User talk:Martin Hogbin/Speed of light set by definition

Section on Speed of light by definition

Perhaps it would be helpful to rewrite this section in a context where problems of succinctness are less severe. Then, with a clear statement of the situation in hand, perhaps a more accurate short intro sentence can be constructed?

I'd suggest this section begin with the pre-1983 definition:

“On October 14, 1960 the Eleventh General Conference on Weights and Measures redefined the International Standard of Length as 1,650,763.73 vacuum wavelengths of light resulting from unperturbed atomic energy level transition 2p₁₀ 5d₅ of the krypton isotope having an atomic weight of 86. The wavelength is

λ = 1 m / 1,650,763.73 = 0.605,780,211 µm

At different times some national laboratories used light sources other than krypton 86 as length standards. Mercury 198 and cadmium 114 were among these and they were accepted by the General Conference as secondary length standards.”

This beginning point has the merit of being perfectly understandable: define the length standard "metre" in terms of a fundamental length of nature, a particular wavelength.

Given this metre and a time measurement, the speed of light in m/s is readily understood as a length / time of transit, and is roughly 299 792 458 m/s.

That introduction then can be followed by an explanation of the 1983 switch to a defined speed of light and a length standard based directly upon time-of-transit. That explanation would clarify why the term "speed of light" in SI units is then to be understood only in the context of length determination as in length = 299 792 458 m/s × time of transit. The number 299 792 458 m/s is explained to be a convention adopted by CODATA, and caution given that it should not be confused with a numerical value for the physical speed of light, which can no longer be expressed in m/s, but can be expressed, for example, in wavelengths of some atomic transition / second.

Of course, references to all critical statements are to be provided, such as Wheeler; Jespersen; Sydenham. What do you all think? Brews ohare (talk) 21:14, 21 August 2009 (UTC)

I think you are wrong. What is you justification for this statement? 'The number 299 792 458 m/s is explained to be a convention adopted by CODATA, and caution given that it should not be confused with a numerical value for the physical speed of light, which can no longer be expressed in m/s, but can be expressed, for example, in wavelengths of some atomic transition / second'. Martin Hogbin (talk) 22:18, 21 August 2009 (UTC)

First, I hope we are clear that this is intended as an outline, not as a finished contribution to the article. Breaking matters up a bit, the statement "the number 299 792 458 m/s is explained to be a convention adopted by CODATA" refers to the cited sources that explain this number to be arbitrary convention. The second portion follows, inasmuch as an arbitrary convention can hardly be considered to be a replacement for a physically observable and measurable quantity. I assume you'd agree that the speed of light is a knowable entity, and not something dreamed up at a convention of metrologists. Brews ohare (talk) 00:32, 22 August 2009 (UTC)

The speed of light (in vacuo) is a natural phenomenon that we have no power to change. The units that we use to describe that speed are exactly the opposite, human constructs that can be any size we want and defined any way that we want. We have chosen to define the second based on the period of a specific radiation from a caesium atom. Do we agree so far? Martin Hogbin (talk) 09:34, 22 August 2009 (UTC)

Martin: We are closer to agreement than I thought. Let me just check that we mean the same things: I agree that units are defined as we wish. I have no problems with the standard for the unit of time. I believe we agree that the number 299 792 458 m/s is adopted for use in the relation length = 299 792 458 m/s × time-of-transit. Perhaps we agree that the real physical speed of light in terms of the wavelength of an atomic transition is a constant of nature, as in c = λ_atomic / (time of transit)? Then the question is: will λ_atomic / (time of transit) = 299 792 458 m/s? That question is more subtle, I think. Brews ohare (talk) 01:46, 24 August 2009 (UTC)

I am not sure what you mean by the 'real physical sped of light'. In simple human terms all we can say is that light goes very fast. If we want to give its speed a value we have no option to define some units of measure. We can do this any way that we like. We can define the unit of time in terms of the rotation of the Earth or the radiation from a chosen atom. We can define distance in terms of the circumference of the Earth, the length of a metal rod, or any other way that we choose. We can, if we choose, define our unit of distance in terms of the speed of light. You may consider this perverse, but you must accept that we can do this. Do you agree? Martin Hogbin (talk) 09:09, 24 August 2009 (UTC)

