Planckons and
elsymons
Part 3
Contents
1. Hypothetical plankonic gas – thoughts versus
cosmological data
2. The question of mutual interaction of
planckons
3. The problem of speed
4. Minimal distance between planckons. The existence of limit (not asymptotic) value
of potential energy and force
5. What is the system’s mass at the
absolutely smallest distance between its elements?
Á
propos. Associations, reflections and thoughts
1. Hypothetical planktonic gas – thoughts versus
cosmological
data
Let’s suppose that at the beginning we had the planckonic
"gas", all the elements of which are equivalent. This gas, even if
quantitatively limited, cannot in the long run create a uniform static
continuum, even if such is its initial state. After all, we remember planckon’s properties.
Hence we have "gas" (in quotes). [By the way, can there be the
absolutely initial state, that is the state from which time begins its
existence? Is the existence of no-time at all possible?]
If the
system is spatially limited, there must be also an uncompensated gravity which attracts
planckons, particularly those located in that uttermost space. In such a
situation the system itself has the centre (also gravitational). In this case,
stability is disturbed.
However,
if the system is unlimited, infinite, then (under the condition of stability
and uniformity) we have a situation in which there is no relative movement as a
result of the full balancing of forces (the resultant force acting on each
element is equal to zero). In the context of thoughts on cosmological
questions, this would be also absolute, timeless eternity. But here we are, the
very existence of the author of this statement precludes such a possibility. [Of
course, assuming that there is no external, transcendental factor which would
initiate movement, that is some "force majeure", primum mobile,
disturbing that eternal peace. Would that be enough to conjure the Universe from
infinite continuum, the Universe with all its changeability? And what about
this "force majeure", when did it deem worth it, and for what reason?
At what moment of no-time...? In other words: Was it at all possible in
nonexistence of time? After all, time implies changeability, and so the will to
act on the part of this transcendent factor already indicates the existence of
time. Something for those who like to mull over such things. As for myself, I
don’t recommend any searches for the reasons and ways by which planckons came
into being]. Fortunately, we are not dealing with transcendental (not to
say theological) factors. We are dealing with the known to us, real Universe,
which is dynamic, not static, has no centre, as it is reflected in cosmological
principle (and thus the Hubble’s law); there is no space outside of it. An existence
of the centre, and an existence of extra space, would go against the
cosmological principle which we assume a priori. It would also contradict the
correctly forecasted temperature of the CMB radiation - obtained in the
empirical study. There is more about it in the article dealing with the CBM
radiation. So far, this is a rather isolated view, even though the cosmological
principle is widely accepted ...
[Currently it is thought that
the diameter of the observable Universe is approx. 92 billion light years; check
the appropriate internet sites, such as: https://en.wikipedia.org/wiki/Observable_universe. Is this the
last word of science? It is the latest word of its current representatives. So
far, the Universe can (potentially) be one way or another - according to the
Friedmann-Einstein equation (with the addition in the form of the cosmological
constant).
If the Universe is inherently flat, things can be a lot simpler, and its
current diameter of the order of 30 billion light years. In addition, if there
was no inflation, which was to push a large part of the Universe beyond visual
range (because there was, after all, the phase transformation, followed by the
Hubble expansion), this 92 billion could be put aside as an oddity from the
turn of the century. So it's not about the expansion of the autonomous space
but only about the relative motion of objects which speed limit defines the
outer border of the flat space occupied by the Universe. The only complication
(here I would turn to mathematicians-topologists) would be the absolute limit on
the birth certificate of existing space so as to keep it within Hubble
dimensions. "If it is flat, it should be infinite," but this is not
the case – which is undoubtedly proved the existence of variation, and the
existence of CMB radiation. This is not the case also because of c limit,
which, in the confrontation with the manner of expansion (relative movements,
rather than expanding space), actually indicates the historicity, the
variability – there was once the beginning of this State of Affairs. The State
of Affairs, rather than the Beginning of Everything.]
