Today, we’re going to talk a little bit about PSI signals but, before that, i’d like to make some additional notes on what has been said earlier.

 

About “unified field theory”

 

In B106, I recalled a relation between the potentials of an electromagnetic field (EM field, in short) and a gravitational one (G field), involving only universal constants. Strictly speaking, the substitution of 1/4pe₀ is –k and not k. So, the relation should rather be:

 

(1)               G_i(x) = (-4pe₀k)^1/2A_i(x) = ±i(4pe₀k)^1/2A_i(x)

 

which corresponds to a rotation of ±p/2 (i = e^ip/2) in a complex plane having axes A_i and G_i. We can keep G_i(x) = (4pe₀k)^1/2A_i(x) if we restrict ourselves to the amplitude alone. But we can do much better, saying any EM field is formally equivalent to a purely imaginary G-field (or conversely) and extend the real-valued G-field to a complex-valued one:

 

(2)               G_i(x) = G_1i(x) + i(4pe₀k)^1/2A_i(x) = G_1i(x) + iG_2i(x)

 

If doing so, we then get a true unification of gravity and electromagnetism, since EM can transform into G and back thanks to G_2i(x) = (4pe₀k)^1/2A_i(x), without the need to enlarge the number of dimensional parameters. We use to talk of Maxwell’s theory as a “unifying theory”, this is not really exact: it’s rather a “grouping” of electricity and magnetism. Sure, the set of 4 equations show that electricity and magnetism are two complementary aspects of a single entity called the “electromagnetic field”, but these two aspects only couple to each other, they don’t transform into one another: we have “electricity” as one feature of the EM field, produced by fixed charges and “magnetism” as the other feature, produced by currents, that is, charges in motion. We could say the same of the electroweak GSW model: the weak field only couples to the EM field, they don’t transform into one another: their “internal” symmetry groups remain different.

Opposite to this, (2) enables us to build a real “electrogravitational” theory. Mass is equivalent to a purely imaginary electrical charge and conversely.

 

About gravity in M_4-

 

The frame we built throughout B102 to 105 included brings new insights in what we call “gravitation” in M_4-, as to know:

 

MOTION G_i(x) IN M₄₊(x) = GRAVITY FIELD IN M_4-

 

Meaning what a biological observer restricted to M_4- will perceive as a “G-field” will send back to the motion of a PSI-object in M₄₊. I checked how pertinent was this choice of G_i as new coordinates, despite their universal nature, trying other possibilities for the xⁱ⁺⁴ in B104, I found the G_is the most suitable ones. The gauge transformation Gⁱ(x) -> Gⁱ(x) + ¶ⁱD(x) not changing the intensities W^ij(x) of the G-field in M_4-, we then deduce that

 

MOTIONS Gⁱ(x) AND Gⁱ(x) + ¶ⁱD(x) IN M₄₊(x) HAVE SAME “VELOCITIES”.

 

This was impossible in Euclidian 3-space E₃: a motion x(t) only had same velocity as x(t) + x₀, this motion translated from a fixed point. This was due to the “poverty” of the dynamical parameters: a single one in E₃(t) against 4 in M₄₊(x).

Consequence: since we can fix a gauge where ¶ⁱG_i(x) = 0, the only prescription on D(x) is:

 

(3)               ¶ⁱ¶_iD(x) = 0

 

meaning the G-field is defined “up to a wave” in M_4-. Hence the behaviour of D(x), which has units m²/s (a scattering coefficient):

 

(4)               D(x) = D(R_pl)R_pl²/x² , x² = xⁱx_i

 

and if we choose D(R_pl) = (4p/3)R_plc (choice is free), we get:

 

(5)               D(x) = cV_pl/x²

 

giving:

 

(6)               ¶ⁱD(x) = -2cV_plxⁱ/x⁴

 

We conclude that:

 

MOTIONS Gⁱ(x) AND Gⁱ(x) – 2cV_plxⁱ/x⁴  IN M₄₊(x) HAVE SAME “VELOCITIES”.

