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A = BC

Continuation from above subsection

The question is fairly simple, and is not different than "what to plug for C in A = BC" if C = 2. The answer is 2. There's no sweeping under the rug, whatever uncertainty there was in c before is now contained in both E and m. Headbomb {_{κοντριβς} – WP Physics} 17:22, 10 September 2009 (UTC)

I didn't follow the A=BC example? Brews ohare (talk) 17:47, 10 September 2009 (UTC)

First put c = 1 and then decide to use incompatible units for A and B which leads to a conversion factor c different from 1 in your equations. Then think about what would happen have happened had people measured A and B separately using different experiments in different units from the start. Then c would have had an uncertainty, but what does that really mean? Physically, this is equivalent to measuring e.g. the same length twice (e.g. using different experimental techinques and expressed in different units). The ratio will have an experimental error, even though it is some fixed constant. Count Iblis (talk) 18:13, 10 September 2009 (UTC)

This is interesting. So the equation in more recognizable notation is ℓ = c t. The suggestion is that we measure time of transit t and use fringe counts to get ℓ. Then c = ℓ / t = so many fringe counts / s ± ε, with ε = measurement error. Now we know c has an exact value, but here it has been measured only to within measurement error.

I hope I;'m following your discussion up to this point. Am I?

Now what is next?

It seems to me that the real meat of the 1983 decision is that pre-1983 lengths were compared by comparing fringe counts. Post-1983 they are compared using times-of-flight. Because we all are willing to accept that c is constant of nature whatever else it is, we suppose that these two comparisons are entirely equivalent, except the time measurement provides a more accurate comparison. So we adopt the 1983 definition.

My view of this development is that in fact it has zero to do with what the numerical value of the speed of light really is, or how accurately we can measure it. It has to do only with fringe counting being a less accurate basis for length comparisons than times-of-transit. Do you agree with some of this?? Brews ohare (talk) 18:35, 10 September 2009 (UTC)

Yes, if you have some experimental technique for measuring lengths (that is normalized in some arbitrary wayway) and and a different experimental techique for measuring time (which is normalized in some other arbitrary way) then the speed of light will be some arbitry number. You can say that the value of the speed has some inherent physical meansing, but then that meaning depends also on the ratio of the lengths and the time intervals that are numerically equal to 1 in these units. Count Iblis (talk) 23:59, 10 September 2009 (UTC)

So, more specifically, I'd say that the pre-1983 approach counted fringes to get lengths (the metre was so many fringes), and that this method is different from a time-of-transit measurement, in your sense of different experimental techniques for length and time. Then c = # of fringes /s is exactly what you mean by a speed that depends upon the units: what wavelength you picked for the basic fringe count and what unit you picked for the second. That is my understanding of how 299 792 458 ± 1.2 m/s was arrived at. Would you agree to that, I wonder? Brews ohare (talk) 00:34, 11 September 2009 (UTC)

Yes, I agree. Count Iblis (talk) 02:49, 11 September 2009 (UTC)

Count Iblis, thanks for your patience. To shift topics a bit, comparing length by comparing fringe counts is a different experimental technique than comparing lengths by comparing transit times, although the two comparisons should provide the same result. For example, if one comparison says the large length is twice the smaller, so should the other.

However, as counting fringes is more error prone than measuring transit times, the comparison based upon fringes is more error prone than that based upon transit times. I take that as the reasoning described by BIPM that led to the switch to transit-time comparisons in 1983. Would you agree with me on that one?

I hope you do, and that because of this, you also agree that the switch in 1983 is not based upon accuracy in measuring the speed of light, which actually has nothing to do with the switch at all. The switch is all about transit-time comparisons being more accurate than fringe comparisons. What do you say? Brews ohare (talk) 05:41, 11 September 2009 (UTC)

Yes, I think this is correct. Count Iblis (talk) 14:49, 12 September 2009 (UTC)

Yes and no. You're right that the change in the definition of the metre was simply so that lengths could be measured more accurately. You're also right that the time measurement doesn't pose a practical problem. Since at least 1973, by far the largest part of the uncertainty in the measured speed of light was the uncertainty in how long a metre actually was: the uncertainty in the "time" part of the measurement was orders of magnitude lower, and hence negligeable. If you can't measure length to more than 4 parts per billion, then you can't measure speed to more than 4 parts per billion, I think we agree on that.

