Who does not believe in ghosts, hey? ;)) I said (warned?) in B130 that "i be BACK", well i am!!!

 

 

I

WHY SEARCHING FOR A POSSIBLE EXISTENCE OF « LIFE AFTER LIFE »?

 

This is not simple curiosity. This is not only to “know” or to answer a question as old as humanity and still less, if it worked, to “leave a name in the history of biophysics”.

This is before all a crucial social issue.

Since humanity emerged on Earth, humans always believed in “spirits”, “gods” and “life after (biological) life”. Despite this, it didn’t prevent them to fight against each other, some, to defend their territory (an anthropomorphism linked to genetics, as at chimpanzees – who are not our cousins by the way, or other animals), some, to try and steal others’ territories. The concept of war is deeply encrypted in the human genome. It’s not only about competition, it’s before all about destruction and self-destruction, the “human paradox”. Biology is able to explain this qualifying the human specie as a “super-predating” one. Before humans,  paleontology revealed that there has been other animal species who behaved like super-predators. They all had an extremely short life (on the geological scale), precisely because of their natural instinct, not only to kill all other species (to feed themselves), but sometimes, to kill members of their own specie. Anyway, the more super-predating a specie, the shorter its life, for a time comes when it remains nothing to feed anymore…

This is exactly what’s happening with our specie. Some days ago, an international congress of specialists confirmed that we had entered the “Anthropocene era”, i.e. major changes in our ecosystem put an end to the “Eocene era” that lasted until recently. They fixed the beginning of that “Anthropoce era” to approximately the middle of the 20^th century, short after World War II. Within less than 50 years, we completely modified the structure of our seas, which had been the most stable medium on Earth since they emerged, billions of years ago. Our actions on hard soil are equally devastating, not to talk about our atmosphere.

This is not evolution. This is destruction and self-destruction, that is, negatively-oriented evolution.

 

There is a strong difference between hoping for life after life, believing in it and in what I would generally call “spiritual entities”, and managing to get the scientific proves of it, at least on the theoretical viewpoint. If we could demonstrate that the sole concept of life after life can enter a known physical or biophysical context, we would acquire evidences.

And this could have decisive impacts on human psychology.

Because there’s a difference between “fearing to sustain the faults committed during bio life” and “being sure these faults will have further consequences, eternally”.

I’m convinced most of people would think twice before doing wrong. But I may keep a part of candour.

 

 

 

II

MAIN MOTIVATION

 

This is the main reason and my main motivation for trying to find a scientific, consistent, answer to the question: is there another form of life after the biological one? As you can see in the long list of previous posts, this is everything but a simple issue. The most difficult thing is to be as consistent as possible with biology. We just cannot collect datas and testimonies from individuals across the world who say had a “paranormal” experience and “suggest” a physical explanation that sounds great, fashion-style, but give no importance to biological and, in particular, neurobiological facts. This is simply not an honest scientific way. An honest scientific theory must before all:

 

a)      stick to the established and well-verified facts;

b)      incorporate new ones (here, testimonies);

c)      propose a wider frame inside which point a gets included, while point b is submitted to thorough analysis and criticism.

 

Finally, the theory itself must be open to criticism: if it bears no criticism, it just cannot be improved, it just reveals the megalomaniac temper of his author.

This begins with not taking for granted all we collect in point b. Some people may tell the truth, others can be honest but deform reality and still others may simply invent. A solid theory has to be able to sort things out, according to criteria that have nothing “universal” but, on the contrary, were built out of point a and consistent extensions of it.

So… the least to say is that I tried many, many ways and none of them fully satisfied me so far (now, I may be difficult…). Talking about self-criticism? I always found obstructions to the models I suggested.

NDEs (Near-Death Experiments) seemed to me to be the “door”, the central point, to a better understanding of parapsychological phenomena. I believed that, if we could understand the different aspects of an NDE scenario, we would be able to go further in the other aspects of so-called “parapsychic phenomena”. I spent a lot of time and numerous posts on this matter. Each time, an obstruction occurred, that forced me to abandon an hypothesis. Amongst these obstructions, the strongest is maybe the necessary requirement that a second body exist. I acquired the conviction that a single body was simply impossible to explain NDEs. With a single body only, you systematically conflict with neurobio.

Why?

Mainly because biology and microbiology proved that what we call “consciousness” is definitely not some kind of “substantial entity”, but a virtual production of the only substance present under our skull: the brain. Consciousness is a process, not a substance. This distinction is determining. It says that, whatever you try, you cannot assign a “body”, whatever its physical nature, to consciousness. It’s both physically and neurobiologically impossible. What neurobio tells us is that the (highly disordered) collection of connected neural cells making the neo-cortex, which makes neural matter, produces a physical field we call “consciousness”. This field is obviously highly complex, as is the neo-cortex, but whatever its complexity, it remains an electrochemical field. The “basic impulses” of that field are the “nervous signal” generated by neurons through their membranes and this signal is an electromagnetic signal produced by electrically-charged atoms (ions): potassium, sodium, calcium.

Now, you cannot attach any physical substance to such a field. It’s fundamentally non material. Quantum physics explains why: because it is submitted to the Bose-Einstein statistics, whereas matter is submitted to the Fermi-Dirac statistics. Only a sign differs between the two, but it changes everything…

The consequence of this is that, in a NDE, disembodiment (Out-of-Body Experiment – OBE) cannot involve consciousness, as it is quite widely assumed.

First, because neurobio asserts that the consciousness field is a radiating field, produced by and inside neural matter and, as such, remains confined inside the organism; and this assertion is proved by MRI examinations.

Second, because, according to “experiencers” themselves, disembodiment involves “a body, but of a different nature”: the patient keeps that strong feeling he/she still have a “body”, but that this body has nothing to do with their previous one anymore.

Get me as clear as possible: they report they were conscious they had “another body”.

So, it must necessarily be something completely apart from consciousness, right?

Anyway, physically, you cannot make a body out of an electromagnetic field, how complex may it be, precisely because of the statistics abovementioned.