 

Up to know, nobody saw any reason to impose a restriction on the xⁱs. But we could well have:

 

(7)               xⁱx_i = x² ³ R_pl²

 

in opposition to formula (6) B104. Such a condition would simply mean what we call “classical” fields in M_4- are defined from a space-time distance R_pl, which corresponds to what the Standard Model supposes. Below R_pl, assuming we can extend the notion of “distance” (expressed in meters) down to zero, we should rather turn to the xⁱ⁺⁴. In other words, the “classical” coordinates xⁱ become meaningless under R_pl, while the “Klein” coordinates xⁱ⁺⁴ become meaningless over R_pl.

However, as I already underlined it, such a “dichotomic” vision of the Universe is only due to our will to maintain the meter as the unit of length and restrict our observations to M_4-. When we turn to M₈, we see (B104-105-106) that, for velocities v > c, one finds no more “ordinary” waves and, for frequencies W > f_pl, one even finds nothing quantum anymore. In this optics, it will mean that, “inside” the Planck volume, one would only find vacuum and fluctuations: no more matter, no radiation, not even PSI matter or PSI radiations. Absolutely nothing realized.

Well, one can agree or not with this scenario, but it is consistent with the Standard Model.

 

About the motion in the “Tunnel”

 

Third and final note I wanted to make, the motion in the Tunnel. If we assume Tunnels have the physical property GⁱG_i = c² or Gⁱ(x)G_i(x) = c² expressed in terms of their G-field in M_4-, then Gⁱ(x) = -cuⁱ as we showed in B89. Examined a bit deeper, this property is really nice and interesting, for it expresses the fact that, in such structures, the “potential velocity” G_i(x) exactly equilibrates the “kinematical velocity” cu_i of an incident object:

 

(8)               v_kinⁱ + v_potⁱ = cuⁱ + Gⁱ(x) = v_totⁱ = 0

 

ALL VELOCITIES BEING OBSERVED BY A BIOLOGICAL OBSERVER IN M_4-, THE TOTAL VELOCITY IS THE RESULTANT OF THE VELOCITIES OF AN INCIDENT BODY MOVING IN M_4-: ITS KINEMATICAL VELOCITY cuⁱ AND THE ADDITIONAL VELOCITY THE G-FIELD COMMUNICATES IT. THIS RESULTANT BEING ZERO, A BIOLOGICAL OBSERVER WILL SEE NO MOTION AT ALL: EVERYTHING WILL HAPPEN AS IF THE BODY WAS AT REST.

 

There’s no paradox at all, only two velocities compensating for each other.

 

Now, add all this:

 

1)      no apparent motion of any “body” in any “Tunnel”;

2)      “PSI” phenomena supposed to hold only at distances lower than the Planck radius;

3)      Nothing concrete subsisting under the Planck horizon, according to the Standard Model;

 

And you’ll be naturally led to conclude that, not only can’t you observe anything “PSI” from M_4-, but that there can be no “PSI” at all!!!

 

If we don’t change frame and add a new system of units, we can even use the Klein hypothesis to extend the dimensions of our world, we won’t find anything “PSI” for as much, and will never be able to link it to the quantum, because this would simply contradict the Standard Model…

 

So, biologists are not the only one: even quantum physicists may not believe in the PSI, if they have no suitable frame to work into.

 

We, at last, come to our first practical application of our new model. And not the faintest one.

 

We take two animals with a central nervous system. Animal A1 will be the emitter, A2 will be the receptor.

The central nervous system (CNS) of A1 produces a mental object. Such an object being electromagnetic, it’s a A_i(x) distributed in a volume V₁ of his CNS. According to what we saw in the previous bidouille, A_i(x) can be transformed into a G-field G_i(x) in M_4- and therefore corresponds to a non material PSI object in M₄₊. So:

 

ANY MENTAL OBJECT PRODUCED BY A CNS IN M_4- IS A NON MATERIAL PSI OBJECT IN M₄₊. ITS PSI MASS IS M_MO(x) = 8p²e₀A²(x) = (2p/k)G²(x).