Regarding your point about defining distance in terms of the wavelength of light, consider this: it is actually the frequency (or period) of the emitted light that is determined by the atom that emits it. The atom cannot determine the wavelength of the radiation. The wavelength is simply set by the distance travelled by the light in one period. Martin Hogbin (talk) 09:12, 24 August 2009 (UTC)

Hi Martin: Thanks for your remarks. What I mean by the "real, physical speed of light" is the entity that decides the speed of transfer of information and the limits upon speed of massive bodies, as per relativity. This speed can be inferred in wavelengths/s for any atomic transition: as you say the wavelength is not determined by the atom. However the selection of a particular transition is necessitated by metrology matters, such as linewidth, that affect the error bars in determining the wavelength. The idea is not that the atom sets the wavelength. That is set by the "real physical speed of light", and is the reason that the whole approach is able to determine this speed in wavelengths/s. Brews ohare (talk) 14:08, 24 August 2009 (UTC)

OK, so we have, 'the entity that decides the speed of transfer of information [etc]'. We agree that is the real, physical, if you like, speed of light, but we cannot give it a numerical value unless we set up a system of units of measurement. However we do this, whether we use a metal rod, the wavelength of a chosen type of light, or any other means, it is always an arbitrary human construct.

The distance measured out by the specified number of wavelengths is identically equal to the distance that light travels in that number of periods. What is there to disagree with about this? Martin Hogbin (talk) 14:21, 24 August 2009 (UTC)

Hi Martin: Thank you once more. Your last paragraph is right on the money, I believe. The distance measured out by the specified number of wavelengths is identically equal to the distance that light travels in that number of periods. This sentence, if I read it correctly, identifies the speed of light as λ_atomic / time-of-transit. I would adopt that as a fundamental constant of nature, although, as you point out, the selection of exactly which transition to use is arbitrary.

What remains for us to discuss is the connection between c = λ_atomic / time-of-transit and c = 299,792,458 m/s. My view of this relation is that the first is an absolute speed of nature, and is independent of man's choice of which atomic transition to choose; in contrast, c = 299,792,458 m/s is an approximate version of the fundamental speed of light obtained by measurement using exactly the first approach in the pre-1983 epoch when the metre was defined in wavelengths. At that time it was well understood that c = 299,792,458 m/s was not exact, but measured, and with error bars. However, post-1983, the metre is redefined so that c = 299,792,458 m/s is exact within the SI units system. That means that c = 299,792,458 m/s is no longer a measured quantity and has been divorced from the real, physical speed of light, and the "error bars" no longer exist. Of course, you may disagree with me; this is simply how I understand the sources. Brews ohare (talk) 14:31, 24 August 2009 (UTC)

Editing break

So you must agree then that a meter is the distance travelled by light in the specified number of periods of the specified krypton radiation? Martin Hogbin (talk) 15:40, 24 August 2009 (UTC)

Martin: This statement seems to me a non sequitor. I've suggested that the pre-1983 evaluation of c was a measured quantity based upon the relation c = λ_atomic / time-of-transit, and that as a measured quantity it was 299 792 458 m/s ± error using the pre-1983 definition of the metre. I have not tinkered with the pre- and post-1983 definitions of the metre. Consequently, I do not know what you're proposing I must agree with. Brews ohare (talk) 16:01, 24 August 2009 (UTC)

Just the statement above. According to the pre-1983 definition the meter was defined as a specified number of krypton light wavelengths. Do you agree that this definition is exactly the same as saying that the pre-1983 meter was the distance travelled by light in the specified number of periods of the specified krypton radiation?

