What a week. On not one night this week did I get home from the lab before 10 pm, and since I didn't get a chance to work on the thesis then, it'll need some attention this weekend...[sigh]
With that said, thanks for your patience - I can't promise I'll get to everyone today, but I'll do my best.
CDL, first things first - And beware, this is REALLY long, it was the only way to properly consider what you sent, and I wanted to be thorough here, and as fair as possible.
I did some research (using SciFinder Scholar, a _great_ indexing service for scientific literature), and I found a bunch of references on the VSL cosmology as they call it (VSL = Variable Speed of Light). It's clearly a serious postulate, it's been written up in some very good journals, and there's a lot of scholarly debate surrounding it, mainly from the last five or ten years, so this is a recent thing. You're correct also in that it typically involves a non-linear change in the speed of light over time.
There are some scientists who argues its advantages, and claim that it solves the "horizon" and "flatness" problems of the current model, i.e. that it could explain certain topological features that our universe apparently has.
There are other scientists who say that the model has serious limitations, mainly having to do with violations with the second lay of thermodynamics.
I will freely admit that I don't have all of the necessary backgound to understand everything these people are doing, so I am happy to provide references, if anyone is interested. It seems to me, from looking at this, that from a theoretical point of view, allowing for the variation of the speed of light is one of a number of possible ways of accounting for some of the difficulties with the current standard model. The reason the debate continues, in the community, is that no one so far seems to have published a paper that definitively proves that the speed of light is varying.
Davies' work, referred to in the links you sent, is excellent stuff, and he's a VSL cosmology proponent - But that is only one of a number of interpretations of his data, which shows a variation in the fine structure constant, not the speed of light. The fine structure constant (alpha), which is the ratio of the speed of an electron in a hydrogen atom to the speed of light, is defined as follows:
alpha = e^2 / [(2)(epsilon-naught)(h)(c)]
...where e is the charge of an electron, epsilon-naught is the dielectric permittivity of free space, h is Planck's constant, and c is the speed of light. The value of alpha is about 1/137, FYI.
There seems to be a lot of debate in the community as well, as to which value(s) could be changing, and what the consequences would be. Some people say varying the speed of light makes the most sense, others say it makes more sense to vary permittivity, for instance, or the electron charge - No one has presented the perfect postulate yet, though, as there seem to be problems with each of them (a lot of them are busy poking holes in each other's theories, basically :)
Two final points, with respect to VSL cosmologies: The magnitude of the measured variation in the fine structure constant seems to be very, very small, and none of the VSL cosmologies seem to make predications boiling down to an explicit c(t) = (something) type expression.
Therefore, the most we can say right now, based on this work, is that, if we believe the data, the fine structure constant is changing very, very slightly, which _could_ mean that the speed of light is changing, which _might_ be consistent with one of a number of VSL cosmologies. I saw one or two papers proposing interesting means of testing variations in the speed of light directly - Hopefully someone will perform one of these tests and see for sure, because right now, based on Davies' work alone we can't say whether the speed of light is changing or not.
I should also say that it appears (and I didn't know this - so this is cool, I learned something!) that the speed of light may be subject to variation by other means. There are postulates that imply that temperature extremes, very strong magnetic fields, and even _direction_ may change the speed of light (the last has to do with the assumption of isotropy in the universe - there might be very slight anisotropy, it seems). Wavelength is another one - If photons are massless, there should be no wavelength dependence, but if they have some exceedingly small but finite mass (this may even be below the Planck mass, making measuring it impossible, at least so far as we know currently), their speed may then be very weakly wavelength dependent - While the previous variations I don't yet understand, that makes more sense to me, having seen de Broglie's equation. Keep this in mind whenever you see the speed of light measured - There are a number of factors, then, not including the uncertainty principle, that may account for very small variations.
