After being absent of the blog for a VERY long time, but not without actively researching for as much, I’m back with a HUGE problem on complex numbers and that’s why I’d like to be back to the old “bidouille” B32 [inside which you’ll be kind enough to replace, in eq (20), T’_-+^- with -T_-+^-]. Here’s indeed a reasoning that leads to a stunning contradiction within the structure itself of the algebraic field C.

 

If we combine the cyclic properties of the imaginary unit i:

 

(1)               i⁰ = 1 , i¹ = i , i² = -1 , i³ = -i , i^4+k = i⁴i^k = i^k

 

for all non-negative integers k, with the relation out of the de Moivre formula,

 

(2)               i = e^ipi/2

 

We’re led to:

 

(3)               pi = 0…

 

which is obviously absurd. Let’s prove it straight away.

 

Eqs (1) shows a base-4 cycle on the integer powers of i. (1a) is not only a convention, it’s also proven by the behavior of power functions near the value zero of the argument. (1b) is the very definition of i as the “imaginary unit” within the field C. (1c) is Cardan’s original definition. Finally, (1d) is the combination of (1a and b), which also defines the complex conjugate of i.

 

Eq (2), again, really looks like a wonderful formula, linking the only two known irrationals e and pi to i. So, let us now use that last relation to compute iⁱ:

 

(4)               iⁱ = (e^ipi/2)ⁱ = e^i²pi/2 = e^-pi/2

 

The result is real-valued and, apparently, irrational. The fact that it’s real-valued is already quite surprising, from a conceptual viewpoint. But, anyway. Let’s take the square of (4):

 

(5)               (iⁱ)² = i²ⁱ = (i²)ⁱ = (-1)ⁱ = e^-pi

 

The problem arises with the square of that square:

 

(6)               (iⁱ)⁴ = i⁴ⁱ = (i⁴)ⁱ = (+1)ⁱ = e^-2pi

 

Let’s point out that we only used here the algebraic properties of the elevation to a power. Now, (+1) elevated to any power, real or complex-valued, should, by definition, give +1. So, we should have:

 

(7)               (+1)ⁱ = +1

 

immediately inducing (3) after taking the Neperian logarithm of (6).

 

Search for the error… I did, and didn’t find any… This totally absurd result is not even due to the cyclic property (1e) or only partially. The true responsible is actually the rule of signs on the multiplication table for real numbers:

 

(8)               (-1)(+1) = i²i⁰ = i² = (-1)  ,  (-1)² = i²i² = i⁴ = i⁰ = +1  ,  (+1)² = i⁰i⁰ = +1

 

which perfectly works when extended to the imaginary unit.

 

In any case, cyclic properties (1), which are formally equivalent to a modulo 4, more than clearly show that i should now be taken as a more fundamental unit than +1 and -1, since both can be generated as integral powers of i. Furthermore, cyclicity offers an infinite countable way of obtaining -1 and +1. In R, we only had a modulo 2 cycle:

 

(9)               (-1)⁰ = +1  ,  (-1)¹ = -1

 

And, because C was built as an algebraic field, it’s both a unifere and integer ring, meaning all its non-zero elements are invertible and it has a unit one. Which should be?... +1, -1, i or 1 + i? The inverse of i is defined (and obtained) as:

 

(10)           i^-1 = i* = -i = i³

 

because of (1e) for k = 0. It’s also confirmed by (2).

 

Get me right: if there had been any contradiction in the algebraic laws upon which C was built, it would have immediately been detected (and corrected). What leads to the absurd result (3) is actually a consequence of the construction of that algebraic field basing oneself on the choice of a unit number: C was actually built mixing real numbers with new ones, the square of which were allowed to be negative, so that C appeared as an algebraic extension of R. But we still need to know which element is to play the role of a unit… K If it’s i, since it looks more fundamental than +1 and -1, then we should find i² = i and i^-1 = i, by the very definition of a unit element…

 

SO… folks… should we REALLY forget about “complex” numbers?... I’m just wondering about this, because we have CONCRETE (and no longer “imaginary”…) CONSTRUCTION PROBLEMS…

 

And I discovered that one only because I was after a physical significance of i. Before quantum theory, i was used as a mere convenient math tool to easy calculations but, ultimately, classical waves appeared as real-valued trigo functions: cos, sin, tan,… Since quantum theory and the de Broglie “wave-corpuscle duality”, it little by little became obvious that we could no longer satisfy ourselves with the “real-part” of a math wave, but that we really had to take both the real and the “imaginary” parts into account and on an equal footing. This, because quantum waves behave like refraction index: they have a “refraction” component and a “reflection” one, and you just can’t neglect the second one. This was going in the direction of i acquiring a physical content, as a “fundamental quantum unit”, namely [see (2) once again], as a quantum wave with unit amplitude and constant phase (or “quantum state”) pi/2. There was no classical equivalent to that wave, since it’s real component is zero…

 

Unfortunately, there are obvious contradictions within the construction of C that does not allow me to go further in that direction.

 

Maybe I’ll need to go back to B32. Maybe I’ll instead have to change from R to R². After all, this is the same as “doubling R” and it’s even much cleaner than identifying C with R². And use M₂(R), where units are correctly defined, for operator ring acting upon 2-component vectors of R².

 

However, the distinction between “classical” and “quantum” will need to be reviewed, because it will then be far less obvious than when introducing an “imaginary unit”.

 

BACK TO THE “POLARITIES” PROBLEM

 

 

 

I’ve studied many times before what I called the problem of “polarities”, in a different sense than the one usually refers to in particle physics (and related to intrinsic rotational momentum of particles – or “spin”). What I mean by “polarities” here refers to the sign of masses or, equivalently, of energies.

Mass is not to be confused with substance: it’s only a property of substance (as is the electric charge or more complicated charges). Besides, we say that a physical body “carries” a mass.

