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Preamble[edit]

This article is not intended to be very technical, but to present in a pretty accessible manner the differences between a ‘time-of-flight’ and a ‘length-and-time’ approach to standard units, a change made in the SI definition of the metre in 1983. Brews ohare (talk) 16:53, 18 July 2010 (UTC)[reply]

Comments by Martin Hogbin[edit]

I tend to agree with JohnBlackburne that this is more of an essay than an encyclopedia article. It seems to be trying to make some kind of point that I cannot fathom. On the other hand I would have no personal objection to it being made into an article so long as you add more references to support the exact points that you make.

If you do make it into an article remember that it will be open to others to edit it. As the originator you cannot claim any kind of ownership to it and it may start to move in a direction that you do not like. If that happens you may be drawn into major edit war to protect 'your baby'. You could leave it as a private essay in your user space but then others might not be want to have a link to it from the SoL article. Martin Hogbin (talk) 17:38, 18 July 2010 (UTC)[reply]

Thanks for commenting. Your remarks are pertinent, and further documentation will be made. I also understand the ownership issues. If you have some particulars you'd like to change, please advise. Brews ohare (talk) 20:37, 18 July 2010 (UTC)[reply]

Comments by John Blackburrne[edit]

I suspect it would not last very long as an article as, even with better references, it's a straightforward POV fork so would probably be quickly deleted. especially given as it's arisen out of disagreements at Talk:Speed of light. The topic "definitions of the metre" should be covered on that page, the points on Speed of light in its article.--JohnBlackburnewordsdeeds 18:06, 18 July 2010 (UTC)[reply]

John, a POV fork is described as follows: “POV forks generally arise when contributors disagree about the content of an article or other page. Instead of resolving that disagreement by consensus, another version of the article (or another article on the same subject) is created to be developed according to a particular point of view.” Now, IMO, this article does not deal with a disagreement over content, and does not develop a particular point of view. All it does is describe two different approaches to standard units and compare them, not with a view that one is better or worse, but just what is the difference. Its role is to provide an expanded discussion of this topic that would be too large a digression on the Speed of light page.
I'd appreciate it a lot if you would make the attempt to explain just how this article can be seen as a POV fork, so that I can change anything that could lead to that opinion. Brews ohare (talk) 20:31, 18 July 2010 (UTC)[reply]

The disagreement was with the content of Speed of light, which you raised at Talk:Speed of light#Measurement. "Definitions of the metre" should clearly be part of Metre, though there is some overlap with Speed of light. If the content split were inadvertent it might only be a content fork, but that doesn't apply here. This instead is a classic example of a POV fork: an attempt to bypass the consensus on the content of Speed of light by creating a new article.--JohnBlackburnewordsdeeds 21:02, 18 July 2010 (UTC)[reply]

John: I would like further comment. IMO, the statements I made at Speed of light were not disagreements over content, but over clarity - a matter of good writing and exposition. Brews ohare (talk) 21:07, 18 July 2010 (UTC)[reply]

It's all content. a large part of the content of an article is how it's presented, the order, the precedence, the emphasis placed on different areas. You wanted to add something, but were unable to convince other editors. Rather than accept that you now want to create a new article with your thoughts on the subject, using a title that clearly is a fork of Metre.--JohnBlackburnewordsdeeds 21:22, 18 July 2010 (UTC)[reply]

In summary, you aren't going to indicate in so many words what constitutes the matters that "other authors" disagree with? I don't think there are any points here at variance with Speed of light. There is simply a more extended discussion of the subject of two definitions for the metre. There is, therefore, no POV fork here at all. Brews ohare (talk) 00:21, 19 July 2010 (UTC)[reply]

See the section you started on Talk:Speed of light for the disagreement, where you again failed to persuade anyone of your views. You can't now ignore consensus and take your ideas to a new article, that's exactly what a POV fork is. If this is a truly different topic then what is it on? It can't be on the metre (as the current title and refs indicate) or the speed of light as there are articles on those already. So what other notable topic is it meant to cover?--JohnBlackburnewordsdeeds 00:37, 19 July 2010 (UTC)[reply]

John: If there was a failure it was to persuade people that the article's saying c was an exact value and then quoting an approximate value with an error bar sounded contradictory to me. You, for one, figured that the reader could read the whole article and infer what was meant, and that was preferable to simply adding a sentence about what was going on. That is hardly a POV regarding subject matter: it's a POV regarding how much effort should be put into being clear. Brews ohare (talk) 02:25, 19 July 2010 (UTC)[reply]
What is the article about? To recapitulate:“this article does not deal with a disagreement over content, and does not develop a particular point of view. All it does is describe two different approaches to standard units and compare them, not with a view that one is better or worse, but just what is the difference. Its role is to provide an expanded discussion of this topic that would be too large a digression on the Speed of light page.”

