Thus, this “G-space-time” seems to be promising. Here’s now another and rather striking confirmation.

We have two different measures of length depending on which space we are working in: in M₄, we have meters; in G-space-time, we have meters per second. Just as in classical 4D relativity, it would be nice, as a synthesis, to work with a single unit. We can choose m/s or stay with meters. If we keep this last option, we can define additional coordinates through:

 

(1)               xⁱ⁺⁴ = Cte x Gⁱ

 

Obviously, for our new xⁱ⁺⁴ to be in meters, we need Cte to be in seconds. Now, as c, this constant must be universal. The only constant of this kind we know so far that is compatible with the Standard Model is the Planck time:

 

(2)               t_pl = R_pl/c = (hk/c⁵)^1/2 = 1,3512808 x 10^-43 s

 

It’s the only quantity solely made of universal constants. Reversing (1) would give:

 

(3)               Gⁱ = f_plxⁱ⁺⁴ , f_pl = 1/t_pl = 7,4003864 x 10⁴² Hz

 

We’ll find a much wider use of that Planck frequency later on. For the time being, we investigated the limit case GⁱG_i = c² in B89. If we stick to this physical limitation in G-space-time, something that seems quite legitimate after all, being still about velocities, then the condition:

 

(4)               GⁱG_i £ c²

 

in G-space-time, this time, that is, on 4D lengths in that frame, together with:

 

(5)               xⁱ⁺⁴ = t_plGⁱ

 

implies that:

 

(6)               xⁱ⁺⁴x_i+4 £ c²t_pl² = R_pl²

 

Makes you remind of something?...

 

THE OSCAR KLEIN HYPOTHESIS.

WE RETRIEVE THE OSCAR KLEIN HYPOTHESIS ON ADDITIONAL DIMENSIONS OF SPACE-TIME.

 

What inequality (6) means is that, is we want to stay causal, i.e. observable, in higher dimensions of space-time, we need 0 £ xⁱ⁺⁴x_i+4. But (6) now requests that xⁱ⁺⁴x_i+4 £ R_pl². So,

 

FROM WHAT AN OBSERVER OF M₄ CAN PERCEIVE,

THE 4 HIGHER DIMENSIONS OF SPACE-TIME, EVALUATED IN METERS, CAN ONLY STAY CONFINED INSIDE THE PLANCK RADIUS IF TO REMAIN CAUSAL.

 

Actually, what is likely to happen?

Simply, (6) shows meter is no longer the appropriate unit to measure distances in the higher dimensions. If we use (3) instead, the only constraint we have is (4), which is interpreted as a kinematical constraint in M₄. No confinement anymore.

 

DIMENSIONAL CONFINEMENT IS AN ARTEFACT APPEARING WHEN WE, BIOLOGICAL OBSERVERS OF M₄, TRY TO KEEP ON MEASURING PHYSICAL OBJECTS AND EVENTS IN THE HIGHER DIMENSIONS WITH THE SAME SYSTEM OF UNITS WE USE IN THE FIRST 4 DIMENSIONS.

 

I’m particularly satisfied with this result, totally unexpected, since I’ve criticized the Klein hypothesis from the very beginning, arguing, as many others, that there was no justification at all for such a choice. Indeed, it was nothing else than getting rid of these additional dimensions that jeopardized the behaviour of fields in the macroscopic.

We now have a justification and even an explanation.

The hypothesis is justified to an M₄-observer’s eyes.

But G-space-time enables us to explain why it’s actually a mere artefact, that disappears in higher dimensions.

 

 

YES-WE-CAN. We can retrieve quantum field theory and quite easily. Here’s how.

