One of the historical misfortunes that put the physics
down in trouble was Minkowski's "sudden" death, one year after his
important spacetime discovery. He did not have a chance to go after and fixed
whichever idea diverged from his own or elaborate his idea that he might not
yet express adequately a).
The crucial issue that Minkowski did not have a chance
to touch was the nature difference of the space and time albeit their complete
union. Einstein took charge on it but with an indecisive elucidation1: "The non-divisibility of the
four-dimensional continuum of events does not at all, however, involve the
equivalence of the space coordinates with the time coordinate. On the contrary,
we must remember that the time coordinate is defined physically wholly differently
from the space coordinates".
Einstein certainly knew that any indivisible continuum
[no matter how many numbers of its dimensions] should be completely symmetric,
homogeneous and isotropic, in the sense that all of its dimensions are
equivalent. However, he did not know why in the real world we experience
with such different kinds of dimensions such as spatial and temporal. He had no
better answer than taking for granted their difference as intrinsic. However,
the cost we have to pay for it is too high.
At those days physicists knew nothing about the
concept of symmetry breaking that would be developed later on in the quantum
theory. The relativity theory has missed this kind of phenomenon which marked
the beginning of the world we know today, a mechanism that broke the spacetime
dimensions into spatial and temporal.
Ocean of Action, the Aeon
The discovery of quantum, if it were interpreted
correctly would make the progress of physics much faster than it is now. Planck
was unaware that he had revealed the fundamental nature of reality i.e., the
union of energy and time (Et), the 4-dimensional quantum of action.
The spacetime, the union of space and time, that
Minkowski had discovered, on the other hand, was merely a geometrical structure
of 4-dimensional ocean of quanta. This ocean of temporal energy resembles eon, a timeless undifferentiated epoch, the
name which we propose to adopt b). As the current
"broken" unit used for quantum does not reflect the inextricability
of energy and time, we may use a more natural unit "eon," so that one
eon = 6.63 10-34 joule-second.
Nobody points to Planck discovery as the unification
of time and energy as what Minkowski did on space and time. Energy and time are
inherently inextricable just as space and time to be. Similarly, the dimensions
of the spacetime in its undivided state are in a complete union; all are
inherently equivalent, i.e. temporal.
A Series of Symmetry
Breakings, the Aeon Split
One of the oft-abused expressions that physicists use
is word creation. In the relativistic world there is no creation but separation
c). Nature tends to break down unity into duality,
and duality into plurality d). It is the
underlying principle of what physicists call spontaneous symmetry breaking.
The beginning that marks any symmetry breaking is
relative as such event happens successively in series. The beginning in physics
always points to a relative one, even if it is about the beginning of the
universe. The absolute beginning is far
away remote in time veiled by layers of worlds of various dimensions came into
being in a series through symmetry breakings happened successively.
The symmetry breaking works on the premise that
everything exists in pair, either in actuality or potentiality. The case also
applies to the eon. Without its opposite partner, the eon will remain sterile.
As such, there will be no reaction or interaction and no world
"creation."
The eon is primordial, can neither be created nor
destroyed. All changes are just the
manifestation of its transformations. In
its primordial state, the eon was extremely unstable as its opposite parts
tended to segregate. As it split apart a
boundary (3-dimensional interface) appeared in between the embedding parts,
which was much more tenser than the surrounding due to its [interfacial]
tension e).
Due to its “rigidity” the dimensions along the
interface f) are no longer equivalent with
those of the surrounding. We perceive the former dimensions as spatial and the
latter temporal, its original nature, and the interface as the space in which
we live.
The Geometry and Reality of
Space
The geometrical elements such as point, line, and
plane are defined conceptually as having zero, one and two dimensions,
respectively. These configurations are only in imagination and utterly
different from those in the real world. However, physicists take those
geometrical elements for granted for their world model both microscopically and
macroscopically.