However, the type of substance will set the sign of its mass (opposite to all other charges) and, reciprocally, knowing the sign of a mass will determine the kind of substance we’re dealing with. It’s usually assumed (one more convention) that the sign of “substance” (matter or radiation) is positive or zero, while the sign of “anti-substance” (antimatter or anti-radiation) is negative or zero.

Galilean physics (space relativity, universal time) assumes that all masses are strictly positive and, indeed, human-scale or cosmological-scale antimatter has never been observed so far. This does not mean for as much there isn’t in our observable universe, but this is now assumed to be very unlikely for, if there was, there would unavoidably be interactions between that antimatter and nearby matter, so that huge radiative jets would be detected with today’s equipment.

This “no see” fact is, after all, rather logical. If we’re fair enough, at the best, only fundamental particles can be considered as keeping a constant mass (off interactions, of course, in which case, there are transformations). All other bodies have a more or less variable mass. Mass varies in time simply because there are no closed systems (apart, maybe, from the whole universe itself), so that physical systems exchange with their surrounding environment and this results, in particular, in substance transfer: you feed, you gain mass (in our approximately constant earth gravity field, this can be seen as equivalently saying we gain weight); you starve, you loose mass (or weight). According to the direction the substance current points towards, substance is brought to a system (from the outside environment into the system) or leaves that system (from the system into the outside environment).

It’s common sense that, given a system with initial mass m(0) > 0, if this system keeps on loosing substance in time, there will be an instant, say t_f (“f” for “final”) when there’s no more substance inside the system’s volume: m(t_f) = 0. It’s then perfectly logical (and fully observable too) to consider there’s no system anymore... So, it would be difficult to take any more substance out of a substance-free volume... That’s the main reason and justification why mass, in Galilean physics, is set to always be strictly positive, whatever its evolution in time: “you can’t loose more than what you have”.

Space-time relativity (Galileo + relative time) does not change this vision of things, despite the famous energy relation E² = p²c² + E₀² with E₀ = m₀c² the “energy at rest” of a physical system (m₀ its mass at rest and c, the velocity of light), enables both signs:

 

(1)               E² = p²c² + E₀²  =>  E_± = ±(p²c² + E₀²)^1/2

 

(and diametrically opposite too) so that, if you set the momentum p to zero (in which case, your system is fixed in space), then (1) gives you:

 

(2)               E_± = ±(E₀²)^1/2 = ±|E₀| = ±|m₀|c²

 

Absolute values of the energy and mass at rest, up to the sign. These are the mathematically allowed solutions to the quadratic (“power 2”) relation (1). Classical spacetime relativity keeps only the (+) solution, still sticking to Galileo’s frame.

Quantum physics allows negative masses, because their justification is now based on a different assumption. The quantization process takes the energy and momentum of a classical system and puts them into the phase of a “wavefunction”, a process known in mathematics as “exponential lifting” (I shall not elaborate here, it’s in all refs online – and extensively on this blog as well - !). As quantum physicists use signals and signal couplings (to describe particle interactions), there’s no more “physical obstruction to the law of common sense” in changing the sign of the phase: both signs are perfectly observed and the same way. As a result, if you keep the same orientation for your space and time, then a change of sign on the phase will change the sign of your momentum (space related) and energy (time related).

Should I precise here that we’re actually talking, from the beginning, of free systems.

The problem on the sign of mass (or energy) concerns free (i.e. non interacting) systems.

In linked systems of bodies, a negative energy of the system is accepted (and observed!) as soon as Galileo’s space relativity. It’s even what characterizes linked systems: that, to set components free (to “dismantle the system”), you need to bring positive energy to that system, from the outside.

The dilemma was on free systems. Classical physics did not observe them. The best spacetime relativity brought was to accept fundamental waves like electromagnetic or gravitational ones as massless substances. “Immaterial”. It allowed the possibility that m₀ = 0, under the (less than “mathematically correct”) condition that such substances “moves” through space at the speed of light. It holds because, so far, no massive bodies have been found to move at c (as Heisenberg said of the Planck constant h and quantum “wave mechanics”, “it holds because that’s what we observe”... – at least, it had the merit of being honest, recognizing the fact that nobody could explain why it was so – which is still the case).

 

However, all this (Galileo, Einstein, quantum physics) was developed (because observed) in a 4-dimensional real geometrical frame.

It no longer holds in a 4-dimensional complex geometrical frame... even if we assume the “hermitian” hypothesis, which is the (very rude) mathematical translation for “mirror symmetry” (the name comes from mathematician Hermite). Usually, theoretical physicists continue assuming real-valued masses. But it’s no longer a pre-requisite, even under super-symmetry, where the masses of partners are equal.

 

Let’s review once again the connections between dynamics and geometry. It goes back up to the late 18^th century – early 19^th, when people began to use the geometrical tool to describe dynamics. As geometry was quickly progressing, they found it useful to “code” dynamics into geometrical terms. So, they intensively began developing a multitude of spaces with geometries suitable for the type of dynamics they were studying. The result was called “analytical mechanics” and received most of its contributions from people like Lagrange, Hamilton and Jacobi, all along the 19^th century. They based themselves on works from geometricians like Gauss, Riemann and (much later, in the second half of the 20^th century) Grassmann. Jordan, not-the-NBA-but-mathematician-trained superstar turned physicist (shame!... what do I say? HERESIA!), brought matrix theory to the quantum formalism in the late 1920s, following 1926 Heisenberg’s description.

