6) The SN1a distance
ladder and the shrinking matter theory.
The Shrinking
Matter Theory is characterized by the possibility of vary the Planck constant along the time as the factor of the redshift of the emissions in the past.
This
justifies the bigger size of the atoms and bodies in the past, as well the
longer wavelength emissions and smaller energy and temperature.
The main
relationship relative to the proprieties of the matter and the redshift is
listed below.
hf = ho (1+Z)1/3 Plank constant
λf = λo (1+Z) wavelength
emissions
rf = ro (1+Z)2/3 Bohr radius,
energetic n level radius, and bodies size.
Ef
= Eo (1+Z) -2/3 Energy of the line
emissions.
WDCf
= WDCo (1+Z)1/3
Wien Displacement Constant
R∞f
= R∞o(1+Z) -1 Rydberg constant
Tf
= To (1+Z)-2/3 Temperature of the line
emissions
The SN1a
distance ladder or "cosmic distance ladder" is a system used to calculate the distances based in the
hypothesis which their luminosity peak is constant, so, as fainter the flux
received in our telescopies, as longer the distance from the Earth. The
relationship between the distances and the flux is:
F1
and D1 are flux and distance of a near and known SN1a, which distance
can be determined by parallax, used as standard reference.
F2 is
the measured flux of a more distant SN1a, and D2 is the unknown distance
to be calculated.
The absolute
magnitude μ is a logarithm scale where:
but,
so,
The adopted
standard distance D1 is
10 pc, so that simplify the equation, since log10 = 1. The equation so becomes:
μ = 5 log D2 - 5 (XX)
D2 : (pc)
This
equation works well for low redshifts, but in the Shrinking Matter Theory the
flux F2 is affected by the redshift. In the past the energy of the
emissions was smaller, and such energies were spread onto a bigger
surface.
The energy
of the emissions in the past is defined by the function Ef
= Eo (1+Z) -2/3, and the surface by the function Sf
= 4 π rf 2.
To nullify
the effects of the redshift in flux F2,
we should replace it by the corrected flux F2c .
The F2c is defined by the
function:
F2c = F2 (1+Z)2 (XXI)
Then, the relationship
between the fluxes and the distances becomes:
The absolute
magnitude function for the Shrinking Matter Theory becomes:
μ = 5 log D2
+
5 log (1+Z) - 5 (XXIII)
D2 : (parsecs)
The graphic
02 presents the comparative evolution of the absolute magnitude μ.
The
evolution of the expected μ to the Shrinking Matter Theory, hypothesis A is in
red color.
The
evolution of the expected μ to the Shrinking Matter Theory, hypothesis B is in
green color.
The
evolution of the expected μ to the Standard Model (expanding universe) is in
black color.
The observed
evolution of the absolute magnitude μ is represented by square blue points,
which were extracted from Betoule et al 2014, Table F1, page 30, “http://arxiv.org/pdf/1401.4064v2.pdf
“.
Graphic 02
The curve
which best fit to the observational data is the hypothesis A of the Shrinking
Matter Theory “shrM A abs mag”. No need for dark energy.
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