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Conference: Photon-splitting and elongation By
invitation (chairman: John Pazmino) New York Skies Astronomy Seminar,
December 7, 2006. Work in Progress: Simulation of the Big-Bang unfolds of the space-time
continuum. Alfred Bennun Abstract The dynamics of primordial
energy could be described as a wave function and allows simulation of a model
in which time and the expansion of space emerge naturally through the
continuous decrease of its initial frequency. The parameters of time and
space were scaled as a function of the increments in the values of time and
volume of l-localization.
Conservation of energy by parametric down conversion would allow wavelength
elongation resulting in an increment in the number of photons, but at a
longer wavelength (l). This was illustrated as a function of the photons at
the Planck energy limit continuously increasing the amplitude of their
wavelength. Each photon resulting into two of twice the length of the
predecessor wave and eventually result in Cosmic Microwave Background
radiation (CMB). The velocity for the changes of phase of sinusoidal waves is not limited by that of light.
The increment of the cosmic radius could therefore be related to the trains
of photons, incrementing their length four times per each duplication event.
The changes in cosmic volume up to scission of strong and weak forces were
correlated by (43)n-1 multiplied by the volume
of l-localization and by the
accumulated number of photons. This formula allows an exponential increase in
base ten of the cosmic volume as a function of the chronological decrease in
the energy of cosmic radiation during the Inflationary time. The expansionary
rate was obtained multiplying only the number of CMB photons by the volume of
CMB l-localization allowing results in
accordance with the size of the universe between the periods of last
scattering and present. It is assumed that the
astronomical survey of this expansionary period may be able to observe
increments of the wavelength of CMB spectra according to cosmic chronology.
However, because CMB only conserves 0.005 % of
the initial critical energy, it was also assumed, and used as a correction,
that at the end of the inflationary period the energy of most photons was
converted into dark energy and ordinary and dark matter. Connes proposes a cosmos geometry describing that, in between two layers of space-time continuum, there is a discrete and non-continuous non-commutative space. If space is geometrically differentiable, this should correspond to thermodynamic structures with differentiable properties. General relativity expanded special relativity by demonstrating that the interaction of matter with the space-time curves the space. However, by not defining if the space-time could exist independently of energy it could be inferred that it does not. Consequentially, the gravitational effect may result from density of energy structuring the geometry of the energy-matter-space-time locus. Hence, gravitational energy may not be characterized as an excisable force as it’s the case for the strong and weak forces. Therefore, may not be a need to postulate a theory proposing gravitons like it does the Grand Unified Theory (GUT). The complementation between continuum and non continuum requires characterization. One may surge from Schrödinger’s equation, which shows that probability density is a function of the square of the amplitude module of the wave. According to the Heisenberg principle, a continuum of wavelength increments with concomitant increments in amplitude would yield a gradient of increasing uncertainty. However, this is a cause-effect relationship. Therefore, the evolution of primordial and, maybe, dark energy, may constitute the thermodynamic structure of a continuum with thermodynamic predictability equivalent to a causality vector, and, the non-continuous geometry, from the transformation of primordial energy into ordinary and dark matter, describable in terms of its intrinsic quantum mechanic properties. Hence, either could show time dependent energy arrows which link within cosmic evolution relativity and quantum mechanics. Also, the radiation continuum with thermodynamic geometry which intrinsically prevents time-symmetry could merge with the non continuum self-connected by energy flows seeking equilibrium. The latter would allow particle level time-symmetry and molecular and local level events with microscopic reversibility modulated by synchronized coupling between downhill and uphill thermodynamic flows. Thus, allowing vector kinetics which characterizes life by its capacity to decrease entropy inside of a cell at the expense of its environmental increment. Introduction The parameters of the changing space-time during the Inflationary Era are described using a different model than that of Guth et al (1) (2) (3) (4) and Linde (5) (6) (7) (8) (9), based in a positive vacuum mechanism. One of the major objections to the presence of a singularity at the initiation of the Big-Bang (10) (11) is that conceptually it should be described as a dimensionless point. The problematic resulting from a physical description of the universe initiated from a non-dimensional geometry with matter at infinite density was an incentive for the development of alternative hypothesis like String Theory (12). To overcome these objections it was inferred that primordial energy could be conceptualized as a radiation that even if not yet characterized its evolution could be described in terms of wave functions. The velocity of the changes of phase of a sinusoidal wave generated by a laser pulse in a cell of caesium gas exceeded by 300 times the velocity of propagation of light in a vacuum (13). Therefore, the primordial radiation changes of phase resulting from the continuous decrease in its frequency and the dissociation of strong, weak and electromagnetic forces and/or transition between a virtual and ordinary time and space of localization could be assumed to occur within the time parameters of the Inflationary Era (14) (15) (16) (17). There is not a theoretical limit to how high could be the frequency of a radiation; the simulation starts at the initial energy quanta the Planck energy limit 1.22 x 1022 MeV (Mega Electron Volt). This allows that the number of primordial photons required to reach the energy equivalent to the critical mass could be confined (18) in a very small but still tri-dimensional space. Accordingly, a radiation of ultra-high frequency could emanate from confinement (19) (within space restrictions which would not hold the kinetic energy required for baryonic particles to reach the temperature needed to start the hot Big-Bang (10) (15). Anton Zeilinger (20) and Y. S. Lee (21) showed that the ultra-violet laser incidence on a non-lineal crystal through the process of parametric down conversion to lower energy photons, allows each photon to divide into two of longer wavelengths. The individual photons energy is inversely proportional to their wavelength. The simulation correlates the evolution of cosmic energy by the increase in the number of photons and their wavelength increment. At temperature equilibriums, photons radiate with the energetic