Question: is there anything known in physics likely to justify only the possibility of the existence of such a “non-biological body”?

I reviewed all I knew about fundamental and complex physics, didn’t find anything.

Quite a lot of serious physicists claim that quantum theory could explain it. I objected that the central point was that quantum theory does not double bodies, but their internal dynamics: the physical medium remains single, but some of its components follow the “classical” laws of dynamics and others follow the “quantum” laws of wave dynamics. So, quantum theory cannot be the explanation. Furthermore, there is a quantum entanglement that shows absolutely incompatible with an eventual separation between the biological body and this “other body”: if this second body was a quantum extension of the biological one, they could never be torn apart whatever you try; you could place one at “one end of the universe” and the other one “at the other end”, they’d still make a single body…

This is definitely not what’s reported in NDEs. So, I told myself “maybe it’s the Tunnel that enables de-entanglement?...”, but then you severely contradict the laws of physics and have to bring an explanation to what is not observed anyway… L

 

 

 

III

SUPERSYMMETRY, A CONSISTENT FRAME?

 

I already explored the supersymmetric hypothesis several times, without success so far. But, did I make the right interpretation of it? Isn’t it, after all, a question of correctly interpreting our most advanced theories or not?

What are the advantages of supersymmetry?

Let me try to explain it the simplest possible.

It’s always about unifying the physical laws to get a more synthetic view of them. With supersymmetry, The idea was to group together matter and radiation. But this amounted to (try and) reconcile two apparently contradictory behaviours: that of matter, following the Fermi-Dirac stat, and that of radiations, following the Bose-Einstein stat. To get a chance to achieve such a goal, it soon appeared obvious that the known symmetries of Nature were not sufficient enough, hence the idea of extending them into wider symmetries, named “super-symmetries”. The concept of symmetry is central to theoretical physics, as it is intimately linked to that of invariance and properties.

So, what these guys did is, they took both stats and put them together, then built a convenient physical frame that would accept such extended symmetries.

The result is a “super-space” or “super-space-time”, as you wish, that has eight dimensions instead of four: the four known ones, three space-like and one time-like, and four new ones, still three space-like and one time-like, but constructed differently. I shall not enter into details, as they soon become extremely technical and this paper is made for the largest public possible. What I will say is that BE statistics for radiations leads to a symmetric geometry, with the mathematical property that, for any two numbers x and y, the product of x and y, xy, is equal to the product of y and x:

 

(1)               xy = yx

 

which can also be written under the form,

 

(2)               xy – yx = 0

 

whereas FD statistics for matter leads to skew-symmetric geometry, with the property that,

 

(3)               xy = -yx

 

or,

 

(4)               xy + yx = 0

 

Such a property is obviously not realized by “usual” numbers, or “c-numbers” (c for commutative), but is realized by mathematical objects called matrices (“tables of numbers”), a generalization of numbers. It’s however possible to somehow get back to “commuting variables”, while keeping the desired properties for matter. For technicians now, as I’m forced to justify this last assertion a bit, the new quadruplet of coordinates is given by:

 

(5)               xⁱ⁺⁴ = qsⁱq* = q^asⁱ_aa’q*^a’

 

where the greek indices are two-component Weyl spinors (a,a’ = 1,2) and latine indices run from 1 to 4 or 0 to 3, it’s up to you, the sⁱ being Pauli’s sigma matrices and the q^as, the skew-commuting “theta-variables” (together with their conjugate representations q*^a’).

This to show why the “supersymmetric spacetime” can be built 8-dimensional, with coordinates (xⁱ,xⁱ⁺⁴) locating any “point-like body”.

From that point, theoretical physicists, who are not completely stupid, told themselves: “well, we’re gonna do field theory just like in 4-dimensional spacetime, but with 8 variables instead of 4”. So, they took a function, say F, assumed to model a physical field, and developed it in powers of the 4 new variables. This gave them “component fields”, namely:

 

(6)               F(x^k,x^k+4) = F₀(x^k) + F_1,i+4(x^k)xⁱ⁺⁴ + ½ F_2,i+4,j+4(x^k)xⁱ⁺⁴x^j+4 + …

 

(… = higher-order contributions). Each expression between two addition operator is a convenient convention (Einstein’s summation convention) to write a sum over all four values in condensed writing (physicists are dramatically lazy…). The field F₀(x^k) is the “zeroth-order contribution” to the “superfield” F(x^k,x^k+4). As it does not explicitly depend on the additional variables x^k+4, it’s identified as a “usual” field over 4-d spacetime. And so are all further contributions F_1,i+4(x^k) (4 components, 1^st order), F_2,i+4,j+4(x^k) (10 components, 2^nd order), etc.

Doing so, they make both radiative and matter fields appear as components of the original “superfield”.

However, this “dichotomy” between “radiative fields” and “matter fields” is, as usual, Cartesian and made necessary because physics is before all a science of observation and detection and we observe and detect only phenomena occurring within our 4 dimensions at reach. Hence the aim of power developments like (6) above: to bring a new physical entity back to accessible ones.

Obviously, this distinction between radiation and matter looses all significance in 8-d super-spacetime: the superfield F(x^k,x^k+4) is “neither radiative nor material”, it is “both of them at the same time”. Only when we project it back into smaller 4-dimensional spacetime do we recover that distinction between “radiation” and “matter”. Otherwise, to be honest, we don’t know how to correctly qualify it, but as a “unified field”.

Before going further, I’d like to make a brief parenthesis on physical dimensions. In people’s mind, it’s usually assumed that additional dimensions are located “above”. There’s no such picture in the world. No dimension is “above” or “below” another one, it doesn’t make sense. The eight dimensions here described are all “at the same level”. What happens is that physical objects can move or not along all dimensions or only a smaller number of them. We evolve every day in a 3-dimensional environment, we can move along the 3 dimensions of space. Particles do exactly the same. What they have more is that, if their velocity is high enough, they can also begin to move along the time direction, what we all do, actually, but can’t perceive it, because our velocities are much slower than that of light. Nonetheless, as soon as we move into 3-space, we induce a very small motion in time as well. So small that it is not perceptible.