To increase the accuracy in length measurements required a change in the wavelength used to (practically) define the metre. But the wavelength had only been chosen in 1960, were people going to have to change the definition every ten or fifteen years or so? How would we know in the future that one wavelength was better than another? The solution was to turn the equation round: instead of measuring speed in terms of an arbitrary fixed wavelength and a precise frequency, it was decided to measure wavelength in terms of an arbitrary fixed speed and a precise frequency. The practical problem is still to measure length, but now you can do it with lots of different light sources and compare the results. Physchim62 (talk) 15:57, 12 September 2009 (UTC)

I got the "yes" part. What is your "no" part? Your discussion describes the evolution of length measurement and how it caused the change to time-of-transit as a basis for length comparison. I think we're in agreement on that. The next step is the definition of length by the BIPM as ℓ = 299 792 458 m/s × t. I imagine we will agree that that is what BIPM did. With that in front of us we can put in the time of transit for the metre as 1/299 792 458 s, and recover the metre. Moreover, we can solve ℓ = c t for c and get c = 299 792 458 m/s for any choice of ℓ and its corresponding transit time t. Do we disagree about any of this??? Brews ohare (talk) 21:57, 12 September 2009 (UTC)

My hesitation is that high-precision measurements of lengths in the order of one metre are not usually done by measuring a transit time for that length. They're still done by counting fringes. so you get ℓ = nλ, n is your wavelength count. You then measure a "transit time", but for one wavelength, that is the inverse of the frequency of the light. The transit time for the length you trying to measure, the t in your comments, is measured as n/f.

Before 1983, you had c = λf as by far the most precise measurement of the speed of light, ℓ = nλ (with λ fixed) as the definition of the metre. The limit of precision in the value of the speed of light was how well you could compare the wavelength of the test frequency with the wavelength of the krypton transition chosen as the standard. Since 1983, you have ℓ = cn/f as the lab-scale measurement of length with c as a defined value; the precision in the measurement of length is limited by the measurement of f, not because it is difficult to measure time but because the sources are not perfectly monochromatic. A practical measurement of length will also have an uncertainty in the value of n, which may well be considerable, but nothing changed in 1983 in that respect.

You can measure length in terms of a transit time over that length, of course, just think of radar. However, the method is not very accurate for lengths which are the same order of magnitude as your test equipment because it's difficult to know whether you've eliminated your systematic errors. You could also measure transit time over a longish terrestrial distance that you've calibrated against some other standard – that's effectively the Michelson–Morley experiment.

You might also be interested in and , which are readable introductions to some of these points. Physchim62 (talk) 23:03, 12 September 2009 (UTC)

Physchim62: I take your point that the practical determination of length may vary depending upon how long a length you are looking at, and possibly some other factors as well. However, the main discussion here, in my view, is what the underlying definitions are about, and I guess we agree upon that. I wonder if you would go so far as to say the adoption of the time-of-transit definition of the metre in preference to the fringe-count definition used before is simply a matter of accuracy in length comparisons, and whatever the actual speed of light might be, it really doesn't enter into these accuracy considerations, which are all about lengths, not speeds? Brews ohare (talk) 23:32, 12 September 2009 (UTC)

"all about lengths, not speeds"? Are you sure that you can separate the two as neatly as you seem to be suggesting? Let me give you an example. You have just come up with a brand new measurement technique that implicitly relies on the speed of light being constant: let's call it "interferometry", and not just for the sake of argument ;) You want to calibrate your new technique, so you go and use it to measure the national length standard, which at the time is a bronze bar. Fair enough, you find that the bronze bar is a certain number of wavelengths long, and so you have the conversion factor between your new method and older measurements. A few years later, you go back to measure the same bronze bar, and you find that the conversion factor is very slightly lower: there are fewer wavelengths to the length of the bar. What has happened between the two measurements? Has the bar gotten shorter or has the speed of light increased?

The answer is that the bronze bars, which formed the standards for length measurements throughout the English-speaking world, were very slowly getting shorter. Fortunately, the platinum–iridium bar used in the metric system didn't seem to have this problem (or at least, the problem wasn't large enough to measure), which led the United States to switch to metric-based standards in… 1893.

The British were rather slower to make the legal change and so, throughout the late nineteenth and early twentieth centuries, the value of the speed of light in Imperial yards per second was slowly but surely increasing. Did this mean that the speed of light was increasing, but only in the British Empire? Would have made for some interesting refraction effects at the borders!

