Testing a Prediction
With a nod to Starts With a Bang, more people are starting to wonder Is the Speed of Light Truly Constant? A new online paper by Lorinzo Iorio looks at Solar System planetary tests of cdot/c Using data on planetary orbits, his paper limits c change to less than 10^{-7} per year. With a little math, we can predict just how little c changes today.
Start with GM = tc^3:
c(t) = (GM)^{1/3} t^{-1/3}
cdot = (-1/3)(GM)^{1/3} t^{-4/3}
cdot/c = -1/3t
Estimating age of the Universe t at 13.7 Gyr, cdot/c is 1 in 41.1 billion years.
In one year c would change by approximately 0.25 x 10^{-10}. From a speed of 3 x 10^8 m/sec, yearly change today is only about 0.75 cm/sec! This is well within the cookie boundaries of Iorio's estimate.
It is impossible to prove experimentally that c is constant, because a more accurate experiment can always prove that wrong.
Measurements of planetary distances are limited by many sources of error. Thanks to the Apollo program, we have accurate distances to one body: the Moon. The Lunar Laser Ranging Experiment (photo) from 1969 allows us to measure lunar distance to cm accuracy or better. According to LLRE, the Moon has been receding at 3.82 ± .07 cm/yr.
Geology and paleontology can tell more precisely how the Moon’s orbit has changed. Starting with today’s LLRE measurement, Bills and Ray [1] have compiled the most accurate estimates of lunar orbital distance.
The Mansfield datum, the most precise, indicates that the Moon has been receding at 2.9 ± 0.6 cm/yr. The LLRE measurement is outside this range. As with Mercury, small discrepancies in orbits can be very significant. When the Moon appears to recede 1/3 faster than geology says, it is a serious anomaly.
If the speed of light slows, that would increase the time for light to return each year, making the Moon appear to recede faster as seen by LLRE. We have cdot/c of 1 in 41.1 Gyr. Multiplied by the Moon’s distance of 384,402 km, that distance will appear to increase an additional 0.935 cm per year. An anomaly in the Moon’s outward drift is precisely accounted for, indicating that c is slowing to this day.
With corroborating data from Type Ia supernovae and the "Faint Young Sun," there is reason to believe that "c change" is happening. Change in c is beyond today's ability to directly measure in the laboratory. That is the essence of scientific prediction: to correctly predict a result before the experiment.
[1] Bills and Ray, Geophysical Research Letters 26, 19, 3045-3048 (October 1, 1999)
Labels: speed of light
posted by L. Riofrio at 6:54 AM
5 Comments:
Hi Louise
Well that answers my question. Glad I gave you something to think about the other day. Though you might want to fix the typo. His name is Lorenzo Iorio... I think you slipped an 'I' or two.
The tidal recession of the Moon has been an interest of mine for some time. From what I've garnered from the different researchers the difference in recession rate with geological time is driven mostly by the sea-level changes and configuration of the continents, as most of the energy loss from the system is in the tidal friction in the shallow continental margins. I'd be surprised if a strong enough light physics signature can be extracted from the 'noise'.
Iorio's paper claims to prove that c-dot/c is equal to zero but that is clearly ridiculous. When I actually read the paper it was clear that he was assuming a particular constant of proportionality between c-dot/c and tilting at that windmill.
Iorio did something a little similar with regard to the use of Mars' moons to prove Einstein's gravitation. See frame dragging and the Mars moons, a reply to his paper on the subject.
qraal, I appreciate the heads-up.
Carl, your work appreciates the value of testable predictions. Testing GR with Martian moons, given how inaccurately their orbits are known, indicates that someone needs to check their figures.
"According to LLRE, the Moon has been receding at 3.82+/-.07 cm/yr.
...
The Mansfield datum, the most precise, indicates that the Moon has been receding at 2.9+/- 0.6 cm/yr. The LLRE measurement is outside this range. As with Mercury, small discrepancies in orbits can be very significant. When the Moon appears to recede 1/3 faster than geology says, it is a serious anomaly."
Dear Louise
I think it's worth pointing out that even though the LLRE measurement is outside the range of the Mansfield estimate, the difference is not statistically significant, since 3.82 is only 1.53 standard errors
away from 2.9 +/- 0.6. The error bars do not represent hard limits, only that there is a (roughly) 68% confidence that the 'true' value of the recession rate lies in the range 2.9 +/- 0.6 cm/yr. At
1.53 std errors, the statistical significance of the difference between LLRE and Mansfield is only 12.6%. In other words, if the 'true' value really was 2.9 cm/yr, over a series of random trials you would expect a difference of this magnitude or larger about 12.6% of the time - not too unlikely.
I'm sure you're aware that most scientists don't consider a difference to be significant unless it's above 3-sigma, so a mere 1.5-sigma difference does not indicate a discrepancy from the LLRE measurements.
Sorry, that should read "In other words, if the 'true' value really was 3.82 cm/yr, over a series of random trials you would expect a difference of this magnitude or larger about 12.6% of the time".
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