Something i really don’t understand: I put the phase transition model aside because of the numerical results I obtained, which seemed to have nothing in common with our purposes. Now, something definitely doesn’t fit. I reviewed in great details my references on statistical physics this time and, if I had to apply them to coma IV, I would find there’s no thermodynamics anymore…

Let me be more precise. According to statistical physics and quantum thermodynamics, even a stellar residue like a black hole keeps on having a thermodynamical activity, usually ruled by the Fermi-Dirac statistics. Again, if the material content of such a body was proven it’s a quark plasma, the thermodynamics inside would be that of flavour dynamics. In Fermi-Dirac quantum bodies, one still find pressure, temperature and density (number of particles) and the feature is that the Fermi pressure is independent of temperature, only proportional to the product of the particle density times the Fermi chemical potential m₀ = k_BT_F, where T_F is Fermi’s temperature (a constant for a given medium). The same occurs for radiative fields, with the Bose-Einstein statistics.

But are those bodies in an “end-of-life” state or can they be considered as “dead”? According to statistical physics, as long as there remains a thermodynamical activity inside matter, this matter is not “completely dead”.

The problem we face with NDEs is the following one: in stage IV, the blood pressure p = 0. The vicious circle is, about 7 mns after the heart stopped beating, the brain ceases to work. So it cannot activate the neurons contracting the heart, which can’t restart by itself. And this remains the case whatever the body temperature T. Obviously, if the biological body stays inactive, T decreases. It will be far from reaching T = 0K, but it significantly decreases, at least in °C or °F. The only thermodynamics inside the inactive biological body is that of destructuring. Now, what about the supposed “PSI body” that is said to “emerge” from the biological one at stage IV? There, is the real challenge.

On one side, it seems to show several similitudes with quantum media: it has no apparent thermal activity, no mass transfert with the biological body, it apparently carries no entropy. And the pressure p = 0. So? So, we would be tempted to deduce from all these characteristics that this “PSI body” has no thermodynamical activity at all. This is only made possible if (and only if) such a body has no molecular structure. Because (I checked), heat transfert in matter is done by phonons at the microscopic level, i.e. quanta of sound excitations travelling through the substantial network from molecules to molecules. Thus, a PSI body could only be made of matter waves.

However, as we just said, both radiative and matter waves still have a thermodynamical activity… that could be detected and measured, just as for quantum media.

So, we should be forced to deduce from all these absences that PSI bodies can’t exist in Nature: mechanics doesn’t fit, quantum theory doesn’t fit, thermodynamics doesn’t fit.

Yet, this is not so easy. For, and I deliberately insist on this point, we have numerous of testimonies from all around the world, different cults and religions, different social classes, all reporting “constants”: the OBE, the Tunnel, the Great White Light, a sort of “Garden”, Entities. I myself experienced a “spontaneous NDE” at the age of 10, out of any medical reason, and I don’t think I’m the kind of guy telling fairytales.

So, there seems to be something, that present-day physics seems unable to explain. Up to now, it only indicated us what does not work. We could establish an entire series of “no-go” theorems on parapsychology and the NDEs! :))

 

Should we play doctor? A competent doctor uses to say: “when I find nothing and there’s apparently something, is the proof that there’s indeed something”.

 

Let’s sum up once more: quantum physics is inadequate; electromagnetism gives a correct description of conscious processes, but leads to no “non-material body” (because its statistics is Bose); thermodynamics doesn’t work: pressure is zero, friction should diseappear.

And the damn whole thing remains desperately unobservable. Even undetectable.

 

It’s already everything but an easy task to find a proper theoretical frame to new physical domains when we can rely on observations, experiments and measurements.

But, when it comes to items where nothing can be certified, neither observation, nor experiments or measurements, the only thing we can do is look at the principles and see if it fits or not. Then, ask ourselves the questions: is this logical, consistent, do we have to enlarge the frame, how?

 

As I said, there’s a lot of analogies with known things: between the frictionless PSI body and quantum fluids; the Tunnel looks like a gravitational black hole (but just can’t be…); the Great White Light, as incoherent light;…

Whatever interesting, all these similitudes face strong physical objections.

 

Let us re-examine the phase transition scenario. It’s not that bad, after all.

We so have two options: the bosonic or the fermionic model. Applied to the global nervous system, the external field implied is the electromagnetic one. Biology learns us that consciousness is not a body, but a process, created by the ionic activities of neuron cells. So, the corresponding potentials are the A_i(x)s. What we can notice is that, in the “living” stage, biological matter is organized. But waves are not necessarily. Assuming there exists a wavepacket for each biological cell, when two cells adhere, they make a structure. However, there’s a (strong) difference between their individual wavepackets interfering and being coherent: interference leads from phase factors exp(ik₁x) and exp(ik₂x) to exp[i(k₁+k₂)x] = exp(ik₁₂x); coherence implies k₁ = k₂, that is, resonance. There’s no more phase shift in a coherent state. As a consequence, substance can be organized, while its wavy properties remain disordered.

That’s the aim of the phase transition model: to assume that, whereas in an unconscious state of in a state of modified consciousness, part of, if not the whole of, individual cellular wavepackets are in resonance. If they are, then there appears a collective behaviour, just as in the theory of neuron groups and it suffices to stimulate one cell to stimulate the whole assembly, simultaneously, would the neurons implied be directly connected or not: the group stimulus does not depend on the distance between the constituants, nor even on the biological topology of the network. That’s why it becomes possible to model comas using the phase transition model. The order parameter of the transition is then the number n of inactive neuron cells per unit volume. This volume can be the cortical volume only or the whole body volume, depending on what you focus on. When I say “inactive” here, it doesn’t mean “temporarily silencious”, but “permanently silencious”. We cannot deduce for as much the cell is dead, for this is not true: it dies only when not correctly fed (or if too old). This number n is a density. It should depend on pressure and temperature for it’s non-zero only when p is lower than a critical threshold p_c and/or T under a critical threshold T_c. In my investigations, I fixed p_c around 15 pulses/mn and T_c around 25°C. If y(x,t;p,T) models the wavepackets for coherent neurons, i.e. “permanently silencious” neurons, the individual wavepackets of which are all in phase (giving a collective – and space distributed - one), then n = |y|² is the number of such inactive neuron cells around point x inside the body, at time t, pressure p and temperature T, per unit volume. In a given volume V, the total number of cells of that kind is N(t,p,T) = ò_V |y(x,t;p,T)|²d³x.