Good question. I'd suggest that exactly may be a bit strong here. According to present theory one could use the word exactly, but of course, present theory has to be continuously subject to test. (For example, it might evolve that corrections for field amplitudes need to be made, or for polarization, or whatever, as accuracy improves.) So, subject to that caveat, I'd say: "Yes, the metre pre-1983 was the distance traveled by light in vacuum from a particular atomic transition in a certain (fractional) number of periods." That is, I believe, the same thing as saying c = λ_atomic / time-of-transit. Brews ohare (talk) 20:56, 24 August 2009 (UTC)

There is nothing strong about 'exactly'. Please explain how any of the factors you mention can make the specified number of wavelengths (including any fractions) not exactly equal to distance travelled by light in the specified number of periods (including any fractions) of the specified krypton radiation? Martin Hogbin (talk) 21:11, 24 August 2009 (UTC)

I don't see any need to go into that; I have agreed with you to all intents. Brews ohare (talk) 21:14, 24 August 2009 (UTC)

So I take it that you agree that, using the pre-1983 definition, the metre is exactly equal to distance travelled by light in the specified number of periods of the krypton radiation.

The definition actually was: definition:

“On October 14, 1960 the Eleventh General Conference on Weights and Measures redefined the International Standard of Length as 1,650,763.73 vacuum wavelengths of light resulting from unperturbed atomic energy level transition 2p₁₀ 5d₅ of the krypton isotope having an atomic weight of 86. The wavelength is

λ = 1 m / 1,650,763.73 = 0.605,780,211 µm Brews ohare (talk) 20:56, 24 August 2009 (UTC)

Yes. Martin Hogbin (talk) 21:11, 24 August 2009 (UTC)

You also have not got around to discussing the last point in the previous section: the connection between c = λ_atomic / time-of-transit and c = 299 792 458 m/s exactly. Brews ohare (talk) 16:06, 24 August 2009 (UTC)

This represents an unknown change to the length of the meter that was immeasurably small at the time of the change but could become significant later. Martin Hogbin (talk) 16:51, 24 August 2009 (UTC)

As Wheeler says: "we have to expect that the speed of light will remain at the decreed figure of 299,792,458 m/s ... any substantial improvement in the accuracy of defining the second will bring with it an identical improvement in the accuracy of defining the metre." I believe that you agree with that statement. It seems to me that ruling out any change in 299,792,458 m/s is in accord with the view that 299,792,458 m/s actually is not the speed of light, as the real, physical speed of light can be determined with better and better accuracy as technique improves. Such improvement with technique is realizable in principle using c = λ_atomic / time-of-transit, but is not realizable even in principle using a fixed value c = 299,792,458 m/s exactly. Brews ohare (talk) 20:56, 24 August 2009 (UTC)

No. It says exacty what I and everyone else have been saying as experimental technique improves the speed of light remains at exactly 299,792,458 m/s but the accuracy of defining (better to say delineating) the metre is improved. Martin Hogbin (talk) 21:11, 24 August 2009 (UTC)

We agree on what Wheeler says. So you dispute the last sentence: "improvement with technique is realizable in principle using c = λ_atomic / time-of-transit, but is not realizable even in principle using a fixed value c = 299,792,458 m/s exactly"? What is being said here is that today's measured value of λ_atomic / time-of-transit may change with technique but an exact defined value of 299,792,458 m/s cannot change. Do you really disagree? Brews ohare (talk) 21:16, 24 August 2009 (UTC)

I am not sure what are Wheeler's words and what are yours. Can you repeat that putting only Wheeler's exact words in quotes please. Martin Hogbin (talk) 17:17, 25 August 2009 (UTC)

Wheeler says: "we have to expect that the speed of light will remain at the decreed figure of 299,792,458 m/s ... any substantial improvement in the accuracy of defining the second will bring with it an identical improvement in the accuracy of defining the metre." He says a lot more if you pursue the link. Among other things he says about 299,792,458: "A fundamental constant of nature? Might as well ask if 5280 is a fundamental constant of nature!" Brews ohare (talk) 19:19, 25 August 2009 (UTC)