distribution of a black body. The finding that at 3.79 x 105 light years from the Big-Bang, a surface of “last scattering” with a temperature equilibrium of 3000 K° originates the CMB photon-packets which could be interpreted as a red shift, z = 3000 K°, to the 2.73 K° observable at present. However, it is commonly accepted that this temperature gradient is a part of the time-temperature axis correlating the chronology of the Big-Bang (14) (22) (23) (24) (25). Radiation temperature and radiation energy are equivalents, but the simulation uses units of energy rather of temperature because the latter, conceptually could be related to the kinetic energy of matter. The latter plays the initial role in the hot big-bang whereas the simulation assumes that primordial energy could be regarded as a mass-less intertwined complex of strong, weak and electromagnetic forces. Even if is not fully characterized, primordial energy could fit the description of electromagnetic radiation through its treatment as a wave function which shows that the possibility to find an energy quanta in a given space-time parameter is a function of the square of its amplitude. Accordingly, a time-temperature parameter could configure only a thermodynamic arrow, whereas a wave function not only provides this arrow, but also allows associating amplitude increases to quantum mechanics description. The increase in wave amplitude decreases the probability density that could be attributed to a single energy quantum. However, if the individual wave functions are expressed as interconnected as a train of continuously decreasing energy and concomitant wave amplitude increment, it configures a probability arrow. If such thermodynamic entity is described as a continuum (26) (27), it would have a thermodynamic tendency to irreversibility (28) (29) (30). Hence, if cosmic evolution could be described as the continuum, individual photons and matter particles would show the characteristic quantum mechanic behaviour of individual energy quanta. However, the expanding of primordial energy would create a decreasing probability arrow that would integrate causality into the relationship of coupling between time-dependent thermodynamic events (31). This would have an oscillatory axis and propagate as a radiation that, after scission of component forces, allows restructuring as ordinary and dark matter, dark energy (32) (33) and relic wave packets of CMB. Oscillations within the same time of localization and/or space of localization would not structure as a thermodynamic dissipative potential. This could be assumed to appear as an arrow of time (34) (35) (36) and space expansion when oscillations propagates from smaller to larger wave localization dimensions. If time and volume of localization of particles bearing mass would not evolve from smaller to larger values, this could not provide an expansionary potential and their role would be to oppose expansion through gravitational attraction. In the context of a time-wavelength axis, at the frontier of last scattering, free electrons interact with photons through Thomson scattering, which couples matter and radiation. Then, the expanding Universe cooled and as the temperature reaches 3,000 K°, the scattering ends and photon packets are released as an emission of a black body as shown by the wavelength spectra of CMB. The astronomical elongation observable of CMB has lead to the perspective that cosmic expansion stretched the photons to longer wavelengths. The simulation may be regarded as intent to reverse that perspective, but, it is truly intended to examine these interrelationships without reaching a conclusion of which is a cause and which is an effect. By a change in perspective it could be assumed that the increase in wavelength of primordial photons and relic CMB may be factors in the dimensioning of the space-time. Methods Assuming that primordial energy in the form of energy packets is not subject to interactions at the initial stages of the cosmos, it could be discussed according to the solution of Schrödinger’s equation for a harmonic oscillation known as a wave function Ψ(x):
Where A is the maximum amplitude of the function; k is the number of wave; w is the angular frequency; φ is the phase of the movement; and x and t are the spatial and the temporary variables. This approach allows that, independently of the lack of characterization of primordial energy, this one could be described in terms of frequency evolution. Hence, time of localization and volume (space) of
localization, emerge naturally. Wavelength is the space or distance for the
wave function between two peaks. The wave amplitude could increase as the
wave propagates. A time dependent cosmic relationships with quantum mechanics
are reflected in that the probability to find the particle in an interval x,
x+dx is the square of the module of the wave function Then, the probability per unit of length (or probability density) to
find the particle in x is Evolution of cosmic energy as a wave function of primordial energy packets could be simulated by treatment as a continuum, linking uncertainty with causality. A Universe inflated by matter, in which the modification of the kinetic energy of particles occurs without that of their resting mass eludes the concept of a continuum. Hence, matter particles that disperse according to temperature-gravitation equilibriums will rather reflect properties that fit within the non-continuum description of the Universe by Connes (37). Therefore, the simulation by treating the evolution of primordial energy as a radiation focalizes into the characterization of the continuum. Number
of stage (N): shows
decreasing by half the Planck energy limit (EPl) according
to progression (1, 1/2, 1/4, 1/8, etc.) ending at 1/ 2106 = 1/ (8.11
x 1031), or the presently residual energy of CMB photons after 106
stages plus initial (0) total 107 stages. Planck energy limit (EPl): the three fundamental
constants: G ( CMB photon packets:
Best fit thermal distribution of a black-body spectrum: actual mean temperature
(T) of 2.725 Kº
converted to 2.35 x 10-10
MeV (Mega Electron Volts). Frequency peak: 1.604 x 1011 Hz; and
wavelength peak: 1.9 x 10- To calculate, according to Wien Law, emission peak for a black body: T=2.897 x 10- Calculation of critical energy: 2.35 x 10-10 MeV multiplied by the actual number of CMB photons (3.74 x 1087) equals 8.79 x 1077 MeV, which only represent 0.005 % of the total energy or critical mass for a self-contained universe (1.702 x 1082 MeV), equivalent to about 2 protons per cubic meter. Energy of wavelength (Eλ): starts at the value of EPl and each
stage decreases by half the energy to end at the actual value of CMB. This procedure
yielded a total number of 107 stages; and allows the dimensioning of the
energy parameter. In Table 1
denominated for primordial energy: Radiation Wavelength (λ) and a Table
2 average λ (black body to the photon packets corresponding to each stage),
according to the formula [c = f x λ], were c = velocity of light (2.997 x Time of λ-localization (tλ-loc): corresponding to each wavelength. According to the relationship for frequency: [tλ-loc= ħ/E=1/f=λ/c]
