a new cosmology
The new cosmology can be found here
He, J. (2007). Real Cosmology. PHILICA.COM Article number 71
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1. What is Creator’s Character?
Does Creator have a character? If does, what is Creator’s character? Nowadays, people consider the world to be magical. Everything is fast-changing, and no stable frame exists for people to rest on. The situation is exemplified by the resort to the superstitious black holes, big bang, superstring, …, all of which are the products or by-products of curved spacetime imagined by bold human. Let us be humble and resort to Creator. Does Creator show his character in the creation of the universe? A little faith to Creator can lead to the truth: Creator is visible, stable, reliable, and yet weighable. Creator weighs on the value: simplicity, diversity, and harmony.
2. Homogeneity: The Base of Creator’s Creation.
Human’s creation is based on illusory spacetime. Creator’s creation of spacetime is based on real existence: photon, electron, quark, and all other real matter. Creator’s first principle is simplicity. Therefore, the ideal universe is characteristic of homogeneity. That is, we can find an inertial reference frame in which the distribution of matter in the universe is both spatially and temporally homogeneous. Because of homogeneity, any test particle is either static or moving straightly in constant speed with respect to the frame. Any other frame which moves straightly in constant speed with respect to the former one is also an inertial frame, that is, it observes uniform particle motion and homogeneous mass distribution. Spacetime is flat and we have rectangular coordinates in any inertial frame:
x, y, z, t (1)
where x, y, z are spatial coordinates and t is time (the coordinate of the fourth dimension of spacetime). All information is causal and can not be transmitted instantly. Therefore, there is the maximum speed of motion. The maximum speed belongs to massless particles like photons. Massless particles have the same speed in all inertial frames. The coordinate transformations between inertial frames are Lorentz ones. Creator puts space and time in equal footing. Any quantity is either an invariable, constant with Lorentz transformations, or a variable tensor whose components change covariantly with the transformations. For example, particle energy is an invariable. The path parameter p which labels particle passing on spacetime must be an invariable. The classical velocity is not covariant,
v = (v1 , v2 , v3) = (dx/dt , dy/dt , dz/dt) (2)
where dx/dt, for instance, is the variance rate of x to t, called the derivative of x with t by mathematician. The velocity has only spatial components and time is a preferred variable. Creator puts space and time in equal footing and the generalized velocity vector is favored,
(U1 , U2 , U3 , U0) = (dx/dp , dy/dp , dz/dp , dτ/dp) (3)
where p is the above-said path parameter, τ =c0 t, and c0 is the constant maximum light speed. Therefore, τ has the unit of length (not time). This description of motion is Einstein special relativity (SR) which holds to the ideal universe of homogeneity.
3. Energy Principle: The Energy and Motion of Particles in Ideal Universe.
We know that in the inertial frame of ideal universe, any particle is either static or moving straightly in constant speed with respect to the frame. Physical universe concerns only motion. To be prepared with more complicated real universe, we seek some principle to describe particle motion. Creator does provide such principle: the energy principle, or generally called Lagrange’s principle which is in fact an optimization principle. Particle’s motion optimizes the summation (integration) of energy along the path on spacetime. That is, for all possible paths on spacetime, the summation of energy along the real path is always the minimum. Consider the case of ideal universe. The formula of particle’s total energy per unit mass is the following
E (x, …, U1 , …)= (1/2) (U1 2 + U2 2 + U3 2 - U0 2 ). (4)
Generally, energy depends on both position variables and components of generalized velocity. In the simple case of ideal universe, however, it depends only on velocity. Velocity is the variance rate of position to path-parameter p. The optimization principle gives the following equations called Lagrange’s equations which describe the real motion,
P1=∂E/∂U1 , ... , P0=∂E/∂U0 ,
dP1/dp=∂E/∂x , … , dP0 /dp=∂E/∂τ , (5)
where P1 , ... , P0 are the components of generalized momentum vector and obtained by taking partial variance rate of E to respective velocity components. For example, P1=∂E/∂U1 is the variance rate of E to U1 by taking all other independent variables x , ..., U2 , ... to be constant. Return to the energy formula of ideal universe (4). Because all variance rates of E to position variables are zero (energy depends only on velocity), the formulas (5) indicate that the generalized momentum is constant
P1 = ∂E/∂U1 = U1 = dx/dp = constant, ….
Therefore, we have proved that any test particle is either static or moving straightly in constant speed with respect to inertial frame. The energy principle does work. We note that the final term -(1/2)U0 2 in (4) involves only temporal velocity component and is potential energy while the remainder involves spatial velocity components and is kinetic energy. Because we deal with causal motion only, energy is always non-positive,
E ≤ 0. (6)
The energy of material particles is negative while the one of massless particles, e.g., photons is zero. In classical relativistic description of photon, its momentum and energy form a vector and energy is its 0th component. Classical energy is proportional to photon frequency. Therefore, the potential energy of photons in our definition, i.e., the final term in (4) or (7), proportionally corresponds to the energy of classical relativistic theory. Why do we have a new definition of invariable energy? This is because our Lagrangian principle leads to the Hamiltonian which is identical to the original Lagrangian itself.