So let's leave the option of a uniform and
static gas on the side. Because of
various interactions taking place in the planckon gas, it can be expected
that it develops in the direction of forming the less or more complex systems,
and elsymon lumps. We are not dealing here with an ideal gas in which the
particles are points which “don’t feel” whether they are attracted or repelled,
and where their encounters are perfectly springy collisions occurring in the
zero range. That’s how it is generally imagined. Actually we are dealing here
with repulsion at a very close range, but not at the zero range¹
2. The question of mutual interaction of
planckons
Planckons,
although very small, create a different world, the world of gravity. This makes
them different from the perfect gas particles just as nature differs from
mathematics (that is, they require different math...). They have certain sizes,
but at the same time they can penetrate into each other (but not permeate
through each other) being (physically) truly elementary creations. All the
substantial matter is built out of them, including radiation and every particle
and each body. So as to create (on paper) the principles of construction of
stable planckon systems, the basis for the construction of elsymons (in the
sense of inner balance and their relative resistance to destructive external
influences), one should, above all, examine the interaction between two planckons
forming an isolated system and connect the findings of this article with the
findings contained in the preceding article, in the section entitled: "How
to build elementary particles?"
At this
stage we will describe a system in a static manner, i.e., without considering
the relative movement of (our two) planckons. [In the particular case, both
orbit around the common centre of mass, if in a circle then such a state is in
fact equivalent to immobility (if you don’t take into account the outside
witnesses). In the extreme case, the vibrations take place along the connecting
them axis.] We’ll explore the dynamics further on. We will calculate the force
of attraction (and repulsion) as the function of distance between their
centres. We have examined the matter in relation to the system of two material
points**. It will be interesting to see whether we’ll get the results
consistent with the results of that study, which has the characteristics of
generality and universality. It’s a kind of test for the planckon model.
As we
know, in a very short range mass deficit becomes an important factor. This must
be therefore taken into account in our research. We should also recognize that
in the case of relative motion of planckons, the results of this research should
remain in force. The planckons set apart attract each other by force of
gravity, and according to the assumptions they make a closed system. Let one of them be at the origin of the coordinate system. Let’s consider the magnitude of force depending on
the distance of the second planckon from
the origin of the coordinate system.
Intuition suggests the graph shown above. Does this graph correspond to reality? We will check it in our study.
We'll
start, obviously, from deriving an equation for calculating force. We will rely
here on the Newton’s law of universal gravitation, and we will take into
account the fact that, with the mutual approach of its components, the mass of
the system gradually decreases. Because in the formula for the resultant mass
there are no restrictions on the value of r, the formula for the force, which
we get, should be valid for any distance. This formula can be considered as a
modification of Newton's law. So as to take into account the mass deficit, we
rely, of course, on the formula:
derived in the first part of this essay (comprising three parts). Thus we
obtain the following formula:
After
dividing by 4, because mass of one element is equal to m*/2, we received an
expression very similar to the formula (7) in an article on material points. We
see that force is positive over the whole range of r values, that this
formula does not indicate the change of the direction of the force (attraction
- repulsion), because it does not recognize, for now, the possibility of
repulsion. We know that it takes place when the distance between the centres of
planckons is less than half the Planck length. To impose this condition, the
formula (**) should include the factor that satisfies our need:
Same as
in the case of interaction of two material points, and in the case when we were
determining the potential energy of planckons’ interaction. Thus we receive:
Let’s explore function F(r). We differentiate it and equate
the derivative to zero in search of extreme (or inflection point):
In the calculation, as one can see, the factor Γ does
not play a role. Most importantly, we see that our function has an extreme (or
an inflection point), and actually in two places. Although it does not fit
intuitive predictions, the r values that we received correspond to those
received in respect of two material points. This is encouraging. By continuing
our research, we find that the first point is a maximum, and the second is the
inflection point (not minimum, as for the smaller r values the force is
negative (factor Γ <0)). Here is the graph:
The force magnitude at
these points:
Exactly the same as what we received with respect to the material points.
Asymptotes, horizontal:
Again we are puzzled by the huge maximum value of the force:
We found it already in the article on material points.
That's a huge number! It's a completely different world! But is it really
different?
Characteristics of nature do not depend on scale. It's
the same nature. Perceptible nature is simply more complex. [If we mix the blue
and yellow powder, we get, in our perception, green colour. Today, our truth is
green.] That what is given to our senses and can reach our consciousness, being
the result of overlapping and mixing of stimuli, appears to us as a different
quality and constitutes the basis for the theories that we invent and develop.
Today's description of nature is necessarily of phenomenological character. Of
course, it's not enough. The world of "sub-dimensions," although it
requires a different approach, is no different. In it, the same fundamental
rules apply.