In real [3-dimensional] world what we call point is,
in reality, a 3-dimensional small grainy object, a line is 3-dimensional small
cross-section thread-like and plane is 3-dimensional thin surface-like. No
wonder, as those elements in the model miss some "thicknesses,"
physicists are confronted with problems such as singularity or infinity in
searching for solutions.
In dealing with the quantum realm where any things are
small, one cannot neglect any thickness whatever small it is. The minimum
thickness that nature allows is 10-33cm or
equivalent to 10-44 second, below which
everything would just disappear into thin air.
Such case also valid for the interface discussed so far in the sense
that its thickness cannot be zero. Its small thickness reflects its brief
lifetime, the universal now. The space as a whole and the universal now are two
different aspects of the same thing.
At such interface exists only in a short time, the
action (Et) is reduced to become [3-dimensional] energy E (Figure-1). It is the
underlying quantization procedure in which a crazy looking differentiation to
time replaces energy: E = iℏ ∂/(∂ t).
On top of the interface's thickness other feature that
most people overlook is its two-sided surface. As the interface is embedded in
the opposite eons, one side that faces the positive eon has positive energy;
the other side has negative energy. These opposing energies are the implicit
solution of the relativistic energy equation E2 = m2c4 + p2c2. The Cashimir
effect experiment demonstrates the existence of negative energy.
As Einstein equation E = mc2 indicates, the side having positive energy will
become the locus of matter while the opposite side the locus of antimatter. The
transformation of energy into matter and vice versa takes place at the pace
equal to the speed of light as implicitly indicated by Einstein equation. It is
the reason why no matter can move faster than the pace of its perpetual
creation.
Grand Cosmos, the Ensemble
of Multidimensional Aeons
As mentioned previously there are many worlds of
various dimensions as a result of symmetry breaking happened successively. Some
recent theories, among other the string theory, support the existence of such
multiple worlds indirectly, hence, the existence of eons of various dimensions.
The ensemble of those worlds, the grand cosmos, can be
described in term of their respective positive and negative (frequency) eons.
At the lowest level, we have 3-dimensional energy (E), at higher levels we have
consecutively 4- aeon, Et1, where t1 is its corresponding time, 5- aeon (Et1)t2, 6- aeon (Et1t2)t3 and so on and ultimately n- aeon (Et1t2t3 …. tn-1)tn, where t2, t3…tn are their
corresponding time, respectively.
The ensemble of positive (frequency) aeons:
F+ = Et1 + Et1t2 + Et1t2t3 + ….. Et1t2t3 ... tn
As those multiverses have their own speed of
[multidimensional] light c1, c2, c3 …. cn, then we may express t1 = i µ1 c1t1, t2 = j µ2 c1t1, t3 = k,
… µ3 c1t1… tn = w µnc1t1,
where µp = cp / c1 , the
relative speed of the higher-dimensional light, in which
p = 1,2…….n, and i,j,k…..w are
imaginary numbers.
For the sake of simplicity we just write c1 as c and t1 as t:
F+ = iµ1cEt + ij (µ1µ2) cEt2 + ijk (µ1µ2µ3) cEt3 + ….. ijk..w (µ1µ2µ 3 … µn) cEtn
F+ = a1 Et + a2 Et2 + a3 Et3 + ….. an Etn
where
a1 = iµ1c, a2 = ij (µ1µ2) c, a3 = ijk (µ1µ2µ3) c, an = ijk..w (µ1µ2µ 3 … µn) c
Similarly the ensemble of negative (frequency) aeons:
F- = a -1 Et-1 + a -2Et-2 + a -3Et-3 + ….. a-n Et-n
The totality of aeons within the grand cosmos g):
F = F+ + E+ F+
which is nothing but the formulation of Laurent
series.