Little by little, they came to the following correspondences:

 

Riemann’s geometrical axiom <-> commutative geometry [xy = yx, see B131, formula (1) or (2)] <-> spaces with a symmetric metric <-> radiations (Bose-Einstein stat, integer spins);

Grassmann’s geometrical axiom <-> anti-commutative geometry [xy = -yx, B131, formulas (3) or (4)] or “projective” geometry (because related with projections onto planes rather than axis) <-> spaces with a skew-symmetric metric <-> matter (Fermi-Dirac stat, half-integer spins);

Kähler’s geometrical axiom, a synthesis of the preceding two, with “enough good regularity conditions” (“smooth” spacetimes or “continua”) <-> complex geometry <-> spaces with a hermitian metric <-> supersymmetry between matter and radiation.

 

It’s worth noticing that Grassman’s geometry was required in connection with the so-called “phase spaces” of analytical mechanics. Typically, these are spaces where the complete “classical” motion of a given body or system of bodies is well described in geometrical terms. To describe such motions, we need to determine, following “classical” laws of motion, both the position of a system in space (or spacetime) and its “quantity of motion” (momentum, the product of mass with velocity, or energy-momentum in spacetime dynamics). This doubles the number of required dimensions of the “configuration space”, as there are as many momentum components as there are coordinates of position, but it does not endow that “enlarged” space with a complex structure for as much. What we get instead is a “symplectic” structure (another vulgar math term) that describes the dynamics in a “space of planes” (planes come to replace axis for “coordinate systems”) and the geometry of such spaces no longer obeys Riemann’s axiom, but rather Grassmann’s. The connection with quantum mechanics was later made when people realized that the spin of a particle can be used as the classical “rotational momentum”, vector product [see B132, § beginning with “but let’s now reverse the problem”, before formula (6)] of the position and the momentum of the system and this, despite the fact that the spin is a purely quantum quantity with no classical equivalent. Hence the use of “q variables” or “coordinates” for spin-1/2 (the most fundamental half-integer spin), with anti-commuting properties and the connection I made in B131, formula (5) between these anti-commuting variables (measured in m^1/2) and “more familiar” commuting variables xⁱ⁺⁴. What enables this are the Pauli “transition” matrices.

 

I had to explain all this before coming to the subject, or the non-familiar reader would have understood nothing (and still, I hope he grabbed something of the brief introduction I made!).

 

What comes directly out of complex geometry is that objects remain single (it’s very important to keep this in mind) but, when projected onto real sub-spaces, they become double: we find what we call in maths a “real part” which is here the state-(1) component of a super-quantity (in z = x+iy, it’s then x) and an “imaginary part” which is the state-(2) component of that super-quantity (that is, y).

And this is pretty understandable, if we think of it carefully. If the frame itself, that is, space and time, is to mathematically complexify, it physically means it oscillates: complex geometries are the siege of oscillating spaces, times and spacetimes. So, if the frame is the very first one to oscillate, then we can legitimately expect that any object, any event and any process within that frame will oscillate as well. We can have amplifications or dumpings, but we will always have, in addition, an oscillatory behaviour that we will never be able to suppress, whatever we do or try: objects become signals and signals become objects.

The supersymmetric frame is “essential fundamental”. It is so fundamental, “in essence”, that it actually gives birth to both matter and radiation. It’s a very “primitive” frame, in the sense of “original”. From this 4-dimensional “oscillating” frame emerge, as 4-dimensional “projections” into real sub-spaces, both matter and radiation fields. The supersymmetric association between them then says that, what is observed as behaving like “matter” (resp. “radiation”) in one of the two available “sub-worlds” will behave like “radiation” (resp. “matter”) in the other sub-world.

 

However, there’s more. Much more. Supersymmetry does not “only” unifies matter and radiation, giving unidentifiable very primitive substance that vaguely resembles “radiating matter” or “material radiation”, to give a rough idea of it (but is actually none of these), it also unifies substance and anti-substance. Yes, dear. And this is thanks to that “new math operation” called complex conjugation, which becomes an inherent property of supersymmetric spacetimes (whereas it desperately remains an “external” operation in real sub-spacetimes). We saw this in formula (7), B132. What complex conjugation does is it reverses the sign of the state-(2) component, while keeping that of the state-(1) component unchanged:

 

(3)               q -> -q  => x -> x , y -> -y

 

It’s also possible to reverse the sign of the state-(1) component while keeping that of the state-(2) unchanged, but it’s a bit more complicated and requires some additional operation. To go from z = x+iy to –z* = –x+iy, we first need to perform complex conjugation, then reverse the sign of the result (z*). As i² = -1, we can also write our result under the form –z* = i²z*. We then use the remarkable (in all sense) properties of the two known (up to now) irrational numbers, e = 2,718281828456... and p = 3,1415926535... which, combined with the imaginary unit i give this:

 

(4)               e^ip = -1  ,  e^ip/2 = i

 

(the 3^rd known fundamental number, the Euler number, is still not formally proven to be an irrational). These above formulas are truly remarkable and probably amongst the most remarkable ones in mathematics, as they “close onto each other”. Applying (4a) to our result gives us –z* = i²z* = e^ipz* = e^ipre^-iq (in polar representation) = re^i(p-q) (additive properties of the argument of the exponential function), that is, a phase shift of p-q from the original angle q. As a conclusion, to reverse the sign of x without touching that of y, we need reverse the sign of the phase angle q of our supersymmetric quantity z, than shift of +p or 180°.

What does this all mean?