But coming
back to that enormous force, it helps illustrate how strong (in an appropriate
scale) is gravity. It’s not the first time that we came to this result. We
could have expected it, remembering the result of exploring the interaction of
two material points, the result which was of a more general character. This solution
confirms also an already expressed view that gravity is the basis of all
interactions (including the strong ones, of course). As for the graph (above),
it is basically identical with the graph describing the interaction of two
identical material points².
It is also noteworthy that within a certain
range (L/2, L) the force increases with distance (until it reaches its maximum
value, which we just discussed). This is not consistent with our habitual
thought (force in the central field decreases with distance). This may be
illustrated by stretching rubber band. Interestingly, such is the character of
gluon-quark interactions. We are talking about the so-called asymptotic freedom
and resulting from it colour confinement, which makes it impossible to observe
quarks directly. Judging by the results of our considerations, it can be expected
that the range of "gluing" of quarks is so short that it can be
compared with Planck length. Perhaps quarks were indeed the primary structural
elements of the panelsymon at the moment preceding the start of expansion. And
what about gluons? In the dual gravity model they kind of lose their raison d’être.
In a fit of arrogance I would even say that the concept indicating the need for
the existence of the "force transmitting" particle in relation to the
gravitational field, is not adequate. This is the fundamental field, base for
other interactions. Gravitons? This is not the right direction. We can do without
them. They are just the product of a particular paradigm. A theory can be
always adjusted (to comply with the paradigm). Some are starting to see (or
just suspect, not being able to substantiate their suspicion) that the search
for graviton is a Sisyphean task. Am I wrong? Let someone prove it. Tip: look
for the facts of nature (rather than arguments based on one theory, or
another), contradicting dual gravity, in other words, give us the facts which cannot
be rationally explained on this basis. It is worth remembering at this point that
this model generates a lot of anticipations that can be checked even now (after
liberating oneself from the current habits of thought).
Field is a being that cannot be separated from
matter. In fact, matter, each body and every particle, is a field, the
gravitational field, in a very condensed form. Even the famous Einstein's
formula (mc²) can serve as an illustration of this fact. But this is not
enough. So as to apprehend the truth about gravity, one must descend much
deeper, toward "sub-dimensions" of elementary gravity, towards
planckons. The derived formula testifies to it. Planckon is the ultimate
condensation of the gravitational field, as well as its elementary source, the
only one that exists. Therefore, there is no infinite continuity into depth, just
as there is no physical singularity. Here resides the source of quantization (and
of the gravitational field).
3. The problem of speed
Let’s
assume that the initial distance between two planckons is very large
(mathematically tends to infinity). Leaving one of them at the origin of the
coordinate system, we can say that the second falls on it unhampered under the
influence of gravitational force. [We do not take into
account the presence of other planckons here, because, as usually, we consider
here the simplest case, "raw material", an elementary system. Physics
of complex systems is not really different, but the aspect of calculation, even
in case of just three components, becomes dominant and requires approximation
methods. For us only the physical aspect is of importance, the concept at its
source. This model is designed for testing.]
During the
fall the force of attraction increases, and therefore acceleration as well.
Interesting, what is the falling speed³. In our study we will answer three
questions, which concern fundamentals:
1. What is the distance between
the centres of planckons at the moment when the speed is maximal?
2. What is the value of the
maximum speed?
3. What is the minimum distance
between their centres at the moment when they come to rest?
The answer to the first question is immediate. This is the distance at
which the force of attraction comes to zero, that is half of the Planck length.
To answer the second question, we have to start by calculating the work of the
propelling force (until it comes to zero) in the range from infinity to half
the Planck length. This work is equal to the increment of kinetic energy.
Therefrom the road to calculate speed. It can be expected that this speed may
reach relativistic values. It immediately evokes serious concern about the
expected in this case computational complexities. Deeper reflection (thanks to
this concern) leads however to the conclusion that in this case the
relativistic effect should not be taken into account. That’s because in Planck
scale this effect does not occur. Planck mass is not subjected to relativistic increase
as it is unequivocally elementary and invariant with respect to any
transformation; independent of the choice of the reference system. More
importantly, we do not need to observe our planckon. Observe? Using photons?