expressed in centimetres. Time (t) expressed in seconds [t x c = 2r] was used to calculate the time of localization for photons, calculated considering 2r = λ results in value of localization for EPl energy limit that equals 5.40 x 10-44 s. Similar value could be obtained according to: tPl
= Photon number (nγ): incrementing according to
the progression: initial value x (2)N-1. The critical mass divided by the Planck Energy
Limit results in the initial value 1.40 x 1060 photons. The values of energy per photon (Eλ), in accordance to the equation: [Eλ =ħ x f], were used to obtain the frequency values in Hz, which were calculated but not included in the table. Volume of λ-localization
(Vλc-loc): according to the formula in cm3: [Vλc-loc= 4/3 x π x λc3]. In the
formula of a sphere, r3
was replaced by λc3. Radius of localization
(λc) based in the Range of values of λc: Table 1: from
stage 0: 1.62 x 10- Radius of the Universe (Ur):
calculated by compounding the lengthening of photon trains by simultaneous
doubling the number of photons and doubling the wavelength and amplitude
according to Ur= (4)N-1
x ((Vλc-loc x nγ) x (3/4) x
(1/π))1/3 in cm x 1.05805 x 10-18,
equivalent in light years as unit of length. This
formula came from the formula for a Universe volume: [UV= (43)N-1 x Vλc-loc x nγ= (4/3) x π x ( The
term (43)N-1 was
developed only for Inflation to provide a volume expression for the separation
of forces. It was assumed that the transversal polarization of the
oscillatory axis of the electromagnetic force results from the scission of the strong force at 1016 MeV, and the
weak at 1012 MeV. The separation of these forces according to
the two complementary axis allows volume to increase according to a cubic
exponential associated to the rate of lengthening of each photon train. Under
non-tabulated values these relationships are formalized. Time of particle localization (tp-loc): according
to the relativistic formula which allows to relate radius of particles (r), to the velocity of light and time
(t) expressed in seconds [t x c
= 2r]. The Planck particle
corresponds with the Planck radius of 1 x 10- Temperature-time axis (t): could be
correlated with Eλ (2nd
column), on the basis that, to decrease
energy either as a wavelength or temperature by half, requires a
corresponding doubling of the preceding elapsed time. This rate of 4 relating
the decrease in energy to an expansion of the associated time may reflect a
rhythm for the enlargement of the space time. This may relate to a
relationship in which it is required that the time of localization increase
by 2 to allow that the radius of localization could also simultaneously
increase by 2. Results The energy
differential between CMB emanating from the surface of last scattering (3.79 x 105 light years) at a
temperature of 3,000 K° and its presently observable 2.73 K° was scaled as
following a decreasing progression in a base of one half which is about 3,000
K° x (1/2)10 = 2.93 K° (table
3). This correlates with a sequence in
which energy per wave packet decreases from 2.59 x 10-7 to 2.35 x 10-10 MeV, halved 10 times or about (1/2)10.
The increase in the Universe radius from the time of last scattering to the present
could be expressed as a 3.63 x 104 radius increment or a progression of about (2.84)10.
Calculation by parametric down conversion shows that, during the same period,
the number of photons would multiply by 210, which is a partial
increment of the total one. Accordingly, the
simulation adopted a gradient or continuum of decreasing energy in terms of
frequency, scaled to show that an increment of wavelength not only decreases
energy by half, but also requires the doubling of the associated elapsing time. This approximation was regarded as acceptable in terms of the
simulation requirements, and astronomical
observations were extrapolated to initial conditions according to Planck
energy limit, which allow calculating that after 107 stages of decreasing energy
by half, it would reach a value concordant with the present one. The time elapsed from the Era of equal particle to radiation number
to the present, shows that a photon number increase over particles by about 231,
suggesting a partial energy conservation mechanism by parametric down
conversion. The discrepancy disappears by taking in account that most of the
energy present as primordial energy was diverted for the formation of
ordinary matter and dark matter and dark energy. Hence, preventing that photon
number could increase by only accounting their formation by parametric down
conversion, the stages allocated for this process are indicated by the
question marks in Table 2. Thus, allowing that only 1/20,000 of the total
initial energy could reach the frontier of last scattering. Calculation
does not represent a physically observable parameter since wavelength
elongation may be observable as a much more gradual decrease in temperature
from last scattering to the present. However, the mathematical artefact of
dividing by two could help to pinpoint the levels of CMB energy within time
and space parameters. The model adopted reference values shown in bold characters from observationally and theoretically accepted concepts to determine best-fitting of the several treated simulations. The one regarded as showing consistence with observations was a cascade scheme. This assumes that, rather than dissipate its energy, the wavelength trains of primordial photons and resulting CMB relic when increasing the amplitude of their wavelength, would conserve the missing energy rather than increasing entropy. The mechanism adopted for energy conservation was parametric down conversion which allows a gradual increase in the total number of photons. This process could be illustrated as a photon number increment within the train of elongating waves or through continuous and simultaneous events decreasing by half the energy of photons to duplicate the photon number. The more gradual mechanism may eventually be shown to better correspond with observational data. However, it was computational convenient to develop a numerical simulation of Inflationary dynamics, schematized as a chain of photon-splitting and elongation cascade scheme (PSEC). The value calculated
for the critical mass divided by the Planck energy limit yielded the initial
number of photons (ng) 1.40 x 1060 shown in 5th column of Table 1. The chronology
established in terms of the energy-time relationship was expanded to include time and volume of
λ-localization (Vλc-loc) as additional requirements to correlate events. The time lapse of inflation would not be limited by the velocity of light propagation in space because of a phase transition of the amplitude of the trains of photons when decompressing the space-time dimensions of the cosmic energy field. Accordingly, the rate of increase of cosmic radius and that of the number of photons formed by the multiplication chain during the Inflationary period were assumed not to be influenced by the insignificant distance travelled by light during this period. The emerging from
confinement of primordial radiation into a continuously unfolding space-time
indicates the convenience to relate the decrease in frequency to a time of
wave localization rather than to relate directly energy evolution to an ordinary time scale.