To me Speed of light makes sense, and if it seems unclear or contradictory to you I recommend you look at some of the sources which go into the subject in much more detail. But the consensus is it is correct, so it has no place for your lengthy, idiosyncratic and unencyclopaedic "digression". That you think there should be a place for it, against consensus, is your point of view - making this a POV fork if it were to become an article. Again I would highlight that the "Definition of the metre" is something that should be and already is covered at Metre, so there is definitely no need for a new article on it.--JohnBlackburnewordsdeeds 11:00, 19 July 2010 (UTC)[reply]

Kilometre[edit]

The article should explain whether the kilometre is a defined or measured value. --Michael C. Price talk 19:23, 18 July 2010 (UTC)[reply]

I'm a bit mystified: isn't the km 1000 metres and therefore subject to whatever considerations go into the metre? Can you elaborate? Brews ohare (talk) 20:35, 18 July 2010 (UTC)[reply]
So is it a defined or measured quantity? A simple question. --Michael C. Price talk 22:35, 18 July 2010 (UTC)[reply]
It is effectively defined as 1000×9,192,631,770/299,792,458 wavelengths of the ground state hyperfine transition of caesium-133. How long said wavelength is one has to measure, though. So what? A. di M. (formerly Army1987) (talk) 23:19, 18 July 2010 (UTC)[reply]
Brews used to claim that something couldn't be both a defined and measured quantity. The kilometre shows this is false, since it is both. Same with c. This should be explained in the putative article since it is something that confused two readers (Brews and Tombe). --Michael C. Price talk 03:49, 19 July 2010 (UTC)[reply]
Michael: It sounds a bit like rhetoric to me. The idea was that if c is defined to have a particular value by the BIPM et al., then that value is not a measured value. It may be they chose the magnitude of their c to be close in value to the previously measured speed of light as a matter of practical convenience, but that doesn't make the defined c both a measured and a defined value, eh? For one thing, the defined value is 100% certain, while the measured value it was based upon is not and was not. What is the point of these word games? Just aiming to cloud things up for your entertainment, maybe? Brews ohare (talk) 04:43, 19 July 2010 (UTC)[reply]
No, I am hoping you will (one day) see the analogy between the kilometre and c. They are both defined and measurable. End of "paradox". --Michael C. Price talk 07:00, 19 July 2010 (UTC)[reply]

OK Michael, maybe you are happy that you understand yourself. Perhaps you could try to be clear enough that I could follow your point too, rather than set up cryptic riddles. For example, π would seem to be defined, as a geometric ratio. And one can try to measure π. So would that classify as defined and measurable? Of course, the measurement cannot determine π, but only an approximate value. Now that situation differs from c in this way: the definition of π as the ratio of two lengths implicitly provides a procedure for its measurement. However, the definition of c does no such thing, and in fact NIST says in so many words that it is "no longer to be measured".Jespersen “One fallout of this new definition was that the speed of light was no longer a measured quantity; it became a defined quantity. The reason is that, by definition, a meter is the distance light travels in a designated length of time, so however we label that distance - one meter, five meters, whatever - the speed of light is automatically determined. And measuring length in terms of time is a prime example of how defining one unit in terms of another removes a constant of nature by turning c into a conversion factor whose value is fixed and arbitrary.” Thus, I'd say that there are examples of things that can be both defined and measurable, but c isn't one of them. Brews ohare (talk) 14:21, 19 July 2010 (UTC)[reply]

Of course, the measurement cannot determine π, but only an approximate value. This is true of any measurement. A. di M. (formerly Army1987) (talk) 14:44, 19 July 2010 (UTC)[reply]
I agree that that is the point. Thus, to fully develop the point, c = 299,792,458 m/s exactly means c is a defined, not a measured value. Brews ohare (talk) 15:41, 19 July 2010 (UTC)[reply]
And yet the kilometre is a defined value (1000 metres) and also measurable. Think of it as a Socratic question, not a cryptic riddle. Why are (as you claim) c and the kilometre different? If you keep on getting tangled up in wall of text answers then perhaps you should consider that they aren't different categories. --Michael C. Price talk 05:45, 20 July 2010 (UTC)[reply]