Here the (observational) effects of the special theory of relativity are
irrelevant. Besides, a truly elementary being must be invariant! So let’s
calculate the work:
dW = -Fdr
Minus
expresses here the fact that during the fall the displacement is negative when
the work is positive (during the approach under the force of attraction). The
repulsion phase will be indicated by the Γ factor. Let’s in the above
expression substitute the value of force on the basis of the formula (***). We
get:
So as to
calculate the maximum speed this expression should be integrated within the
appropriate limits:
Here Γ factor is positive, therefore it is omitted. We calculate this integral and obtain the following:
because:
Assuming:
We get:
Let’s
note that the coefficient 2/3 already occurred in the article dealing with the
potential energy. It also appears in cosmological considerations based on the
Friedmann equation (after all this is also worth noticing). If we accept as
well-founded the basic definition of kinetic energy, which should not be a
problem also in relation to planckons, we get:
Thus this
speed is greater than the speed of light. This should not cause trouble due to
the invariance of planckon (I pointed this out above). This corresponds to our
hypothesis regarding the very early phase of Big Bang (URELA), although we are
talking here about the approach, not expansion. But in accordance with the
principle of conservation of energy, these speeds should be the same, because
after stopping, planckon accelerates under repulsive forces. The obtained speed
is the relative speed of the nearest neighbours. The relative speed of the
elements most distant from each other may be much greater. Let’s note also that
in the description of complex systems - and such was the exploding Universe -
simple extrapolations lead nowhere. The calculation of that "much
greater" speed using the apparatus used here is not possible, given also
the specific topology of the system, certainly different than the one known to
us from the autopsy, given the non-linearity of spatial relations.
We
received speed greater than c. By how much? This is easy to calculate. Here is
the source of excessive kinetic energy, which dissipated during the phase
transformation, giving birth to temperature. It's also the kind of indication
for estimating the initial temperature (the highest in the history of
Universe), and at the same time for confirming the whole concept.
So let us
now answer the third question: "What is the minimum distance?"
Our planckon, while approaching, crossed the point at which the force came to
zero, and the speed reached the maximum value. Continuing its motion it faces
resistance. As it moves on it meets the growing repulsive force. Finally it
stops. What's next, you already know. We are interested in the minimum distance
corresponding to zero speed. To calculate it, let's start with the calculation
of the value of work (integral) over the new interval:
Let’s
note that this time factor Γ is negative, hence the lack of a minus in the
expression for work. In addition, the searched for distance x we express using
Planck length: x = nL . Our aim is thus to find the value n. Let us therefore take note of the change in kinetic energy:
So we get:
It has only one solution: n = 1/4. Therefore,
the minimum distance is equal to the quarter of the Planck length. A clear
solution was to be expected. No solution or more than one solution would render
questionable all my efforts, since the solution should be unequivocal. The
concept itself would have to be rejected. I was therefore under considerable
stress when I was solving this equation for the first time (checked it several
times).
The result was a source of a powerful experience. The fact that this
result surprises with its elegance can mean that we are pretty close to the
truth. But this is not the end, because the gravitational mass of such a system
immediately arouses curiosity. Calculating it was not a problem. For now,
however, please be patient. I think we should first calculate the potential
energy at the moment of the closest approach. We need to hurry up before the
start of repulsion, so as to make it before the Big Bang.
4. Minimal distance between
planckons
Let us return to the preceding article.
For the record, there we dealt with, inter alia, the potential energy of
planckons’ interaction. The graph shown there asymptotically approaches the
energy axis (OY). As it turns out, there is the minimum distance at which two
planckons can approach each other. It is equal to quarter of Planck length. It
is easy to calculate that the corresponding potential energy is four times
greater than the plankon’s rest energy. So there is no asymptote. Graph ends in
a certain place. This is significant. There is one truth and the asymptote does
not lead to it. This is however shown only in the (truly) elementary systems.
But if that’s the case there, then in the whole matter – use of asymptote in
the description of macroscopic systems it is only apparent and is means
that there are limitations in the given method of description. Here's one more,
this time "philosophical" confirmation, if not of the validity of the
chosen path, then at least the legitimacy of investigations in this direction.
Is it only for the philosophical elegance? This seemingly trivial statement,
carry nonetheless some weight.
And what
is the magnitude of the repulsive force at that threshold distance? Finding it is no longer a problem.
Substituting in the general formula for force (***), taking into account Γ = – 1, and
using the familiar formula:
we get:
The
maximum repulsive force is thus 64 times greater than the maximum force of
attraction. So here as well, there is no asymptote. The story ends at this
value of the force. Pauli exclusion
principle is the direct consequence
of this very fact.
5. What is the system’s mass at the absolutely smallest distance between
its elements?