It means that, when it comes to considering a quantity like mass, we now have to deal with an oscillating mass:

 

(5)               M = m₁ + im₂ = mexp(iq) = mcosq + isinq

 

measuring the amount of “substance” contained inside an oscillating “super-object” (with an oscillating volume, by the way) and only the magnitude m of that mass, which is a real-valued quantity, is assumed to always be positive or zero. This is because the sign of the magnitude doesn’t matter anymore, since it’s now assured by the value of the phase angle q, so that m can always be set non negative once for all:

 

-         if 0 < q < p/2 (sector I on the unit-radius circle), both m₁ and m₂ are > 0, this is interpreted in sub-worlds as “matter and radiation”;

-         if p/2 < q < p (sector II), m₁ < 0 while m₂ > 0, “antimatter and radiation”;

-         if p < q < 3p/2 (sector III – diametrically opposed to sector I), both m₁ and m₂ < 0, “antimatter and anti-radiation”;

-         if 3p/2 < q < p (sector IV – diametrically opposed to sector II), m₁ > 0 while m₂ < 0, “matter and anti-radiation”.

 

Special values are for (up to 2p):

 

-         q = 0, m₁ = m > 0, m₂ = 0 (massless substance);

-         q = p/2, m₁ = 0, m₂ = m > 0;

-         q = p, m₁ = -m < 0, m₂ = 0, and

-         q = 3p/2, m₁ = 0, m₂ = -m < 0.

 

We can already combine “everything with everything”: substance, anti-substance, massless substance, which, again, is nothing craft ;) but perfectly logical: if “super-substance” is to give birth to both matter and radiation, it has to give birth to antimatter and anti-radiation just the same, “in an equal way”, since the sign attributed to a substance is, after all, a mere question of human convention: we would have chose the (-) sign for all the substances we observe “at our scale and beyond it”, we would have counted masses with a common negative sign...

Notice that sectors are well defined and delimited:

 

-         adjacent sectors I and II are separated by q = p/2 (turning round counter-clockwise or trigonometric sense), where state-(1) is filled with massless bodies (such as photons, for instance, quanta of electromagnetic light);

-         adjacent sectors II and III are separated by q = p, where state-(2) is filled with massless bodies;

-         adjacent sectors III and IV are separated by q = 3p/2, where again state-(1)’s filled with masless bodies;

-         finally, adjacent sectors IV and I are separated by q = 2p (or 0, since we’re back to our starting point – we’ve accomplished a complete turn round the “counter-clock”), where again, state-(2)’s filled with massless bodies.

 

We can be even more precise. As m₁ changes sign when “jumping” from sector I to sector II, on the I-side, m₁ tends towards 0⁺ (massless substance), while, on the II-side, it turns to 0^- (massless anti-substance): the simple fact of changing sector changes the sign of the concerned mass component and therefore of the type of substance we’re dealing with.

This is very unlikely to be possible for “ordinary” matter or radiation, for the reason we saw at the beginning of this bidouille: in a real geometrical frame, you can’t withdraw more substance than you have.

What I want to point out here is that, in “super-substance”, there’s no reason why this should still be forbidden. No physical laws now oppose to this and this faculty is in full agreement with the fact that the notions of “substance” (m > 0) and “anti-substance” (m < 0) loose all meaning, since complex mass M being no longer a real-valued quantity, comparisons like M > 0 or M < 0 have no sense. The only relation which has a sense is M = 0, which is an equality. In this case, m₁ = m₂ = 0 as the magnitude m of M is zero. The magnitude m is the only real-valued mass that can be submitted to a comparison with the “universal reference” zero, indicating the absence of substance and we saw that, by convention, we can always set m ³ 0...

 

This was all about constant masses. But we said above that, because of substance transfers, from and to the surrounding environment, masses, in practice, were not expected to remain constant all the time. Can we extend the time-dependence of mass to the complex frame? Absolutely, taking a complex time T = t₁ + it₂ = te^ia = tcosa + itsina, we even have four ways to decompose our mass function M(T) in components:

 

(6)               M(T) = m₁(t₁,t₂) + im₂(t₁,t₂) = m₁(t,a) + im₂(t,a) = m(t₁,t₂)exp[iq(t₁,t₂)] =

= m(t,a)exp[iq(t,a)]

 

as we have two possible representations for time (planar or polar) and two others for mass.

Let’s look at the last one. The magnitude m(t,a) is now variable. It can varies with t ³ 0 as with the time orientation angle a. The condition:

 

(7)               m(t,a) ³ 0             for all t ³ 0 and all 0 £ a < 2p

 

is not restrictive at all, since the sign of the mass components m₁(t,a) and m₂(t,a) is still assured by the mass angle q(t,a) [for physicists now, this “mass angle” would be found in associated isospace-time, time-like component – B131, unitary group SU(3,1)]. This mass angle is now variable as well (it has no reason to remain constant). Variable! Meaning it can change... with time... (and time angle, but this is more abstract to us).

Does this mean that each mass component can now change sign?

That’s an interesting question.

Both m₁(t,a) and m₂(t,a) are oscillating, since:

 

(8)               m₁(t,a) = m(t,a)cosq(t,a)  ,  m₂(t,a) = m(t,a)sinq(t,a)

 

Let’s fix t = 0 to be the instant we start our observation. At this instant, q(0,a) = q₀(a) still depends on a. So, it’s still variable. We need a stronger condition on a, say a = 0 set to be the time angle at which we begin observing. And let q₀(0) = 0 for simplicity (it all starts at zero degree angles). Then, our initial masses are m₁(0,0) = m(0,0) > 0 and m₂(0,0) = 0 [an m(0,0) = 0 magnitude would have no interest at all]. Suppose q(t,a) increases. If its evolution is not bounded between 0 and p/2, then, when q(t,a) will become greater than p/2, m₁(t,a) will change sign. Okay, we will then go from sector I to sector II, so it may happen that the “conversion” is no longer observable to a human observer.

The same will obviously hold for m₂(t,a), when going into sectors III and IV. Anyway, the simple fact of substituting M(T) for its complex conjugate [M(T)]* = M*(T*), which is a function of T*, as a development in powers of T* immediately shows, suffices to reverse the sign of m₂(t,a).

Can we really withdraw more substance than available?...