So the km is a defined function of a measured quantity. So what? So π is defined and measurable, so what? Brews ohare (talk) 11:33, 20 July 2010 (UTC)[reply]

So c is defined and measurable. So what? Exactly; that's what everybody thinks. What is the big deal with c and the metre? Answer: it is no big deal at all. --Michael C. Price talk 13:36, 20 July 2010 (UTC)[reply]

Comments from A. di M.[edit]

  • "A change in the meaning of the term speed of light ..." Nope. It was a change in the meaning of the term metre.
  • Some problems in deciding whether c changes with time are theoretical and even philosophical, as well as experimental. For example, you need to define what exactly "over a fixed distance" means. Note that if c changed with all other things being equal, since the size of objects are determined by the size of atoms and molecules which are determined by the electromagnetic interactions, it could be the case that any yardstick you could use would shrink by such a factor that you'd never be able to measure the change in c. (see e.g. Variable_speed_of_light#Varying_c_in_time, and Planck_units#Planck_units_and_the_invariant_scaling_of_nature). A. di M. (formerly Army1987) (talk) 19:50, 18 July 2010 (UTC)[reply]
Thanks. I'll have to assimilate your remarks and see what to do about it. Maybe you have some suggestions? Brews ohare (talk) 20:33, 18 July 2010 (UTC)[reply]
Yes, I was considering making similar remarks to A. di M. Is this really an essay on 'What I think distance is'? Martin Hogbin (talk) 20:40, 18 July 2010 (UTC)[reply]

Some things I was thinking about, of which Count Iblis's post reminded me: I said you need to define what exactly "over a fixed distance" means. I can think of several things this could mean:

  • The distance between A and B today is the same as the distance between A and B yesterday if the same platinum bar which yesterday fit between A and B fits today (assuming no atoms left or joined the bar, the temperature of and pressure on the bar stayed the same, etc.). (This assumes the size of a platinum atom, and hence the Bohr radius, stay constant.)
  • The distance between A and B today is the same as the distance between A and B yesterday if the same number of wavelengths of such-and-such radiation fit between A and B today as did yesterday. (This assumes the wavelength of said radiation stays constant.)
  • In the time elapsed by light to go to A and B, my clock ticks the same number of times as yesterday. (This assumes the product of the speed of light and my clock's rate stay constant.)

And so on, and so forth. Whatever experimentally verifiable definition you give to the statement that a distance stays constant, you need to assume that some other quantity stays constant. So the statement that the distance between A and B stays constant, without further specifications, is devoid of meaning; you can only ask whether the ratio of the distance between A and B and "something else" stays constant. The same applies if you replace "the distance between A and B" with "the distance travelled by light in one second". The question of whether the distance travelled by light in one second is constant only makes sense if you specify compared to what it has to be constant. A. di M. (formerly Army1987) (talk) 21:12, 18 July 2010 (UTC)[reply]

I'll have to read your remarks a few times. But I'd like to ask if you are suggesting that it is impossible to determine whether the speed of light is the same today as it was yesterday? Or, over many millennia? Brews ohare (talk) 00:17, 19 July 2010 (UTC)[reply]
I'm saying that the question whether the speed of light is the same today as it was yesterday only makes sense if you specify standards of lengths and times (which you assume to be constant) to compare it with. In any experiment, you can't actually measure a dimensionful constant: you have to compare it with some standard so as to have a dimensionless ratio, as explained in Planck units#Planck units and the invariant scaling of nature and the references cited in it. A. di M. (formerly Army1987) (talk) 01:30, 19 July 2010 (UTC)[reply]

So help me out here. If I pick a metal bar and measure the time-of-flight along the bar today, and do the same tomorrow, there are some questions about the bar that can be asked. For example, is it the same bar, or was it swapped? Is it at the same temperature? And so forth. Whatever "fixed" length I choose to measure along, there are questions about whether it has changed or not, and one answers them as best as they can be answered. That will leave some estimated Δ𝓁 that is the possible change in length between measurements. I don't actually have to know 𝓁 itself, only Δ𝓁. Then there are similar errors Δt regarding the time interval. The end result is c today is the same as c yesterday within ±Δc based upon Δ𝓁, Δt. The constancy (or not) of c "makes sense" to within the error bars. How does that sound? Brews ohare (talk) 02:00, 19 July 2010 (UTC)[reply]