Accordingly, in Table 1, this parameter allows not to ignore that the
theoretical meaning of time of localization provides, as a function of its
energy, a physical lower limit for the cosmos existential time required for a
wave dimensioning into or within the space-time. Example: If shutter timer
allows only the emission of a single violet photon, the same timing would not
allow the emission of a red photon which would occur only if the timer is set
to increase to the time dimension of the latter photon. The time of
localization could be calculated by using the relativistic formula that
relates the radius (r) of particles
to the velocity of light (c) and
time (t): The Planck energy limit (EPl) is the same quantity for an energy packet either
particle or wave (1.22 x 1022 MeV). However, it could
be assumed based in that duality as either photon or wave allows description
in terms of different space-time conformations, but could be useful to only
differentiate by assigning the denomination time of λ-localization for
waves (tλ-loc) and
in the equation refers 2r as equal to λ, and for particles or photons, the
time of particles localization (tp-loc)
referring 2r as equal
to the diameter. Table The dispersion of trains of increasing number of photons, would conform an arrow of time according to the increment in time of
localization and would inflate space by the increase in their number and volume of photon
localization. In Table 1 the scission of strong force at 1016
MeV and weak at 1012 MeV relates to a change of phase that would
occur at much greater velocity than that allowed by the celerity of light. Table 1 emphasizes the role of time localization in generating the
Inflationary time and its ending at the time of the scission of the weak
force. At stage 33, the energy per photon corresponds to a tλ-loc of 2.91 x 10-33
s., a time usually assumed to end Inflation. At the end of inflation the initial number
CMB photons (1.40 x 1060 photons)
multiplied by 233 (or 8.59 x 109)
have increased to 1.20 x 1070 photons, but
since the radius has increased according to (4) N-1 x
rλc to 2.35 x At stage 56, the energy of wavelength (Eλ) has decreased to 1.69 x 105 MeV, which, according to Connes mathematical treatment (37), is the value that allows the appearance of the Higgs boson. When the dimensions of the cosmic time axis exceed that required for tλ-loc for a single wave, the tendency to further expansion becomes less dependent of subsequent tλ-loc increment and more of the incremental volume of photons localization and their increase in number. During the Expansionary time the velocity of light propagation in space could make a substantial contribution to the rate of increase in the value of the cosmic radius. Table 2 shows that at the moment of the Higgs boson formation corresponds to a value 2.5 x 10-11 s. in the time-temperature axis. This value greatly exceeds the tp-loc required for localization of all the listed particles, which indicates that particle formation is not limited by time requirements and will mainly depend of the cosmic energy level. Table 1 shows that matter particles could not have occupied
ordinary three-dimensional space during most of the Inflationary Era but only
at its ending. The generation of mass would thereafter oppose the
expansionary tendency of radiation. The latter, would be acting as a
quintessence or Einstein's cosmological
constant (26) (38), in opposition to the attracting force
of gravity, but at a rate limited by the
thermodynamics of time-space dilation. Table 2 takes into account
that, after formation of ordinary matter and dark matter and energy, only
1/20,000 of the total initial energy would reach the frontier of last
scattering. Therefore,
transformation of an energy gradient of radiating wave packets into dark
energy and matter, and ordinary matter, may have followed a sequence of
stages. At these stages, photons still would be
duplicating, but also disappearing by converting their energy into the
equivalent resting mass of particles. The corresponding extrapolation for the
number of photons column was not done because it could have been less than
accurate. This was resolved bypassing stages 56 to 70 by using the question
mark symbols. Table 2 shows that at
the stage 60 the energy level still exceeds that required to create the
masses corresponding to quarks (according to E=mc2) expressed in MeV, which are: charm: 5 x 103,
bottom: 1.6 x 103 and up, down and strange below 1.5 x 102.