Yes, IF we count negative masses as positive anti-masses. We reduce the (positive) mass of a substantial body down to make it completely disappear (m = 0). We can no longer “pump” substance “out”, right? But, what we can do is to replace the vanished substance with anti-substance. And quantum physics actually says (and shows!) that this process is absolutely equivalent to keeping on pumping substance out of the vacuum! Equivalent too, but not feasible for as much. Hence the introduction of the concept of anti-matter by Dirac, to “fill” the (relativistic) holes left by matter in energy bands. Recall that this was allowed because the wavefunctions were complex-valued quantities with magnitude and phase.

Well, this is exactly what we have here with mass, charges, and everything, including space and time themselves!

Of course, if we “stick” to “our” 4-dimensional “sub-world”, then not only all phase angles will be everywhere constant, but set to zero and we’ll recover that m₁(t,0) = m(t,0) > 0, m₂(t,0) = 0 for all t.

 

Okay. Let’s turn to biophysics and see the implications of all this.

 

Supersymmetry not only says, it asserts, again, based on well-observed and reproduced evidences, that the true geometry of Nature is not real but complex. It means that “we have an observation problem”. Or, in other terms, “we’re not completely blind, but nearly”... we see rigid bodies where we should see oscillating bodies. We see substance on one side, anti-substance on the other. We don’t see one transforming into the other. We are subject to observational limits. Even in our particle accelerators, we are limited by the levels of energy our apparatus can deliver: if they’re not powerful enough, we have to wait for the next generation (if not too long in distance!) to expect observing something.

You take a biological body: this is “real” substance, it’s the tip of the iceberg.

You take biological fields: these are “real” radiation fields, again, tip of the iceberg.

We take absolutely no phase into account. We don’t see this is actually imbedded into a wavy world. What we observe and study are limited properties.

I don’t say it, supersymmetry says it!

I never asserted anything, by the way, I always looked at what physics said...

 

I have an animal body in front of me. I’m a state-(1) observer and so is that body. I assume he’s material. He first has a supersymmetric partner in state-(2) which is radiative, that is out of my reach, since my observations are “confined” to state-(1). According to an operation that is out of my reach too, they both have an anti-counterpart. And all this actually makes a single “super-body”... all the rest are mere transformations. What’s the true substance? I just can’t define, it all looks and sounds contradictory to me... to me, if I look at the physical laws I can observe in my real geometrical state-(1) “restricted world”, it should all disappear into light. It should all neutralize. Now, it’s not the case, or I wouldn’t be there to observe and the animal in front of me wouldn’t be there either. So, why can it be so? I don’t know. The only thing I can say is that “it’s all-in-one”.

I am in front of an oscillating substance in an oscillating universe, extremely primal, where “all is in one”: matter, radiation, antimatter, anti-radiation. It all transforms under one of these 4 forms and it’s none of them at the same time. That’s the best I can describe from where I stand. To me, it’s absurd physics...

This animal in front of me has a conscience, which is an electromagnetic process. This conscience has a supersymmetric partner in state-(2) which is a material plasma of photinos: a material substance! I have light propagating along neuron cells in state-(1), I have matter particles (photinos) propagating along “virtual neuron cells” in state-(2). My photons (the ones I observe) are massless, my photinos have non-zero mass. If supersymmetry is respected, these photinos should be massless as well, but in another “state of life”.

Assume all these masses remain constant in time. There still remains the time orientation angle... that I did not take into account in my observations... According to (8) above, I can still have a dependence:

 

 

(9)               m₁(a) = m(a)cosq(a)  ,  m₂(a) = m(a)sinq(a)

 

I would have to fix my time angle a to get a fix mass angle q. That would require very restrictive physical laws... so restrictive, actually, I would have to justify them... understand: there’s nothing natural in these restrictions. It’s so unnatural that, should if set a = 0, i would fix my time arrow to t₁ = t > 0, t₂ = 0 and, if I set a = p, I would fix my time arrow to t₁ = -t < 0, t₂ = 0: in the first case, I would be unable to define a “past” in state-(1) and, in the second case, a “future” (as I would still less have complex conjugation, I wouldn’t be able to use it to reverse my time arrow...). THAT is weird... :)

 

Relations (9) should be clear enough by now and (8) even more: beginning with m₁ and m₂ both positive, I can end in many ways. Nine, to be precise (3²):

 

(m₁ > 0 , m₂ > 0) , (m₁ > 0 , m₂ = 0) , (m₁ > 0 , m₂ < 0)

(m₁ = 0 , m₂ > 0) , (m₁ = 0 , m₂ = 0) , (m₁ = 0 , m₂ < 0)

(m₁ < 0 , m₂ > 0) , (m₁ < 0 , m₂ = 0) , (m₁ < 0 , m₂ < 0)

 

Physical interpretations should now be easy...

(m₁ = 0 , m₂ = 0) in particular = NO SUBSTANCE. NOTHING REMAINING. Mere “quantum super-light”. Or super-substantial vacuum.

 

The Bible says that “God made us His image”. For long, it made me blink... However, if our true physical reality is to be supersymmetric entities, then, we’re all of the same original nature and it fits with the Bible’s assertion. Recall that, in the Old Testimony, nothing is referred to as a “Universal Evil”: God grants and punishes. He’s at the same time “positive for those who build and create”, “negative for those who destroy”. This, again, fits much better with supersymmetric physics. What we call the “Devil” didn’t even exist in St John’s Apocalypse: he only mentioned the “beast”, who actually referred to Caesar Neron. That “dichotomy”, that “split” between the “Essentially Positive” and the “Essentially Negative” was done much later, in the Middle Age: then came this idea of a “Universal Evil” aimed at destroying and punishing everything and everybody. That notion of a “Creator” on one side and a “Destroyer” or “Annihilator” on the other, who “fell from Heaven”.

