE CAN ALWAYS ASSOCIATE A “CORPUSCLE” WITH IT, BUT NOTHING ALLOWS US TO GO BEYOND THIS PURELY UNFORMAL ASSOCIATION.

 

The Compton effect is not set back into question at all. Instead of saying “an atomic electron emit a (corpuscular) photon”, it’s much better to say it emits “a single quantum of electromagnetic radiation”, a single “wavy object called the photon”. Compton’s relation is even better confirmed, if we rewrite it l = h/p_wav: p_wav, not p_corp!!! p_corp is zero for the photon.

 

THE VERY SAME PROBLEM HOLDS FOR THE NEUTRINO, IF THIS MATTER PARTICLE IS TO REMAIN REALLY MASSLESS: DESPITE THE FACT IT’S A FERMION, THE MASSLESS NEUTRINO CAN HAVE NOTHING SUBSTANTIAL.

 

Let’s get back to history again. Pauli first wrote the spontaneous decay of the free neutron: n⁰ -> p⁺ + e^-. Energy was conserved. 3-momentum was conserved. But the spin was not: n⁰ is spin ½, the pair (p⁺,e^-) has spin 1. Now, in order to be allowed, the spin has to be conserved. So, Pauli was forced to introduce a new particle, n⁰, electrically neutral (to conserve the electric charge in the reaction), he called “neutrino”, “little neutron”. The complete reaction now writes: n⁰ -> p⁺ + e^- + n_e*, n_e* being the electronic antineutrino. Since n_e* did not contribute for corpuscular energy nor 3-momentum and was ejected at the speed of light out of the decaying neutron, Pauli deduced, still from space-time relativity, that the mass at rest of n_e* (and thus n_e) should be zero. However, n_e* does have an energy, and even a 3-momentum, for it contributes to the energy of spin. 1) spin is a purely quantum quantity, with no classical equivalent at all (not even the kinetic momentum); 2) n_e and n_e* are pure wavy, yet material, objects.

 

THE DISCOVERY OF THE NEUTRINO WAS ACTUALLY THE FIRST PHYSICAL PROOF OF THE EXISTENCE OF NON-SUBSTANTIAL MATTER.

 

Just like the photon only has two polarization states instead of the three required for a spin 1, the neutrino only has one polarization state instead of the two awaited for a spin ½. The origin of this is well-known, it’s due to the zero mass.

 

SO, BASICALLY, THERE’S NO PROBLEM OF PRINCIPLE IN ENCOUTERING MASSLESS FERMIONS IN NATURE. RIGHT ON THE CONTRARY, IT OPENS US WIDE THE GATE TO “WAVY MATTER”, I.E. MATTER WITH NO CLASSICAL EQUIVALENT.

 

Which does not prevent these fermions to contribute to the (wavy) energy of the Universe. But certainly not to the corpuscular one. Besides, we find no neutrino contribution to the classical energy of the Universe. The “neutrino problem” is a purely quantum one.

Massless fermions only hurt our conception of matter, since we’re used to reason in terms of classical, corpuscular, matter. That’s all.

 

This existence of non-substantial matter, revealed in the particle accelerators, is a first important step in our own researches, about the possible nature of a second physical body.

The second step is harder to make, as it’s about the separation between the corpuscle and the wave. Once more, Prigogine can save us.

 

LOCALLY, I.E. AT THE MICROSCOPIC LEVEL OF DESCRIPTION (INDIVIDUAL TRAJECTORIES), THE CORPUSCLE IS INDISTINGUISHABLE FROM THE WAVE FOR MASSIVE PARTICLES, A PROPERTY INTERPRETED AS QUANTUM INTRICATION, ALLOWING TO ASSOCIATE A “PSEUDO-CORPUSCLE” TO ANY MASSLESS PARTICLE.

 

“interpreted as” is very important. At this elementary level, we find both classical trajectories x(t), xⁱ(t) for corpuscles and wave trajectories y(x,t) (spinor or tensor). The De Broglie duality then means we cannot distinguish between what we will call a “corpuscle” and what we will call a “wave”: any particle has both nature, the “quantum” nature.

This assertion has no reason to hold at the macroscopic level. The reason is, we go from individual objects and separated motions to collections of objects and sheaves of trajectories. A non-reversible process.