This predictable question was asked
at the end of the third chapter. As we shall see, it was a good one.
It is
obvious that at this particular moment the mass of the system is negative. Its
value is expressed by the equation which we already know:
along
with this, a reminder:
So we get
the following:
As we
know, from the defining formulas (Planck dimensions) it comes out that:
Here's
the final result:
Amazing,
although by intuition it was to be expected. Absolute symmetry! When they are
infinitely far from one another, their total mass is, of course, equal to 2M. The system has the same mass when the distance between its
elements is minimal, but the mass is negative. Yes, minimal! They can’t get any
closer to each other, just as there is no greater distance than infinite. Also,
the rule of conservation of energy remains valid and categorically excludes any
further approach (it’s the question of the magnitude of mass). Again the Pauli exclusion
principle! And actually, it is also an expression of the principle of
conservation of energy. And probably just here lies its mystery. Is it not like
quantization (gravity)? Infinity on the "one side of the mirror"
becomes a definite quantity on its other side. Alleluia! This cry expresses
everything...
Á propos
Associations,
reflections and thoughts
¹) It is interesting
from the psychological point of view that something like this is even considered
(perfectly springing rebound in the zero range), as if it really took place in
nature. Collisions of free electrons with individual photons, treated as
central springy collisions of bullets, may serve here as a particular example*.
In any case that’s the way the matter is perceived by young people interested
in science. And that’s how the Compton effect is often presented in schools
(wrongly of course, but for a somewhat different reason). However, physically (perfectly
springy rebound in the zero range) is simply absurd. "But this is just the
kind of approximation" – one could say... An approximation distancing from
reality, deceiving imagination which we want to develop in the young so that they
would grasp this reality in the best way possible. If already in school such
and similar assumptions are used a priori, it is no wonder that quite often
even scientists are automatically and mindlessly prone to incorrect judgements.
Stereotypes formed in youth live their own lives and the more irrational, the
stronger they are. I do not want to give examples from outside physics. Ad rem.
Let's try to describe (qualitatively), what can happen when an electron
approaches a photon. [Let's try to describe it in a kind of mechanistic way, without
referring to quantum mechanics. Which does not mean that it's a better one. It
means that it’s worth trying.] The speed of the electron relative to other
bodies is here of no importance. Other bodies have nothing to do with
it, are far beyond our system, and know nothing about that electron. In
addition, their varied speeds, from zero to the speed of light, in relation to
our electron, makes it pointless do deal with its kinetic energy, the value of
which depends on the reference system – unambiguity is out of the question. And
yet, among astronomers there are some (I deliberately not cite names, because
they are quite well known and quoted - so I know about them) who explain the
cosmic X-radiation as follows: "high energy electrons during a collision
with photons of the CMB radiation transmit their energy making these X-ray, or
even gamma radiation photons."
Let's stop the shot at the moment of closest approach
of an electron to a photon. Both players are elsymons. The gravitational field
of the electron when it approaches the photon causes deformation of both of
them. Polarization occurs in the system of constituent planckons’ vibrations -
gravitational induction). Thus, the photon becomes a source of uncompensated
gravitational field. It attracts the electron (itself being attracted). [For
this reason light is deflected in a strong gravitational field (not necessarily
due to the curvature of space).] Here we have an analogy in relation to
electrostatics - electrostatic induction (as scraps of paper in the field of
rubbed object). In our system there is the gravitational interaction. As we
know, in the gravitational field the wavelength of radiation increases (contrary
to popular belief, not because of the gravitational time dilation, anyway, so I
dare to believe), but it takes place only at the moment of contact***. Immediately
after comes radiation, and thus the photon returns to its original state, to
its original energy. This cannot be captured in an experiment. Possible to
observe, however, is the dispersion in accordance with the principle of
conservation of momentum. Already this suggests that the model of gravitational
photon as elsymon is consistent. The change of momentum itself proves that it participates in the
interaction. What interaction? Of course, gravitational.
By the way, returning to the interaction of the photon, it is worth
noting that disruptions occurring in its internal vibrations, and thus its gravity caused by induction, can
result only from massive particles (even electron). Photon alone is not the
source of the gravitational field. Not surprisingly, the light beams do not
interact with each other. The planckon model explains this fact as well. [And
if the particle has negative mass? Then photon deflects in the opposite direction.