Well, superparticles are allowed to move along up to 8 dimensions. Also, “super-volumes” can be 6-dimensional. They can move along two time-like directions instead of a single one.

And this completely, radically, fundamentally changes the properties and dynamics of physical objects. So completely, so radically, so fundamentally that there’s no possible comparison with the objects we are familiar with or can detect in a restricted 4-dimensional world. Physicists focused so far on the implications on elementary particles, because their research is directed towards the unification of the fundamental laws of physics and, ultimately, the birth of the (4-d) universe.

But the basic principles of supersymmetry are:

 

a)      there’s no longer such things called “radiation” or “matter”, these two concepts now derive from a unified “super-physics”, once projected into a 4-dimensional world;

b)      to each known particle can be attributed a “super-partner”, which is a new particle with same characteristics, but only different spin (the intrinsic rotation momentum about the particle’s axis);

c)      particle and its supersymmetric partner are not entangled together as “body mechanics” and “wave mechanics” are in quantum theory.

 

Let’s take a typical example to illustrate this. The electron is a light particle with mass at rest m_e, electric charge q_e (taken as the conventional unit) and spin ½ (fermion, matter, half-integer spins). Its super-partner is the “selectron”. It’s assumed to have same mass m_e, same electric charge q_e, but spin 0 (ie no rotation). So, if it wasn’t about its spin, it would be seen as the same particle. Now, if the selectron had same mass at rest as the electron, it would have been detected for long, which is still not the case. Is it that the theory is based on uncorrect assertions? No, it only shows that there are restrictions to be made. The restriction in question is on the mass of the two partners. Why isn’t the selectron detected yet? Because its mass at rest must actually be much heavier than that of the electron.

But why, since supersymmetry based itself on the equality of masses???

Because of a process known as symmetry breaking.

So, the fact that super-partners are not observed yet is explained by the spontaneous breaking of supersymmetry.

But, wait a minute. What are we actually talking about? We’re talking about accessible observations, okay, even if they hold in particle accelerators. It means, phenomena are reported to the 4-dimensional world. Where symmetry is MUCH lower than in an 8-dimensional world.

So, nothing actually prevent supersymmetry to hold (one says: to be restored) in its natural frame. And, again, only when we are back to our 4 accessible dimensions do we observe a breaking of this symmetry…

Could this be justified by group-theoretical arguments (underlying the concept of symmetry)?

Supersymmetry is supposed to combine “external” symmetries (i.e. 4D) with “internal” symmetries.

“External” symmetries are described by the Lorentz rotation group in a 4D world. This group has 6 rotation planes, 3 space-like and 3 spacetime-like (they mix a space dimension with a time one).

In an 8D world, the corresponding rotation group would have 28 rotation planes: that’s nearly five times more! 15 space-like, 1 time-like and 12 spacetime-like. Uh: a time plane appears, in addition!

One can reduce the number of rotation planes by nearly a half, going from real geometry to complex hermitian one. Without entering the details, the new symmetry group has 8 space-like planes, 1 time-like plane and 6 spacetime-like planes. And it’s more powerful than the previous one, because it exhibits properties that do not occur in real geometry!!!

Well, this last symmetry group, I name it, because it definitely has interesting properties: it’s the unitary group SU(3,1).

And it’s a nice candidate to the unification of the four fundamental interactions and fundamental matter too. Here, I cannot do otherwise than being a bit technical.

In previous posts, I talked about the canonical decomposition of that group:

 

(7)               SU(3,1) » SU_s(3) x SU_st(2) x SU_st(2) x U_t(1)

 

The sub-groups (restricted rotations) are respectively: space-like for SU_s(3) (the 8 planes above), spacetime-like for the two SU_st(2) (the 2x6 = 12 planes above) and time-like for U_t(1) (the time plane above). Remember how hard I wondered what the heck could the second SU_st(2) refer to? Well, if I write a second isomorphism (similarity in polite English…):

 

(8)               SU_st(2) » U(1) x Spin(1)

 

and insert this in (7), I find,

 

(9)               SU(3,1) » SU_c(3) x SU_w(2) x U_em(1) x U_g(1) x Spin(1)

 

Translation (! – from martian):

-         strong nuclear interaction [QCD – Quantum ChromoDynamics – model, symmetry group SU_c(3), here space-like];

-         weak nuclear interaction [the chiral model, symmetry group SU_w(2), spacetime-like];

-         electromagnetic interaction [Maxwell model, symmetry group U_em(1), spacetime-like];

-         fundamental matter field [Clifford spin group Spin(1), dimension 2, spacetime-like];

-         gravitational interaction [Maxwell model, symmetry group U_g(1), time-like].

 

All-in-one, provided we take for gravity the same linear model as for electromagnetism, which is not the end of the world, after all.

 

Otherwise said: the supersymmetric spacetime shows self-sufficient to unify all known fundamental fields of physics.

 

 

 

IV

BACK TO BIOPHYSICS

 

And now, we’re back to “down-to-earth” subjects. What possible implication on biophysics?

 

Let’s first retake our electron. We now assume it is an excited state. It will naturally de-excitate, producing a photon (a quantum of electromagnetic field):

 

(10)           e^- -> e^- + g⁰

 

In this reaction balance, energy, kinetic momentum and charge are conserved. Since e^- has spin ½ and g⁰, spin 1, spin will also be conserved provided that the de-excited electron has its original spin reversed: +½ -> -½ + 1. “conventional matter” emits “conventional radiation”, microscopic version of “matter emits a field”.

What does this become when super-particles are involved?