 

This PSI object is located at point Gⁱ in M₄₊. The aim is to connect it to a PSI object G’ⁱ of the same nature. This can only be done through a trajectory Gⁱ(x) in M₄₊(x), with G₁ⁱ = Gⁱ(x₁) and G’ⁱ = G₂ⁱ = G(x₂). So, A1 is located at point 1 in M_4- and A₂ at point x₂. The trajectory Gⁱ(x) is a G-field in M_4-. However, it should be obvious it’s different from the G-fields produced by both animals. Actually, we don’t need any source for this Gⁱ(x). So, why introducing any? The simplest scenario can use a G-wave.

So, we have a first animal, A1, emitting a mental object MO1, which is a PSI object and we want this PSI object to be sent to a second animal A2, the receptor. In our scenario, this can be done with the help of a G-wave in M_4-: this wave carries the information of MO1 from A1 to A2. For MO1 to be properly received by A2, we then need:

 

(1)               G₁ⁱ = Gⁱ(x₁) = G₂ⁱ = G(x₂)

 

First conclusion:

 

THE G-WAVE SUPPOSED TO CARRY THE MESSAGE FROM A1 TO A2 CANNOT BE NEWTONIAN.

 

For if it was, it would continuously decrease as 1/xⁱx_i from A1 and we could never obtain (1). So, whether Gⁱ(x) is constant, at least from x₁ to x₂, but A1 and A2 can a priori be arbitrarily distant from one another, or this Gⁱ(x) is oscillating. I prefer the second possibility, more general. So, I consider a monochromatic G-wave (for it’s enough):

 

(2)               Gⁱ(x) = gⁱcos kx

 

with constant amplitude gⁱ and constant k_is. (1) is satisfied for:

 

(3)               cos(kx₁) = cos(kx₂)

 

that is:

 

(4)               kx₁ = kx₂ – 2np  ,  n Î Z*

 

or:

 

(5)               x₂ⁱ = x₁ⁱ + 2np/k_i = x₁ⁱ + nlⁱ  ,  lⁱ = 2p/k_i

 

FOR THE MENTAL OBJECT A1 PRODUCED TO BE FAITHFULLY SENT TO A2, A1 AND A2 HAVE TO BE DISTANT OF AN INTEGER MULTIPLE OF A 4-WAVELENGTH.

 

If n > 0, A2 will stand “on the right of A1”; if n < 0, he will stand “on the left of A1”.

What if this condition is not satisfied? We then have:

 

(6)               x₂ⁱ = x₁ⁱ + alⁱ  ,  a Î R*

 

This corresponds to a phase in (2). Consequence:

 

IF THE ABOVE CONDITION IS NOT SATISFIED, THE MENTAL OBJECT PRODUCED BY A1 CAN STILL BE RECEIVED BY A2, BUT ROTATED FROM AN ANGLE 2pa.

 

This explains why Mrs Cant-Remember-Her-Name-Gotta-Review-My-Literature received a horseshoe with a screw in the middle where a marine anchor was sent to her: rotation 90° with respect to the vertical. This case corresponds to a = ±¼.

 

IN OUR NEW 8D FRAME, TELEPATHY CAN FIND A POSSIBLE EXPLANATION AS A COMMUNICATION USING GRAVITATIONAL WAVES.

 

Tricky! You can isolate A1 in a closed room protected against electromagnetic field, the process will still be possible: gravitational fields and waves have nothing to do with those kinds of “obstacles”. Fortunately enough! For we would be at zero gravity as soon as we would be in such a room…

Furthermore, G-waves are far less energetic than electromagnetic ones: if truly this way, the process is extremely weak.

Finally, you’ll never be sure the message is correctly transmitted, for there are interferences between the G-field carrying the message, the G-fields produced by the animals and the G-field of the Earth. All these interferences, and many others, “second-order”, regarding the weakness of the process, can seriously damage the content of the message or jeopardize its transmission. Dissipation is easy.