Whereas we work in the bosonic or the fermionic model, the wavepacket actes as a source for the electromagnetic field A_i(x). This means that, in addition to the “disordered” electric 4-current j_i(x,t) (charge density and related current) we observe in the active stage, there’s an “ordered” current s_i(x,t) generated by y(x,t;p,T). In the bosonic model, s_i(x,t) = (ħq/m)n¶_iq, it depends on the ratio (charge/mass at rest) and on the variations of the phase q of the wavepacket in space and time: the bosonic model is second-order. In the fermionic model, s_i(x,t) = qcy*g_iy, where the g_i are the 4x4 Dirac (constant) matrices. Rigourously, I should have written j_i(x,t,p,T) and s_i(x,t,p,T), since we take the two thermodynamical parameter inside matter into account. From y(x,t;p,T) º 0 for p ³ p_c and/or T ³ T_c, we derive s_i(x,t;p,T) º 0 for p ³ p_c and/or T ³ T_c: in the “normal” situation, the only 4-current is the “normal” j_i(x,t,p,T).

What does a “real vacuum state” represent there? It’s a state of ordered wavepackets minimizing the potential energy of the system. Great. What else? If we interpret things well, it’s the state where there remains no substance, only fluctuations. This should precisely be what we search for, as we want to get rid of the biological substance to see what remains. The interesting situation is the one where all coefficients in the potential energy of the system only depend on the thermodynamical parameters, neither on the location in space, nor in time. Such coefficients are said to be “global” (in space-time): they keep the same value everywhere, for a fixed pressure and temperature. When this is so, then the number of inactive neurons per unit volume only depends on p and T: n₀ = n₀(p,T). T = 0 being unreachable, especially for biological systems, we expect to have n₀(0,T) maximal at p = 0, meaning all neurons of the whole nervous system targeted are inactive. One more reason to “forget about” them and focus on the collective wavepacket they make. Since n₀ is maximal at p = 0, the “intensity” of this “global” wavepacket is maximal: it covers, whether the whole cortex or the whole body.

As it’s made of no molecular, nor even atomic, structure anymore, it’s automatically frictionless. Carries zero entropy: s =0. No heat transfert, just like in superfluids. So, nothing relevant should change if we take n₀ independent of T. Besides, that’s what medical datas seems to show. If this is correct, then everything inside this wavepacket would seem to happen as if T was zero. Anyway, we find s = 0, p = 0, T = 0 or Cte for the “completely ordered wavy body”. All thermodynamics stands in the biological part. The wavy part is thermodynamically reversible, and it’s even a trivial result, since there’s no thermodynamical activity anymore at p = 0 (there is, obviously, between p_c and 0).

Until now, it seems to fit. The model shows that, below p_c, there would be a larger and larger part of “conceptual functioning” typical of the collective wavepacket: works global, reasons global, reacts global, everything global. No need for signal transmission. No delay. It’s no longer propagative, it’s correlative.

The point is, I already underlined it: y(x,t;p,T) is actually not a physical body, but a motion.

Where’s the body? The model says nothing about it. It only describes the motion inside it.

Where’s the body? What is it made of? Surely not of ordinary substance.

What rushes inside the Tunnel is a body, not a motion or a process. What we developed here is a possible description of a “coherent consciousness”, the source of which would be the wavepacket. And still: in the vacuum state, the source disappears in the bosonic model (but not in the fermionic one).

If we follow the quantum description, we only have one neuron cell, with two different dynamics: the “incoherent” one, with membrane current j_i(x,t,p,T) (K⁺, Na⁺, Ca²⁺ ions) and the “coherent” one, with current s_i(x,t,p,T), unrealized for p ³ p_c and/or T ³ T_c.

It should be clear this approach is not the right one, shouldn’t it? We can make an analogy at the best.

Now, again, we’re not very logical with ourselves when we say, on one side, that a wavepacket is not a medium but a motion and, on the other side, that the electromagnetic potentials are wavepackets. Because the electromagnetic field is considered as a physical medium…

Okay, so much for me: A_i(x) is a physical medium in space-time; in an “electromagnetic space-time” (coordinates Aⁱ), it’s a motion. Same for y: y(x,p,T) is a physical medium in space-time, but a motion in a “psi-space” (coordinates y, y*).

So?

Could y(x,p,T) partially or totally replace the inactive biological nervous system in space-time? Or rather its vacuum y₀(p,T)? y(x,p,T) fills in a 4D-volume of space-time and its value changes from point to point inside this 4-volume, for each value of pressure p and temperature T. y₀(p,T) does the same, simply it keeps the same value over the whole 4D-volume.

Looks like it could fit, doesn’t it?

At p = 0, y₀(0,T) is completely formed (since it’s maximal). Over p_c, it does not exist (as a collective state, I mean).

 

We’ll follow this discussion later on.

 

So… in the end… it seems it wasn’t a question of quantum behaviour at all, but a question of thermodynamics…

Still, it’s not completely done. Because, thermodynamics in a science of matter. Now, what gave me consistent results in the last bidouille uses a thermodynamical frame. As I underlined it, it works much better, if we accept the idea of changing frame, going from a mechanical space-time to a thermodynamical one. So, we can’t limit ourselves to saying “it’s a question of thermodynamics”, for present thermodynamics still uses conventional space-time. We have to build a new frame. A frame adapted to thermodynamics, as space-time was a frame adapted to mechanics.