Let’s designate by E^- and G⁰ the corresponding extensions of the electron and the photon. If we report these super-particles to 4D components, we represent each of them as a doublet of particles, namely: E^- = (e^-,se^-) = (electron, selectron), G⁰ = (g⁰,sg⁰) = (photon, photino). The reaction above turns out to become:

 

(11)           E^- -> E^- + G⁰

 

Okay? Not difficult. We merely transcript. And this gives four possible reactions: (10) as above plus,

 

(12)           e^- -> e^- + sg⁰

(13)           se^- -> se^- + g⁰

(14)           se^- -> se^- + sg⁰

 

Let’s examine the three new ones. The photino sg⁰ has spin ½, it’s a particle of matter. So, (12) gives ½ -> ½ + ½ = 1 or ½ -> -½ + ½ = 0; The selectron se^- has spin 0, so (13) gives 0 -> 0 + 1: again, spin not conserved; finally, (14) gives 0 -> 0 + ½. In all three reactions, spin is not conserved, the reaction should not be allowed (extremely weak branching ratios). In (12), matter is therefore not expected to emit matter; in (13) and (14), radiation is expected to emit neither radiation nor matter. The only reaction likely to happen is matter emitting radiation, that is, (10).

But let’s now consider a de-excitation of sg⁰, since it has same spin as e^-:

 

(15)           sg⁰ -> sg⁰ + g⁰

 

or even any other neutral particle with spin 0 or 1 in place of the photon. This time, spin is conserved, just as in (10). To conclude, e^- and sg⁰ decay separately, both emitting a photon, while se^- cannot decay this way, it can only be emitting a spin-0 neutral particle, and this is precisely what theoreticians actually mean by “supersymmetry breaking”, because that spin-0 neutral particle is usually assume to be a Higgs particle, which is responsible for spontaneous symmetry breaking in the electroweak unified model of Glashow, Salam and Weinberg:

 

(16)           se^- -> se^- + H⁰

 

and the mass at rest of the H⁰ is much heavier than that of the electron. So, the inverse reaction is the absorption of a Higgs by a se^- with initially same mass as the e^-, leading to a massive selectron:

 

(17)           se^- + H⁰ -> se^-

 

To sum up:

 

-         4D “conventional matter” emits “conventional radiation” (we knew it, but it’s confirmed);

-         supersymmetry forecasts the existence of a “super-partner” to “conventional matter” as well as a “super-partner” to “conventional radiation”; the first “super-partner” is a radiation, while the second one is a matter field;

-         the super-partner of conventional matter emits conventional radiation.

 

This is the interpretation of things when brought back to a 4D world. In an 8D world now, there’s neither “super-matter” nor “super-radiation”, physical objects are both and none of them at the same time.

 

A biological body is a macroscopic object, no matter the complexity of it, we consider it globally. For electrically neutral macroscopic object, the only significant field produced is the gravity field of the object, and it’s produced by its mass. So, as any such object, the biological body produced its own gravitational field, which is a radiating field. In addition, each cell has an electric and magnetic activity, so that the organism as a whole does also produce an electromagnetic field but, as it is globally neutral, the biological body there behaves as a plasma, that is, electrical currents propagate inside of it but the resultant of these currents is zero, so that there’s no residual charge.

As we saw it above, none of these fields, the substantial biological one, the gravitational one or the electromagnetic one is and can be the “supersymmetric partner” of the biological body.

In a unified 8D world, there’s a single “body”.

In a restricted, accessible 4D world, there are two bodies: the biological one, which plays the role of the “conventional body” and a “super-partner”, which makes “another body”.

These two bodies are not entangled, so that they can “separate” (if any, which is not even necessary) and evolve entirely on their own. They both produce their own radiating fields.

In particular, consciousness, seen as a plasma of photons, has for super-partner a plasma of photinos, which is now substantial.

In other words: we have “dematerialized consciousness” on one hand and “materialized consciousness” on the other hand. However, this is far from being enough to make a complex organized body. To get one, we need to go into the details of the biological machinery, down to the atomic and molecular structure, because it’s all a question of spin. So, we have ions, molecules, proteins, and so on which behave like fermions if their resulting spin is half-integer and like bosons if their resulting spin is integer.

As the conventional body is a highly complex mixing of “matter-like” and “radiation-like” components, so is its super-partner.

Therefore, there’s no apparent physical objection to the making and existence of “second bodies”, assuming we work within the frame of supersymmetry.

For what concerns specific aspects of NDEs and other parapsychic phenomena now, they have to be examined one by one, but we can already see why we can legitimately expect a radical change in the laws of thermodynamics which are responsible for the alteration of systems and, ultimately, their “death”: in the supersymmetric world, there are two dimensions of time instead of one, as we saw it, implying two energies and two temperatures.

That new possibility of systems ruled by two temperatures means that, instead of “suffering” an “arrow of time”, from past to future, birth to death, there can now be loops in both times and temperatures, allowing to go back in time and in temperature without violating the laws of thermodynamics. As an immediate consequence of this, Boltzmann’s “H” theorem asserting that systems in contact with their environment can only increase in entropy (i.e. they can only go from a more ordered phase to a less ordered one) now falls into default, as it always becomes possible to reverse entropy. This means:

 

a)      “to beat death”;

b)      to become thermodynamically reversible, i.e. eternal.

 

Supersymmetric systems are neverending systems, precisely because they are unified systems.

 

Supersymmetry may also not be incompatible with that weird concept of “Light Beings” reported by NDE experiencers, if we interpret it as “Beings being both substantial and radiating at the same time, without the possibility to separate these two aspects”. Simultaneously “substance” and “light”.

 

Quite an interesting working frame, in the end.

