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3.6 Energy density and cosmological constant

To be able to formulate the Theory of Relativity free from contradictions, Einstein once had eliminated the space ether. His radical demand was, light waves need no medium (ether) for their propagation, but also can spread in an absolutely empty space.
This view is not longer viable today, since the quantum field theory teaches us, even the absolute vacuum still contains energy.
 [19], p. 319:
„This is related to the fact that the so- called zero point fluctuations of a quantum field can never be suppressed. Besides, such a quantum field has the interesting property that it is Lorentz invariant, so that its spectrum character looks the same from any inertial system. The special relativistic Einstein equivalence principle therefore seems to be adhered to against such a vacuum."
It is very strange now, between that energy density deducible from the quantum field theory and that admissible from observations, there gapes the huge discrepancy of  120 powers of ten (= 10 120), which is regarded as a fundamental physical problem by some scientists.
The following quotations will underline this even more:
[20]: “The fact that we can realize our surroundings unto the far distant galaxies at all, therefore sets an upper limit to the cosmological constant and, with it, to the vacuum energy: namely 120 powers of ten smaller than according to the so- called theoretical estimation. This discrepancy between quantum field theory of the vacuum and cosmology presents one of the big unsolved problems in modern physics.”
[20]: „A still unknown natural law with an unbelievable fine tuning must take care of the energy of the vacuum to decrease by 120 powers of ten, against the former calculations – a precision which no other physical theory knows.”
 [19]: "But there remains the urgent question of the absolute value of this energy density, as well as those of the other quantum fields, and the question  of the variability of these energy densities at a metric of the universe that varies with time. Now, as before,, there is not even a trace of an answer."
[21]: „If we reject the possibility that the cosmological constant is only by accidence infinitesimally small, then we must accept radical consequences for physics."
Before we can find an approach for the solution of this problem at all, we must clarify how the vacuum energy density is calculated from the quantum field theory [22], p. 128:
"In the equation of the available quantum field theory, the energy density diverges (ultra violet divergence), i. e. the integral over all wave numbers k diverges."
 
 
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