Thermodynamics is the macroscopic version of statistical physics. Amongst many other things, it learns us the internal dynamics of matter can be described with only two “thermodynamical variables”, all the others being derived from these two. I chose pressure and temperature to be these two “fundamental variables”. Usually, pressure p is only the projection of a (mechanical) force f onto the normal to the surface of a given body. I extended this definition from a scalar to a vector quantity p, taking the other two tangential projections of f into account. So, we could equivalently write p = (p_x,p_y,p_z) in Cartesian coordinates, or p = (p_^,p_//1,p_//2) in curvilinear coordinates. Then pressure will be the orthogonal component p_^; p_//1, the projection of f tangent (or locally parallel) to the first family of curves that compose the surface and p_//2, the projection of f tangent to the second family of curves (I recall a surface can be drawn as the geometrical locus of two families of curves intersecting – a curved generalization of a plane).

Anyway, this vector p will play the role of x in conventional 3-space and temperature T, the role of time. As p and T are chosen as our thermodynamical variables, the suitable energy is free enthalpy G. It’s a function of p and T that can be defined through the differential relation:

 

(1)               dG(p,T) = -S(p,T)dT + V(p,T)n.dp = -S(p,T)dT + V(p,T)dp_^

 

The coefficient S is usually known as entropy. In my literature, I found only functions of T: entropy there is defined as S = -(¶G/¶T)_p taken at constant pressure. This does not prevent us from extending this definition to:

 

(2)               S(p,T) = -¶G(p,T)/¶T

 

since (1) is a total differential. Similarly, the volume V of a given body may vary with both temperature and pressure. So:

 

(3)               V(p,T) = -¶G(p,T)/¶p_^

 

In mechanical space-time, (2) and (3) lead to functionals, as both pressure and temperature are fields over space and time. In thermodynamical space-time, they become functions, i.e. fields over “thermodynamical space” and “thermodynamical time”.

The temptation is high to make a 4-vector out of these variables. To achieve this, we need a physical constant. If we simply write (ST, pV) or [(S/V)T,p], there will be nothing “universal”, since both S and V will (strongly) depend on the properties of the matter a given body is made of. Now, if we want to build a frame, we have to consider these four variables as coordinates in a physical frame independent of any kind of matter, that is, in a vaccum.

Well, the only combination I know so far that could fit both a thermodynamical vaccum and the Standard model is the Planck volume:

 

(4)               V_pl = (4p/3)R_pl³ = 6,648158 x 10^-104 m³

 

assuming this volume is spherical. This is the limit of “classical” distance in the Standard Model:

 

(5)               R_pl = (hk/c³)^1/2 = 4,0510454 x 10^-35 m

 

Making use of the Boltzmann constant k_B = 1,38 x 10^-23 J/K, we get:

 

(6)               s = k_B/V_pl = 4,955519 x 10⁷⁹ J/Km³

 

for the constant transforming temperature into a fourth pressure:

 

(7)               p⁰ = sT

 

This value of s is very high, but Planck’s pressure is extremely high, seen the smallness of the Planck volume: we’re not “at the classical limit” for nothing… J

What would it imply?

A relation like p(T) is commonly seen as a state equation for matter. Here, it becomes a trajectory in thermo space-time. The difference is that it no longer depends on any material medium, just as a trajectory into space, x(t), is not a property of any body. p(T) is now a motion into thermo space. The instantaneous “velocity” of this motion is dp(T)/dT. As before, if we think “Galilean” (relative pressure, absolute temperature), dp(T)/dT is unlimited; if we think “einsteinian” (relative pressure and temperature), to remain causal, we must have:

 

(8)               0 £ |dp(T)/dT| £ s

 

which is already not so bad… J (what now becomes limited is the number of letters we need to name constants – later on, do not confuse s with the Stefan constant)

The important value of s guarantees most of temperatures to keep their “absolute” nature: only temperatures close to T_pl become significantly relative in this frame. I don’t think we’ll reach such temperatures in parapsychology (or maybe in Hell… lol) and I rather expect to work inside a Galilean frame. On the contrary, s (as c) will almost probably appear useful in the theory of signals.

Unfortunately, for the time being, my system of units strops here…

For we can now go further, of course, and simply imitates mechanics.

We can introduce “PSI matter” in our frame, through a “PSI mass” m_y(T) that we can obtain from a “PSI mass density” m_y(p,T):

 

(9)               m_y(T) = òòò m_y(p,T)d³p

 

over a “thermodynamical volume”. Such matter will now distribute inside a finite pressure volume. Formula (9) says a PSI mass do not depend on time t at all. If it varies, it varies with temperature. Consequently:

 

ANY “PSI BODY” WILL LOOK “IMMORTAL” WITH RESPECT TO CONVENTIONAL TIME, AS ITS MASS WILL ALWAYS REMAIN CONSTANT IN TIME.

 

You could ask yourselves why I didn’t choose to transform pressure and temperature into new space-like and time-like coordinates, using, for instance, thermal wavelengths. The reason is that, if I do this then try to transform my BL metric in the previous bidouille back into a space-time metric (in m²), all the satisfying results I obtained are spoiled. In particular, the value of p₁[(2k+1)p/2] diverges, indicating the poles of the ergosphere are rejected to infinity. It definitely doesn’t fit. We need change frame. Simply changing our system of lengths would keep us inside the space-time frame and, in such frames, we know we have a serious observability problem. We already encountered it with the quantum approach. Because we’re not observable, nor even perceptible, we ought to completely change frame. With now the question of finding new systems of physical units…

I won’t go any further for today, since I’m still searching “meaningful results”. I’d only like to add a comment on B99.

We shouldn’t be that surprised to quit space-time when going through the ergosphere of a black hole for the reason that, from the gravitational radius r_g down to the centre r = 0, we are supposed to move inside matter… Remember all classical field theory: it says that, outside sources, we’re in “the vacuum”, i.e. in space-time, whereas inside sources, we’re in matter. So, maybe shouldn’t I say we quit space-time, rather we quit the external vacuum. Obviously, space-time is still present inside matter, but sources mathematically appear as “singularities” inside the space-time continuum. And they become particularly singular in the case of degenerated stellar objects with initial mass over the Chandrasekhar limit. The remaining matter is typically quantum, so it has nothing consistent anymore. In the case of black holes, a hypothesis is that the degenerated core would be made of a “quark soap”. This is a plasma. Ruled by (quantum) thermodynamics… Nothing classical anymore. So, talking of classical motions becomes meaningless…

Besides, something does not fit in the common description of the motion under the ergosphere. I don’t know if I already mentioned this. We’re supposed to reach the ergosphere at the speed of light. Then? The central body is still attracting… and the closer to its centre, the higher the attraction… How would you expect your speed to remain lower than c inside the ergosphere?... there’s a contradiction somewhere…

If you want to respect space-time relativity, you’re forced to admit that, from the ergosphere, you cannot keep on working in classical space-time. Or you face the risk to contradict yourself. I prefer to look at this ergosphere as a “physical limit to mechanical space-time”, the “frontier” of a collapsar, inside which we enter a new kind of space-time. A thermodynamical space-time, much more suitable to describe matter inside.