But you then are assuming that if the bar has the same temperature and the same pressure as it had yesterday and it has neither lost nor gained any atoms, then its length stays constant. To do this you have (among other things) to assume that the Bohr radius stays constant. Now, the Bohr radius is the distance travelled by light in a time ħ/αme, much like the metre is the distance travelled by light in a time nτ (where n is a particular number and τ is the period of a particular caesium-133 radiation). The philosophical difference between the two is much less than one could believe. A. di M. (formerly Army1987) (talk) 10:23, 19 July 2010 (UTC)[reply]
I am not assuming anything: the idea is to remeasure such things as temperature etc. and put error bars on the measurements. If there are changes that conspire to be undetectable, of course they can't be detected, and get left out. So I can't say with certainty such things have not happened. They are philosophically outside the system. I can handle only the things that are observable. I don't think BIPM intended at any time to deal with changes that conspire to be invisible. Brews ohare (talk) 14:07, 19 July 2010 (UTC)[reply]

I got around to looking at the link you provided. Thanks. It suggests that as long as dimensionless ratios are unaltered, it doesn't matter if c changes or not. But α must stay the same or we'd see a difference. I believe this line of argument takes the article a bit astray. What is needed for this article is the ability to determine to within what error the standard speed of light is realized in a time-of-flight measurement. We don't really care what “the value” is. However, in establishing that the standard speed has been realized, we do need to know what factors can affect that speed, so that they can be controlled (or corrected for) during the time-of-flight measurement. Brews ohare (talk) 03:43, 19 July 2010 (UTC)[reply]

Comments by Count Iblis[edit]

In principle there is always relation between the constants implied by merely defining a standard for a unit, albeit it that in practice one cannot see this relation.

If you have a meter stick then this has some in practice unknown exact description in terms of the atoms it consists of. If you know this exact relation, then the length of the meter stick is in principle determined. But that length depends on the fundamental constants plus the formal specification of the meter stick (which is unknown in practice).

So, merely saying that: "here is my metre", already implies an (unknown to us) mathematical relation between the constants. The only real difference with the definition of the speed of light is that we can actually make the relation that eliminates one constant explicit and thus make use of it to reduce uncertainties in certain measurements. Count Iblis (talk) 20:43, 18 July 2010 (UTC)[reply]

I'm a bit vague about your meaning. Could it be as follows? Given an adequate understanding of inter-atomic and intermolecular forces we could specify a "metre" by saying it was the length occupied by n atoms of (say) aluminum assembled by a certain process, kept at a certain temperature and suspended in some particular fashion in a standard receptacle with a standard atmosphere. Supposing that all could be calculated using the "generalized space-time-quantum theory", can you explain further what you are driving at? Brews ohare (talk) 21:03, 18 July 2010 (UTC)[reply]
I take your comment as a very fundamental point, suggesting that prior to 1983 we were in effect measuring a length and a time to find c, when in fact the length was a redundant or superfluous complication, being basically something like a function of c in the first place. Thus, in some sense the pre-1983 approach was wrong-headed, if not wrong. Is that your meaning? Brews ohare (talk) 04:29, 19 July 2010 (UTC)[reply]
That view seems to me possibly to require the theory of relativity to posit the properties of the speed of light. So if we view these properties as valid only to a high accuracy, and not to be inviolate, perhaps the pre-1983 approach has as much logical standing as the time-of-flight approach? Brews ohare (talk) 04:33, 19 July 2010 (UTC)[reply]
Jespersen says “It is the hope of some metrologists that eventually all seven base standards - time, length, mass, current, temperature, amount of substance, and luminous intensity - will be replaced with a single base standard, time.” Is this remark in keeping with your observations? Brews ohare (talk) 14:26, 19 July 2010 (UTC)[reply]
Brews, yes, in principle, one can use one standard, say for time, and then that would be the standard for everything else. I think the best way to see what it going on is to consider that Nature is described by some laws of physics and that these laws have certain scaling properties; if we consider phenomena on time scales and lengths scales that are large relative to some fundamental microcopic scale (say the atomic scale) then you can eliminate the microscopic lenght scales form the equations with negligible error, the error becoming smaller the farther you are removed from the fundamental length scale. For observers who live in this asymptotic regime there is then no preferred way to choose the unit for length.
In some sense what is going is is trivial. If you take some equations and you rescale the variables in some way such that the limit to infinite rescaling exists and thus described by a limit equation, then rescaling the variables further in that limit equation will leave that limit equation invariant (otherwise the limit would not exist). In case of special relativity, you can derive the classical limit in this way, by rescaling length relative to time, see here. So, the classical limit has an extra scaling property that the original relativistic equations do not have. This is the reason why we have separate units for time and distances; they were invented before we knew about realtivity and the world we live in, is to a good approximation non-relativistic.
You can understand the appearance of all the units we have in this way. The corresponding constants that would relate the different units can be understood to be scaling constants with the world we effectively live in being approximately the scaling limit in which these constants are either very large or very small. E.g., Planck's constant is extremely small when expressed in SI units, speed of light is very large, Boltzmann's constant is very small and the gravitational constant is very small. Count Iblis (talk) 16:24, 19 July 2010 (UTC)[reply]