We take advantage of the fact that M(x) is a density of inertia to search it under the form:

 

(1)               M(x) = Iy*(x)y(x) = Ir(x)

 

where I is an inertia (Js² = kgm²). In the bosonic model, we get this:

 

(2)               ¶ⁱ¶_iM(x) = I(y*¶ⁱ¶_iy + y¶ⁱ¶_iy* + 2¶ⁱy¶_iy*)(x) = (4mI/ħ²)£_y

 

where £_y is the Lagrangian density for the free field y:

 

(3)               £_y = (ħ²/2m)¶ⁱy¶_iy* - ½ mc²yy*

 

To establish (2), I made use of the field equation:

 

(4)               ¶ⁱ¶_iy = -(mc/ħ)²y

 

derived from (3). We get a better idea of the thing with y = r^1/2e^iq. The field equation (4) and the Lagrangian (3) become the system:

 

(5)               ¶ⁱr¶_iq + r¶ⁱ¶_iq = 0

(6)               (1/2r)²¶ⁱr¶_ir - (1/2r)¶ⁱ¶_ir + ¶ⁱq¶_iq = (mc/ħ)²

(7)               £_y = (ħ²/8mr)¶ⁱr¶_ir + (ħ²/2m)[¶ⁱq¶_iq - (mc/ħ)²]r

 

so that, if we use (2):

 

(8)               ¶ⁱ¶_iM(x) = 2Ir[(1/2r)²¶ⁱr¶_ir + ¶ⁱq¶_iq - (mc/ħ)²] = I¶ⁱ¶_ir = (I/m)¶ⁱ¶_im

 

with m(x) = mr(x) the mass density. Integration gives:

 

(9)               M(x) = (I/m)m(x)

 

hence the result:

 

IN THE BOSONIC MODEL, THE “PSI” MASS M(x) IS INDEED LINKED AND PROPORTIONAL TO THE LOCAL MASS m(x) = m|y(x)|² OF A WAVY BODY GIVEN BY QUANTUM FIELD THEORY.

 

We can be led to the very same conclusion in the fermionic case. However, as it is a first-order model, the simplest way to proceed is to start from the general relation:

 

(10)           ¶ⁱ¶_iM(x) = £_y/c²

 

holding in both situations.

Our constant of inertia I is left free. If we choose:

 

(11)           I = h²/3mc²

 

we obtain:

 

(12)           M(x) = 1/3 (h/mc)²m(x)

 

This choice is motivated by what follows. We first have the identities:

 

(13)           m_pl² = hc/k , R_pl² = hk/c³ , c²/k = m_pl/R_pl , hc = m_plR_pl

 

These identities show very useful in the (important) case of:

 

(14)           M(x) = cte = c²/4pk

 

the coupling constant of gravity (in M₄). We then get:

 

(15)           m(x) = cte = m²/m_plV_pl = (m/m_pl)²m_pl, V_pl = (4p/3)R_pl³

 

and when m = m_pl,

 

(16)           m(x) = m_pl = m_pl/V_pl

 

that is, precisely, the Planck density for a spherical Planck particle.

 

What does all this mean?

It shows that the body we search for at stage IV is confirmed to be purely wavy, with mass density in M₄ given by RQFT (Relativistic Quantum Field Theory). This mass distribution m(x) = mr(x) then indicates the way wavy matter distributes in space and time. Notice that, opposite to classical mechanics, the time dependence is no longer contained into m, but reported into the number r(x) of elements involved, per unit volume.

Following that, what we showed here is that m(x) is actually proportional to what we defined in B102 as the “PSI mass” (to stick to our context), that is, the mass of a physical body, no longer in M₄, but in the higher dimensions of a gravitational space-time. The calculation from (11) to (16) above is interesting in itself, but its aim is to prove that we retrieve all the properties of the original Planck particle, the existence of which is intimately associated with the birth of our Universe. It was necessary to show this in order to consolidate our reasoning.

 

Just a tiny correction before we go on: in the bosonic vacuum state, the source does not necessarily vanish, since its phase can still vary in space-time.

Okay. We’ve already established something: that “PSI” bodies, if existing, can only be made of wavepackets. No substance of any kind anywhere.

Next question: under such conditions, what could be the physical frame inside which wavy bodies could form and evolve?

Forget about space-time. We have to find something else.

We identified PSI matter: organized systems of material wavepackets. It’s already something.

Ordinary matter being distributed in 3-space, PSI matter can only distribute in a space of wavepackets. If it distributed in 3-space as well, it would be observable.

But a “space of wavepackets” is a functional space, a mathematical space. If we think in terms of wavepackets, our physical frame remains ordinary space-time M₄. We can do mechanics, quantum field theory and thermodynamics inside it, but nothing “PSI”: in M₄, PSI is desperately trivial and leads to nothing interesting at all.