4. Real Universe: Variable Density of Matter Distribution.
Homogeneity is the base of Creator’s creation of the universe. However, complete homogeneity means no vigor and ideal universe is dead creation. Therefore, Creator allows for both spatial and temporal variance of matter distribution in the universe. By physical view, the variance introduces force upon particle motion and test particles no longer keep static or moving straightly in constant speeds with respect to inertial frames. When observing local solar system, we ignore temporal variance of mass distribution and only spatial variance is involved. The resultant force is the gravity as we know. However, when observing distant galaxies and intergalactic matter, the density of large-scale mass distribution is spatially homogeneous but changes with time. Because of spatial homogeneity, the resultant force exerts in all spatial directions with equal magnitude on any particle, which resembles fluid pressure. The present article concerns cosmology and only the latter force is involved. We call the force temporal pressure which is the spatial force due to temporally varying density of spatially homogeneous mass distribution. Now we understand that gravity as well as temporal pressure results from variance of matter distribution. As we know in the following, it is temporal pressure that leads to a birth and a death of the universe, and it is the simple energy principle alone that gives results which meet current astronomic observations.
5. Energy Formula for Spatially Homogeneous Universe.
Nowadays, cosmological study becomes an observational science and astronomical data does indicate that the large-scale universe is spatially homogeneous. That is, the universe is isotropic so that each observer sees the same in all directions. This is very strongly suggested by the observation of cosmic microwave background radiation (CMB). Therefore, the energy formula in the inertial frame which observes spatially homogeneous density of matter distribution, is the following,
E (x, …, U1 , …)= (1/2) A (U1 2 + U2 2 + U3 2) - (1/2) B U0 2 (7)
where neither A nor B is a constant. Otherwise the energy would be equivalent to the one which describes ideal universe. Both A (>0) and B (>0) change with time only (temporally variable density of spatially homogeneous mass distribution),
A=A(τ), B=B(τ). (8)
Because Creator allows for diversity (variance of mass distribution), Einstein special relativity is no longer perfectly true. As we show in the following, light speed changes with time and one inertial frame is preferred which is called the absolute (or unique) inertial frame of the universe. The absolute frame is meaningful because all test particles (e.g., galaxies) slow down their motion with respect to the frame. To show which conditions must be satisfied by the quantities A and B to meet current astronomic observations, we firstly present the Lagrange’s equations suggested by (7) and their solution under arbitrary A and B.
6. Lagrange’s Equations and the Solution.
The Lagrange’s equations given by (5) are as follows,
P1 = AU1 = constant , …, P3 = AU3 = constant,
dP0/dp - ∂E/∂τ = - B dU0 /dp - (1/2) B′ U0 2
- (1/2) A′ (U1 2 + U2 2 + U3 2) (9)
where A′ = dA(τ)/dτ is the variance rate of A to τ and similarly for B′. We define the constant spatial momentum (conservative spatial momentum),
M2 = (P1)2 + (P2)2 + (P3)2. (10)
The solution of the Lagrange’s equations is,
dτ/dp = √((M2- 2EA)/(AB)),
dx/dτ = P1√(B/((M2- 2EA)A)), … (11)
where E is the constant total energy (conservative total energy). The explanation to all current astronomic observations is based on the solution.
Astronomic observation is the reception of electromagnetic waves from the universe. Atomic transitions give out electromagnetic waves and different atoms present different spectra. Because large-scale universe suffers only temporal pressure which exerts in all directions with the same magnitude on any particle (e.g., galaxy), we expect that local physical processes are identical, independent of spacetime positions in the universe. This is approximately true and the accurate observations should see a change with time in the local laws of physics especially near the time of birth of the universe. People found that atomic spectra from distant galaxies are red-shifted. That is, compared with the wavelengths of atomic spectra from earth, the ones from distant galaxies are systematically longer. Because atoms in earlier time in fact give out identical spectra as in today, we expect the waves gradually change their wavelengths while on their road to the earth of modern times. This can be shown to be true straightforwardly if we assume that A=A(τ) increases with time. What we need is to determine how the potential energy of on-road photons changes with time. Photon motion is given by the equations (11) with total energy E being zero. Only potential energy Ep is useful which is,
Ep = (1/2) B U0 2 = (1/2) B (dτ/dp)2 = M2/ (2A(τ)) (12)
where M is constant spatial momentum. Because photon potential energy is proportional to its wave frequency, we see that photon wave frequency does change with time. At the initial time τ0, photon had the frequency ν ~ 1/A(τ0), which is the same as the one on earth. After a long journey to earth at the time τ, the frequency becomes ν0 ~ 1/A(τ). The ratio of the two frequencies is
ν / ν0 = A(τ)/A(τ0). (13)
The quantity redshift defined by astronomer is the difference of the normal frequency ν given by earth atoms from the observed frequency ν0 given by distant atoms, divided by the latter,
z = ν / ν0 – 1 = A(τ)/A(τ0) – 1. (14)
Because distant galaxies or other cosmic matters give redshifted spectra, i.e., z > 1, we have the result that A(τ) increases with time. In the following we see that the increase with time of A(τ) (not decrease) is also the requirement by other astronomic observations. Note that our explanation of redshift by the temporal pressure on traveling photons, i.e. by the evolving universe, is different from the one by the expanding universe of curved spacetime. However, we will see that our explanation is simple and consistent to current astronomic observation.