No surprise there’s a lot of failures with mediums.

And no surprise you don’t do it every day.

 

Today, two things: we’re first going to talk about observability. New insights about it, thanks to the enlarged frame. Then, a surprise. I’ll let you discover about it in the next paper.

 

We first rename our frames, for more convenience. We’ll call M_4- the usual 4D Minkowski flat space-time with coordinates xⁱ (in meters) M₄₊ what we called the “gravitational space-time”, that is, a second 4D Minkowskian space-time with coordinates Gⁱ (in meters per seconds) and M₈ = M₄₊xM_4- the Euclidian product of it, which makes the enlarged 8D physical frame. We can no longer say M₈ is Minkowskian: strictly speaking, a Minkowski space-time is a space-time with a single time-like dimension. We can only say M₈ is either “non-Euclidian”, “pseudo-Euclidian” or “hyperbolic”.

What we showed in the 3 last bidouilles (103, 104 and 105) suggests us to take a 8D flat metric on M₈ of the following form:

 

(1)               ds₈² = ds₄²[1 – W²(x)/f_pl²]

(2)               W²(x) = W_ij(x)W^ij(x) = W²(x)/c² - W²(x)

(3)               ds₄² = c²dt²[1 – v²(t)/c²]

 

The field W(x) is the “electric-like” part of the gravitational field on M₄₊, W(x) is its “magnetic-like” part.

Before going further, a little remark about physical dimensions. When we say M₄₊ is “over” M_4-, we have to precise what we mean. Mathematically speaking, none of the dimensions we use are “over” others: in any reference frame where we choose a given point as our origin, all the axes start from that point, so that all directions are actually “at the same level”. We can choose to use all of them or only a part of them. For instance, in a 3D reference frame, we draw rectangular axes x, y and z, all “at the same level”. They simply indicate that, in such a space, we can move along any or all of the dimensions available: along axes x, y or z; along planes (x,y), (y,z) or (z,x) or in the volume (x,y,z). The same holds for an arbitrary number of dimensions, with only more possible combinations.

Physically speaking, we’re allowed to say that M₄₊ is “over” M_4- provided we justify the physical conditions about this. In our present purpose, the central condition is: to reach the 4 next physical dimensions, we need our velocity v to be greater than c, at least, to an observer’s eyes who stayed in M_4-. Now, if we assume the world to be larger than only 4 dimensions, it becomes obvious that everything inside such a world is imbedded in the 8 dimensions. That’s what explains why we could discover the quantum behaviours: as we saw in B103, what we called the “PSI mass” is proportional to the mass density of a wavepacket in M_4-. Not all wavepackets are quantum. But the ones we considered precisely are, since they represent a probability amplitude of presence and a wavy extension of a point-like rigid body.

What we showed in B103 was nothing else than “any wavy object in M_4- corresponds to a PSI object in M₄₊”. If the wavepacket is material, the corresponding PSI object will be material (but obviously not substantial); if the wavepacket is radiative (boson-like), the corresponding PSI object will be radiative.

The metric (1) expresses what is observable and what is not in M_4-, M₄₊ and M₈.

To be observable in M_4-, we need to be causal: ds₄² > 0. This is done for 0 £ v £ c. The value v = c is an upper limit to observability in M_4-. It means that “ordinary” waves propagates at c in the vacuum and, beyond c, one finds no “ordinary” signals: the only components of a signal propagating at v > c are its nodes and since they have zero amplitude, they carry no information at all.