 

But i had nothing new to bring so far, that's all. So, i spent these past months to review once again the mathematical tools at my disposal: as you could see reading the papers on this blog, i'm overall specialized in the study of structures.
Well, thus far, the spectral way seems to be the most convincing of all. In all cases, it's the only one able to justify the necessary presence of two bodies in the NDE experience. I found interesting properties of spectrum analysis that might bring nothing really new to the mathematics, but do bring a synthetized vision in physics, linking spectroscopy to the Heisenberg-Schrödinger's quantum description and Connes non-commutative spaces. I'll explaian this in more details in a paper to come, rather soon now, i think. The basic idea is that, separately, both ordinary space(-time) and spectral space(-time) are commutative worlds, while the transition between them is non-commutative. This loss of commutativity better explains, i think, the fundamental changes in the physical laws between ordinary and spectral frames.
Unfortunately, it still does not bring any satisfying answer to the processes reported in NDEs. One thing for sure: nothing happens in ordinary space-time. But i still have to understand why a wormhole should form, and where, and why the thermodynamical laws shouldn't apply anymore to spectral bodies. Until now, the only argument i found is purely physical and based on the fact that, assuming a spectral body (starting hypothesis) has nothing substantial, there can be no friction between its elements and therefore, no dissipation, making its entropy a constant. However, this explanation is not precised enough: i'd prefer to find physical mechanisms behind, that would justify it much better.
There it is for the time being. I should be back soon, hopefully with advances.
Hopefully... :)

We've been quite far in the analysis of the mathematical tools at our disposal in modern physics. We've investigated many aspects of the parasychological problem, in connection with neurobiology. It's now time to make a synthesis of all this and justify our choices.
 

We have a biological body, which is a (highly) complex autonomous system, able to self-regulate, interact with its surrounding environment and adapt to it. However, if we choose to consider it globally, we can "forget" about all this complexity and model it as a "macroscopic (touchable) matter", that is, as a mass distribution inside a finite volume of space with internal pressure p, temperature T and other thermodynamical parameters describing the different chemical concentrations. This is the "global" description of "substantial" matter.

Through its mass, this body produces a gravitational field. In addition, it has a nervous system, which produces an electromagnetic field through its electrical charges: the nervous system behaves like a "plasma", producing electrical currents, while keeping its global charge to zero [actually, all biological cells have an electromagnetic activity, but neurons are amongst those cells that are (re)activable].

These three complementary aspects of the animal body orientated us toward a macroscopic description of it with these three interacting components: substantial matter, G-field and EM-field. The complexity of the biological mechanisms inside the body demanded a generalization of the much-too-simple Maxwell model. We proposed such an extension, taking into account the feedbacks of the fields on their sources. As a result, any change in the behavior of, say, the field of consciousness, dynamically modifies the distribution of charges inside the nervous system, that is, active paths in the neuron graphs which, in turn, modify the field, and so on, until possible (but not systematic) equilibrium situations are found. Physically speaking, the memorization process can be described as a charge retention.

It goes the same for the G-field. Since its source is complex, so will it be. Any change in the distribution of substantial matter inside the body will then modify the G-field and back. This will be much less noticeable as the electromagnetic activity of the nervous system since the coupling constant of gravitation is far lower than that of electromagnetism. Still, it exists and we shouldn't forget about it, even if we can legitimately consider it's completely negligible in organic bodies.
 

Then, we introduced (or re-introduced) general relativity and we showed that elastic deformations of space-time were actually induced by material sources. The much larger freedom of choice in designating "matter" including, not only "substantial" one, but fields themselves, i.e. "non-substantial ones", showed that the induced deformations actually had nothing to do with gravity, which was now a source of space-time deformations like macroscopic matter and the EM-field. Our reviewed interpretation of GR was confirmed by the existence of non-trivial solutions of the Einstein equations keeping space-time plane (and not only flat) and that could therefore be produced by no kind of matter at all, may it be substantial or not.

When matter is present, it curves space-time. But we should be very careful which part of space-time we're dealing with. For the equations of GR with material sources actually describe the curvature of space-time inside matter.

Inside. Not outside.

Outside matter, the equations are those "in the vacuum".

And we can no longer superpose both types of solutions, for the equations of GR are no longer linear.
 

Why am i now strongly insisting on the qualitative difference between them?
 

Because i came to the conclusion that the only way to bring a physically consistent explanation of comas was to accept the idea that space-time was truly deformed inside the body.
 

I'd like to emphasize here the essential difference there is between psychotic behaviors and the NDE. Because there lays a possible explanation of the "Tunnel".
 

In psychotic behaviors, the patient has an altered perception of external surrounding space-time. These alterations are mostly due to dysfunctions inside the nervous system (severe disconnections of entire bundles of fibers in the brain, for instance). But it remains a mere perception of things. Actually, as we can check it, reality around us is altered nowhere. The patient incorrectly observes his environment, that's all. Inside and outside of him, there's no perceptible deformation of space nor time. The origin of this false, or pseudo-alteration, of both inner and outer realities is purely organic.

On the opposite, NDEs have nothing psychotic at all. The "Tunnel" can only form if, and only if, space-time inside the patient's body is significantly altered. In this case, the deformation of both space and time is not fictitious, but real. It's not perceived outside the patient, because it remains confined inside of him.

There can be no perceptive process anyway, since there's no more cerebral activity in the neocortex...

In the psychotic brain, there remains an activity, even if wrong.

In NDEs, we can no longer argue there's any. It just don't hold.
 

Why should space-time be altered inside the patient's body?

Because the functioning of the body is itself altered. As soon as it's placed in a coma state, even artificial, part if not all of the nervous functions are blocked. "Frozen". As they command all of the biological functions inside the body, this "freezing", even partial, has direct and quick consequences on the rest of the body. For instance, in "artificial coma" (anesthesia), both the sensor and the motor systems are blocked, so that the body is already no longer in «nominal» functioning.
 

The novelty holds in the fact that, opposite to what we could think, this restriction alone suffices to change the nature of space and/or time inside the body.

We indeed have to stick to the observational facts. And the facts tell us that, as soon as stage I, the patient looses the notion of time. Yet, outside his body, time keeps on being perceived the same. So, the change can only stand within him.
 

The physical explanation is to be found in the equations of GR inside his body, not outside.

We can restrict ourselves to a single thermodynamical parameter, the blood pressure p. Inside matter, the metrical coefficients describing the (local) deformations of space-time explicitly depend on p, g_ij = g_ij(x,p). The result is a family of metrics and not a single one, as would be in a vacuum: for each value of p, space-time inherits a geometry described with the metrical coefficients g_ij(x,p=cte). When p changes, these metrical coefficients can change and we go from a geometry to another one. For instance, g_ij(x,p=p₀) = g_0,ij(x) gives a geometry, g_ij(x,p=p₁) = g_1,ij(x) gives another.
 