FYI the Internet Physics FAQ you linked to (marked as "hermes" in your original post, the one I posted the update link to) may need to be updated in light of Davies' work, as it says that "to the best of our current ability to observe, the fundamental constants really are constant" :)
All of this brings me to your first link, the one where Montgomery and Dolphin do a statistical analysis of 120 measurements of the speed of light, and conclude that it's decreasing with time. The paper is interesting, and the statistical methods they use are generally accepted - No problems there. They did a least-squares regression, but they don't give the fit-type - I can only assume it's linear, because we're presuming (approximate) linearity over the time frame we look at.
With that said, and as I'm sure you are aware (Cvengr can back me up on this as well, I'm betting, it sounds like he's got the background for it), the famous Twain quote regarding "lies, damned lies, and statistics", while a humorous if somewhat cynical exaggeration, has a grain of truth to it. If you set up your analysis properly, you can get a variety of results, not all of which will agree. This is usually not due to improper application of statistics or bias on the intent of the researcher so much as the fact that statistical analysis is necessarily limited, being based on probability, and can never be said to be said to be 100% correct and accurate. Montgomery and Dolphin analyzed _selected_ data, which they admit is the weakest point of their study. If we define the proper selection procedures, we can come up with a variety of results. In addition, while they show a lot of statistics on their data, they did not show the statistics (i.e. the predicatble statistical error) on their statistics :) This is very important.
Here's a good example of what I mean. I typed the 120 data points [phew!] they had into MicroCal Origin 6.1 (Excel won't do regressions) and took a look myself (if you want the file, I'll be happy to send it along). The mean value of c I found is identical to the one they report, so I don't think I made any typos, BTW. Here's what I found:
A linear regression, fitting to c(t) = A + B(year), gives me A = 311968.66461 and B = -6.3209. Well, fine, you say, it's going down, right? Not so fast :) The adjusted R-squared value for these coefficients is 0.31926(!) And worse yet, while the t-value for A is quite high (194.88342), the one for B is dismal (-7.53716).
I direct anyone unfamiliar with these measures to this good, brief explanation of R-squared and t-values, here:
http://www.som.yale.edu/faculty/pks4/files/teaching/handouts/r2_tstat_explained.pdf
The statistical implications are clear - We can't be at all sure of the B coefficient, which is what defines the trend, therefore we can't be sure of the trend. We're a little more sure of relevance of A, however - The R-squared is poor, but the t-test value for A is quite high. This makes sense, as it's (roughly) the speed of light, as we know it.
In addition, when I tell Origin to perform the regression using error weighting, based on the error in each measurement as reported by Montgomery and Dolphin, I get a horizontal line, with A = 299792.48738 (i.e. nearly dead-on the accepted value; t-value = 2.54298 MILLION here). The R-squared value is horrendously low, for obvious reasons - The line fails to pass anywhere near a few early measurements - But the reported error in those measurements is so large compared to the more recent ones that the error weighted fit comes out this way. In this case, B = -0.0000144815, +/- 0.0000595668 (yes, the error is larger than the value :) The t-value is -0.24311 here, though in this you don't need the negative t-value to judge that this doesn't mean much, with the error as large as it is.
Now, we can get into more complicated data fits (exponential, polynomial, power law) and do the same thing, but in those cases it will be the trend itself that disproves the fit, since the equation we will get will predict much larger variations in the speed of light in just the past 500 years than we can reasonably accept, even based on current VSL cosmologies. I'm happy to show you any sort of fit Origin is capable of, however, if you're so inclined - Just let me know what you want.
In summary: Montgomery and Dolphin did a smart thing, and I don't think they (intentionally) biased the data by their selection criteria. However, the statistics of a linear least-squares regression analysis of the data show that any trends we get from that data set cannot be trusted, and an error-weighted analysis indicates that the idea of a constant value of c, over the time-period studied, is much more reasonable. I invite you to try this and see what you think - You should get the same numbers.