Quantum physics assigns to each particle a minimum volume of localization
which corresponds to the radius of 3 x 102 Fermis for an electron
and 1/10th of Fermis or 10- However, it has been
postulated that in the earlier space-time the value of the radius of
particles were smaller than in the present. If so, a proportionality factor,
alpha (α), should be used to correct these values: α x Table 2 and 3 shows
that, from the era in where radiation and particles were in equal proportion
(2 x 1078) to the present, the photon number increased as illustrated
from about stage 75 to the present by a factor close to the one reported in
the literature of 1.9 x 109 CMB photons per each baryonic particle. Table 3 includes
observational values obtained by the astronomical survey of CMB, within the
parameter from the era of last scattering to the present, which shows these
photons as decreasing in energy, but, as we assumed increasing in number. At
the CMB emerging from recombination temperature of 3,000 Kº, the corresponding number of photons
would be 3.44 x 1084, which will progressively increment from stage 97 to
107 to reach a photon number of 3.78 x 1087, which closely corresponds to the observed one. These 10 stages of
halving energy were related to the exponential increase of Universe Radius
according to the exponential 2.84. Hence, from
the actual age of the universe, 13.76 x 109 light years, were
subtracted first 8.92 x 109 light years to obtain the initial time
framing of the last division. To the resulting number 4.85 x 109 was thereafter subtracted 3.14 x 109 light years. The ten-stage
subtractions ended at 3.79 x 105 light years which is
regarded as the time of recombination at the end of last scattering. This is one of the relationships that allow extrapolating astronomically
observable values with those obtained by simulation. The Radius in
light years corresponds to the chronometric scale of time based in the
velocity of light. Dividing the actual Universe volume
(9.34 x 1084
cm3) by the CMB packets photon number (3.78 x 1087), it obtained a volume
of λ-localization of about 2.43 x 10-3 cm3 similar
to the one calculated
using the mean value of the CMB wavelength packet. Obviously, it is unlikely, that the present time could correspond to the end of the last division. Therefore, Table 3 partial simulation of a period of the expansionary time, should be regarded as only an illustrative draft. However, it may provide a theoretical framework for a more rigorous computational analysis plotting the elongation and cooling down of CMB radiation to characterize the Expansionary Era. |
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Table
1: Simulation defining Inflation as a function of time of λ-localization
and space by wavelength elongation and photon increment by parametric down
conversion |
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N are stages in the progressions that applies to all
columns, but only 15 stages are reported from the total 57. The column of energy of wavelength was used to calculate frequency (f) values, for an omitted column, according to f=E/ħ, and from there, the values of radiation wavelength (λ), according to λ = c/f. Subsequent columns according to methods Emphasized
in bold numbers: The Energy of Wavelength values proximal to the scissions of
strong (1 x 1016 MeV) and weak force (1 x 1012
MeV), and the required for the Higgs boson according to Connes (1.6 x 105
MeV). Time of λ-localization of 2.91 x 10-33 sec. is close to
the one in the time-temperature scale regarded as the end of the Rapid
Inflationary Period, and corresponds to a Universe Radius of 249 light years. Radius of
localization (λc): from stage
equal to 0: 1.62 x 10- |
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Table 2: Energy and time of particles localization as
chronological limits for the generation of particles |
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The table shows, in
bold characters, the values intercalated for particles. 1st
column: N is stages in the progressions applied to all columns,
but only 20 stages are reported from the total 41. 2nd column: describes time related Events. 3rd column: Energy of
Wavelength (Eλ). 4th column: Number of photons (ng). These values were
calculated as described in methods. The question symbol (?) indicates values
which could not be obtained by extrapolation. 5th column calculates Time of particle localization (tp-loc) according to the relativistic formula which allows to
relate radius of particles (r), to
the velocity of light and time (t) expressed
in seconds [t x c = 2r]. The Planck particle corresponds with the Planck radius of 1 x
10- |
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Table 3: The cosmic radius as a function of the
increments in volume of localization and number of CMB photons |
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The final 11 stages are reported plus an initial one,
added to compares Eλ of stage 96 with that
corresponding to the frontier of last scattering, which is rather out of
scale. Energy
decreases by half, and photons duplicate in number with average λ corresponds to the mean of the
distribution of radiation emitted by a black body. The
table relates the energy in CMB packets, after most of primordial energy,
generated ordinary matter, dark energy and dark matter, from last scattering
to the present, as the summation of energy per photon x number of photon as total 8.89 x 1077 MeV. This value
corresponds to a 1/20,000 remnant from the total initial value shown in table
1= 1.71 x 1082 MeV. Astronomically
observable values in bold characters for CMB photons packets radiating from
the time of last scattering of 3.79 x
105 light years radius at a mean temperature 3000 K (2.59 x 10-07 MeV), to the
present Universe of 13.76 x 1010 light
years radius at 2.73 K (2.35 x 10-10 MeV) with a number of photons
of 3.78 x 1087. The Universe Radius ( |
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Discussion The purpose of the simulation is to illustrate that there are
energy-space-time relationships, which are physically ingrained in wavelength
elongation as described by the model and may be verifiable by concordance
with astronomical observation. The NASA, COBE and WASP space probes (22) (23) (24) (25) show
a flat cosmic geometry that, if not to require a very exact critical mass, indicates
that at the Universe origin, a mass-less primordial energy describable by a
wave function could have preceded the formation of matter. Accordingly, the primordial quanta of energy at the earlier Inflationary time may be
mass-less as it is the presently detectable electromagnetic radiation. This
proposition is required in order to elude that mass density, at the initial
stages of the Big Bang, would lead to a non-physically describable
dimensionless singularity (39) (40). Hence, even if at present matter