If we agree with the classification of comas into 4 stages (which is not the only one possible), we need 4 critical values of p: p_c1, p_c2, p_c3 and p_c4. Each time the blood pressure falls down one of these critical values, the patient enters another stage of coma. At each critical threshold, something happens in what we call the «main directions» of the strain quadric, i.e. in at least one of the diagonal coefficients g_ii(x,p). Let us detail this, in the transition model based on pressure.
 

In the awaken state of consciousness we can classify as «stage 0», the sane patient perceives time and space as should be. This is described by g₀₀(x,p) > 0 and g_aa(x,p) < 0 (a = 1,2,3).

When p reaches the first critical value p_c1, g₀₀(x,p_c1) vanishes, while g_aa(x,p_c1) remains < 0. This vanishing is sufficient to deeply change the properties of space-time inside the body, because it means that, at p = p_c1, «the notion of time disappears».

Between p_c1 and p_c2, g₀₀(x,p) becomes < 0, meaning the patient looses the notion of time. He keeps that of space, since g_aa(x,p) remains < 0. He can remain perfectly conscious (at least in his subconscious) he’s having a surgery, he can even ask the medical staff questions sometimes (he won‘t remember), but he has no idea of how long it takes.
 

It should already be clear we changed geometry since, above p_c1, we had one time dimension and 3 space dimensions and, below p_c1, we get four space dimensions.
 

Let’s argue that, at p = p_c2, the patient also looses the notion of space itself. He enters stage II, «light coma», g₀₀(x,p_c2) remains < 0 and at least one of the three g_aa(x,p_c2) now vanishes.

Between p_c2 and p_c3, he’s in stage II, he has lost both the notion of time and that of space, because we now have g₀₀(x,p) < 0 and (at least one of the) g_aa(x,p) > 0. It wouldn’t mean much to interpret it saying «he now has the notion of only one space dimension and (between one and ) 3 time dimensions».
 

At p = p_c3, he enters stage III, «deep coma». There, g₀₀(x,p_c3) is still negative, but g_aa(x,p_c3) vanishes again. The patient «begins to recover the notion of space».

Between p_c3 and p_c4 we will set to zero, he still has no idea of time, but has that of space again, since g_aa(x,p) < 0 again.
 

At p = p_c4 = 0, he’s in stage IV. There, g₀₀(x,0) = 0, while g_aa(x,0) < 0.
 

Let us proceed «　stage by stage　» :).
 

Each time one of the diagonal coefficient g_ii vanishes (i = 0,1,2,3), we stand on a «critical hypersurface». As we want GR to hold whatever the pressure, from above p_c1 down to zero included, the determinant of the metric, g(x,p) = det[g_ij(x,p)] is expected to remain < 0 for all p. This means we exclude «essential singularities», that would set GR into default. What we get instead, which is physically meaningful, is a «fictitious singularity» at each critical value of the blood pressure. Such a fictitious singularity, or critical hypersurface (of dimension 3), precisely indicates a change in the geometry of space or time.
 

However, we have to slightly modify the usual definition GR gave of a fictitious singularity.
 

In the original theory of GR founded on changes of coordinate systems, such a singularity was defined by:
 

THERE EXISTS A LOCAL COORDINATE SYSTEM IN WHICH THE ZEROS OF THE gii(x) ARE REPLACED WITH NON-ZERO VALUES.

In other words,
 

THE VANISHING OF AT LEAST ONE OF THE gii(x) IN A GIVEN LOCAL COORDINATE SYSTEM ONLY INDICATES THAT THIS SYSTEM IS NOT THE SUITABLE ONE.

In an adapted system, none of the g_ii(x) vanish. The (more than familiar) example of this is the static black hole: in the Schwarzschild system (spherical coordinates + time), a singularity appears at a distance-to-the-centre equal to the gravitational radius of the source body. This singularity is seen to be fictitious because g(x), the determinant of g_ij(x), does not vanish at r = r_g for as much. Going then from the Schwarzschild system to the more adapted Lemaitre system of local coordinates, the singularity in question disappears and light rays are found instead.
 

We have to modify this definition for we’re no longer playing with coordinate systems, but with true physical deformations (or strains) of space-time. In this context, we will rather say:
 

A SINGULARITY IN THE METRICAL PROPERTIES OF SPACE-TIME WILL BE CONSIDERED «FICTITIOUS» IF THE DETERMINANT OF THE METRICAL TENSOR REMAINS < 0, SO THAT ONE CAN ALWAYS FIND A LOCAL STRAIN FOR WHICH THIS SINGULARITY DISAPPEARS TO THE BENEFIT OF NON-ZERO, FINITE AND SIGN-DEFINITE VALUES.

Indeed, if you go back to the previous bidouille, you will realize that we have established the following result:

 

THERE EXISTS A NON-TRIVIAL LOCAL STRAIN FOR WHICH SPACE-TIME REMAINS PLANE.

Well, at each critical values of the blood pressure of our model of comas, there always exists a local strain y(x) for which the zeros disappear, regularizing geometry.
 

To obtain a Tunnel at p = 0, i have two options.

Whether i exclude that final critical value from the three other fictitious and consider we now face an essential singularity, for which g(x,0) = 0 and then i’ll have (unsolvable) problems with the equations of GR, as the inverse of my metrical tensor won’t be found, or

i consider it the fourth fictitious and its regularization should have the topological S²xR symmetry: a 3D spatial sphere as basis and time as axis. With g(x,0) < 0 and finite, there necessarily exists a local strain for which the tube structure appears.
 

And we get what we call in astrophysics a wormhole. A «tunnel» through space and time.
 

Why should this tubular structure appear only at stage IV? Good question. The answer might be found in the set of all coupled field equations in curved space-time: the 10 GRs, the 4 complex Gs, the 4 complex EMs + the equation of state and the 4 equations of motion for substantial matter. A total of 23 strongly non-linear coupled equations. Good luck...