I think that in the future it will be possible to check it. Scattering of light
on neutrinos? Perhaps in this way it will be discovered that neutrinos actually
have negative mass... About neutrinos in an essay devoted to them.]
Although all this sounds rather logical, research is
essential... even if you, dear reader, consider it all as "fantasy for the
poor." If that’s what you think, it means that you either have not read
everything, or you are already programmed. Experiment is of crucial importance
and so far none has even attempted to refute the model that with a good dose of
arrogance I have present in my works. The known facts rather confirm it (at
least do not contradict).
²) This enormous force makes me think at this point of the
hypothesis of inflation. There also some huge force caused the sudden, even an
exponential increase in the size of this (This? Actually singularity, in spite of
being zero...), which was to become the Universe. [Just for the record,
inflation was expected to start (because of this singular zero) only after some
time. Sly dodge. Would this make it more credible?] In that case it was some
not fully specified force, vacuum energy, but we know that it was gravity.
Moreover, this force (surprisingly) is called repulsive gravity, and is based
on a known Planck mass, incomparably larger that the mass of any known particle.
I invented the absolutely elementary being (with that mass), thanks to which
the vacuum energy has its specific source. Inflation is the expression of
intuition, and Urela based on the dual gravity concretises things on the basis
of causality (and not according to the scheme: empirical fact → fitting
hypotheses, hypotheses based on the currently in force paradigms and
theories, resulting from creative inventiveness of those involved in the
subject.). It is significant that Allan Guth invented some "repulsive
gravity" yet hadn’t thought about the possibility of dual gravity. It is
thanks to the concept of dual gravity that there is no need to use such
hyper-abstract ideas as Higgs bosons, Higgs fields, the energy of vacuum, false
vacuum, inflation field; there is no need (in this field of research) to use hyper-mathematics,
and no need for hyperspace and supersymmetry. So that what was achieved
starting from the quantum premises and from the top, deserves great admiration.
From the top, that is on the basis of observable data; moreover, without taking
into account gravity, which is, after all, (according to the common habit of
thought) a super-weak interaction. Yes, without taking into account gravity,
and yet, in spite of all, taking it into account at the Planck level in a
contrived hypothesis (inflation) without a sound conceptual basis. It is
praiseworthy (for intuition). For me it was a lot easier because I recognized
gravity as the basic interaction, and all others resulting from complexity, and
I accepted its duality as the base. Moreover, my view was not obstructed by
sky-high fluctuations (existing in this range of dimensions), excluding insight
because of the quantum conditions (already a priori). This is not a great
revolution. It’s a minor treatment, a small step forward (rather than backward).
By the way, this convergence (Inflation with Urela) would indirectly
indicate that indeed gravity is the key to everything. No wonder that it wasn’t
possible to co-opt it to other interactions as some secondary Cinderella. The
fact that now (probably not only in my work) it triumphs by its magnitude, fully
justifies the previous failures. The obtained (directly in several ways)
"universal force" could be an indication. On this occasion it is
worth pointing out that the existence of gravitational repulsion is, according
to our concept, a natural consequence of the existence of attraction. Awareness
of the existence of gravitational mass deficit also enabled clear understanding
of why gravity in our observable surroundings is so weak.
³)
Can the relative speed of plankons be different than c? Judging by their
absolute elementarity? Other speeds are relative, so is the magnitude of
force... But that’s from the point of view of an observer... who actually does
not exist... In our testing planckons are material point, and their internal
features of absolutely elementary beings are actually beyond this research.
Planckon feels that it is attracted (or repelled). By what? It's none of its
business. Let’s add to this that during the first phase of the Explosion the
relative speed was to exceed, even by much, the invariant speed (c). It is,
however, about the pace of expansion, the speed at which increased the radius
of the Universe. Or maybe, in fact, the relative speed was equal exclusively to
c? The speed of the nearest neighbours,
of course. And as for the speed of further neighbours? There must have been
quite a lot of these neighbours in every direction, and also in this set up the
cosmological principle - which is the expression of symmetry, homogeneity and
isotropy in global scale - was certainly in force****. According to this
principle the relative speed is proportional to the mutual distance. In this
case, it would be a multiple of the invariant c. Was then "c"
the only possible basis for the relative speed? Is it possible that there was
no acceleration in the initial phase? No Urela (or inflation)?? Or maybe the
view that the relative speed of planckons could not be other than c is wrong, anyway according to
the suggestion at the beginning of this digression. Because if it cannot be
other than c, then why is it (in
line with the cosmological principle) n-fold greater in relation to the more
distant neighbours? This relativity would actually contradict its invariance.