Thanks. I am not sure what your point is. Nobody claims that 299,792,458 is a fundamental constant of nature but it is the exact speed of light in units of metres per second. The catch is that although we have a very good idea how long a metre is, we do not know its length exactly and never will. Martin Hogbin (talk) 21:40, 25 August 2009 (UTC)

You asked what Wheeler said: I've given you the link, made some exact quotes. Do you agree with what is said? Brews ohare (talk) 00:22, 26 August 2009 (UTC)

I agree with what Wheeler says. I do not agree with your interpretation of it. Martin Hogbin (talk) 08:20, 26 August 2009 (UTC)

Could you point out, please, what is my interpretation of it? I don't know what you think that I think, so I don't know what you disagree with. Brews ohare (talk) 14:03, 26 August 2009 (UTC)

I have no idea what your interpretation is, except that it is not what he says. Martin Hogbin (talk) 14:51, 27 August 2009 (UTC)

Martin: You're being oblique here. You have some objection to my "interpretation". I take the stance that I have no "interpretation" but take Wheeler literally. So I have no idea what you think the discrepancy is between myself and Wheeler, to which you object. You must have some notion of to what you object, eh? What is it? Brews ohare (talk) 16:31, 27 August 2009 (UTC)

Before 1983

Before 1983 the metre was exactly equal to distance travelled by light in the specified number of periods of the specified krypton radiation. Do you agree? Martin Hogbin (talk) 21:42, 25 August 2009 (UTC)

I've quoted the CODATA definition. It is more or less what you say. It specifies the number of wavelengths of a certain transition. The period of that transition is known, so the time taken for the transit of the specified number of wavelengths is known (to within an error bar). Therefore, c = number of wavelengths / time of transit. Brews ohare (talk) 00:16, 26 August 2009 (UTC)

Brews, you seem to be evading this question. Do you agree with my statement above? Martin Hogbin (talk) 08:18, 26 August 2009 (UTC)

Before 1983 the metre was given by the CODATA definition: I'll agree to that. Proceed from there. Brews ohare (talk) 13:18, 26 August 2009 (UTC)

The definition actually was: definition:

“On October 14, 1960 the Eleventh General Conference on Weights and Measures redefined the International Standard of Length as 1,650,763.73 vacuum wavelengths of light resulting from unperturbed atomic energy level transition 2p₁₀ 5d₅ of the krypton isotope having an atomic weight of 86. The wavelength is

λ = 1 m / 1,650,763.73 = 0.605,780,211 µm

I think this statement with the standard for time is tantamount to c = number of wavelengths / time of transit. I take it that the number of wavelengths is a fringe count (a measurement, subject to error) and the second is measured, also subject to error, making c determined in this fashion dependent upon measured quantities, and therefore subject to experimental error (that is, not exact). Refinements in technique will lead to better estimates. The SI conversion factor 299 792 458 m/s, however, is not altered by change in technique because the metre adapts, making 299 792 458 m/s not a fundamental constant. With the pre-1983 metre, with advances in technique the speed of light might become c = 299 792 458.0001 m/s ± ε (say) but in post-1983 metres it will stay at 299 792 458 m/s and the metre will change. Thus, the term speed of light applied to 299 792 458 m/s is a meaning different from speed of light applied to c = number of wavelengths / time of transit. Brews ohare (talk) 14:22, 26 August 2009 (UTC)

Let me ask my question again, with real numbers if it makes you happier. Do you agree that, before 1983 the metre was exactly equal to distance travelled by light in 1,650,763.73 periods of the light resulting from unperturbed atomic energy level transition 2p₁₀ 5d₅ of the krypton isotope having an atomic weight of 86? Please do not evade the question, either you agree or you do not. Martin Hogbin (talk) 16:18, 26 August 2009 (UTC)