This is not very consistent with physics.

What’s consistent with physics is that ability to turn evil or turn good. Change polarities.

What’s also consistent with physics is the “Judgement of Souls”. Assuming we consider as “souls” a whole supersymmetric body. It does not matter if the “biological projection” into state-(1) or state-(2) ceases functioning, we saw in B132 that this actually has no incidence whatsoever on the supersymmetric body, because it had assimilated that from the beginning (IF such a notion of a “beginning” and an “end” can still be given meaning). We now see that, in addition, that “biological mass” measuring the amount of biological substance (consciousness included) in an animal body can well fall down to zero (which takes a long time...), it only transforms the supersymmetric body. But it does not change it for something else, since all these transformations are also “coded” inside it! The only think that can change is m₁ = m₂ = 0, that is, M = 0 permanently.

 

Now, mix all these polarization possibilities with what monotheist religions say and make your own deductions. The way your conscience drives your acts, etc.

 

FINALLY SOLVING THAT PAINSTAKING OBSERVABILITY PROBLEM

 

 

In a complex-valued geometry, you can basically describe things two ways: whether using “planar components” or “polar” ones. Both obviously make use of the (excellent!) mathematical properties of the so-called “imaginary unit” i, the square of which is negative, equal to -1: i² = -1. Let’s explicit this in real dimension 2, that’s complex dimension 1 (and you’ll see why right now). We thus have a single object, say z, the physical significance of which has no importance for the time being. z is a complex-valued quantity. In planar components, it decomposes as z = x + iy, which is the complex transcript form of “the pair of real-valued quantities” (x,y). In polar components, it decomposes as modulus (or amplitude) and argument (or phase angle) as z = r exp(iq). Since both writings are absolutely equivalent (these are mere representations of the same object), using de Moivre formula:

 

(1)               exp(iq) = cosq + i sinq

 

we find a one-to-one correspondence between these two possible representations, namely:

 

(2)               x = r cosq , y = r sinq

 

or, conversely,

 

(3)               r² = x² + y²  ,  tan q = y/x

 

What this shows in practice is that, in the structure of space as in that of time itself, there appears orientation angles, that do not exist in real geometry. This is essentially due to the fact that, for each physical dimension, we no longer work along a corresponding line, but inside a whole corresponding plane: mathematically, the real plane (real dimension 2) can be made formally equivalent to the complex line (complex dimension 1, see above), assuming the properties of the imaginary unit. So, we’re back to the same notions, lines associated to each dimension, but in the frame of complex geometry: when we go from real to complex, we double the number of dimensions, when we go from complex to real, with divide the number of dimensions by two. We therefore find a time plane in place of the former time line and, similarly, three space planes in place of the former three space lines. Or, equivalently, a single complex time line and three complex space lines.

I’d like to be as clear as possible on this general aspect of things, as it’s essential: before doing anything else or going any further, you have to make your mind to the fact that, in complex geometry, there are no such things as “amplitudes” and “phase angles”, or “first and second projections” (in planar components), these are all real-valued quantities, therefore referring to real geometry. In complex geometry, the only thing we have is the complex-valued object z above. Full stop. Planar or polar representations of it appear when we report this object to real quantities.

This is absolutely crucial or you won’t understand the world of supersymmetry. The object z is a completely new object. And the notion of complex dimension also has to be viewed as a completely new notion.

Complex objects, events and dimensions have no equivalent in the physical world. At the best, they admit real representations, once projected into half-less dimensions.

Let’s take the example of time. Real time, we all understand what it is. We can feel it progressing.

Complex time?... Can anybody tell me what it is?... I can’t. All I can figure out about it is a “time plane”, or “a two-component time” or a “time with an amplitude and an orientation”, when I report that concept to my knowledge and experience of real time. I have no idea at all of what “complex time” really is, so I merely represent me two real times, “orthogonal” to them, despite I’m unable to explain what “orthogonality” is for time (nor space, by the way), since I don’t feel it in my daily life...

I find it easier to make me to the concept of a single “complex time”, for it looks more like the single real time I’m familiar with...

And look: as soon as you report that complex time to real ones, you find... “absurdities”; you find an “arrows of time” that can be shorten, even if you keep on going the same direction, and this, because of the presence of a “time orientation angle”... Look back at expressions (2): both cosine and sine are basic trigonometric functions bounded by -1 and +1:

 

(4)               -1 £ cosq , sinq £ +1

 

whatever the involved angle. So, here I now find myself with two projections of my initial complex time, as to know, x = r cosq and y = r sinq that are both bounded by ±r:

 

(5)               -r £ x , y £ +r

 

Question #1: where is the time I’m supposed to measure in state (1) (“my biological state”)? Is it r or is it x? It should be x, since it’s the projection of z in state (1). But, x is generally shorter than expected! So, according to the orientation I would have in the (real) time plane, the measured time in both states would “oscillate” between –r in the past and +r in the future... WHAT THE HELL DOES IT MEAN???... Assume I’m following the conventional “arrow of time” in any of these two real states, that is, starting at present, time flows towards future. For q = 0, my time interval is +r (> 0); for q = p/4 (that’s 45°), it’s already +r/Ö2 » 0,707 r, for the very same distance through space.

What the hell does it mean?... is it some “new kind of time relativity”? Not even...

As a “biological observer of state (1)”, as to any hypothetical “non biological observer of state (2)”, it sounds absurd to me or I would have perceived these “time and space oscillations” for long...