That’s what B99 suggests: that you travel a thermodynamical space-time inside a black hole structure, but non-gravitational (remember I showed, in a previous work, that General Relativity was actually a general frame for all kind of classical or semi-classical interactions, a second-order theory, not specific of gravity at all), down to the centre of its central singularity. There, a wormhole, an Einstein-Rosen bridge, connects you to “another place”. Apparently, in “another space-time” in our context.

If you go directly from the conscious state to stade 4, only the central singularity may appear. Penrose’s censorship has not been formally proven, after all. There’s no perturbation in mechanical space-time anyway, since we’re not gravitational and the structure appears in a completely different physical frame.

Unnoticed.

 

Yesterday evening, i had what you could call a « revelation ». Well, it’s not, actually. Numerical calculations simply forced me to take a brand new way. I already talked about the fact that numerical results gave me things completely aside of the problem. These last days, the very same happened. So, I tried something completely different… and it worked.

So, no real “revelation” at all: no one came to me at night to bring me the solution on a plate, unfortunately… J

Better don’t ask me how I was led to it, it would be far too difficult to explain. What’s coming up is really what you’re allowed to call “trafficking”. If some kind of “revelation” there can be, it will be on our way to see how things work inside a wormhole.

So, we begin with a new model of comas, that will bring us to the Tunnel. And probably to the rest.

I took the Boyer-Lindquist metric (1967) to start with. It’s another version of the Kerr metric for rotating black holes. As it’s rather complicated, I will write it in several parts:

 

(1)               ds² = g₀₀c²dt² + g₁₁dr² + g₂₂r²dq² + g₃₃r²dj² + 2g₀₃rcdtdj

(2)               g₀₀ = 1 – r_gr/r² , r² = r² + a²cos²q

(3)               g₁₁ = -r²/D , D = r² - r_gr + a²

(4)               g₂₂ = -r²/r² , g₃₃ = -(1 + a²/r² + r_ga²sin²q/rr²)sin²q , g₀₃ = r_gasin²q/r²

(5)               r_g = km/c² , a = M/mc

 

the metric coefficients g_ij having to be unit-free. m is the mass at rest of the attracting body, M is its kinetical momentum (in Js). The BL metric actually covers a 2-parameters dependent family of space-time metrics. These two parameters are r_g and a. They’re both expressed in meters. When a = 0 (fixed source), BL gives Schwarzschild back.

The fictive singularities of (1-5) are obtained for g₀₀ = 0 and for 1/g₁₁ = 0. The first one gives two ellipsoidal surfaces:

 

(6)       r₁(q) = ½ r_g{1 + [1 – (2a/r_g)²cos²q]^1/2}            (ergosphere)

(7)       r₄(q) = ½ r_g{1 - [1 – (2a/r_g)²cos²q]^1/2} (central singularity)

 

The second one gives two spherical surfaces:

 

(8)       r₂ = ½ r_g{1 + [1 – (2a/r_g)²]^1/2}                         (external horizon)

(9)       r₃ = ½ r_g{1 - [1 – (2a/r_g)²]^1/2}                         (internal horizon)

 

One has:

 

(10)           0 £ r₄ £ r₃ £ r₂ £ r₁ £ r_g

 

For r > r₁, g₀₀ > 0 and g₁₁ < 0: outside the black hole, the observer has the notion of both time (through g₀₀ > 0) and space (through g_aa < 0, a = 1,2,3), he can see a causal link between causes and effects for any matter travelling at v < c.

For r₂ < r < r₁, g₀₀ < 0 and g₁₁ < 0: inside the ergosphere, he looses the notion of time, since time looses its nature; instead, he rather perceives four space dimensions. You can see here the analogy with the Wick rotation in quantum mechanics. In classical mechanics, this is rather interpreted as the disappearance of a frame at rest: inside the ergosphere, matter is assumed to be in constant motion.

For r₃ < r < r₂, g₀₀ < 0 and g₁₁ > 0: under the external horizon, it’s worse, as the time and space directions are permuted. In classical mechanics, this would correspond to a tachyonic motion (motion at a speed > c).

For r₄ < r < r₃, g₀₀ < 0 and g₁₁ < 0: again, we’re Euclidian, as in the ergosphere.

Finally, for 0 £ r < r₄, g₀₀ > 0 and g₁₁ < 0: we’re back to a situation analogous to what occurs outside the black hole, despite we’re inside the central singularity.

 

Once more, I made calculations and once more, I got absurd results. The gravitational radius of a mass m » 70 kgs, for instance, is 5,2 x 10^-26 m… and anyway, we kept on having this base problem of a black hole created by a gravity field: whether it would be much too small to apply to anything interesting for us, or it would be much too heavy and would have absorbed everything around for long, as I already underlined in a previous work.

So, why did I turn to BL, then? Because this space-time structure offers 4 levels corresponding to 4 critical surfaces and values of the distance to the centre of the black hole.

And we have 4 states of coma. So putting the two closer and building an analogy was quite interesting to experiment.

However, it does not work as a space-time structure, independent from gravitation: I tried with electrically charged plasmas, I quickly abandoned.

Then comes to me a hateful question: could the analogy continue to hold, with different variables?

After all, I can always reduce my space-time variables xⁱ into unit-free variables.

Why would I do that?

Because my variables for comas are thermodynamical: blood pressure, body temperature, chemical concentrations.

Now, the BL model is purely mechanical. Hence my hateful question: could I keep it while using thermodynamical variables instead of mechanical ones?

