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# Deflating the Expanding Universe

The value of the Hubble constant

can be identified with a simple

group of fundamental physical

constants which describe the

properties of local spacetime.

According to the standard viewpoint of cosmological thought, we live in an expanding Universe created by the Big Bang event nearly 14 billion years ago. Spacetime is everywhere becoming bigger as time goes on, carrying all the galaxies with it. Except for the nearest few galaxies, all of them show a measurable displacement of their light emission towards the red end of the visible spectrum, the so-called redshift. One way to interpret this is as the result of motion in a direction away from us, or recession, which would create a relativistic Doppler effect.

Another interpretation is available,
however, which is the basis for this article. To begin with, we need
to know something about how a particular number called the Hubble
constant is measured, and its value. Hubble's law links recession
velocity, *v*, which can be determined from the measured
redshift, to the distance a light-emitting object such as a galaxy is
from us, *D*. This distance can be measured independently over a
very large range using various overlapping techniques. When this is
done, it becomes reasonable to suppose from the data results that a
linear relationship, or law, exists between recession velocity,
conveniently measured in kilometres per second (km s^{-1}),
and distance in millions of parsecs, or megaparsecs (Mpc), again for
convenience.

That law is expressed by *v* =
H_{0}*D*, where H_{0} is the Hubble constant.
The trick is to measure it exactly. For several decades after an
early measurement in 1958 placed it around 75 km s^{-1}
Mpc^{-1}, there was a dispute between two extremes of about
50 and 100 km s^{-1} Mpc^{-1}. This was settled in
2001 by a team led by Wendy Freedman, who used the Hubble Space
Telescope (HST) to arrive at a measured value of H_{0} equal
to 72 plus or minus (+/-) 8 km s^{-1} Mpc^{-1}. In
2003, this was refined by the WMAP spaceprobe to 71 +/- 4 km s^{-1}
Mpc^{-1}. Further measurements have given 73.2 +/- 3.2 (WMAP,
2006), 71.9 +/-2.7 (WMAP, 2008) and 74.2 +/- 3.6 (HST, 2009). NASA
has summarised the existing data to give H_{0} = 70.8 +/- 1.6
km s^{-1} Mpc^{-1} for gravitationally flat spacetime
(the usually assumed case), otherwise known as Minkowski space.

The reason why I've gone into these
results in some detail is that it is possible to find a theoretical
solution for H_{0} which has nothing to do with recession,
but has everything to do with spacetime, electromagnetism and gravity
acting together. This comes about because we don't need to define H_{0}
in units of velocity per distance, as velocity is already distance
per time. That means we can eliminate the length units of kilometres
per megaparsec. This simplification inserts a conversion constant,
which is just a number, to replace the description "one kilometre
per megaparsec", leaving the remaining unit of H_{0},
that of inverse seconds (s^{-1}), to define its dimension.

To do the conversion, the value of H_{0}
in km s^{-1} Mpc^{-1} only needs to be multiplied by
whatever the value of one kilometre per megaparsec happens to be.
Since a parsec is closely equal to 3.086 x 10^{13} km, and a
megaparsec is 10^{6} parsecs, one kilometre per megaparsec
inverts both these figures together to give:

1 km Mpc^{-1}
= 3.241 x 10^{-20}

This conversion constant can now be
multiplied into any of the H_{0} values shown previously to
give its value in units of s^{-1}. For the NASA summary
value, we find that:

(NASA) H_{0} = 70.8 +/-1.6 km
s^{-1} Mpc^{-1} = (2.295 +/- 0.052) x 10^{-18}
s^{-1 } (1)

Suppose we now take a small group of
fundamental physical constants from an advanced physics textbook or
website. First of all, we need something called the gravitational
coupling constant, *β*
say, which measures the tiny gravitational attraction between two
protons compared to a reference force of spacetime. This has the
value of *β* = 5.906
x 10^{-39}, and is dimensionless; that is, without any units
of mass, length or time. Next comes the Compton wavelength of the
electron, λ_{e},
which measures how much its mass-energy is spread out as a wave in
spacetime. That one is λ_{e}
= 2.426 x 10^{-12} metres (m). Lastly, we have to use the
speed of light, *c* = 2.998 x 10^{8} m s^{-1}.
Two out of three of the constants have much better values than the
approximations given here, but we don't need the extra accuracy.

If we put these three values together in such a way that the dimension of the group is inverse seconds, and multiply in the close approximation for the circular constant π = 3.1416, look what happens:

πβ*c*/λ_{e
}= 2.293 x 10^{-18} s^{-1} = 70.7 km s^{-1}
Mpc^{-1} (2)

Of course, in this equation the second
number is nothing more than a theoretical reconstruction from the
first one in the same equation, using the conversion constant 1 km
Mpc^{-1} given above in its inverted form; that is, as one
megaparsec per kilometre. Notice, however, that this particular group
of fundamental physical constants isn't going anywhere, and has
nothing to do with redshifted galaxies and their inferred recession
velocities. I've put that second number in to show that the value of
the Hubble constant in Equation (1), for all its tortuous measurement
permutations and error refinements over the past ten years
especially, seems to have a lot in common with the collective value
of theoretical constants which have never been near a telescope.