What does supersymmetry tells me? It tells me that, at the microscopic structure, these orientation angles come from an initial spin structure. It also explains me why I don’t feel this spin structure effect anymore at “my” scales: because of spin combinations in composite matter. Spin effects even tend to neutralize, as they randomly distribute in matter under “nominal” (i.e. non extreme) conditions (which is the case, in particular, of all biological matter). Even ferromagnetism is a large-scale display of collective spins and it reveals only under external influence, leading to magnets, when atomic spins collectively orientate in the direction of a magnetic field. So, at “my” scale, if nothing external to “my” surrounding medium comes to collectively favour a spin direction, I will not perceive anything from it, it will all be drown into statistical fluctuations, and I’ll still less feel anything like any incidence on space and even less on time. In other words, to my perception, the orientation angles of space and time will all be dramatically close to zero, up to an integer multiple of p (180°). The best I’ll be able to perceive, once taken an origin, will be “future” (q = 0, cos 0 = +1, positive orientation of my time arrow) and “past” (q = p, cos p = -1, negative orientation of my time arrow). That’s all...

The very same is expected to happen in state (2) for q = p/2, sin p/2 = +1 (“future”) and q = 3p/2, sin 3p/2 = -1 (“past”).

As you can see, there are much more implications to take into account in physics as there are in mathematics. Mathematics would let you believe that “great! I find a brand new property!”, physics immediately warns you “your brand new property is observed, at the best, at the level of particle physics...”, where effects are no longer drown by statistical fluctuations or dumped by any other collective or combination process.

To sum up: at the particle scale of supersymmetric theories, we do have a “brand new property”; at all higher scales, including the atomic one, we rather have a “brand new frame” occupied by “brand new objects”. Opposite to what mathematics seems to show, projecting this new frame and new objects onto any of the two possible 4-dimensional “sub-worlds” do not generate perceptible effects for as much... It’s a bit more complicated than that...

 

But let now reverse the problem. Assume that I want to detect anything “complex” from my state (1). I CAN’T! How would I do this? It would require me to imbed in a higher-dimensional world and, still, it won’t be enough! Why? Because an 8-dimensional real geometry is not a 4-dimensional complex one!

Consider our decompositions again. We had a mathematical correspondence between a pair of real-valued quantities (x,y) and the complex quantity z = x + iy. But, wait a minute... if I reason within the frame of real geometry, than the product of two pairs (x,y) and (x’,y’) will be... what? (x,y) actually makes a two-component vector. So, I first have to specify what kind of product I want to perform: if it’s scalar multiplication, I’ll find (x,y) x (x’,y’) = xx’ + yy’, that I can identify with (xx’+yy’,0); if it’s vector multiplication, I’ll find (x,y) x (x’,y’) = xy’ – x’y = (xy’-x’y,0). Let’s compare with the product of two complexes z and z’:

 

(6)               zz’ = (x+ iy)(x’ + iy’) = xx’ – yy’ + i(xy’ + x’y)

 

since i² = -1. The two products do not correspond at all... However, I have a “magic new property” in complex geometry, which is complex conjugation:

 

(7)               z* = x – iy = r exp(-iq)

 

Again, an operation that does not exist in real geometry. Let’s calculate zz’*:

 

(8)               zz’* = (x + iy)(x’ – iy’) = xx’ + yy’ – i(xy’ – x’y)

 

Now, I find both my scalar product and my vector one at the same time, in a single expression, using a single (complex) product.

What this reveals should be crystal-clear: that, if I try to extend anything from the real geometry to the complex one, I’ll fail for sure, whereas, if I use the suitable quantities in complex geometry, I’ll fall for sure onto the correct real ones...

This is therefore not only about doubling the number of dimensions: the imaginary unit i was introduced by Cartan precisely because no one could find explicit solutions of the cubic equation x³ + 3px + 2q = 0 in the frame of real numbers... and, indeed, i has no equivalent in real numbers. Only it’s square, i², has, since it’s defined as being -1, a negative real number. Negative squares were actually required to solve for the cubic above.

What is real-valued is zz*, equal, according to (8) with z’ = z, to x² + y² = r². This quantity is always real and non negative.

 

In conclusion, it’s better to reason within the frame of complex geometry, with complex objects, events and processes, then to project the results on each real states, assuming these results will be different from those we use to measure in our state, because of the presence of orientation angles, or spin structures.

 

If we do this, then we do find “new possibilities”, such as the vanishing of one component only over the two. And, when this component [the “state-(1) component”, to be explicit] is the 4-dimensional momentum, what it implies is that the momentum (“quantity of motion through space”) and the energy (“quantity of motion through time”) of a supersymmetric object, turn out to be zero, simultaneously, in state (1), making this object mechanically undetectable in this state [whereas it has a priori no reason to be so in state (2)]. Conversely, if the “state-(2) component” of this object identically vanishes, it will be undetectable in state (2), but will have no reason to be in state (1).

Usually, this is obtained fixing the values of the orientation angle: for q = kp, k integer, cosq = (-1)^k, while sinq = 0 and consequently, x = (-1)^kr, while y = 0; for q = (2k+1)p/2, cosq = 0, while sinq = (-1)^k and then, x = 0, while y = (-1)^kr. This is the most general situation where the amplitude of a given complex quantity is not required to identically vanish, which would make it vanish in the whole “super space” and, as a result, in both states (practically, in physics, no amplitude = no existence – even the vacuum has amplitude...).

 

Complex geometry, supersymmetry and that concept of a “super spacetime” actually solve numerous problems encountered in the frame of parapsychology. Just to mention:

 

-         non-observability or non-reproducibility of “paranormal events” [zero quantities in state (1)];

-         space, time and space-time distortions [orientation angles];

-         thermodynamical reversibility [complex temperature and entropy...];

-         tunnelling structures: complex analysis shows that, because of orientation angles, there’s a natural link between functions of complex variables (super fields over super spacetime) and cylindrical symmetries (axial symmetries).