could be described as distributed uniformly, at the origin of the universe
only radiation was present and the absence of matter prevented an initial
curving of space-time. The model basically provides a mechanism to conserve a finite cosmic
energy by evolving, by parametric down conversion, as a cosmic energy density
decrease. A cascade or gradient of primordial
radiation decreasing its energy density could not be fully described by a
time-temperature parameter, because the cosmic existential time may not
suffice to provide the volume and/or time of localization for the increasing
size of the expanding in space-time energy packets. Hence, for Table 1,
was elaborated a time parameter based in the time of λ-localization and,
at the same time, this was a check for consistency with the more generally
accepted axis of time-temperature. The model leads to assume that a space-time-framework for energy
dispersion exists which would be detected by examining observational data. The logic behind
these arguments was based in that wavelength elongation by incrementing space
and time of λ-localization may impose a cosmic Inflation-Expansion
requirement. Treating wavelength elongation not as a continuous increment but
as a series of numerical increments allows to formulating comparative scales
more easily. The methodology of dividing by half the energy and, by
parametric down conversion, doubling the number of photons versus time should
only be regarded as a way to scale thermodynamic correlations between the
parameters of time, energy and space. The relative size of the Cosmos versus time has been usually
described as a continuously growing sphere with a space-time radius that if
it were to be scaled as to display bidirectional surfaces it would behave
like an inflating rubber globe were all points recede from each other. The
unidirectional nature of time allows that the photon duplication chain will
shape the space dispersion of observable CMB as conical along a single axis
of time, showing a sequential decrease in the size of the universe which
becomes smaller and smaller until converging onto the surface of last
scattering. The period of
continuous decrease of velocity of the space-expansion was followed 5 x 109
light-years ago by a period of expansionary reacceleration. Reacceleration of the rate of expansion may be explained by the
increasing distance between galaxies decreasing their mutual gravitational
attraction, whereas the increment in the number of photons and simultaneous
wavelength increment could exponentially extend the distance between
recessionary galaxies moving away as a function of a time-temperature axis,
or as discussed, a time-wavelength increment axis. CMB
photons need to travel along no less than two space parameters to show the
influence of a gravitational depending curving of space. The conical nature of CMB dispersion, along a single axis of time,
may allow that at the large geometrical scale, CMB observations could show a
flat universe. Accordingly,
all CMB observers from all directions would have lines of vision that could
only converge into the same axis of time to ultimately reach a single vision
corresponding to the initial state of the universe. Hence, at the largest
scale of deep space, the universe could be characterized by its observable
isotropy meaning it would look the same wherever the position of the CMB
observer would be. The expansionary tendency of radiation follows the pattern of a
non-equilibrium thermodynamics structure, in which time dilation and the
dispersive dissipative potential of primordial energy, by expanding
wavelength and number of photons, acts like Einstein’s cosmological constant opposing the centripetal force of gravity. The intrinsic time-reversibility of the microscopic laws of physics
constitute the “arrow of time” problem. The kinetic and thermodynamics events
associated to a photon-splitting cascade could be deduced by assuming that
the division of one photon into a train of two photons expanding into space
is thermodynamically more favoured event than the association of two photons
to reconstitute into one of higher energy. The forward direction for the
progress of photon division generating trains of elongated photons of lower
energy will be the one favoured. The lowering of frequency associated to time
dilation also means that dissipation of the energy potential between high and
lower wavelength frequency would oppose any intrinsic tendency for
time-reversal. Hence, time symmetry could not be manifested as long as the
dissipative potential is not exhausted. This creates an arrow of time between
the past associated to higher frequency photons and the present and the
future that is associated to their lowering frequency. Thus, according to the
illustrative concept of arrow, the thermodynamic (11) and the
kinetic events could integrate to give a vector direction to both
Inflationary and Expansionary times allowing black energy and primordial and
relic radiation to conform the continuum space-time. As discussed, an arrow of time emerges from the kinetic and thermodynamic
structuring of a system rather than emanating from special asymmetric
properties of the universe. Connes geometry, as discussed in the abstract, could be used to differentiate between intrinsic properties of the thermodynamic
continuum and non continuum structures. For instance, the continuum may
produce the gauge bosons W and Z which mediate the weak force, and the non
continuum creates the massive Higgs particles (1.6 x 105 MeV).
Therefore, ordinary matter and, maybe, dark matter could be regarded as
integrating the discrete space where individual atoms could be regarded as
showing time symmetry. At the molecular level, apparent violations of microscopic
reversibility could be observed, a concept related to the conceptual
understanding of time symmetry. To illustrate the role of time in integrating thermodynamics
structures in the non continuum, photo-phosphorylation will be described in
terms of a synchronized cross-coupling between a space configured
electron-transport chains with downhill energy flow, and uphill energy
transfer for ADP-phosphorylation to generate ATP (41). In this example, time controls coupling through the synchronization
between a sequential temporary increases in reactivity of the electron
carriers and the chloroplast membrane localized enzyme ATPase. The
interactions of the latter, with the electron-transport-chain and surrounding
molecules would let the enzyme to change its states of association with
electron carriers, protons, water, and ions. Simultaneously, the enzyme will
sequentially modify the interaction order with substrates and products. These
would be equivalent to a spatial propagation of the energy of activation
(Ea). Thus, generating a sequence of energy of activation peaks corresponding
to intermediate reactions (Ea1→Ea2→ Ea3→ Ea4→…→Eax).