The same happens in M₄₊: we are causal for W² £ f_pl². The value f_pl is the upper limit. What this now means is that “PSI waves” propagate at f_pl in the vacuum of M₄₊, as any other “PSI signal” and, beyond f_pl, one finds no PSI signal anymore. No more PSI information of any kind. This actually corresponds to what is assumed to have occurred at the birth of the Universe, according to the Standard Model: frequencies f > f_pl correspond to temperatures T > T_pl and pressures p > p_pl. In this earliest age of the Universe, gravity was so gigantic that nothing could stand, no matter, no radiation, absolutely nothing, only a quantum vacuum. Now, we said that PSI signals had a quantum origin in the microscopic (in the macroscopic, we find more general wavepackets). We now see that, below the Planck time, that is, from t = 0 to t = t_pl, there was no ordinary signal, nor even PSI ones, i.e. nothing even quantum. Only fluctuations of the primordial vacuum. A t = t_pl, the PSI emerged from this vacuum and, with it, elementary quantum wavepackets.

According to (1), we are observable in all M₈ for ds₈² > 0, that is for (v < c, |W| < f_pl) or for (v > c, |W| > f_pl). The first situation corresponds to current processes: we’re observable in both M_4- (v < c) and M₄₊ (|W| < f_pl). The second situation corresponds to “before the Planck age”: the Universe is then observable, but there’s nothing concrete to observe… (and there’s no observer yet, anyway! J).

We loose observability in M₈ for ds₈² < 0, i.e. (v > c, |W| < f_pl) and for (v < c, |W| > f_pl). The first situation corresponds to no ordinary signal in M_4- but PSI signals in M₄₊; the second situation, to ordinary signals in M_4- but no PSI signals in M₄₊.

We see our metric (1-3) is inclusive: if any over the two 4D space-times is out of observation, the whole 8D process is out of observation.

 

TO AN M_4- BIOLOGICAL OBSERVER’S EYES, (v > c, |W| < f_pl) CORRESPONDS TO THE END OF THE TUNNEL (B89): THE WAVY BODY REACHES THE GREAT WHITE LIGHT AT v = c, THEN GETS OUT OF OBSERVATION. BUT, AS A PSI BODY, ITS REAL SPEED IS NO LONGER v, BUT W (B105). AS A CONSEQUENCE, IT REMAINS OBSERVABLE IN M₄₊. WE LOOSE OBSERVABILITY IN M₈ BECAUSE WE LOOSE IT IN M_4-.

 

If there was no Tunnel, we would be able to observe (with the help of suitable instruments) a wavepacket with group velocity v_gr < c, accelerating up to v = c, then disappearing. Unfortunately, without the help of a convenient structure, relativity in M_4- prevents us from reaching c within a finite relative time. So, such a process would take “an infinity” (while the proper time attached to the wavepacket could remain finite).

Besides, we can compute the intensities and the source of a “limit” G-field verifying G_iGⁱ = c² (B89). If we made no mistake, we have W = 0, so that m = 0, that is, a constant G-wave. However, even waves in M_4- have a PSI mass. That of a G-wave is:

 

(4)               M_G(x) = (2p/k)G²(x)

 

and that of an electromagnetic wave,

 

(5)               M_EM(x) = (8p²e₀)A²

 

which can always be transformed back into a M_G(x) through the correspondence A² = G²/(4pke₀). Only when G² = 0, i.e. G_i is light-like, which is not the case of a Tunnel, is M_G(x) = 0. For a Tunnel:

 

(6)               M_G(x) = 2pc²/k = 2pm_pl/R_pl          (Tunnel)

 

is a constant. When G_i is time-like, M_G(x) > 0; it’s < 0 when G_i is space-like.

There’s a difference between the quantum mass and the PSI mass for massless fields: their quantum mass is zero, while their PSI mass is given by the general formula (10), B103, using the Lagrangian density of the massless free field in M_4-.

It means that massless fields in M_4- also become, in turn, PSI sources for PSI fields in M₄₊ and this is perfectly logical, since a massless field like G_i(x) or A_i(x) is its own quantum wavepacket. These are two examples of PSI bodies being non material: G_i(x) is made of gravitons, A_i(x) of photons.

 

ANY FORM OF LIGHT IN M_4- SENDS BACK TO A NON-MATERIAL PSI BODY IN M₄₊ AND THUS, TO A CORRESPONDING PSI SOURCE THERE.