Now, that group of constants is not an
accidental combination. If we invert Equation (1) so that the
measured value becomes H_{0}^{-1}, this is equivalent
to the age of the Universe, for which the most recent WMAP value
(2010) is H_{0}^{-1} = 13.75 +/- 0.11 billion years.
This is sometimes referred to as the look-back time. Inverting
Equation (2) also produces a time dimension, and can be split into
two factors multiplied together to give:

β^{-1}
(λ_{e}/π*c*)
= 4.361 x 10^{17} s = 13.82 billion years
(3)

The first factor, which is the inverse
gravitational coupling constant, has a value of β^{-1}
= 1.693 x 10^{38}, and represents the strength of spacetime
to the weakness of gravity between two protons. The second factor is
harder to interpret, but could be equivalent to the time taken for
light to cross some region of spacetime comparable to the theoretical
diameter of the electron.

In other words, there is what appears to be a meaningful coincidence between the accurately- measured age of the Universe, and the transit time of light across some precise measure of electron width, which has been boosted enormously by a fairly-exact fundamental constant created by a combination of spacetime and gravity.

If true, it means we might be looking
at a natural unification between the electromagnetic force which
deals with light, electrons and protons, and the gravitational force
over the largest distance scale of the Universe. A similar though
obviously much more comprehensive kind of unified field theory was
the subject of a continual search by Albert Einstein over the two
decades leading up to his death in 1955. However, any approach using
the Hubble constant appears to have the disadvantage that over the
next billion years or so the coincidence might expand itself out of
existence as the Universe becomes older and H_{0} smaller in
value. On the other hand, could the highly-improbable similarity of
Equation (3) to the age of the Universe mean that the Universe itself
might not actually be getting any older?

Recall that at the beginning of this
article I said that an alternative explanation for the redshift was
available. The units of inverse seconds for H_{0} indicate
that it could be an absorption coefficient for light through
spacetime. During its long journey energy might be continuously
subtracted from the frequency of that light, which would produce the
measured wavelength shift towards the red end of the spectrum.

The basic idea has been around since the 1930s, when it was originally referred to as the tired light hypothesis. Unfortunately, in the absence of a luminiferous aether to absorb the energy it has naturally been assumed that light from distant galaxies and quasars doesn't have a plausible excuse for feeling tired, no matter how far it might have travelled. More recently, measurements of the light curves of a type of supernova published in 2008 have indicated that time dilation is present for those supernovae with larger redshifts which are therefore further away from us. This is now generally taken as confirmation that the Universe is indeed expanding.

Alternatively, could spacetime be
capable of absorbing energy and time together? After all, these are
just the dimensions of Planck's constant *h*, which defines
spacetime interactions. It would have the two-for-one advantage of
not only absorbing energy-time in an incident direction, but also
reradiating it at a much lower energy in a more diffuse form in
almost-perfect thermodynamic equilibrium as the 2.7^{0}K
cosmic background radiation.

These are completely new ideas, as-yet unpublished elsewhere. We should remember that at present our Universe has no meaningful resolution in terms of life and consciousness. Speculative cosmology has taken physics far beyond any event we are likely to encounter on Earth, yet many physicists believe that only through increasingly exotic conjecture might unification of the forces be one day theoretically proven.

Even if it were in principle possible to do so, how would they then be able to relate what they had discovered to a world of people with varying degrees of intelligence and ability? Above all else, any unified theory needs to refer back to things we have already experienced, not just what we know. Otherwise it will inevitably lose contact with the reality of conscious awareness, which may have a holistic existence every bit as important as the objectivity of science.

**© 2010 profcrumble**

## Comments

I do not talk of the General Principle ... or the Basic Idea ... I talk in the Definitive ... I talk Specifics that correctly Define ... the Existential's Reality ...

I define ... what your Sciences, Logics, Technologies, Philosophies, Religions, and Caballing, can never Define.

"The basic idea has been around since the 1930s"

"These are completely new ideas"

The Physical Universe is not a Balloon, Expanding, into an Infinite emptiness ... It is a Finite State of Creation.

In, the Islamic Concept ... The Created Form, only Exists in the Living Human's Awareness, in State of Distinct Paired Singularities ... Defining Creation, with Distinct Forms.

That, In, The Ordained Manifestation of Form, the Form, Generates the Formal's Compositors ... Matter, Space, Time, and Energy ...

That, Quantum of Formal Space, Is Directly Proportionate to the Physical Form's Manifestation Generated Matter.

So are the Form's Manifestation Generated Energy, and Duration of Existence ... Time.

Hell and Heaven, transcend the Physical, for these are the Soul's Internal States ... not, external to the Soul ... Forms.

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