 

GLOBALLY, I.E. AT THE MACROSCOPIC LEVEL OF DESCRIPTION, WE HAVE TO DISTINGUISH BETWEEN THE CORPUSCLE (POINT-LIKE BODY) AND THE WAVE, A CHANGE INTERPRETED, THIS TIME, AS QUANTUM DISINTRICATION. HOWEVER, THE WAVEPACKET DOES NOT VANISH, IT’S NOT EVEN “SEPARATED FROM” THE SUBSTANCE, WE NEED TO MAKE THE DISTINCTION BETWEEN THE TWO.

 

I’m going to try and justify all this. If we want the wave-corpuscle duality to include massless particles, we have no other solution than to consider that the wave carries no mass at all. The concept of mass is therefore purely corpuscular and the wave can be endowed, at the best, a “mass equivalent” hf/c², where f is the frequency of the wave. But this “mass equivalent” has nothing substantial. Then and only then can massless particles be properly represented as some “intricated pair” made of a wave, to which we merely associate a corresponding pseudo-corpuscle of zero mass.

This is not a true intrication. A true intrication would be a non-separable pair made of two physical objects, may they have different natures, exchanging their informations. Now, in massless systems, there can be no mass transfert from a “corpuscle” to a wave, since there’s no substantial mass anywhere… Instead and according to space-time relativity, there’s energy and 3-momentum. Both can be converted from one form to another one. And this is exactly what the De Broglie relations tell us: when they hold, the corpuscular energy can be converted into a wavy energy and back, as corpuscular 3-momentum can be converted into wavy 3-momentum and back.

But this actually corresponds to a situation of equilibrium: the De Broglie equivalence relations (3) can be read as equilibrium relations, where the corpuscular energy and 3-momentum of a system become equal to their wavy counterparts.

If we read it this way and then, turn back to Prigogine, we see that such an equilibrium situation can only be local. First, because it’s purely mechanical, between the dynamics of a corpuscle and the dynamics of a wave, for each particle (the corresponding wave is thus the individual wavepacket). Second, because there is no dissipation: all the corpuscular energy and 3-momentum is converted (and back) into the corresponding wavy energy and 3-momentum. Immediate consequence of this: these conversion processes are fully reversible, typical of “ideal” mechanics involving no friction and there’s no “time arrow”. Schrödinger is reversible, Klein-Gordon is reversible, even Ginzburg-Landau is (with respect to the inversion of thermodynamical parameters).

This should justify, once again, the general principles of quantum theory at the microscopic level.

As soon as the mesoscopic scale, this is no longer true. It’s still less true for complex systems, because of chaos. Chaos is a typical non-equilibrium situation. There, the De Broglie equivalence relations do not hold anymore, since we now have to distinguish between the substance and the wave. Both remain present. As we’ve seen before, a complex wavepacket made of more fundamental wavepackets remains a wavepacket (with only sub-structures) and there’s no reason why a wavepacket should vanish at higher scales, because of “information dissipation”. What chaos does is to “cut the system off its past”. In the present case, off its dual nature.

If a wavepacket had to vanish, there could be no light at all… no electromagnetic field… no gravitation… nothing.

The wavepacket is not even “separated from the corpuscle”, we have “substance” on one side and “non-substance” on the other side, carrying their own physical properties. They still can interact. The action of a wave upon a substance is identified with an external force.

The emission of a wave by a substance is identified with a “field of forces” and the substance in question as “the source of the force field”.

At the macroscopic level, the distinction is complete: we observe a world made of “substance with no wave properties at all” and “wave made of no substance at all”.

But we observe both. Both, “separately”. Distinctively.

 

There’s a straight parallel with fermions and bosons: at high temperatures, we don’t need to distinguish between fermions and bosons anymore; at low temperatures, we need to do it.

 

IF WE NOW COMBINE MASSLESS MATTER AND COMPLEXITY, WE ARE LED TO THE POSSIBILITY OF THE PHYSICAL EXISTENCE OF “NON SUBSTANTIAL” BODIES WITH PURELY WAVY PROPERTIES, COMPACT VOLUMES (AS WAVEPACKETS), TO BE DISTINGUISHED WITH SUBSTANTIAL BODIES.