For the purposes of this article, what do you see as the ramifications of these ideas? I really did not expect to end up in a deep philosophical discussion: I simply wanted to point out that the naive treatment of separate length and time standards was clumsy and led to greater uncertainty than a time-of-flight standard. Ostensibly that is because counting fringes is sloppy. Is it necessary to go any deeper than that in this article? Brews ohare (talk) 17:09, 19 July 2010 (UTC)[reply]

In the sections "What do we know about the speed of light?" and further there is a discussion about more fundamental issues. It is, of course, a matter of taste what else to discuss. Count Iblis (talk) 00:46, 20 July 2010 (UTC)[reply]

Interferometry[edit]

It might be clearer if we look at what actually goes on when you measure a length by interferometry. To make the measurement, you need to know the wavelength of the light your using. Until 1976, you would simply measure the wavelength against a length standard (with an associated measurement uncertainty) and that was almost that. In the early 1970s, NIST came up with a method for directly measuring optical frequencies by linking them to the microwave frequencies used by atomic clocks. Hence, with independent measurement of wavelength and frequency for the same light, they were able to provide the most accurate determination ever of the speed of light from c = λf.

In 1976, the CIPM introduced a conventional speed of light to be used for interferometry measurements, the same value that was adopted for the definition of the metre for all purposes in 1983. Now, instead of measuring the wavelength of a light source against a standard length, you measure its frequency (with a measurement uncertainty) and then calculate the wavelength: because the speed of light is fixed in this system, the relative uncertainty in the wavelength is the same as the relative uncertainty in the frequency.

Now most interferometry is done in air, not in vacuum: there's nothing stopping you from doing interferometry in a practical vacuum, except it's more fiddly and usually unnecessary. So you have to correct for the effect of the air: this is usually expressed as a proportional correction to the wavelength but, of course, this is equivalent to applying a correction to the speed of light. It's expressed as a wavelength correction because the vacuum wavelengths are tabulated and what you are looking to find is the practical wavelength. There are published formulae for this correction. Of course, the correction depends on measured properties such as temperature, pressure and content of CO2 and water, so the correction also has a measurement uncertainty: fortunately, this uncertainty is "second-order" in the final length result – it is an uncertainty in a small correction to the initial result – which is why you can do interferometry in air with acceptible results. You can measure length by time-of-flight measurements as well – it's called radar – but the most accurate measurements are by interferometry, where you can get relative uncertainties of about 10−12.

So what happens if the speed of light varies with frequency? At the moment, we know that any variation is below the level of uncertainty in our frequency measurements but we never know what the future might hold. Well the CIPM would have to specify a frequency for the light used to define the metre: no problem, this sort of clarification to the definitions of base units happens from time to time, see the mole for one example. Also, there would have to be an additional correction to the vacuum wavelengths published by the CIPM for practical interferometry: again, not a serious problem. The uncertainty in the wavelength would no longer be the same as the uncertainty in the frequency, but again, this is hardly going to cause anyone to lose any sleep compared with the other physical implications of massive photons or a changing fine-structure constant! So if we were to realize that the speed of light in vacuum (in all its facets) is not a single value but a range of values, we would simply choose one of the values to be the standard and apply a correction to the rest. Note that this is already what is done most of the time in interferometry, to avoid the hassle of having to work in high vacuum: I can set the speed of light to any value I want, but I can't force the speed of light to be the same in air as in vacuum. Physchim62 (talk) 14:44, 19 July 2010 (UTC)[reply]