Given the theory of relativity, I'd take that as an equivalent statement. However, the measurement of wavelength is a physical measurement separate from time, and so, for example, if light exhibited departures from the theory of relativity, the pre-1983 definition if implemented with more exact measuring methods, could reveal these departures. For example, anisotropy or wavelength dependence of the metre could be discovered. So the absolutely pinned down answer is "no". The answer with a caveat is "yes". Brews ohare (talk) 18:56, 26 August 2009 (UTC)

Brews, you sound more like a politician being interviewed on the TV than a scientist. Do you agree with my statement or not? It is not a trick question. Martin Hogbin (talk) 19:56, 26 August 2009 (UTC)

No. I've given you a careful answer, but you want a binary answer. The binary answer is "No". Brews ohare (talk) 23:05, 26 August 2009 (UTC)

Perhaps you could explain then what is incorrect about my statement. Martin Hogbin (talk) 08:04, 27 August 2009 (UTC)

Martin: My thinking is that the counting of fringes to establish how many wavelengths constitute a specific length provides physical information additional to measuring transit time along that length. According to our present understanding the two are related by the physical speed of light, which speed has certain properties in theory, but measuring both transit time and length in wavelengths provides physical information independent of theory, namely, the actual speed of light instead of a conversion factor . Brews ohare (talk) 12:03, 27 August 2009 (UTC)

You say, 'According to our present understanding the two are related by the physical speed of light', this is true, but it is truer than you think according to any reasonable understanding wavelength is related to speed. Suppose, for example, it was found that light travelled slightly faster in an east-west direction than a north-south direction (unrealistically) then light would travel further in a given time in an E-W direction than it would in a N-S direction in the same time, but the wavelength would also be shorter in the E-W direction. The wavelength always depends on the speed, whatever rules apply to the speed. Martin Hogbin (talk) 14:19, 27 August 2009 (UTC)

I have no problem with that. The question is "what is the speed". The NIST paper largely is a discussion of how improvements in measurement of the actual speed of light were pursued. Microwave measurements gave good frequency but poor wavelength accuracy. Improvement in clocks allowed a shift to optical frequencies where wavelength was more accurate than microwaves, and clock accuracy was comparable. “This careful measurement resulted in a reduction of the uncertainty of the speed of light by a factor of nearly 100.” However, the 1983 switch to time-of-transit comparisons meant that the actual speed of light became irrelevant.

The actual, physical speed of light simply cancels out in any length comparison:

${\frac {\ell _{1}}{\ell _{2}}}={\frac {c\ t_{1}}{c\ t_{2}}}={\frac {t_{1}}{t_{2}}}\ ,$

any length comparison is "equivalent" to a "time-of-transit" comparison. It is totally irrelevant what the actual value of c might be, so long as one can be sure that the same value appeared in both lengths. Consequently, one is free to choose any value for c whatsoever. In addition, one never needs to measure the value of c .

A consequence of this definition is that the speed of light is now a defined constant, not to be measured again. NIST paper

The definition of the metre by BIPM and NIST is really not a length definition at all, but the identification of a standard time of transit namely t_standard = 1/299 792 458 s. When one says a length is so many metres, one really is saying the length has a transit time in vacuum of so many t_standard units. Brews ohare (talk) 14:28, 27 August 2009 (UTC)

Speed is distance travelled in unit time. It is fundamental that wavelength = speed / frequency. Are you saying that this is wrong? Martin Hogbin (talk) 14:34, 27 August 2009 (UTC)

Of course not. Martin, this whole mess is just a result of the confusion engendered when the literature uses the same exact wording for different concepts. It happens again and again. Examples are centrifugal force and Faraday's law and electromotive force. In this case, BIPM refers to an arbitrary conversion factor with absolutely no physical significance as the speed of light, while the structure of spacetime also uses the notion of speed of light in an entirely different way.