Hence, the reactivity peaks involved in the initial state of the sequence of
reactions could dissipate at a time when the intermediate and final energy peaks are reaching the energy
potential required for progress of the reaction. The time separation between
each of the energy activation peaks of the reaction allows compartmentalized time in reaction stages. Hence, chemical interaction would allow
energy for the forward direction of the reaction at the time that dissipates
the energy required for the backward direction (42) (43). Progress of the reaction will occur without reversibility allowing an
apparent overcoming of microscopic reversibility. For a self-contained
universe, the chronology of the Big-Bang shows not only time-dependent
dimensional changes but also time-dependent changes in the structure of the
thermodynamic relationship between space and the energy of CMB as measured by
photon density and wavelength frequency. |
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Conclusions The time-temperature parameter restricts description to an energy
parameter whereas in the concept of a decreasing wave frequency is not only
implicit in this parameter, but many others. These include space oscillation,
time oscillation, phase, polarization (fitting in a tri-dimensional space),
angular momentum which allows to transfer kinetic energy into mass, and wave
amplitude. The increase in amplitude of each individual wave
packet of energy corresponds to a characteristic quantum mechanic behaviour
decreasing its probability density as a square of the module of the wave
function. However, because the wavelength increment becomes a time structured continuum
of energy decreasing tendency, and its amplitude increment also configures a
thermodynamic structuring to a decreasing quantum mechanistic probability.
These structures merge into an arrow enhancing relativistic causality along
cosmic evolution. The concept of frequency leads to the conclusion that elongation of a wavelength would allow to develop a chronology in which time naturally appears as a function of changes in the Eλ of expanding space. The latter process could be characterized as resulting from simultaneous increments in the intrinsic time of λ-localization (∆ tλ-loc), in the volume of λc-localization (∆Vλc), and in the photon number ∆ nγ by parametric down conversion. These ones could be used as the reference thermodynamic parameters of the cosmic energy evolution structuring the space-time continuum. The model suggests
that by describing primordial energy not shaped as particles, but as if it
had the frequency property of photons, their energy dissipative
potential when surging from
confinement by increasing in number and dispersing in unfolding space evolve
as expected according to
the dynamics of an Einstein universe. In this one, the continuous nature of
the space-time requires that time and space could expand simultaneously. The
linkage to time dilation would not surge naturally from the description of a
universe emerging by the inflow of particles to conform space according to
the prevalent mechanistic description of Inflation. The Expansionary tendency
of radiation would be acting as a quintessence or Einstein’s cosmological
constant, but at a rate limited by time dilation. Therefore, it would be in
opposition to the centripetal
tendency of gravity, resulting from the
event of creation of dark and ordinary matter. The simulation fits numerical data published within a differentiable
mechanism from other propositions like that of Guth’s positive vacuum
pressure. In addition to providing an alternative mechanism, its physics
allow a framework that could be verified by observation of the correspondence
between CMB time-dependent number of photons and their time-dependent
elongation. Furthermore, the simulation reveals that time dilation structures
the correspondence between energy dispersion and space dimensional changes.
Accordingly, the simulation measures how feasible it is to relate through a
single mechanism several observable phenomena for the modelling of Inflation
and Expansion within a viable physical mechanism capable to theoretically
describe the Big-Bang scenario. Consequently, the simulation framework could
be compared to other theoretical propositions independently from the need to
revise its initial data. The purpose of the simulation, therefore, is to illustrate this model by emphasizing that there are energy-space-time relationships, which are physically ingrained in wavelength elongation and which would be verifiable by astronomical observation. These observations appear to suggest that astronomical verification could be used to analyse the validity of the model on the basis of the included partial Table 3 of the Expansionary Era simulation, whereas the same treatment for Inflation within a different time scale appears to be farther into the future. The purpose was to uncover the relationships between time and space dilation versus photon multiplication and wavelength elongation, and how Connes geometrical description could be thermodynamically described to allow for coexistence and complementation between continuous and non-continuous constituents of a single self-contained Universe. Both geometries could be differentiated in terms of how they structure the space time interrelationships. The continuum surges from the thermodynamic structuring of primordial radiation and relic CMB without time-reversibility. The non continuum surges from the quantum mechanics structuring of matter, which allow time symmetry restricted to the particle and atomic levels. At the molecular or higher levels, apparent violations of microscopic reversibility may be observable, but, this could be explained by synchronized coupling between downhill and uphill energy flows. These ones create the integrative texture of the thermodynamic structure of the non continuum. |