 

Otherwise said, “Tunnels” can form in a complex world as rather common dynamical structures, whereas this is far from obvious in a real world, where axial symmetry is usually seen as a lower symmetry than the most isotropic one, the spherical symmetry. For instance, evolved animals (particularly mammals), show axial symmetry as a result of the development of the embryo along the nervous system. The helicoidal symmetry of the double DNA macro-molecule is also a product of evolution. All these structures are not a fundamental property of state (1) (“our observable 4D universe”). The only one observed so far is attached to the neutrino.

 

Let’s come back a bit more on this question of thermodynamical reversibility, as it’s one of the most important one, since it determines if a super system can or cannot be altered in any way. We have no other choice than being a little bit technical here, as we have to perform some calculations to justify our conclusions. I’ll try to be as clear as possible.

Boltzmann’s “H” theorem established that the entropy s of a given system made of many “particles” (typically, molecules) is a function of time, s(t), and can only increase with time: ds(t)/dt ³ 0, the instantaneous variation of entropy with respect to time cannot be negative, indicating that a system always downgrades. This result was obviously obtained within the frame of real geometry.

If we try to simply “replicate” it in the frame of complex geometry, we then have to consider a complex time T and a complex entropy S. S remains a function of T, S(T) and we have to calculate its instantaneous variation. With T = t₁ + it₂, we have:

 

(9)               d/dT = ½ (¶/¶t₁ - i¶/¶t₂)

 

giving:

 

(10)           dS(T)/dT = ½ (¶/¶t₁ - i¶/¶t₂)[s₁(t₁,t₂) + is₂(t₁,t₂)] = ½ [¶s₁(t₁,t₂)/¶t₁ + ¶s₂(t₁,t₂)/¶t₂] +

+ ½ i[¶s₂(t₁,t₂)/¶t₁ - ¶s₁(t₁,t₂)/¶t₂]

 

[the calculation is similar to the product of complexes we performed in (6) above]

First, both s₁(t₁,t₂) and s₂(t₁,t₂) are real-valued entropies functions of now both real-valued times. For s₁, which identifies with s₁(t₁) in the former real-valued context of Boltzmann, it’s already an extension, and not a small one.

The quantity dS(T)/dT being complex-valued, it’s now meaningless to set dS(T)/dT ³ 0: this comparison can only concern real-valued quantities (as zero is a real number...). As for the idea of setting the amplitude of dS(T)/dT to be non negative, it’s stupid, because obvious. So, this wouldn’t learn us anything more.

We have to examine each component of dS(T)/dT. And what do:

 

(11)           ¶s₁(t₁,t₂)/¶t₁ + ¶s₂(t₁,t₂)/¶t₂ ³ 0

 

or

 

(12)           ¶s₂(t₁,t₂)/¶t₁ - ¶s₁(t₁,t₂)/¶t₂ ³ 0

 

now learn us? Nothing... AB-SO-LU-TE-LY NOTHING.

Boltzmann’s H theorem, ruling ALL physically allowed processes in state (1) as in state (2) becomes totally useless and meaningless in super space...

So, it’s not only “because of a time plane”, that’s mechanical reversibility; it’s also and overall because of entropies in each state depending on both times.

Of course, as soon as we fix the time angle to kp, t₂ is fixed at zero and, in state (1), s₁ becomes a function of t₁ alone: s₁(t₁,0) = s_1,0(t₁). We recover Boltzmann.

When we fix the angle to (2k+1)p/2, t₁ is fixed to zero (or “frozen at present”, if you choose it as a time origin of measurement) and s₂ becomes a function of t₂ alone: s₂(0,t₂) = s_2,0(t₂) and we equivalently recover Boltzmann in state (2).

Otherwise... peanuts. You can’t talk about “downgrading” nor about “upgrading”, it has no sense. On the contrary: downgrade s₁ in state (1), as in a biological system for instance. That’s ¶s₁(t₁,t₂)/¶t₁ ³ 0, okay? Assume the requirement (11) to hold. What will you deduce from both? That, if s₂ downgrades as well in state (2), then ¶s₂(t₁,t₂)/¶t₂ ³ 0 too and (11) is automatically fulfilled. Otherwise, we only need ¶s₁(t₁,t₂)/¶t₁ ³ -¶s₂(t₁,t₂)/¶t₂ ³ 0, allowing s₂ to upgrade in state (2)...: you go older, he goes younger...

 

What shall we rather deduce from supersymmetric objects?

That they are self-regenerative. In essence.

They neither “downgrade” nor “upgrade”, despite they can carry entropy. And this helps distinguish them from quantum media, for quantum media usually carry no entropy. What happens here is fundamentally different from the wavy component of fluids or solids: there can be entropy, and therefore, ordered phase and disordered ones, but its time evolution is submitted to no particular constraint. Supersymmetric systems can evolve the way they want, without contradicting physical laws nor leading to paradoxes.

And THIS is essential. Because THIS is actually the key to “everlasting systems”.

The “biological component” can well downgrade, it has no impact whatsoever on the “super body”, because this possibility is integrated within the larger system. As is the possibility of a downgrading of the “super partner”.

It has nothing to do with consciousness, even nothing to do with “survival after biological death”, it’s an inherent property of “timeless” super systems: everything can “loop”, everything can “go back in time”, than “into the future again”, everything can reverse, refresh. This would systematically lead to paradoxes in real geometry, it does not in complex geometry. Right on the contrary, it’s now a fundamental property of the physical frame itself.

No “beginning”, no “end”: these notions are linked to an “arrow of time” and loose all sense in super spacetime.

 

I’M DEAD, SO WHAT?

 

I’m a product of natural evolution. I’m not artificially made. I begin a new cycle, that’s all.

(as always, i hope everybody will be able to properly read the math symbols introduced in the text, as the view seems to depend on the processor used)

 

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... :)