Now, we know that an expression like x(t) means “a motion of a substantial body in ordinary 3-space E₃ (x-space) in time”.

So, we deduce from this that y(x,t) means “a motion of a wavy body in a space of wavepackets (y-space) in space and time, that is, ‘over’ M₄”.

We’re sent back to a new physical frame.

And, as this space can only stand “over” M₄, we have no other choice than to introduce new physical dimensions.

Let it be. What kind of dimensions wouldn’t change well-established behaviours in both classical and quantum dynamics?

We have 3 space dimensions measuring lengths and distances, unit meter; one time dimension measuring… time, unit second. So, we already have no problem with using different physical dimensions expressed in different physical units.

Let’s introduce new physical dimensions with still other physical units. No distances, no time, something else. y-units, m^-3/2? No: first, we need something the most general possible; second, we need something “in a vacuum”, i.e. outside of any matter. y-coordinates are made for PSI bodies (material waves), they can help localize PSI matter inside this new frame. But, as in M₄, space-time is defined independent of any ordinary matter. That’s why we can’t use y.

The best candidate I found is the gravitational field in M₄. It’s the most general, as any other interaction can express with it [example: A_i(x) = (q/m)G_i(x)]. It’s spin 1 and therefore a wavefunction for quantum theory. This G-field G_i(x) sends us back to a wave space with coordinates Gⁱ, units m/s. A kind of “potential velocity”.

If we do this, then we get 4 new physical dimensions Gⁱ, to add to the four xⁱ. Or to the 3 x and the single t.

A “motion” in this “gravitational space-time” is a gravitational field Gⁱ(x): that’s what a biological observer in M₄ can observe. If you go from a point G₁ⁱ to another G₂ⁱ, you’re on a trajectory Gⁱ(x) such that Gⁱ(x₁) = G₁ⁱ and Gⁱ(x₂) = G₂ⁱ: your M₄-observer will see a given G-field taking two different values at two different points of space-time.

What we now say is that such an observation sends us back to a motion in G-space.

Do I face difficulties with physical units in this G-space? Not really:

 

-         “distances” and “lengths” are measured in m/s, they are observed as velocities in M₄;

-         “time” is now 4D-space-time, in m;

-         “velocities” ¶_iG_j(x) to replace dx(t)/dt: Hz, frequencies in M₄;

-         “accelerations” ¶_i¶_jG_k(x), in Hz/m;

-         “energies”? Given by the field Lagrangian in M₄, £_G = (c²/8pk)W_ij(x)W^ij(x), with W_ij(x) “velocities”: £_G in J/m³. So “energies” are energy densities in M₄;

-         “masses”? Consequence of “energies”: the coupling constant c²/8pk is measured in Js²/m³ in M₄, hence a density of inertia; “masses” in G-space are only generalizations of this factor, so that £_G reproduces Galilean motion in G-space, £_G = ½ M(x)W_ij(x)W^ij(x); we deduce M(x) in Js²/m³;

-         “forces”? Deduced from the Maxwell-like potential part of £_G this time: p_i(x)Gⁱ(x) in J/m³ => p_i(x) in (kgm/s)/m³: densities of momentum and energy.

 

Do I have to fear modifications in the behaviour of fields in M₄? Obviously, no, since I’m now gonna work with “PSI fields” Y(G,x) in the total 8D frame. First terms near Gⁱ = 0, corresponding to no gravity or a weak one in M₄ gives me:

 

(1)               Y(G,x) = Y₀(x) + Y_1i(x)Gⁱ + ½ Y_2ij(x)GⁱG^j +…

 

Zeroth-order term Y₀(x) = field in M₄. For other M₄-observable contributions, just consider the functional Y[G(x),x]. Y can, for instance, express a PSI body, than Y₀(x) is its material wavepacket in M₄. It can be statistical or not. If we completely neglect gravity, Y will reduce to Y₀ in this (rough) approximation.

I’m now working on functionals like Y[G(x),x] when Y is in m^-3/2, to see if we properly retrieve quantum field theory in M₄. Answer next time.

 

NB: a G-space over M₄ will mean that a biological observer “imbedded in these higher dimensions” would see everything around him “plunged into a gravitational light”. That’s the way he would perceive the vacuum there, with his 4D senses.

 

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.