Nothing to loose: let’s try.

I keep the angles and I make the following changes:

 

(11)           r -> p (pressure) , r_g -> p_c (critical pressure) , a -> a (in J/m³) , ct -> k_BT/V₃

 

where V₃ is a 3-volume and T is temperature.

The expressions for the metric coefficients (2-4) don’t change. My new metric writes:

 

(12)           dp² = g₀₀(k_B/V₃)²dT² + g₁₁dp² + g₂₂p²dq² + g₃₃p²dj² + 2g₀₃(k_B/V₃)pdTdj

(13)           g₀₀ = 1 – p_cp/r² , r² = p² + a²cos²q

(14)           g₁₁ = -r²/D , D = p² - p_cp + a²

(15)           g₂₂ = -r²/p² , g₃₃ = -(1 + a²/p² + p_ca²sin²q/pr²)sin²q , g₀₃ = p_casin²q/r²

 

My surface element is now in (J/m³)² and nowhere is it still question of mass, nor of space or time.

 

WE LEFT OUR FAMILIAR MECHANICAL SPACE-TIME TO GO WORK INTO A THERMODYNAMICAL SPACE-TIME.

 

So? Nothing more than another fictitious frame, after all…

Not sure. Wait and see.

We now have four singular structures corresponding to four critical values of the blood pressure, that we will call p_c, p_c1, p_c2, p_c3 and p_c4. We fix p_c » 15 pulses/mn. We have:

 

(16)           0 £ p_c4 £ p_c3 £ p_c2 £ p_c1 £ p_c

 

For p > p_c1, g₀₀ > 0 and g₁₁ < 0: we’re in the state of conscious awakeness (active process, sleep included). The patient perceives his surrounding environment. He has the notion of both time and space, of the succession of events and of causality (p = thermodynamical space, T = thermodynamical time).

For p_c2 < p < p_c1, g₀₀ < 0 and g₁₁ < 0: we’re in the stade 1 of coma (artificial coma).

 

THE PATIENT LOOSES THE NOTION OF TIME, WHILE KEEPING THAT OF SPACE. THIS STAGE IS REVERSIBLE: ONCE IN, ONE CAN ALWAYS GET OUT.

 

For p_c3 < p < p_c2, g₀₀ < 0 and g₁₁ > 0: stade 2, light coma.

 

AFTER LOOSING THE NOTION OF TIME, THE PATIENT LOOSES THAT OF SPACE. HE CAN STILL RECEIVE INFORMATIONS FROM THE OUTSIDE, BUT IT’S IMPOSSIBLE FOR HIM TO COMMUNICATE WITH THE OUTSIDE. THIS STATE IS NON-REVERSIBLE: ONCE IN, YOU CAN’T GET THE PATIENT OUT, WHATEVER YOU TRY. IF HE’S TO COME OUT OF IT, IT CAN ONLY BE BY HIMSELF.

 

For p_c4 < p < p_c3, g₀₀ < 0 and g₁₁ < 0: stade 3, sound (or deep) coma.

 

THE PATIENT RECOVERS THE NOTION OF SPACE, BUT NOT OF TIME. HE CAN STILL RECEIVE INFORMATIONS FROM THE OUTSIDE, BUT REMAINS UNABLE TO COMMUNICATE BACK WITH IT AND HE CAN STILL LESS GET OUT OF HIS COMA.

 

Finally, for 0 £ p < p_c4, g₀₀ > 0 and g₁₁ < 0: we enter stade 4. Clinical death (rigorously, p = 0). Against all odds:

 

THE PATIENT WAKES UP!!! 8((((

EVERYTHING HAPPENS AS IN HIS AWAKEN STATE: HE RECOVERS THE NOTION OF TIME, SPACE AND CAUSALITY. HE’S FULLY CONSCIOUS AGAIN.

NOW, HIS BODY STOPPED WORKING.

SO, HE CANNOT BE CONSCIOUS AS BEFORE, I.E. INSIDE HIS BODY.

8(((((

 

Just what to cool you down…

He wakes up… outside his body.

What happened?

Wormhole general theory brings hints of the answer.

For 0 £ p < p_c4, the patient is “inside the (thermodynamical) central singularity”. At p = 0, he’s located right at the centre of it. Now, a wormhole is supposed to “open” there, with the central singularity has its “borders”: the (3D) section of the wormhole is made by the central singularity. Beyond it, in the BL mechanical model, r should be counted negatively, as Penrose suggested, adding this should be physically interpreted as a repulsive gravity field. The point is, r is assumed to be the radius, a non negative quantity. Hence Penrose’s interpretation. Here, we should have p < 0 beyond the entry of the Tunnel. This too is absurd, since the patient’s body doesn’t work anymore. Anyway, even if it did, his blood cannot run counter-streaming.

This all means that, mechanically, we cannot go beyond the point r = 0 and thermodynamically, we cannot go beyond the point (blood pressure p = 0).

So, we have two options: we forget about wormholes or we find a non-mechanical kind of motion inside of them.

It’s natural for us, when dealing with a mechanical problem from the start to search for mechanical extensions. Sounds logical, doesn’t it?

Well, sometimes, logic doesn’t work. What does work is this, as surprising as it is:

 

BEYOND THE CENTRAL SINGULARITY, ALONG THE WORMHOLE, WE LEAVE THE MECHANICAL SPACE-TIME BEHIND TO ENTER A THERMODYNAMICAL SPACE-TIME, WHERE “LENGTHS” ARE MEASURED IN J/m³ (or Pa) AND “TIME” IN °K. THERE IS INDEED A MOTION THROUGH THE WORMHOLE, BUT IT’S OF THE FORM p = p(T): NOTHING HAPPENS IN SPACE NOR TIME ANYMORE.

 

For those who watched the movie “Contact”, in his novel, Carl Sagan based himself on the hypothesis of additional dimensions, enabling “space-time short-cuts”. During the trial, Jody Foster was told: “you pretend you travelled through the universe to another ET civilization, but here, all that happened was that you fell down into water…”

Sagan and al explain this lack of observability using quantum mechanics and additional dimensions, an inheritance of O. Klein and supersymmetry (“hidden dimensions”).