“NON SUBSTANTIAL BODIES” ARE “SUBSTANTIALLY MASSLESS”. THEIR ENERGY IS THAT OF THEIR WAVEPACKET.

THEY ARE ALSO GLOBALLY ELECTRICALLY NEUTRAL.

 

This would imply all physical objects are actually “double made”: a substantial one and a non-substantial one.

 

Why then would the non-substantial body remain non-observable?

 

HEY: MASSLESS AND ELECTRICALLY NEUTRAL!

J

 

Try to catch him with an MRI!... :))

Or feel its presence with your consciousness (an electrochemical process!)…

                                                                                                                                                      

 

 

J’ai encore eu une intuition subite hier, qui m’a tout d’abord parue un peu biscornue mais qui, somme toute, est parfaitement logique. Il s’agit de mettre à profit au maximum le fait que les G_i(x) sont les composantes d’un champ de 4-vitesses dans l’espace-temps. Si l’on veut que le principe de relativité 4D soit respecté, il faut alors imposer la condition :

 

(1)               G_iGⁱ £ c²

 

afin que le champ reste causal (i.e. du genre temps). Voyons ce que cela implique à la limite :

 

(2)               G_iGⁱ = c²

 

Dans ce cas,

 

(3)               G_i(x) = -cu_i  ,  u_iuⁱ = 1

 

Pour la composante G₀(x,t) = f(x,t)/c :

 

(4)               f(x,t) = -c²/(1 – v²/c²)^1/2

 

Où v est la vitesse du corps incident dans l’espace. En explicitant les dépendances paramétriques :

 

(5)               f[x(t),t] = -c²/[1 – v²(t)/c²]^1/2

 

pour un corps incident solide. Il en résulte :

 

(6)               v(t) = cn{1 – c⁴/f²[x(t),t]}^1/2

 

avec n, direction de la normale extérieure, n² = 1. On voit déjà que le domaine du mouvement réel sera :

 

(7)               f[x(t),t] ³ c²

 

Pour f[x(t),t] = c², v(t) = 0, la position du solide est fixe dans l’espace. Pour f[x(t),t] -> -¥, v(t) -> cn. Prenons le cas simple, mais intéressant, d’une source fixe dans l’espace, sans rotation propre et supposée ponctuelle. Dans ce cas, f[x(t),t] ne dépend pas explicitement de t et est à symétrie centrale :

 

(8)               f[x(t),t] = f[x(t)] = -km’/|x(t)|

 

(m’ = masse de la source). D’après (6), on obtient :

 

(9)               v(t) = cn{1 – |x(t)|²/R_g’²}^1/2

 

(R_g’ = km’/c = rayon gravitationnel de la source). Utilisons la paramétrisation :

 

(10)           x(t) = -nR_g’cos(t/T_g’)  ,  T_g’ = R_g’/c

 

Le mouvement incident pointe vers la source. Alors :

 

(11)           v(t) = ±cn|sin(t/T_g’)|

 

On a les deux possibilités : soit le vecteur vitesse incident pointe vers la source, soit il pointe vers « l’horizon » R_g’. Quant à l’accélération :

 

(12)           a(t) = dv(t)/dt = ±(c/T_g’)n|cos(t/T_g’)| = ±(c²/R_g’)n|cos(t/T_g’)|

 

(signe identique à celui de la vitesse). Au départ du mouvement :

 

(13)           x(0) = -nR_g’  ,  v(0) = 0  ,  a(t) = ±(c²/R_g’)n

 

LE MOUVEMENT PART DU RAYON GRAVITATIONNEL DE LA SOURCE A VITESSE NULLE ET ACCELERATION a(t) = c²/R_g’ ET SE DIRIGE VERS LE CENTRE DE CELLE-CI.

 

A l’arrivée, on doit avoir x(t_f) = 0. De (10), on en tire la durée du mouvement :

 

(14)           t_f(q) = ½ p(2q+1)T_g’  ,  q Î Z

 

tandis que :

 

(15)           v[t_f(q)] = ±cn  ,  a[t_f(q)] = 0

 

LE CORPS INCIDENT ATTEINT DONC LE CENTRE DE LA SOURCE EN UN TEMPS FINI, MULTIPLE DEMI-ENTIER DE pT_g’, SA VITESSE EST CELLE DE LA LUMIERE ET SON ACCELERATION EST NULLE.