All i can say is that no testimony so far as ever evoked a Tunnel in any other stage of coma. Not all NDEs have a Tunnel: it may not even be systematic. Some patients have nothing particular to report.

The answers surely lay in the complexity of the metabolism.

 

　

　

　

Mostly text today, as calculations are easy and i would prefer to discuss the point.

There's already a bidouille about zero-energy motions. We're now going to talk about zero-curvature space-times. That is, plane space-times. I'll limit myself to 4D space-times, as generalization is straightforward.

Let then M be a space-time with a single time dimension and 3 space dimensions, x a point of M (anywhere) and y(x) a deformation sending that point x onto the point x'(x) = x + y(x). We compute the metrical tensor g_ij(x) from the surface element around x'(x) and derive the Christoffel symbols C_k,ij(x). The result is very simple:
 

(1)     C_k,ij(x) = [g⁽⁰⁾_kl + d_ky_l(x)]d_id_jy^l(x)

where g⁽⁰⁾_kl is, as usual, Minkowski metrical tensor.

The question i asked myself was: are there solutions of
 

(2)     C_k,ij(x) = 0     globally on M

other than the trivial translation y(x) = a = cte?

The answer is yes. There are even plenty of such solutions, with the form:
 

(3)     yⁱ(x) = aⁱ + S_n=1^N aⁱ_i1...inxⁱ¹...xⁱⁿ/n!

with N finite or not. And these are the only possible solutions. Calculating for the first and second derivatives and inserting them into (2) leads to a set of 2(n-1) conditions on the coefficients of (3). We can check that the first derivatives of the Christoffel symbols then globally vanish, so that the Riemann curvature tensor is indeed everywhere zero, making M plane. Yet, not only is there a deformation in M, but it can be highly non-linear. Physically, this means that not only is M elastic, but it's also plastic!

All this is essentially due to the pseudo-Euclidian geometry of M. In Euclidian geometry, we can easily verify that all coefficients of (3) but aⁱ and aⁱ_i1 vanish, reducing the deformation to a translation + a dilatation/contraction. On the contrary, in pseudo-Euclidian geometry, squares like V^lV_l are no longer positive-definite, leading to new possibilities (light-like ones).
 

It was quite natural for me to wonder what the hell could well be those deformations not affecting the geometry of M anywhere. Indeed, if M was to remain elastic and even plastic, we should expect it to curve...
 

The thing is, (3) describes a anharmonic (= multi-frequency) spring. The pullback is guaranteed by the non-negative powers of the xⁱ. It’s a typically confined solution. The only satisfying physical interpretation i found was that the higher the order N, the more rigid M.

In other words, the development of (3) in higher and higher powers reinforces the flatness of M, assuming, of course, the coefficients satisfy (2).

We can as easily check that all negative powers of the coordinates, leading to non-confined solutions, can never satisfy (2) everywhere, so that M is always curved.
 

This thoroughly changes the familiar picture of flatness we have: reasoning on the metrical coefficients as the «field potentials» of the geometry of M, we consider flatness as constant metrical coefficients.

But the deformation y(x) is more fundamental than the metric. And variable deformations of the form (3) all lead to flatness, despite the metric is variable. This means that these variations actually do not contribute to the curvature of M. In the opposite, they make it more and more rigid.
 

This mechanism might explain how a stochastic geometry of space-time induced by a genuine vacuum could lead to a flat geometry afterwards. The stress tensor field T_ij(x) can always be defined as the invariant of the elasticity tensor field T_ijkl(x) of M:
 

(4)     T_jl(x) = T_ijkl(x)g^ik(x)

If we want the Einstein equations to hold in M, we must connect this elasticity tensor field to the curvature tensor of M, with the same symmetry properties. This is done through a linear combination of R_ijkl(x) and its invariant, the Ricci curvature tensor R_ij(x) and the Gauss scalar curvature R(x). Now, if R_ijkl(x) is to vanish everywhere on flat space-time, the stress tensor field T_ij(x) must equally vanish. This confirms the fact that a plane space-time is necessarily empty of any kind of matter. But, more fundamentally, T_ijkl(x) vanishes everywhere, so that all elasticity coefficients of M are identically zero.

Limiting ourselves to N = 2, which gives a harmonic oscillator, we can reduce (3) to the canonical form and see no coordinate transformation can globally eliminate the deformation: there is a deformation of M, and a variable strain tensor (the metrical one), but it’s induced by no matter, leads to no curvature and gives no information at all on the elastic properties of M.
 

I’d like to end this short paper making a remark about Einstein’s equations. We use to say that they only give informations on the local geometry of space-time. I disagree. Einstein’s formalism is based on the Riemann axiom. Locally, i.e. in the immediate neighbourhood of any point of M, we can always find a coordinate system in which the Christoffel symbols will vanish. However, their first derivatives won’t vanish simultaneously. First of all, it’s therefore a question of reasoning on fixed points of M (despite it has also been shown that this holds on geodesic paths) and, in any of such neighbourhoods, the Riemann curvature tensor is linear and so are its invariants. Consequently, Einstein’s equations are locally linear. So, if we deal with the non-linear set of equations, it automatically refers to the global geometry of space-time, since only globally can’t the Christoffel symbols be eliminated.
 

Another feature surprises me too.
 

Einstein’s reasoning is based on Newton’s Equivalence Principle. From the equality between the inert mass and the «heavy» mass, he deduced that gravity behaved like a «pseudo-force», a «force of inertia», according to D’Alembert’s terminology, and this led him to bring gravity back to a mere effect of the geometry of space-time. The argument was that we could always find a local reference frame in which «we no longer feel the force of gravity», orientating toward the Riemann axiom of geometry. Kaluza and al went even much further, turning all physical forces into geometrical effects.

This really surprises me since, when you feel gravity («feet on the ground»), whatever the coordinate system you choose, you keep on feeling gravity, or you would «loose yourself in space»...

Now, if you have a force opposing gravity, as soon as this force has equal magnitude than that of gravity, you obviously «levitate». Whatever the coordinate system you choose...