We recalled many times the problem of adding new dimensions, especially space-like ones: the change in the space behaviour of fields, tidal effects that are not observed, etc.

That was precisely the aim of Klein’s hypothesis: to throw these “extra-dimensions” inside the Planck volume…

When we confront this mechanical approach with NDEs, we see it just don’t hold…

What gives results in (very) good agreement with reality is thermodynamics.

I investigated the relations:

 

(17)           p_c1 – p_c2 = p_c2 – p_c3 = p_c3 – p_c4 = p_c4 – 0 = p_c4

 

using the same expressions as in (6-9) with the new variables and parameters. From

 

(18)           p_c1 = 4p_c4, p_c2 = 3p_c4, p_c3 = 2p_c4, p_c2 = 3p_c3/2

 

one finds:

 

(19)           a = p_c/5^1/2 » 6,71 pulses/mn

 

which fixes the model and:

 

(20)           p_c2 = (5^1/2 + 1)p_c/2 x 5^1/2 » 72,36% p_c » 10,854 pulses/mn

(21)           p_c3 = (5^1/2 - 1)p_c/2 x 5^1/2  » 27,64% p_c » 4,146 pulses/mn

 

Still more interesting is the great come-back of good old… gold number:

 

(22)           p_c2 = p_cN_or/(2N_or – 1)  ,  p_c3 = p_c(N_or – 1)/(2N_or – 1)

 

It remains a model, of course. The difference is: results are no longer absurd (orders of magnitude over or below anything censed to expect) as they are in mechanical space-time.

And we get another explanation of why nothing at all was observed in the Contact experiment, from the outside.

Nothing observed… and nothing even perceived!

 

IN MECHANICAL SPACE-TIME, NO “BLACK HOLE” OF ANY KIND FORMS, NOTHING PARTICULAR HAPPENS. YOU’RE DEAD, THAT’S ALL.

 

So, when you wake up and tell you’ve travelled “to a magic land”, common sense answers: “what the… hell are you talking about???” lol

 

We’re talking about leaving mechanical space-time for thermodynamical one.

We’re talking about “changing skin”, going from matter spread in space to matter spread in… pressure. Surely a very different type of matter!

We’re talking about meeting “Entities” made of such matter.

We’re talking about a thermodynamical Universe.

Where “feeling heat” means “getting the perception of time”. Becoming conscious of this “new” Universe.

 

Finally for today, a lot of experiencers, especially those who had heart attacks, reported they went into the Tunnel, then found themselves out of their body.

If there’s no motion in mechanical space-time… you don’t leave the room… if you’re back somewhere at the end of the Tunnel… you’re back to the same place. At the same time.

 

 

I may have found an easy way to extend point mechanics, so as to include the scale effects.

Consider first replacing the traditional point xⁱ with a vector field xⁱ(l^j) = xⁱ(l,T). We call the xⁱ(l^j) the sizes of the spot. l^j measures the distance from the spot xⁱ(l^j) to an observer in the direction j. When the l^js tend to infinity, we are at the macroscopic scale and we expect the xⁱs to tend to zero: an observer that is far away from the object will see it as a “point”. On the opposite, when the l^js tend to zero, the observer is very close to the object, which appears very large to him: the xⁱs tend to infinity, meaning the object occupies all the vision field.

We can build a dynamics from these xⁱ(l). The first criterion is the velocity, we define as:

 

(1)               v_ij(l) = c(¶x_j/¶lⁱ - ¶x_i/¶l^j)

 

It’s a skew-symmetric 2-tensor field. Following that, the mass of a point-like body is replaced with a spectral mass density m^(l,T), still measured in kg/m³. It’s spectral because it’s a density function over spectral space-time. We’ll see a more conventional definition of the mass density later on. The integral of this spectral mass density over a finite spectral 3-volume V^ gives the spectral mass of the incident body:

 

(2)               m^(T) = ò_V^ m^(l,T)d³l

 

This quantity depends only on the spectral time T (the period in the signal description). It’s immediately global on original space-time. In particular, it no longer depends on the original time t. From this point of view, it’s always a conserved quantity with respect to evolution in original space-time.

Next step: we form the Maxwellian Lagrange density

 

(3)               £^ = ½ m^(l)v_ij(l)v^ij(l) + f_j(l)xⁱ(l)

 

As £^ is in J/m³, f_i(l) is in N/m³ (force density). In the field description, m^(l) is more suitable than m^(T). The momentum density is:

 

(4)               p_ij(l) = ¶£^/¶v^ij(l) = m^(l)v_ij(l)

 

and the equations of motion:

 

(5)               c¶p_ij(l)/¶l_i = f_j(l)

 

They give the evolution of the spot xⁱ(l) in spectral space-time, knowing the external constraints f_i(l). We have the usual gauge invariance on the velocity field:

 

(6)               x_i(l) -> x_i(l) + ¶g^(l)/¶lⁱ

 

with g^(l) an arbitrary spectral scalar field expressed in m². This freedom enables us to set up the condition:

 

(7)               ¶xⁱ(l)/¶lⁱ = 0

 

What’s interesting here is that, not only original space x but also original time t are now allowed to change with the 4 lⁱ, i.e. from scale to scale (or wavelength to wavelength in the signal description). We knew they were both relative with respect to the velocity of a moving frame, we now see they can also, in addition, be relative with respect to the characteristic scales in all 4 directions of spectral space-time: none of the equations of motions (5) nor the transversality condition (7) depend on x or t. The dynamics is global, not only on original space, but on the whole original space-time and everything actually happens in spectral space-time: for a “conscious” observer standing in original space-time, there’s no particular motion at all. Nothing happens. The only way he can deduce “something” is going on “somewhere” is to observe scale variations on the size of a physical object, in space and time directions. And still: most of the time, a scale variation is for our observer a mere homothety, that is, a forward or backward zoom on the size of the object he observes. Here, such a zoom would be a very particular case of a much wider class of behaviours xⁱ(l), according to the form of the external constraints f_i(l) acting upon a… a what? A spectral body, of course, since the matter distribution of the incident object we considered is spectral: m^(l,T).