Very nice exposition. I hope to include such a discussion in the measurement section. What is your opinion of a need for a fuller exploration of this topic on WP? Brews ohare (talk) 14:50, 19 July 2010 (UTC)[reply]
I don't think it's useful to dedicate a whole article to the 1983 redefinition of the metre. Apart from anything else, it is very difficult for editors to get their hands on documents from the relevant period (which really stretches back to the first list of CODATA recommended values, published in 1973). We are also talking about a very specialized topic: I could probably find a reliable source that most practical interferometry is done in air with wavelength correction, for example: but I wouldn't like to give the equation for the wavelength correction, because I couldn't be sure that the one I would quote was the current best practice.
I think it's rather more interesting for our readers to look ahead towards the "New SI" (also called "Quantum SI"). Our article on the kilogram already has a lengthy section on the possible future redefinition (and there are subsidiary articles which describe the technical points in even greater detail). It's possible that the mole, the ampere and the kelvin will also be redefined in the near future, maybe next year. All of these redefinitions will imply the fixing of physical constants within the SI or they won't happen at all: that much we can say because the relevant documents are much more widely available than their counterparts from nearly thirty years ago. In the case of the ampere, it will mean that the magnetic constant will become "unfixed", as I understand things.
Now the "New SI" has all the philosophical problems that you wish to address in relation to the redefinition of the metre; so did the "old SI", for that matter! Basically, you exchange a measurement uncertainty in the value of a physical constant for a realization uncertainty in the corresponding unit. You can't eliminate the uncertainty, nor does anyone pretend that you can. Physchim62 (talk) 22:46, 19 July 2010 (UTC)[reply]
Your phrase “exchange a measurement uncertainty in the value of a physical constant for a realization uncertainty in the corresponding unit” is a neat summary. I like it a lot. I don't think the Speed of light article makes this point though, do you? Brews ohare (talk) 00:52, 20 July 2010 (UTC)[reply]

Comments[edit]

    • It was enough of a subject in its own right to prompt this 5 full page article at the time:
      • Tom Wilkie (1983-10-27). "Time to remeasure the metre". New Scientist. pp. 258–263.
    • As well as this 2 page precursory coverage a fortnight earlier:
      • G. W. E. Beekman (1983-10-13). "Hunt for the speed of light". New Scientist. pp. 101–102.
    • And all of these journal articles and book chapters:
      • P Giacomo (October 1983). "The new definition of the metre". European Journal of Physics. 4 (4): 190. doi:10.1088/0143-0807/4/4/001.
      • B. W. Petley (1983). "New definition of the metre". Nature. 202 (5916): 373–376. Bibcode:1983Natur.303..373P. doi:10.1038/303373a0.}
      • Pierre Giacomo (March 1983). "Laser Frequency Measurements and the Redefinition of the Meter". IEEE Transactions on Instrumentation and Measurement. 32 (1). Braunschweig, Germany: 244–246. doi:10.1109/TIM.1983.4315052. ISSN 0018-9456.
      • K. M. Evenson (1983). "Frequency Measurements from the Microwave to the Visible, the Speed of Light and the Redefinition of the Meter". In P. H. Cutler and A. A. Lucas (ed.). Quantum Metrology and Fundamental Physical Constants. NATO AS1 Series B-98. New York: Plenum Press.
    • It's remained enough of a subject since to warrant this conference paper some years later:
      • K. M. Evenson (1994). T. W. Hansch and M. Inguscio (ed.). A History of Laser Frequency Measurements (1967-1983): The Final Measurement of the Speed of Light and the Redefinition of the Meter. Frontiers in Laser Spectroscopy : Varenna on Lake Como, Villa Monastero 23 June–3 July 1992 (Proceedings of the International School of Physics). ISBN 9780444819444.
    • A quick search for sources turns up the original papers on the science underpinning this from the Boulder Group, as cited in the references section of a summary written by David R. Lide of NIST in 2002:
    • As well as this:
      • "Documents Concerning the New Definition of the Meter". Metrologia. 19: 163–177. 1984.
    • Lide is, like others, is specifically addressing the laser measurement of the speed of light and the definition and redefinition of the metre:
      • David R. Lide (2002). "Speed of Light from Direct Frequency and Wavelength Measurements". A century of excellence in measurements, standards, and technology. CRC Press. pp. 191–193. ISBN 0849312477. {{cite book}}: Unknown parameter |isbn13= ignored (help)
    • Uncle G (talk) 15:26, 30 July 2010 (UTC)[reply]
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