 

Autrement dit, la condition limite (2) permet, dans tous les cas, de partir d’une position de repos à R_g’ et d’atteindre c en un temps fini, donné par (14). On constate par ailleurs que, pour r > R_g’, (9) fourni un résultat imaginaire. On n’est même pas dans le tachyonique. Interprétation :

 

LE MOUVEMENT CAUSAL SOUS LE RAYON GRAVITATIONNEL S’EFFECTUE « DANS L’IMAGINAIRE DE L’OBSERVATEUR EXTERIEUR » : POUR CE DERNIER, IL N’EXISTE TOUT SIMPLEMENT PAS, PARCE QU’IL SORT COMPLETEMENT DE SON DOMAINE PHYSIQUE.

 

Il était fort tentant d’associer un tel mouvement au « Tunnel » et la source, à la « Grande Lumière Blanche ». Malheureusement, ça ne résiste pas longtemps à la réalité des applications numériques. En effet, pour obtenir un trajet s’effectuant en un peu moins de 8s, ce qui est déjà court, il faudrait disposer d’une source de masse 10⁶ M_ʘ : 1 million de masses solaires…, pour un trajet d’un peu moins de 1,5 millions de kms.

Soyons larges d’esprit, admettons. Le problème est que la proximité immédiate d’un tel corps, qui resterait quand même bien réel (seule la dynamique sous R_g’ sort du domaine physique de l’observateur extérieur), non seulement se saurait (ou plutôt se serait su), mais entraînerait tout avec lui sur un rayon d’environ 1,5 x 10⁶ kms, sans compter les perturbations occasionnées dans une sphère d’influence beaucoup plus vaste encore. C’est évidemment hors de question. Et, comme nous avons besoin d’une masse, qu’il s’agisse de matière (normale ou condensée) ou de rayonnement, c’est rôti… et même plus que rôti.

Ces résultats peuvent tout au plus intéresser l’astrophysique, mais pas la parapsychologie…

 

Il me reste une option, qui demande encore approfondissement : la capillarité.

 

Quant au modèle de GL appliqué à notre contexte, il est censé décrire un grand nombre de cellules « mortes » (= biologiquement inactives) en interaction gravitationnelle les unes avec les autres, à une échelle mésoscopique, grande devant les dimensions d’une cellule, mais restant petite devant les dimensions de l’animal (d’où le terme de « quasi-classique »). L’avantage, c’est qu’il garantit la cohésion du système, en phase « froide ». L’inconvénient, c’est que les deux principaux paramètres du modèle [longueur de cohérence x = ħ/m_cellc, pour le condensat et longueur de pénétration l = 1/(R_g|y|²)^1/2 du champ dans le super-corps] ne correspondent à rien de réaliste : à p = 0 qui nous intéresse, x est de l’ordre du rayon de Planck, alors que l est de l’ordre de 10¹⁰ m, soit 10 millions de kms. C’est, certes, une portée finie… mais « un petit peu trop grande de quelques ordres de grandeur »…

En clair, ça ressemble plus aux supercordes qu’à une théorie réaliste… :))

On est à côté de la plaque, mais seulement de la taille d’un dinosaure, dilaté plusieurs milliers de fois… lol

 

Chose promise, chose due : nous allons donc revenir encore une fois sur ce « Tunnel » des EMIs, qui me donne décidément beaucoup de fil à retordre… J

Mais, avant de réaborder le sujet, une petite remarque, qui va encore faire grincer. Quelque chose me choque en effet sur l’un des fondements de la Relativité Générale (RG), à savoir, considérer que le champ de gravitation n’est qu’un effet géométrique de la courbure de l’espace-temps, qui permet d’incorporer le potentiel de champ dans un mouvement géodésique et ainsi, de se ramener à de la cinétique pure, mais en géométrie courbe.