This representation provides us with a deeper insight
into nature. We may recall that these
Laurent series can be holomorphically mapped as Riemann sphere with its respective
annulus of convergence (Figure-2). F is expressed as a sum of the positive
frequency part (F+) which extends
holomorphically into the southern hemisphere together with the negative
frequency part (F-) extending
holomorphically into the northern hemisphere. The energy (E) as the constant
term of F is located at the equator of the Riemann sphere.
This Riemann sphere represents reality faithfully. Its
annulus of convergence indicates that nature abhors the singularity and
infinity. The Big Bang and the black hole theories which heavily rely on the
possible existence of such singularity may be unphysical. Likewise, the
universe is forbidden to expand forever to infinity. In the future, as the world becomes extremely
unstable, it would be broken apart … the doomsday.
Notes:
a. Minkowski
concluded2:” We should then have in the world no
longer space, but an infinite number of spaces, analogously as there are in
three-dimensional space an infinite number of planes. Three-dimensional
geometry becomes a chapter in four-dimensional physics…” Physicists seemed
at lost as he did not elaborate explicitly whether those spaces may exist
simultaneously or potentially. They refute the existence of even a single
[universal] space.
To avoid further confusion,
I wish to make it clear that all those spaces exist in successive order, in the
sense that the individual space appears and disappears one after another
successively [at the pace equal to the speed of light]. It is the underlying
mechanism of what we perceive as the succession of time.
Now, from a time
perspective, we see all things upside down. We say that we have a different
space for each moment in time. Penrose defined this "alarming"
situation as Galilean spacetime3: “space seems
to be of something that evaporates completely as one moment passes, and
reappears as a completely different space as the next moment arrives."
Nobody knows that this is precisely the reason why the [quantum] world looks so
bizarre. It underlies quantum jump and quantum entanglement phenomenon. The
former is a kind of inherent micro-teleportation across time while the latter
is the mechanism required to avoid chaotic teleportation from one fading space
to the next arising space as a whole.
b. We better
use the term 'eon' instead of action to underline the tangibility of this ocean
of temporal-energy continuum. What we perceive as fields are nothing but the
"surface" manifestations of the 4-dimensional ocean of this
immaterial substance. Nature only allows the use of this action modestly and
economically.
c. In a
simple ordinary case, when one rubs the glass rod with a piece of silk, the
glass rod becomes charged with positive electricity and the silk with a
precisely equal negative charge. The friction does not generate but only
separate the two kinds of electrification.
d. The
dynamics undergo from simplicity to complexity and from the state of higher
order into disorder. The measure of such changes is the entropy of the system.
e. From an
earthly perspective, this tension is equivalent to what we know as the
gravitational constant.
f. It is
more convenient to use the concept of a hypersurface, which is an extrinsic
concept of the world as a system together with the surrounding rather than
hyperspace which is an intrinsic view covering only the system.
The brane theory also
adopts the concept of the hypersurface but in the wrong design. The dimensions
along the brane should be a strictly spatial while off the brane temporal.
Another hint to fix the theory is that the graviton should not allow floating
off the brane; otherwise, the brane will be broken apart.
g. This
expression clearly shows that time is intrinsically multidimensional. The extra
dimensions are invisible because they are temporal. We used to see the world
upside down. Time dimensions are more fundamental than space dimensions. Space,
no matter their dimensions, is incidental and ephemeral.
Physicists, like anybody
else, used to consider that time is unique. They believe that there can be only
the same time dimension prevails in the universe and anywhere beyond. Moreover,
physicists hold that all spatial dimensions other than the ordinary three
should be curled-up into tiny loops; hence, their invisibility. It leads us to
exceedingly complex formulations with its many possible solutions.
References:
1. Einstein, A.:" The Meaning of Relativity,"
Princeton University Press, New Jersey, 1954, p. 31.
2. Einstein, A. et al.:” The Principle of Relativity,”
Dover Publication, Inc., New York, 1952, p. 79-80.
3.
Penrose, R.:" The Road to Reality," Vintage Books, London, 2005, p. 387.Bottom of Form