It sounds a bit obvious, yet:

 

A SPECTRAL BODY MOVES IN SPECTRAL SPACE-TIME.

IN ORIGINAL SPACE-TIME, NOTHING HAPPENS (NO MOTION, NO MATTER).

 

Nothing to observe => no existence. Wrong deduction. It is not because we cannot observe something that this something cannot exist. Only the converse is true, as to know: no existence => nothing to observe.

More sophisticated models are of course possible, I only took the simplest one to illustrate.

Let’s try a “Newtonian” solution like:

 

(8)               x_i(l) = n_iV_pl/l^kl_k

 

where V_pl is the Planck volume and n_i a unit vector. We get:

 

(9)               v_ij(l) = cV_pl(l_in_j – l_jn_i)/(l^kl_k)²

(10)           p_ij(l) = m^(l)cV_pl(l_in_j – l_jn_i)/(l^kl_k)²

(11)           f_j(l) = c²V_pl{(l_in_j – l_jn_i)l^kl_k¶m^(l)/¶l_i + m^(l)(4lⁱl_jn_i - n_jl^kl_k)}/(l^kl_k)³

 

Gauge condition (7) would lead to additional, but subsidiary, n_ilⁱ = 0. Since we started from a solution, the equations of motion (5) must give us the related force density. Surprinsigly enough, this force density does not demand that m^(l) be point-like, i.e. of the form m^(l) = m^(T)d(l). Besides, as you can check, this last form doesn’t give anything interesting for f_j(l), except derivatives of the Dirac pulse, nobody really cares of… :)) This actually means the “point-like” distribution has nothing natural anymore.

Solution (8) has two poles: l^k = 0 and l^kl_k = 0. We discussed l^k = 0. When the scale 4-vector is light-like, everything happens as in the microscopic. Yet, c²T² - l² = 0 only gives v_ph = c! So, it only means the (spectral) light cone is singular towards the Newtonian solution, making the spot size diverge.

 

We have a “reverse” model, permutating the xⁱs and the lⁱs. We then find familiar field theory using the space-time coordinates as field parameters. Instead of the spectral mass density, we find an original mass density m(x,t) and an original mass m(t) for an original volume V of original 3-space (these repetitions, despite necessary, have nothing original anymore… lol).

Mechanical features of this kind of motion (in original space-time – okay, tomorrow, I stop) are the field velocity V_ij(x), the momentum density P_ij(x) and the force density F_j(x) (all originals – STOP IT!). A Newtonian solution is now l_i(x) = n_iV_pl/x^kx_k, with singularity on the (…) light cone. At the origin x^k = 0 (got ya, mate!), l_i(0) = ¥: we’re macro; same on the (…) light cone, whereas x^k -> ¥ gives lⁱ -> 0: micro.

I find this reverse model less interesting, as l_i(x) describes local changes of scales. Moreover, matter distributions being in m(x,t), they describe only scale-invariant (…) matter, which does not include biological bodies as we saw it in the former bidouille. I mentioned it anyway, just to be complete.

 

Non deformable solids are of course mere idealizations: they don’t exist in Nature. All natural bodies sustain elastic deformations and this is precisely what this extension of the “point” expresses: that natural bodies can never be reduced to their centre of gravity or, if we prefer to keep this approach, then this cog can no longer be considered as point-like, but must be viewed as a spot, with sizes varying according to how far it is from an external observer.

We then see a spectral mechanics naturally emerges from such an extension.

 

We can mix both in a (careful!) 8D fictitious space-time with 4 space dimensions, 4 time dimensions and Minkowskian metric:

 

(12)           ds₈² = dxⁱdx_i – dlⁱdl_i = c²dt² - dx² - c²dT² + dl² = c²dt²(1 – v²/c²) – c²dT²(1 – v_gr²/c²)

 

When v < c and v_gr < c, the original space-time is causal (observable), but the spectral space-time is not (dlⁱdl_i > 0 => -dlⁱdl_i < 0).

When v < c and v_gr > c, the whole 8D space-time is causal, but an observer in the original space-time will receive no information from the spectral.

When v > c and v_gr < c, the whole 8D space-time is no longer observable (ds₈² < 0).

Finally, when v > c and v_gr > c, the spectral space-time is causal (observable), but the original space-time is not.

Furthermore, we have:

 

(13)           ds₈² = 0  <=>  dxⁱdx_i – dlⁱdl_i  <=>  (dT/dt)² = (1 – v²/c²)/(1 – v_gr²/c²)

 

The physical reality is much more a 4D space-time with “original state” on “one side of the light cone” and “spectral state” on “the other side”. A 2-state space-time. The metric (12) then expresses the fact that, when one state is observable, the other is not, for they are separated by light. On one side, coordinates are expressed by xⁱ; on the other side, by lⁱ. But these are all distances, all in meters. We could right as well x^ia = (xⁱ,lⁱ), where a = 1,2 is the state label.

 

 

The attentive reader will have noticed (for long) that, throughout these papers, i kind of repeat myself many times, always turning around the very same items. Only the approaches change. Thus, in bidouille 10 to 12, you’ll find the same argumentation (quantum, discrete space and time, stochasticity, wavepackets) as in the last bidouilles.

 

Could we actually be victims of appearances?...

 

Prigogine himself explained in great details the similitude between “classical” and “quantum” complexity: both are founded on a distribution law in the suitable phase space. I think I remember a bidouille where I showed that even classical mechanics could be rewritten in terms of operators acting on dynamical variables, that is, a non-commutative way…

 

I worked a little bit on different forms of distribution laws this week and I finally asked myself:

 

IS PARAPSYCHOLOGY A QUANTUM SCIENCE OR RATHER A SCIENCE OF COMPLEXITY?

 

For it appeared to me that:

 

QUANTUM PHYSICS CAN BE VIEWED AS A PARTICULAR CASE OF COMPLEXITY THEORY, WHEN THE SCALES lⁱ REPRESENT WAVELENGTHS.