With that said, I should also mention that I am very curious as to where the error values reported in Montgomery and Dolphin's table come from. As I'm sure everyone here can agree, scientists are often tempted to overstate the accuracy of their numbers, and in any case, error values are often simple "best estimates", or based solely on statistical error, (i.e. not including experimental error). Therefore I suspect that the error values used are likely a bit too low - Though admittedly I cannot prove this :)
In any case, nothing is truly proved here - It's possible that there are variations in the speed of light with time, I've simply shown that that conclusion cannot be drawn from this data set. In fact, the simplest explanation that explains this data is that c is constant.
So we're back to square one :)
VSL cosmologies are taken seriously, and have been for the last ten years, so while the scientific community may have been skeptical or dismissive of the idea before, they should not be now. Clearly this is not some wacky, off-the-wall idea - This really could be what's going on! But we need to show it, and so far, the scientific evidence is not quite there.
Anyway, this was cool 'cause I learned something - Besides refreshing my statistics, I also found out about a number of different environmentally induced variations in c that have been postulated, and I have you to thank for inspiring me to look up the VSL theories in the first place - I wasn't aware they were as popular or as much talked about as they are these days! Hopefully you folks found this informative as well...
Wow, I'm beat. I'm gonna save additional responses for another time. In the meantime, I hope we can agree on the above - That this is important, that it might be happening, but that no one has shown it yet.
Thanks for reading, DFS
http://pla.blogspot.com/2003_01_26_pla_archive.html#88396751
Quoting excerpts in italics / bold:
Dr. Dini refused to write a letter of recommendation for his student, because Mr. Spradling, although wanting further education and a career in biological sciences, could not “truthfully and forthrightly affirm a scientific answer” to the question of the origins of the human species. Mr. Spradling, apparently, does not believe in evolution.
Mr. Spradling responded to the refusal to write the letter by suing both Dr. Dini and the school, Texas Tech.
We think that Dr. Dini should settle the suit by writing the letter for Mr. Spradling.
Our perspective is not that of an academic, an ethicist, a philospher, a scientist or a cleric. We view this from the perspective of a litigator.
Litigating over an issue as trivial as a letter of recommendation is absurd. The money spent by Texas Tech paying lawyers to defend Dr. Dini’s letter of recommendation policy would be better spent improving the biology department of Texas Tech. The money Dr. Dini does not spend on litigation could fund a trip to the Galapogos Islands to study the length of bird beaks.
The letter might read something like this:
I understand that Micah Spradling has applied to your fine institution in an effort to further his training in the biological sciences. I have been asked to write this letter by Mr. Spradling.
I know Mr. Spadling fairly well as he has taken lower level and upper level courses from me. I have also met with him in my office to discuss matters of biology.
In our meetings, the issue of the origin of the human species arose. Despite four years of training in the biological sciences, Mr. Spradling was unable to truthfully and forthrightly affirm a scientific answer to that question.
As a result of that inability, I declined to write a letter of recommendation for Mr. Spradling. When I declined, Mr. Spradling sued me as well as Texas Tech.
This letter is written under the terms of the settlement of that suit and you should regard it as such.
If you seek litigious students who, after four years of training in biology, are unable to state a scientific basis for the origin of the human species, then Mr. Spradling would be a fine addition to your program.
Sincerely Yours
We cannot expect professors to do more than provide truthful letters that contain an honest assessment of a student. The above letter is both.
Comments on our overly litigious society welcome :)
DFS
At any rate VLS is at least the classical definition of a theory in that it has both the potential to be proven, and the potential to be disproven. Obviously, from the tone of your post, you're already thinking of the implications of the theory if proven...the portal of the mind of God. It truly gives a new perspective to the citation below:
1)The heavens declare the glory of God: and the firmament showeth his handiwork.
2) Day unto day uttereth speech, and night unto night showeth knowledge.
3) There is no speech nor language, where their voice is not heard.
4) Their line is gone out through all the earth, and their words to the end of the world. In them hath he set a tabernacle for the sun.
Truth never becomes "truer", but the light does become brighter...Walter Martin.
regards,
CDL