Thus, either all planckons moved in relation to all others at the speed c, regardless of the distance
between them, or this speed is not a necessity, that is the relative speed
may be other than c. In the
first case there is no question of the expansion, of development. Only absolute
stasis, as all relative to all others move at the same speed, or put it
otherwise, do not move at all. Just
a reminder, we are interested in mutual repulsion in the first phase of the Big
Bang. This case therefore can be dismissed. So we have the second case. Which
means that the invariant c
inherently lies in the planckon itself, while outside of it the case is open. Let’s
note that space is built of a progressive movement, the relative movement (as already
observed in the text proper). So there wouldn’t be any expansion if the only
speed would be the invariant speed c.
Besides, planckons are endowed with mass. Photons are something else. The mutual
c speed is reserved exclusively for
them. It is a kind of external parameter, unlike in case of planckons for which
c is something internal. For the
record, photons appeared at a moment when the mass of the system was equal to
zero (at the end of Urela, and commencement of phase transformation). As for
the system of two planckons, the distance between their centres in this state
is equal to half the Planck length. Á propos, such (field-like) is the meaning
of Planck length. And what about the "crust" that determines the
planckon’s dimensions? Encrusted is our imagination. Later was chaos, and the
space began to expand with the speed constituting the upper limit of the
relative speeds of elements endowed with mass. We will soon learn that the
minimum distance at the beginning of the Big Bang, was equal to a quarter of
Planck length. This will give some foothold for further research.
Planckons, actually only them, repelled each other (in
a very short range), although their assemblies which formed particles attracted
each other, attracted by relatively small forces, being gravitationally almost saturated
systems. Hence the weakness of gravity within our perception. It is interesting
that our poor planckon is personally responsible for this whole mess called the
Universe.
*) Let's leave aside quantum
mechanics with its uncertainty. The "mechanistic" approach should
suffice. According to certain hypothesis which tries to explain the formation
of the X-ray somewhere in space, electrons with great kinetic energy transmit,
through collision, part of their energy to photons of the CMB radiation
(microwaves), transforming them into photons of X-radiation and even gamma
radiation. Sounds nice. The problem is that the kinetic energy is relative,
that is, its magnitude depends on the reference system. It may be, for example,
zero in respect of one of its observers. While the photon energy is as it is,
and no other (hv), and it determines the type of radiation. "And what
about Doppler effect?" It does not apply in the case, because there is no
source of radiation. Photon relative to any observer moves at an invariant
speed. This is what takes place between an electron and an encountered photon,
has nothing to do with the infinite number of other objects outside the system.
Thus, even the "great energy of an electron" (free) in relation to
some of these objects, cannot affect the result of its interaction with a
photon. And what kind of interaction we are having here? We know, as we
remember that photon is electrically neutral.
**) Article (first in this series) entitled: “The dual nature of gravity”
***) The existence
of gravitational time dilation (here, in particular with regard to the photon
in our example), it something quite troublesome, if you look at it as a whole.
We would have, among other things, local time mismatch to global cosmic time,
uncountable number of such mismatches (even without digging into the black
hole). Which of the measured times is actually the global time? Or maybe this
global, shared one, simply does not exist. So, how did it happen that the
Universe exploded as a whole at one moment, being the self-adjusted object for
the whole duration of Urela (or inflation)? How is it that the horizon of the Universe,
no matter which way we look, is equally far away, that there is a cosmological
principle, which observable confirmation is the Hubble’s law? Is H factor (which,
as it is known, determines the age of the Universe) in relation to equidistant
(from us) objects absolutely equal in every one of them? Or maybe it differs
because of the different gravitational environment? So we have an additional
possible cause of uncertainty in determining the value of this coefficient. And
more generally, could there be global processes (of a cosmological nature)
without full time coordination? Or maybe they don’t happen (and no dark
energy...) Nothing but trouble.
Less troublesome solution would result from dispensing with the time
dilation (or recognizing it as a mental shortcut releasing from mathematical
requirements, and not an actual physical effect). Energy of a photon passing in
the gravitational field consists of: its own hv energy (in the
non-gravitational area) and negative potential energy of the photon at a given point
in the gravitational field. The total energy is therefore smaller, which
manifests itself in the longer wave. By this reasoning we come to a formula very
similar to that predicted by GTR. Without involving time. Changing the speed of
the passage of time makes the "new" photon’s features permanent,
because it just "missed the train". After leaving the gravity field,
if it came too late, photon does not return to its primary form.