Voici ce qui me gêne. On le voit dès la relativité de Galilée. Inutile, donc, de compliquer les choses. Dans le lagrangien censé décrire le mouvement d’un corps incident de masse m_I et de vitesse v(t) à l’instant t plongé dans le champ de gravité (newtonien) produit par un corps source de masse m_S :

 

(1)    L = ½ m_Iv²(t) - m_If(x,t) = L_cin + L_pot

 

la partie cinétique décrit le mouvement du corps incident et non du corps source, tandis que la partie potentielle décrit le champ issu de la source selon l’équation de Poisson :

 

(2)    Df(x,t) = 4pkm(x,t)

 

où m(x,t) est la densité de masse de la source et k, la constante gravitationnelle de Newton. Le point x est le point de l’espace où l’on observe le champ. Les équations du mouvement dérivées de (1) sont :

 

(3)    d[m_Iv(t)]/dt = -m_IÑf(x,t)

 

Il est bien évidemment que le corps incident ne subira l’influence du champ de gravité de la source que ssi le point d’observation x coïncide avec la position x(t) du corps incident à l’instant t. Je crois avoir déjà débattu de ce point. Si j’ai laissé m_I entre parenthèse dans le membre de gauche de (3) c’est parce que les corps macroscopiques « normaux » ont en réalité des masses variables au cours du temps (cf. bidouille précédente). Donc, en fin de compte, la mécanique classique tient compte de corps « parfaits » de masse rigoureusement constante… sans pour autant savoir les traiter. Mais ceci est un autre débat.

Mathématiquement, je peux toujours ramener le membre de droite de (3) à gauche :

 

(4)    d[m_Iv(t)]/dt + m_IÑf(x,t) = 0

 

Ok. Idéalisons les choses et supposons, même si c’est faux, que m_I = cte tout le temps. Ça ne change rien au fond du problème. Je simplifie par m_I, j’obtiens un mouvement indépendant de la masse du corps incident :

 

(5)     dv(t)/dt + Ñf(x,t) = 0

 

Maintenant, je dis que ce mouvement, perturbé dans l’espace plan, se ramène à un mouvement libre dans un espace courbe, à la manière du Principe de d’Alembert qui ramène la dynamique à la statique ? Essayons. J’introduis donc des symboles de Christoffel Cⁱ_jk et une dérivée covariante :

 

(6)    Dvⁱ(t)/dt = dvⁱ(t)/dt + Cⁱ_jkv^j(t)v^k(t) = 0

 

Cette expression doit, logiquement, être équivalente à (5), d’où j’en tire que :

 

(7)  Cⁱ_jkv^j(t)v^k(t) = ¶ⁱf(x,t)

 

D’accord ? Ces dernières relations sont algébriques. De deux choses l’une : soient les Cⁱ_jk dépendent de la vitesse v(t) du corps incident, soit c’est cette vitesse qui dépend de ¶ⁱf(x,t) et des Cⁱ_jk, mais alors, elle dépend aussi du point d’observation, ce qui n’a pas lieu d’être.

Dans les deux cas, il est difficile de voir en les Cⁱ_jk, qui sont censés dépendre de x (point d’observation) et de t [mais, a priori, pas de v(t)], des « intensités du champ de gravité », d’autant plus qu’on peut toujours les éliminer dans un système de coordonnées adéquat, alors qu’on ne voit pas bien le rapport entre le fait que le mouvement des corps incidents dans un champ de gravité extérieur à eux puisse se faire indépendamment de la masse de ces corps et le fait que la gravitation ne soit qu’une « pseudo-force »…

On abuse un peu vite de d’Alembert et du concept d’inertie, non ?

Si la gravitation était une pseudo-force, elle ne pourrait, au mieux, être produite que par des « pseudo-sources » possédant une « pseudo-masse »…

 

Conclusions identiques en dim 4, en remplaçant le temps par le temps propre.

 

Vous ne m’en voudrez donc pas de « m’obstiner » à préférer un modèle vectoriel de la gravitation et à continuer de la considérer comme une véritable force, produite par une véritable source, dotée d’une véritable masse.

Ce qui n’empêche nullement les partisans de la RG de poursuivre dans cette voie.

Chacun son style, je développe mon propre point de vue, sans chercher à l’imposer, comme toujours.

 

On passe au « Tunnel ».