 

 

 

Wow, wow, wow! Smells better and better, that stuff!... J

Well, let’s now get back to good old classical relativistic mechanics, but in G-space-time. How can we do it? Just as in M₄, we need a “speed limit”, a velocity over which events are no longer observable in higher dimensions. Why? For three reasons: first, to be able to introduce the notion of “PSI waves” and propagation in higher dimensions; second, to obtain finer results in a theory of “weak PSI fields” and third, to have a suitable frame for strong PSI fields.

In B104, we introduced such a universal constraint: f_pl, the Planck frequency. It plays the role of c in G-space-time. But now, we demand:

 

(1)               0 £ W_ijW^ij = W² £ f_pl²

 

to be the causal condition in that frame. The Lorentz-like correction factor is now:

 

(2)               (1 – W²/f_pl²)^1/2 » 1 – W²/2f_pl² + O(W⁴)

 

in the weak field approximation. Seen the enormous value of f_pl compared to c (= 2,99793 x 10⁸ m/s), the range for observable motions in G-space-time is rather large…

The rest consists in copying relativistic mechanics. We start from a Lagrangian density for free motion:

 

(3)               £ = -M(x)f_pl²(1 – W²/f_pl²)^1/2 » -M(x)f_pl² + ½ M(x)W_ijW^ij – O(W⁴)  in J/m³

 

showing the quadratic term ½ M(x)W_ijW^ij as a “Galilean motion” in G-space-time for weak gravitational fields in M₄ (W² << f_pl²). M(x)f_pl² is the “PSI energy at rest” of a PSI body in G-space-time. It behaves as an energy density in M₄.

 

(4)               P_ij = M(x)W_ij/(1 – W²/f_pl²)^1/2 = -P_ji

 

is its “PSI-momentum” tensor, in Js/m³. It behaves as a density of action in M₄. The corresponding PSI energy tensor is:

 

(5)               T_ij = ½ (P_ikW_j^k + P_jkW_i^k) – ¼ g_ij£ = T_ji

 

It has scalar invariant:

 

(6)               H = T_iⁱ = M(x)f_pl²/(1 – W²/f_pl²)^1/2

 

and behaves as an energy density in M₄, as requested. For weak fields:

 

(7)               H » M(x)f_pl² + ½ M(x)W_ijW^ij + O(W⁴)

 

We have the identity:

 

(8)               P_ijP^ijf_pl² + H₀² = H²

 

with:

 

(9)               H₀ = M(x)f_pl²

 

Action can be defined through a differential relation:

 

(10)           dS_i = T_ijdx^j - P_ijdG^j

 

or, for constant T_ij and P_ij, through the algebraic relation:

 

(11)           S_i = T_ijx^j - P_ijG^j

 

This is the case for motions with “definite PSI energy and momentum”. In G-space-time, “PSI action” is a 4-vector, due to the presence of four dynamical parameters (the 4 xⁱs). So, we have 4 components of a PSI action, one along each of the dimensions of M₄. Dimensional analysis shows that these S_is are in J/m². They behave like the strength coefficient of a spring in M₄. Finally:

 

(12)           I = ò S_idxⁱ

 

is PSI inertia. It’s measured in J/m = N:

 

PSI INERTIA IN G-SPACE-TIME BEHAVES LIKE A FORCE IN M₄.

CONVERSELY, A FORCE IN M₄ CAN SEND BACK TO AN INERTIA IN G-SPACE-TIME.

 

It’s legitimate to ask ourselves what kind of force in M₄ could correspond to a PSI inertia in G-space-time. To get an idea of it, let’s make the following hypothesis:

 

1)      Reference frame at rest: W_ij = 0 <=> G_i(x) = ¶_iD(x) in M₄, with D(x) in m²/s behaving like a scattering coefficient in M₄;

2)      Constant wavy density: r(x) = r₀. This seems to fit with the wavy body in stage IV.