It’s not a question of coordinate systems, but of equilibrium: if the system of forces is in equilibrium, if there’s a force exactly compensating for gravity, you no longer feel it.

Because the point is, if you all bring back to mere geometrical effects, you end in doing «pseudo-physics», with «pseudo-fields» and «pseudo-forces»... everything resulting from inertia...

But, if gravity was a «pseudo-force» then, according to Einstein’s equations, the «matter field» would necessarily be «pseudo» as well.
Well, that’s precisely the idea underlying supersymmetry, with its Kähler geometry!!!
Turning all real physics into «pseudo»... fundamental interactions as curvatures of space-time, fundamental matter as torsion of space-time...
 

So, what are we to do? (3) above shows without ambiguity that deformations of space-time have nothing to do with coordinate transformations, nor with any matter... The presence of multiple-order deformations in flat space-time is only due to its non-Euclidian nature. Nothing else.

If we are to review the context of GR, we have to come back on the concept of motion in a curved space-time.

We started from the principle that a matter field, whatever its nature, causes local deformations in the space-time structure. A point x of space-time is therefore sent onto a point x'(x) = x + y(x), according to deformation theory. That point x is now fixed, it's not mobile anymore. If dx is a small variation around this fixed point x, the corresponding variation around x'(x) will be dx'(x) = dx + dy(x) and the metrical tensor of curved space-time will be expressed in terms of the derivatives of y(x) along all four directions of space-time.

But this has nothing to do with the motion of an incident point-like body in a gravitational field. This now refers to the elastic property of space-time under an "external" constraint, namely, the presence of matter within the frame, or even "intrinsically", in the absence of any «perturbation».

This is a radically different approach of the problem of GR. The equations of motion for material bodies are contained in the conservation law for the energy-momentum tensor of the matter field:
 

(1)     DⁱT_ij(x) = 0

where D is the Levi-Civita covariant derivative associated with the curved metric. They have nothing to do anymore with the geodesic equations:
 

(2)     Duⁱ/ds = 0
 

in curved space-time.

In the absence of deformations, x’(x) = x, space-time is plane and the metrical tensor is Minkowski’s. The dual of xⁱ = (ct,x) is x_i = g⁽⁰⁾_ijx^j = (ct,-x) and it’s everywhere the same.

In the presence of deformations, i can build my curved surface element two equivalent ways: whether keeping Minkowski’s metrical tensor g⁽⁰⁾_ij and using coordinates x’ⁱ(x) or keeping my genuine coordinates xⁱ and introducing a variable metrical tensor g_ij(x),
 

(3)     ds²(x) = g⁽⁰⁾_ijdx’ⁱ(x)dx’^j(x) = g_ij(x)dxⁱdx^j

Developing the first expression gives me:
 

g⁽⁰⁾_ij[dxⁱ + dyⁱ(x)][dx^j + dy^j(x)] = g⁽⁰⁾_ij[dxⁱdx^j + dxⁱdy^j(x) + dx^jdyⁱ(x) + dyⁱ(x)dy^j(x)]

= g⁽⁰⁾_ij[dxⁱdx^j + dxⁱ(dy^j/dx^k)(x)dx^k + dx^j(dy^i/dx^k)(x)dx^k + (dyⁱ/dx^k)(x)(dy^j/dx^l)(x)dx^kdx^l]

= g⁽⁰⁾_ij[dⁱ_kd^j_l + dⁱ_l(dy^j/dx^k)(x) + d^j_l(dyⁱ/dx^k)(x) + (dyⁱ/dx^k)(x)(dy^j/dx^l)(x)]dx^kdx^l

so that
 

(4)     g_kl(x) = g⁽⁰⁾_kl + 2g⁽⁰⁾_j^l(dy^j/dx^k)(x) + g⁽⁰⁾_ij(dyⁱ/dx^k)(x)(dy^j/dx^l)(x)

Careful: this is not a usual coordinate transformation, as in the Einstein-Grossmann context, but a true local disturbance of the Minkowski metric!
 

The unit tangent vector is defined as the ratio of the variation dx’(x) around x’(x) on the variation ds(x):
 

(5)     uⁱ(x) = dx’ⁱ(x)/ds(x) = dxⁱ/ds(x) + dyⁱ(x)/ds(x)

when y(x) is everywhere zero or even constant, which corresponds to a mere displacement in space and time, g_kl(x) = g⁽⁰⁾_kl, ds²(x) = ds(0)² = g⁽⁰⁾_ijdxⁱdx^j and uⁱ(x) = dxⁱ/ds(x) is the unit tangent vector defined in the neighbourhood of the fixed point x.

You’ll have noticed that this unit vector is no longer a function of the curvilinear distance s, as in the problem of motion, but a field over points of space-time. There’s no motion of any material objects there, substantial or not. That kind of motion is in (1). The «motion» (5) stands for deformations of the frame. It can happen with or without matter. However, as before, equations (1) tell us that a given matter distribution will locally affect the flatness of space-time, which in turn, will affect the matter distribution, and so on. Consequently, the motion of any point-like body will be affected by these local deformations.
But the dynamics of fields as well.
 

It’s still possible to link uⁱ(x) to a velocity. But this will now be a velocity field, first, and it will relate to the speed at which space-time deforms. The velocity of point-like bodies stands in the energy-momentum tensor. It’s like making the difference between the velocity of electrical charges and the phase velocity of the electromagnetic field produced. The geodesic equations:
 

(6)     Duⁱ(x)/ds(x) = duⁱ(x)/ds(x) + Cⁱ_jk(x)u^j(x)dx’^k(x)/ds(x) = duⁱ(x)/ds(x) + Cⁱ_jk(x)u^j(x)u^k(x) = 0

now serve determining the smallest deformations and can give indications on the «accelerations» of deformations.
 

This autonomous dynamics is obviously independent from any mass. It has nothing to do anymore with the Equivalence Principle asserting that the «　weighting mass　» equals the «　inert mass　», a principle that concerns gravitation, not space-time elasticity...