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____________________________________________________________________ References: 1. Guth, A. H., The Inflationary universe: a possible solution to the flatness problems, Phys. Rev. D 23, 347-356 (1981) 2. Guth, A. H. and Pi, S. Y., Fluctuations in the new inflationary universe, Phys. Rev. Lett. 49, 1110–1113 (1982) 3. Guth, A. H. and Steinhardt, P. J., The Inflationary Universe, in Scientific American, 250, pp. 90 (1984) 4. Guth, A. H., The Inflationary Universe: The Quest for a New Theory of Cosmic Origins (1998) Publisher: Perseus Books; 1st edition (March, 1998) 5. Linde, A. D., A New Inflationary Universe Scenario: a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems, Phys. Lett. B, 108, 389-393 (1982) 6. Linde, A. D., Chaotic Inflation, Phys. Lett. B 129, 177-181 (1983) 7. Linde, A. D., Eternally existing self-reproducing chaotic inflationary universe. Phys. Lett. B 175, 395–400 (1986) 8. Linde, A. D., The Self-Reproducing Inflationary Universe, in Scientific American, November (1994) 9. Linde, A. D.,
Inflation, quantum cosmology and the anthropic principle. 10. Gamow, G., Mr. Tompkins, 11. Albrecht, A. and Steinhardt, P. J., Cosmology for grand unified theories with radiatively induced symmetry breaking, Phys. Rev. Lett. 48, 1220-1223 (1982) 12. Greene, B., The Elegant Universe: Superstrings, Hidden
Dimensions and the Quest for the Ultimate Theory, W. W. Norton &
Company, 13. Wang, L. J., Kuzmich, A. and Dogariu, A., “Gain-assisted superluminal light propagation”, Nature, 406, 277-279, (2000). 14. Liddle, A. and Lyth, D., Cosmological
Inflation and Large-scale Structure, 15. Liddle, A., An Introduction to Modern Cosmology, Wiley, West Sussex, 16. Boyanovsky, D., de Vega, H. J. y Sanchez, N., The Classical and
Quantum Inflation: The Precise Inflationary Potential and Quantum Inflation
Decay after WMAP, in Nuclear Physics
B (Proc. Suppl.) 148 (2005) 96-107 17. Boyanovsky, D., de Vega, H. J. y Sanchez, N., Clarifying inflation
models: Slows roll as an expansion in 1/N
efolds, in Physical Review
D 73, 023008 (2006) 18. Rindler, W., Relativity
special, general and cosmological, Oxford University Press, (2001) 19. Vestergaard Hau, L., Harris, S. E., Dutton, Z. and Behroozi, C.
H., Light speed reduction to 20. Ferrero, M., Información Cuántica. Shows an image obtained by
Zeilinger, A. et al. at 21. Y.-S. Lee, T. Meade, M. DeCamp, T. B. Norris, y A. Galvanauskas, “Generation of Narrow-Band Terahertz Radiation via Optical Rectification in Periodically Poled-Lithium Niobate, Appied Physics Letter, 76, pp. 2505 (2000) 22. Smoot, G., Observational
Tests of Cosmological Inflation, ed T. Shanks et al., Kluver, p.395 23. Smoot, G. F. et al, ApJ,
396, L1 (1992) 24. Smoot, G., COBE Observations and Results,
<arXiv:astro-ph/9902027> (1999) 25. Tegmark, M., The angular power spectrum of the four-year COBE
data, The Astrophysical Journal, 464: L35-L38 (1996) 26. Einstein, A., The Meaning of
Relativity, 27. Ho, C. M. y Boyanovksy, D., Space-time propagation of neutrino wave packets at high temperature and density, in Physical Review D 73, 125014 (2006) 28. Prigogine, I, El Nacimiento
del Tiempo, Tusquets Editores, Buenos Aires (2006) 29. Buma, T. y Norris, T. B., “Time Reversal 3-D Imaging Using Single-Cycle Terahertz Pulses” submitted to Appl. Phys. Lett. 30. Rufin, A. B., Decker, J., Sanchez-Palencia, L., Le Hors, L., Withaker, J. F., Norris, T. B. y Rudd, V., “Time Reversal THz Imaging”, IEEE J. Quant. Electron., 38, pp. 1110 (2002) 31. Bennun, A., Hypothesis for Coupling Energy Transduction with ATP Synthesis or ATP Hydrolysis, in Nature New Biology, 233, No. 35, pp. 5-8 (1971) 32. Cline, D. B., Sources and Detection of Dark Matter and Dark Energy in the Universe, Springer Verlag (2001) 33. Cline, D. B., 34. Daubechies, 35. Hawking, S., The Universe in a Nutshell, Bantam
Books, 36. Sorli A., Sorli K., “Does Time Really Exist as a Fourth Dimension of Space?”, in Journal of Theoretics, Vol.6-3, (2004) 37. Connes, A. & Marcolli, M., Renormalization and motivic Galois theory, International Math. Research Notices, 76, pp. 4073-4092 (2004) 38. Caroll, Sean, “The Cosmological Constant” Living Rev. Relativity, 4, (2001) 39. Reeves, H., La
première seconde. Dernières nouvelles du
cosmos 2,
Editions du Seuil, 40. Hu, W. & White. M., The Cosmic
Symphony, in Scientific American,
290, 1, pp. 44-53 (2004) 41. Bennun, A. & Avron, M., The Relation of
the Light-Dependent and Light-Triggered Adenosine Triphosphatases to Photophosphorylation,
in Biochimica et Biophysica Acta,
109, pp. 117-127 (1965) 42. Bennun, A.,
Hypothesis on the Role of Liganded States of Proteins in Energy Transducing
Systems, in Biosytems, 7, pp.
230-244 (1975) 43. Heripsime Ohanian,
Kamran Borhanian, Salette de Farias, and Alfred Bennun, “A model for the
Regulation of Brain Adenylate Cyclase by Ionic Equilibria”, in Journal of Bioenergetics and Biomembranes,
Vol.13, Nos. 5/6, pp. 317-355 (1981) *The author is a full professor retired
from |
, which integrated is:
and is related to the square of the wave amplitude.
= 1.22 
; and to determine the time of localization: 
.
arXiv:hepth/0211048
(2002)