Speed of Light as a Function of Time

The Hubble Parameter could be interpreted as a measure of the rate at which the speed of light ( c ) is changing with time. Then, the amount of red shift of an object is related to c at the time of emission. Distant objects are not constrained to be moving at any particular velocity. The universe is expanding with respect to the speed of light.

The Hubble Parameter could also be seen to measure the rate at which current events occur, to what they occurred back when. Then, the amount of red shift of an object is related to the rate of time passage at the time of omission. Distant objects are still not constrained to be moving at any particular velocity. The universe is speeding up with age, much like a an inflated balloon speeding up as the neck is released and air allowed to escape. Some current interpretations of the General Theory of Relativity indicate that this might be the correct model.

Arguments for a Decreasing Speed of Light

The observations I will offer are as follows:

• historical measurements of c, from 1960 to 1983,
• discrepancy in the recession of the Earth's Moon,

At the outset, let me state a few facts. The meter has been redefined three times since 1791, so that measurements based on the meter may have discontinuities at the various points of redefinition. In the 1940s, improvements were made in how time standards were transferred. In 1983, the meter (and the foot) were tied to the speed of light over a period of time. Any further observed variation in c will be due to 'calibration error'. The value of Hubble's Parameter is listed by NIST as 50 to 100 km/sec/megaparsec. This value can also be expressed as 15 to 30 km/sec / million years (or a change in c of 10^-11 per year).

Historical Measurements of c

The data for this observation were gleaned from Barry Setterfield's and Trevor Norman's work, and can be found at: The Atomic Constants, Light, and Time

For data in the period 1726 to 1960, the data supports a line of negative slope. Least squares gives the slope a value of -3.9 km/sec/year. To arrive at this value of slope, I applied a weight to each data point. The weight selected was the inverse of its reported measurement error. The value of the slope is dominated by the increasing number of seconds in a day from the Earth's rotation. This slope would indicate that the Earth-based clock is losing 6.8 minutes per year (speeding up), as compared to Atomic Clocks. The unit of time (the second) changed in 1967 from being based on the rotation of the Earth (officially slowing), to being based on the Atomic Clock. I cannot explain how the Earth can be speeding up and slowing down, other than to say that different observations are involved.

The graphing software I used was KyPlot, which is Freeware, and can be found at:

KyPlot: a professional data-analyzing, graphing and drawing application

In the period 1940 to 1960, after time standards were improved, the data supports a negative slope when weighted as noted before. The slope of this data is on the order of 10^-8. Note that the meter is still defined by a platinum-iridium bar at this time. NIST found steel and Invar measurement bars to be changing size by this magnitude (see 3.6.3.1 one got shorter... increasing c, one got longer... decreasing c):

The NIST Length Scale Interferometer

In the period 1960 to 1967, both the meter and the second were redefined.

The data from 1967 until 1983 also supports a line of negative slope. The slope of this line has a value of -1.2*10^-4 km/sec/year (or 120 km/sec / million years). This value is less than one order of magnitude higher than Hubble's Parameter (Constant). Again, the weight for each data point was set as the inverse of its reported measurement error.

I have personally verified three of the values used in this particular graph. The sum-of-the-squares-of-the-errors is 2.6*10^-5 and the Coefficient of Determination is 0.997. The sum-of-the-squares-of-the-errors for a constant 299792.458 km/sec is 2.7*10^-5.

These data would tend to indicate that either c is decreasing over time, or the wrong 'constant' value of c was chosen for the period. Political decisions can be wrong, so this should not be discounted out of hand.

Increase in Moon's Orbit

Some energy & momentum is transferred to the Moon by the Earth to increase the Moon's orbit radius. The ocean tides are responsible for this transfer, since the center-of-mass of the ocean is different than the center-of-mass of the Earth-Moon system. This is much like a placer miner accelerating the water in his pan by shifting the pan slightly ahead of the water in a circular motion.

NIST reports the increase in distance to be 3.72 cm/year. The Moon's orbit is measured by firing a very tight laser beam at the moon. One of the Apollo missions left a mirror package on the Moon's surface (Lunar Laser Ranging). The laser beam bounces off the surface of this mirror, and returns to the Earth. The amount that this distance apparently increases is 0.0372 meters per year.

The Moon's period has more-or-less been constantly changing over the last 650 million years, as evidenced in tidally deposited sediments (tidal rhythmites). This set of data has the Moon receding at 2.16 cm/year. This determination (presumably) ignores any increase in the Earth-Moon system's mass from meteorites, etc. Skip down to "The Paleontological Evidence", the third paragraph to get the skinny.

The Recession of the Moon and the Age of the Earth-Moon System

The two data sets error bars are mutually exclusive, indicating that the distance change is different based on the two methods. This equates to a change of about 30 km/sec/megaparsec, and 10^-11/year in magnitude. This value is lower than what NIST publishes, but their values are based on measurements of objects that radiated light millions of years ago. The value of the Hubble Parameter has been noted to be decreasing for nearer objects. This may be a method of determining the Hubble Parameter in the here and now.

Conclusion

It would appear that the speed of light may effectively be decreasing with each passing year. If this is true, then the length of the meter is also decreasing, by its current definition. Observations of near galaxies indicate that this variation should be linear (or nearly so) over millions of years.

The description of the property on which you live is described as distances from latitude/longitude sets, and your neighbor's property lines. The variation isn't much, and won't be for a million years, but what you own is shrinking. Wait until someone figures out a way to sell the extra square mile or so the Earth is increasing by each year!

What would the Universe look like if this Hubble Parameter could be factored out?

• If the change is in the speed of light, the light cone now has a variable slope, instead of constant.
• If the change is in the speed of light, all light must be 'braked' periodically to keep it at the current limit. The mechanism could be similar to Cerenkov radiation, which is a mechanism that does not blur. The excess momentum & energy could be responsible for pumping intergalactic matter to radiate the observed microwave background level (UMB). If the energy were subtracted out through decreasing the frequency, then the wavelength we observe now is the wavelength at the time of emission.
• Finally, if these corrections to speed occurred in discrete chunks (some function of UMB, perhaps), this would explain why distant objects appear to be red shifted to discrete levels (see a discussions at Red Shift Riddles, More Evidence for Galactic "Shells" or "Something Else", or W. Tifft himself). The variations in wavelength will start affecting light-based communications (Internet, etc.) as the wavelength of various sources drifts out of the 'sweet spot' designed into optical fibers. Fixed length antennas and inverters will not have this problem.
• If the decrease in time passage were the cause of the observed changes, this raises some unpleasant questions relating to the nature of time, and where the energy comes-from/went-to to change the pace of the Universe. It is possible that the wavelength we perceive now was the wavelength at the time of emission.

Further research could:

• repeat the speed of light measurement using the exact equipment, formulae and constants that were used by NIST in the 1983 determination. This would nail down the change in c with time.
• measure the period of the Moon's orbit accurately on two separate occasions.
• measure the wavelength of characteristic "signature" materials on two occasions sufficiently removed in time that their uncertainties in wavelength will not preclude a clear determination of a change in value of 10^-11 per year. This might take a few hundred years...