8. Hubble Redshift-distance Relation and ‘Accelerated Expanding’ Universe.
Hubble discovered the important law that the distances of the sources (galaxies, etc.) which give out spectra, are proportional to their corresponding redshifts observed on earth. The proportional factor is called the Hubble constant H0. The law proves to be true if we assume that the second evolving factor B(τ) be dependent on the first one,
B(τ) = A′ 2/ (N2A3). (15)
where N is another constant. Photon motion is given by the equations (11) with total energy E being zero. Therefore, in its propagation direction, photon has the speed,
dx/dt = c0√(B(τ)/A(τ)) = c0 A′/ NA2 . (16)
From the initial time τ0 to the current time τ on earth, the distance D traveled by photons is
D = ∫(dx/dτ)dτ = ∫( A′/NA2)dτ
=1/NA(τ0) - 1/NA(τ) = (A(τ)/A(τ0) – 1)/ NA(τ) (17)
= z/NA(τ) = z/H0
where Hubble Redshift-distance Relation is proved and Hubble constant H0 at current time is the following,
H0 = NA(τ). (18)
Because redshift requires increasing A(τ), we see that Hubble constant H0 increases with time too. This result is also an observational law. Here we see that the law is simply the result of galactic redshift. However, Big Bang Theory (BBT) has a separate explanation of the law to be the accelerated expansion of the universe. Because general relativity expects a decelerated expansion, BBT assumes the existence of large amount of negative-pressure dark energy. It is dark because it refuses direct human observation.
9. Infinite Light Speed and the Birth of the Universe.
Positive and increasing quantity A(τ) indicates a time τ0 when A(τ0) = 0. This is the starting time of the universe. We can choose τ0 = 0 to be the time of birth. Currently we do not know the exact physics at the hot birth. One thing is sure that light speed at the time must be infinite. Only infinite speed of communication could result in a later spatially homogeneous mass distribution in the infinite flat universe. This resolves the horizon and flatness problems due to birth. Infinite initial light speed indicates a decrease of light speed with time. Observation during the last decade does support the result of decreasing light-speed with time. The formula of light speed is (16). Therefore, decreasing light speed imposes further condition on the evolving factor A(τ),
AA'' ≤ 2 A' 2 (19)
where A'' = d2A(τ)/dτ2 is the second variance rate of A to τ. There is observational evidence that Hubble Redshift-distance law was not true during the early time of the universe and B(τ) did not obey the relation (15).
10. Light Speed Constancy and the Death of the Universe.
However, there is strong evidence that light speed is approximately constant during mature stage of the universe. Constant light speed with time means that A(τ) and B(τ) are the same
A(τ) ≡ B(τ). (20)
They serve as the scaling factor. Hubble Redshift-distance law completely determines the scaling factor,
1/B(τ) ≡ 1/A(τ) = 1/A0 – N(τ - τ0) (21)
where A0 = A(τ0). This formula indicates a finite time τ1 when N(τ1 - τ0) = 1/A0. This is the ending time of the universe because the scaling factor reaches infinity. The possibility of a rebirth needs further investigation.
11. The Absolute Inertial Frame of the Universe.
Our calculation and results are reference-frames depended. For example, photon frequency is dependent on reference frames. Our results are meaningful only when single preferred inertial frame of the universe exists and the results are calculated with respect to the frame. The absolute frame is meaningful only when all components (e.g., galaxies) of the universe have convergent motion with respect to the frame. That is, all components slow down their speed of motion with respect to the frame. Since the 19th century, scientific report on the evidences of absolute inertial frame has never stopped. Because of light speed constancy we have B(τ) ≡ A(τ) in the formula (11). We can see that the absolute speed of material particles (galaxies) does decrease with time, slowing-down motion with respect to the absolute inertial frame. Note that -E > 0 for material particles. Here we know that the existence of absolute inertial frame is once again the direct result of galactic redshift.
Real cosmology is simple and consistent to all astronomic observation. Creator’s creation is based on the value of simplicity, diversity, and harmony. What a beautiful creation!
He, Jin: http://www.arxiv.org/abs/astro-ph/0512614
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