By introducing wavelength, a true length is invoked. On the other hand, the present-day metre is actually not a length, but a new name for a standard transit time of 1/299 792 458 s. This time is converted to a length by a fictitious dimensional conversion factor. Brews ohare (talk) 14:38, 27 August 2009 (UTC)

So the wavelength of a given frequency of light is exactly equal the period of that radiation multiplied by the speed of light, agreed? Martin Hogbin (talk) 14:48, 27 August 2009 (UTC)

Some math

Yes, the wavelength of a given frequency of light is exactly equal to the period of that radiation multiplied by the actual, physical speed of light, not the BIPM arbitrary conversion factor. BIPM is interested only in length comparisons:

${\frac {\ell _{1}}{\ell _{2}}}={\frac {c\ t_{1}}{c\ t_{2}}}={\frac {t_{1}}{t_{2}}}\ ,$

where c can be any arbitrary speed (for example, the approximate pre-1983 value 299 792 458 m/s); and are not interested in lengths per se:

$\ell =c\ t\ ,$

which require the actual, physical speed of light (preferably measured using 2009 techniques), not an arbitrary conversion factor. Brews ohare (talk) 15:19, 27 August 2009 (UTC)

I have not mentioned any 'conversion factors' they are all figments of your imagination. There is only one speed of light, the speed that light travels at free space.

So now can you please confirm that you agree that the wavelength of a given frequency of light is exactly equal the period of that radiation multiplied by the speed of light. Martin Hogbin (talk) 20:13, 28 August 2009 (UTC)

Martin: This is the problem: there is only one speed of light, as you say, which is the physical speed of light that enters special relativity and the rest of physics. It determines length in vacuum via the equation:

$\ell =c\ t\ .$

However, this fundamental speed of light is not the SI units conversion factor 299,792,458 m/s for re-expressing transit times, which is an arbitrary number set by committee as stated in so many words by Wheeler, and by Jespersen and by Sydenham.

To progress you have to address these sources and the fact that the SI units deal only with transit-times, not with actual lengths. Brews ohare (talk) 02:22, 29 August 2009 (UTC)

Brews you are jumping ahead of me putting up Aunt Sally (strawman) arguments, which are not mine, so that you can knock them down again. I have not yet mentioned SI or any other system of units.

You have agreed that there is only one speed of light. Let us agree to refer to this exact and specific meaning thus: the speed of light, in italics.

Can you please answer this question. Do you agree that the wavelength of a given frequency of light is exactly equal the period of that radiation multiplied by the speed of light? Martin Hogbin (talk) 11:15, 29 August 2009 (UTC)

I'll join you in this word game, though it all seems silly to me as the issues have been laid out along with the sources, and you have responded to neither. It appears you want to use Socratic method, so yes, it is my belief that wavelength is given by speed of light times period. Next, what do you think "speed of light" means? Brews ohare (talk) 19:18, 29 August 2009 (UTC)

Brews, it is you who is playing word games, I just want you to answer a simple question, where we have both already agreed exactly what the speed of light means. Just to restate I mean what you call the 'actual physical' speed at which light travels (in free space etc). Please will you answer my exact question with a yes or no, then we can move on. Do you agree that the wavelength of a given frequency of light is exactly equal the period of that radiation multiplied by the speed of light? Martin Hogbin (talk) 20:12, 29 August 2009 (UTC)

I'll join you in this word game, though it all seems silly to me as the issues have been laid out along with the sources, and you have responded to neither. It appears you want to use Socratic method, so yes, it is my belief that wavelength is given by speed of light times period. Yes, yes, yes. Brews ohare (talk) 22:18, 29 August 2009 (UTC)

So I guess you would also agree that 1,650,763.73 wavelengths of a particular wavelength of light is exactly equal to 1,650,763.73 periods of that radiation multiplied by the speed of light? Martin Hogbin (talk) 22:47, 29 August 2009 (UTC)

Yep. I'd also suggest that one wavelength is equal to one period times the speed of light; I believe the relation is linear (to within experimental error). Brews ohare (talk) 00:00, 30 August 2009 (UTC)

Please note that I said exactly. You still agree?

Do you also agree that 1,650,763.73 periods of a particular radiation represents a time interval? Martin Hogbin (talk) 12:35, 31 August 2009 (UTC)