 

I’ve been looking for explanations in the quantum theory. Is it the right frame or isn’t it rather a question of complexity? Probability laws are constructed the same…

Consider a distribution of matter m(x,t) in original 3-space. Such a distribution depends on x, but not on l nor T. It describes a matter that is inhomogeneous (x-dependence) but scale-invariante (l-independence), that is, homogeneous from one scale to the other: should you change scale, the distribution of this matter would remain exactly the same, at each point, each time.

Consider now the spectral image m^(l,T) in spectral 3-space. Such a distribution depends on l, but not on x nor t. It describes this time a matter that is homogeneous (x-independence) but inhomogeneous from one scale to the other: should you change position in space-time, the distribution of this matter would remain exactly the same, at each scale, each period.

Consider finally both, m(x,t,l,T), and assume m explicitly depends on the ratios xⁱ/lⁱ (i = 1,2,3,4, x⁴ = ct, l⁴ = cT), for reasons of physical units. Such a distribution of matter is inhomogeneous in both original and spectral 3-spaces: not only does it change from one point to the other, but also from one scale to the other.

The distribution m(x,t) is not complex: it’s the same as at the microscopic level (lⁱ = 0). We usually use it to describe corpuscular matter.

The distribution m^(l,T) is complex and global.

As for m(x,t,l,T), we use it to describe “quantum” matter when the lⁱ’s are wavelengths. Then, the sum of the ratios xⁱ/lⁱ represents the phase of a monochromatic wave and å_i=1⁴ò dxⁱ/lⁱ(x) the phase of a polychromatic wave, in a parametric representation lⁱ(x) (and up to a 2p factor).

 

When the lⁱ’s are not especially wavelengths, we find complexity theory.

 

If quantum theory was “merely” a particular case of complexity theory, what kind of physical link could we build between them?

m(x,t) models the corpuscle. It’s clearly elementary (what’s not complex is elementary – or simple…).

m^(l,T) models its spectra. It carries all the complexity (and nothing else!).

So, if m(x,t,l,T) is supposed to model quantum matter than, in such matter, all the complexity is carried by the wavepacket.

That would mean that, at super-high energies (l⁴ -> 0), we indeed retrieve the “corpuscular approximate” (almost-Dirac); at super-low energies (l⁴ -> ¥), we retrieve the “wave approximate” (almost-flat). In between, we are “quantum”, i.e. a “mixing of corpuscular and wavy behaviours”.

So-called “intrication” proceeds through lⁱ-dependence. When lⁱ -> 0, we’re at the “geometrical limit” of classical optics (“rays”), no intrication.

What do we actually call the “microscopic”? It relates to the average size of physical objects, with respect to “our” sizes. Particles and atoms are therefore “microscopic” to us. We can see here the neat distinction with l⁴ -> 0, which relates to the energy level of the object. If quantum physics was confined into “the microscopic”, we would find no “macroscopic” effects, i.e. effects on physical objects with average sizes much greater than ours.

Once again, confusion is easy between lⁱ as wavelengths, quantum-associated with energy and momentum and lⁱ as complexity scales or sizes: in the quantum context, the “size” of an object is the width of its wavepacket…

There’s a possible way to find “quantum disintrication”, at least as an interpretation of things, if we assume, as we saw above that the property “in a quantum object, the corpuscle have zero complexity, while the wavepacket has full complexity” is typical of objects of microscopic sizes, while the “reverse” property “in a classical object, organized matter have full complexity, while the wavepacket has zero complexity” is typical of objects of macroscopic sizes. There’s then a “complexity transfert” from the wavepacket to substantial matter as the system organizes and expands into space. At small distances, we would then observe quantum effects, whereas at large distances, we would observe substantial effects and the wavy ones would have disappeared from our observation, unless we observe a collective phenomenon, i.e. as long as we’re not critical.

Anyway, it’s really all a question of scale, since we observe quantum effects again as soon as we zoom forward back to the microscopic… J

This, again, can be seen as the property of the quantum to be scale-dependent, as any other complex systems. Notice a point-like body is not scale-dependent: it remains a point-like body at all scales. A corpuscle remains a corpuscle. Wave mechanics add a wave to it, but don’t expand it!...

 

Let’s now make a little calculation. We will limit ourselves to orders of magnitude, it’s far enough. The mean mass of a living cell is around 10^-8 kg (that’s about ten micrograms). Taking it circular (for simplicity, but it doesn’t change a lot the result), its ray is about 1 micron (10^-6m) and its thickness, about 1 nanometer (10^-9m). This gives a volume pr²h around 3 x 10^-21 m³ and a mean density m_cell around 3 x 10^-12 kg/m³. The mean mass of a human body is around 70 kgs. Taking it axial, its ray is about 0.5 m and its height, 1.7m. This gives a volume of order 1.335 m³ and a mean density m_human around 52.4 kgs/m³. The ratio between the two densities is 52.4/3 x 10^-12 = 1.75 x 10¹³ = (4.2 x 10⁶)². The ratio between the scale of a cell and that of a human being of order 10⁶, we come to the conclusion that the density of biological matter strongly depends on the scale, roughly as 1/l².

Is it due to some quantum expansion?

Obviously not. It’s rather due to complexification.

Hence my first question above: is parapsychology a question of quantum behaviour or rather a complexity problem, if complexity theory includes quantum theory?

With quantum theory, we face problems, difficulties and legitimate oppositions.

With complexity theory, we no longer face such problems, but we have to look for other evolution stages of organized matter. A new class of problems…

I can keep all the work I’ve done so far on the quantum context, but send it back to the microscopic domain where it belongs in non-critical situations.

And I enlarge the context replacing it with complexity theory.

 

Matter evolves. When reaching a certain complexity level, it’s evolved enough to become autonomous: matter becomes “alive”. It manages itself, it reproduces… but it still strongly depends on thermodynamics. It “gets old”.

 

My question now is: is there another complexity level above which “dead” matter do not depend on thermodynamics anymore?

Surely the physical state of such matter would be fundamentally different from that of “alive” matter.

We yet have a guideline, as the properties reported by NDEs seem to show that “dead” matter has many properties similar to those of quantum media.

Now, we can use quantum equations to help us move forward in complexity theory. So we’re (in principle) allowed to draw some similitudes with quantum matter, as long as they remain similitudes.