 

Hypothesis 1 gives:

 

P_ij = 0,

T_ij = ¼ g_ijM(x)f_pl² = [(m_plc)²/12m]r₀g_ij = ctes

S_i = T_ijx^j

I = ½ T_ijxⁱx^j = [(m_plc)²/24m]r₀xⁱx_i

 

As we can see, I is proportional to the square of the space-time length in M₄. This is typical of a pullback force. Inertial confinement.

Clearly, PSI inertia behaves in M₄ like a “spring”: the more distant you are from the centre xⁱx_i = 0 (the more stretched the spring), the stronger the force to bring you back.

 

REGARDING M₄, HOMOGENEOUS PSI MATTER AT REST (IN “HIGHER DIMENSIONS”) LOOKS “CONFINED” INSIDE A TYPICAL RADIUS OF [24m/(m_plc)²r₀]^1/2 » 0,2995078(m/r₀)^1/2, VERY CLOSE TO (1/3)(m/r₀)^1/2.

 

Numerical applications.

 

For m = 70 kgs, we find I = 0,1592522 r₀xⁱx_i Newtons;

For m = m_cell = m_pl and r₀ = 10¹¹ silencious neurons, I = 2,0431849 x 10¹⁹ xⁱx_i Newtons, typical M₄ radius = 7,3864876 A.

 

Crystal-clear: this time, the results are significant even in the macroscopic. This is mainly due to the value of the Planck mass (around 5 x 10^-8 kg). So, in the first situation, for a wave density of 1 at 1 m, we still find 0,16 N: far from being negligible, but rather weak; in the second situation, even at the Angström scale xⁱx_i = 10^-20 m², we still find 0,2 N: something like “asymptotic freedom in QCD” appears, but the strength is not negligible yet.

 

This is all very natural: inertia is a property of matter. Not to be confused with the force of inertia, which opposes motion in the D’Alembert Principle. What is particularly interesting here is that this property of PSI matter gives birth to a physical interaction that is interpreted as a pullback force by a biological observer of M₄.

The result is striking in the second situation: the base element is the neuron cell; we’ve assumed that the totality of these neurons were silencious at stage IV (that’s about 100 billions in the human nervous system – 60 billions in the brain + 40 billions in the rest). Not only is the “pullback force” still important at the atomic scale, but the biological observer would find a typical “range” of a bit more than 7A only. He will so deduce that “PSI matter is confined inside the atomic scale at best”.

 

Well, what we proved here is that all this good observation and deduction, that seem so natural and logical to us… is spoiled by our dimensional restriction: WE are “confined” into the first 4 dimensions of the universe and make wrong deductions on things happening “over or beyond our space-time” precisely because of this.

The result we got for m = m_cell and r₀ = 10¹¹ are correct and reasonable, they’re not many orders of magnitude greater or smaller than expected, like the ones I previously obtained, yet they have nothing to do with reality…

They only have to do with the reality we can perceive.

“PSI reality” in G-space-time reduces to say: “we have a PSI inertia I = 2,0431849 x 10¹⁹ xⁱx_i and it has to be measured in ‘kg-psi times (length-psi)²’, which is equivalent to the Newton in M₄”. But there’s no “force” of any kind there.

Force is G-space-time is measured in (kgm/s)/m³, it’s a momentum density in M₄.

 

We interpret as a “force” what is not a force. And there is our mistake! J

 

 

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

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

 

(1)               xⁱ⁺⁴ = Cte x Gⁱ

 

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

 

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

 

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

 

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

 

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

 

(4)               GⁱG_i £ c²

 

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

 

(5)               xⁱ⁺⁴ = t_plGⁱ

 

implies that:

 

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

 

Makes you remind of something?...

 

THE OSCAR KLEIN HYPOTHESIS.

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

 

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

 

FROM WHAT AN OBSERVER OF M₄ CAN PERCEIVE,

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

 

Actually, what is likely to happen?

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

 

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

 

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

We now have a justification and even an explanation.

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

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