However, gamma rays or X-rays from the vicinity of neutron stars and (possibly,
black holes) - gravitational field is there very strong - rather testifies to
the possibility that photons - "weakened" after leaving the gravity
field - return to their original form.
"And what about black holes?" one may immediately ask this
spontaneous question. I have resolved this problem as well, and of course, on
the basis of dual gravity. Black hole is an object gravitationally closed,
without singularities, and the matter inside is well known to us, though (in former
stars) very condensed. The average density of such an object is inversely
proportional to the square of its mass. It is easy to calculate and check with
respect to an appropriately massive galactic nucleus. It may even be lower than
the density of water. Most importantly in the context of our discussion, there
is no time dilation. It is simply not needed - everything can fit without it.
Dilation would rather disrupt (this playing with the false t).
Time dilation - yes there is, though not gravitational-local, but
kinematic, also global, cosmological, observed in distant objects because of
their relatively high receding speed. This can be noted (can be even
calculated), because the space of the Universe is flat. [I dealt with this
matter in a series of articles under the title "Horizontal Disaster",
and of course, in one of the books already published.] Discovered
observationally (empirically) Hubble's law, indirectly means also the existence
of global time. Let’s add to that the amazing uniformity of background
radiation (Penzias, Wilson). Its minor heterogeneity is not caused by the
heterogeneity of the passage of time, but by chaos that formed during the phase
transformation - the chaos and the local non-homogeneities in temperature
already at the very beginning of Hubble’s expansion.
****) By the way, as we already know, this original network
of the panelsymon didn’t have to be, and rather wasn’t a network of identical
cubes (as we may imagine). [Although in this case isotropy concerns not the
basic elements, but the basic systems.] Rather regular tetrahedra and regular dodecahedrons
connected by planckonic bridges. They are the ones, one might suppose, which
constitute the structural basis of all particles (including photons). As a
result, the masses of all the particles are (relatively) similar. It is a very
important conclusion (see the preceding article). Moreover, this
"crystal" structure forms the basis for the short range anisotropy, which
does not, however, affect the homogeneity of the whole. [It is exactly this
anisotropy that played its role during the dispersion of elements of that
monocrystal during the phase transformation. Played it role by affecting the
development of matter so that it gained the qualities of chaos. If absolute
isotropy was at the beginning, if only planckons formed the network, then chaos
could not happen during the phase transformation, and fluctuations could not take
place. There would be no large-scale structures, there would be no galaxies and
we wouldn’t exist. The primary anisotropy of the panelsymon was also the source
of known today fractalization of matter.] Hence
the diversity of the types of particles and limited (not infinite) number of
their kinds. Maybe that is also the cause of the predominance of matter over
antimatter. After bursting of panelsymon (phase transformation) only those
systems remained that could exist as stable/permanent (without interference
from outside). Perhaps these are the systems internally resonant, variable in a
cyclical (reversible) manner. Thanks to this, (when in isolation) they do not
emit any radiation – these are the particles that have the right to exist. [
"Radiation"? Of course, in principle it would not be electromagnetic
radiation. So what kind? "Gravitational"? (On the subject of gravitons
I have already spoken. I’d like to remind that the system is stable when
changes occurring in it are cyclical, and its energy does not change.) Probably none. And if there was an internally
resonant particle? That’ll be the day! - systems other than possible could not
be formed, if only for reasons of energy. Here any speculations just don’t make
sense.] The fact that most of them (those internally resonant) decay means that
there is an external factor that causes decay. I have already drawn attention
to this in the preceding article (in the reference with three stars). This
factor is mainly neutrinos (or photons. With their secret gravity inductively
induced? Very possible.) Local
anisotropy could also result in the release of free planckons or very massive
aggregates, all of them with considerable mass and minimal dimensions, creating
global network of dark matter. With the passage of time, around their local
densifications (fluctuations) accumulated matter (as we know it), and the first
swarms of stars (already 200 million years after the Big Beginning), and after
approx. one billion years they started creating systems which we detect as
quasars. These, over the next few billion years, will evolve into galaxies. About
the formation of galaxies I wrote in another place, in an essay devoted to this
topic).
December 2013
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