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 = H0D, where H0 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 H0 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 H0 = 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 H0 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 H0 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 H0, that of inverse seconds (s-1), to define its dimension.
To do the conversion, the value of H0 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 1013 km, and a megaparsec is 106 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 H0 values shown previously to give its value in units of s-1. For the NASA summary value, we find that:
(NASA) H0 = 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, λe, which measures how much its mass-energy is spread out as a wave in spacetime. That one is λe = 2.426 x 10-12 metres (m). Lastly, we have to use the speed of light, c = 2.998 x 108 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:
πβc/λe = 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 H0-1, this is equivalent to the age of the Universe, for which the most recent WMAP value (2010) is H0-1 = 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 (λe/πc) = 4.361 x 1017 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 1038, 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 H0 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 H0 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 2.70K 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