We know from measurements that the total energy of the cosmic microwave background (CMB) is only 1 / 1,100'th of its original energy (original = when the radiation was created).
Tuomo Suntola has developed a cosmological model Dynamic Universe (1990 -), in which total energy is conserved, even though CMB loses energy. Let us check if the Dynamic Universe is consistent with measurement data.
The inflating balloon model
Let us analyze the motion of a freely moving particle m on the surface of a spherical balloon which is being inflated.
The angular momentum of the particle must stay constant. Let v₀ be the velocity when the size of the balloon is
a = 1.
The velocity for an arbitrary size a (or scale factor a) is
v = v₀ / a.
Very simple.
A photon, or a wave packet, always moves at the speed of light, c. To conserve the angular momentum, its energy E must go as
E = h f = E₀ / a,
where E₀ is the energy of the photon or the wave packet when a = 1.
The balloon model explains well why the cosmic microwavebackground looks like black body radiation. The wavelength changes as
~ a,
the density of wave packets goes as
~ 1 / a³,
and the energy of a wave packet goes as
~ 1 / a.
The temperature is
T ~ 1 / a,
and the energy density of radiation is
~ 1 / a⁴ ~ T⁴,
as it should be. On October 10, 2024 we showed that the Einstein-Hilbert action does not allow the energy of a wave packet to change. General relativity predicts that the energy density is
~ T³,
which is clearly wrong.
The Milne model probably gets T⁴ right, but we did not check that yet.
A gravity explosion seems to keep black body radiation black body
Imagine an explosion under newtonian gravity, where baryon matter climbs up from a gravity potential well.
If a photon is moving toward the center of the explosion, it gains energy in a blueshift?
On the other hand, an equivalence principle says that for freely falling matter, things should look symmetric: the orientation of the center of the explosion should not be visible.
Is the CMB spectrum in this case automatically black body?
An observer in the future receives each photon from a lower gravity potential. He should see a redshift regardless of the Doppler effect?
Let us have a clock which tics and produces a laser beam whose cycle time is one tic. When the laser beam was sent, the clock was at a lower gravity potential: it ticked slower. We conclude that the future observer does see a redshift even though there were no Doppler effect included.
The mirror principle of gas. Suppose that the volume of a cloud of uniform gas (or a cloud of photons) somehow changes in a uniform way. Then we can assume that the gas is divided into smaller chambers whose walls reflect the gas atoms.
Proof. Let us divide the volume into smaller "compartments".
compartment compartment
| • --> v | v <-- • |
atom atom
Let there be a very large number of atoms in each compartment. If an atom moves to the neighboring compartment, then we can imagine that an equivalent atom moves to the opposite direction.
And we can imagine that, actually, both atoms bounce from each other at the location of the compartment wall.
That is, we can think that the gas is under an "adiabatic" process. QED.
Let the compartments (their walls) fall freely under gravity. Then one would expect that the photon gas inside the compartment is compressed (or expanded) adiabtically, and the gas remains black body.
Literature seems to say that black body radiation remains black body under an adiabatic process. The following conjecture is now plausible:
Conjecture. An explosion where gravity satisfied an equivalence principle, keeps black body radiation black body. It is equivalent to an adiabatic expansion or compression of the radiation.
Energy conservation in the Tuomo Suntola dynamic universe
Let us check how Tuomo Suntola handles energy conservation. In the inflating balloon model, energy conservation follows from newtonian mechanics. Is the Suntola model somewhat similar?
In equation 1.1.2:1, Suntola sets the total energy of the universe to zero. The energy Em above denotes the "kinetic energy" of all matter in the universe. The energy Eg is the negative "gravitational potential" of all matter. If the total energy is defined in this way, it is conserved, as the sum is always zero.
In section 1.1.4, Suntola says that c₀ is the "expansion velocity of space into the direction of the 4-radius". In the balloon analogy, it would be the radial speed of the expanding rubber sheet.
We have to check if energy is conserved also locally.
The energy formula above looks like a newtonian collapse of dust where the particles have a very small rest mass and are initially far away from each other. A half of the negative gravitational potential (the binding energy) is converted into kinetic energy of particles as the dust collapses.
The book by Tuomo Suntola does not seem to contain a clear formula for the energy content of the universe in a mord complex case where there are stars, galaxies, and the cosmic microwave background.
Conclusions
The cosmological model of Tuomo Suntola has energy conservation, in some sense. But the details are missing in his book.
Section 6.2 of the book contains a strange claim that the apparent angular size of galaxies in the sky, for a redshift z > 1 does not match the FLRW model.
Modern data from quasars at distances up to z = 2.8 supports FLRW and refutes Tuomo Suntola's model. However, recent data from James Webb fits Suntola's model better. See our December 18, 2024 blog post about James Webb.
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