Of course, the speed of light that was being measured was the same, whether it was measured in London, Paris or Washington, DC. There was no "Imperial speed of light" and "metric speed of light", simply a physical constant that had different values in different systems of units. Similarly, today, there is no "actual speed of light" vs. a "BIPM speed of light".

But, you say, the "actual speed of light" must be measured! Fine, go find me a length standard. Now measure the length in metres of your chosen length standard using interferometry: you will find you have a measurement uncertainty. This uncertainty is exactly the same as the measurement uncertainty in the speed of light relative to your chosen length standard… Physchim62 (talk) 11:01, 13 September 2009 (UTC)

Physchim62: We seem to have become disrailed. I did not say the "actual speed of light must be measured". I said: "whatever the actual speed of light might be, it really doesn't enter into these accuracy considerations, which are all about lengths, not speeds." In other words, the actual speed of light does not have to measured; its numerical value is irrelevant to the decision to switch from fringe count measures of length to time-of-transit measures of length. The decision to switch definitions is based upon fringe-count measurements being less accurate than time-of-transit measurements. Do you agree with me on this? Brews ohare (talk) 15:12, 13 September 2009 (UTC)

The problem is that you are still speaking of the "actual speed of light" as it were not the same as the speed of light in the 1983 definition of the metre. In which case, what you speak of as the "actual speed of light" is a very different beast from the one the rest of us are trying to describe. Why I speak of the speed of light I'm talking about the one that was measured by Rømer, Fizeau and Michaelson; also about the one that enters into the Lorentz transformations and E =mc, at least to within a difference which has completely escaped measurement so far, despite many efforts; and also the one used to define the SI metre since 1983. What are you talking about when you refer to the "actual speed of light"? Physchim62 (talk) 17:08, 13 September 2009 (UTC)

I think I refer to the same "actual speed of light" that you mention in connection with Fizeau and with the Lorentz transformation. I wish to distinguish that from the integer number 299,792,458 m/s that occurs in the SI units. This number is used to define lengths in terms of transit times. It also is called "the speed of light" but has a somewhat different meaning than the actual speed of light, because in fact, this number could be chosen to be anything the CIPM committee wanted it to be, unlike the actual speed of light that is a constant independent of man's definitions. This ability to make 299,792,458 m/s any number the CIPM wanted is made possible because the metre changes to adapt to whatever number they might pick. I think you know all that. So the point here is just that there is this difference, and I believe baldly stating without further comment that 299,792,458 m/s is "the exact" speed of light violates WP:Astonish. A tempest in a tea pot, I'd say. Do you agree?

The other point is that the switch from fringe comparisons to time-of-transit comparisons for length has nothing to do with either the actual speed of light or the number 299,792,458 m/s. It has to do with the greater accuracy of the time-of-transit comparisons. Again, a simple point, eh? Brews ohare (talk) 05:12, 14 September 2009 (UTC)

Brews, I think I've asked a few times for sources, and that I have stated that you have provided any, that promote this point of view that the measurable speed of light is not the same thing as the speed of light referred to in the 1983 definition. I think this is just a mental juggling trick that you've made up; if I'm wrong, show us the source that says these two things are different. Dicklyon (talk) 05:39, 14 September 2009 (UTC)

Dicklyon: Let me begin at the beginning this time around. Is it necessary to persuade you of these points personally, or is this just you with your official WP hat on asking for sources? If the former, arguments from sourced precepts should suffice. If the latter, a contribution to the main page is under consideration, a situation that I very much find unlikely. Brews ohare (talk) 13:23, 14 September 2009 (UTC)

Another argument

Given the known laws of physics, you can pretend that time intervals and spatial lengths are physically of the same nature (in the same eay that lengths in the x and y direction are physically the same). That is how you can interpret the known laws of physics, regardless of if it is actually correct or not. No experiment can prove this interpretation wrong if such an experiment does not also contradict the known laws of physics.

Compare this to discussons about the Many World interpretation of quantum mechanics. Barring some exotic thought experiments involving artificial intelligence implemented by a quantum computer as an observer, MWI will yield the same predictions as the Copenhagen Interpretation, so you cannot point to some experimental result and then argue that the wavefunction does in fact collapse (unless that experient is in conflict with some basic postulate of quantum mechanics itself).

This then closes the argument about c as the space-time constant. The fact that c is also the speed of light follows from the validity of the theories that describe light as an electromagnetic wave (Maxwell's equations). Count Iblis (talk) 15:35, 13 September 2009 (UTC)

Count Iblis: I am unsure which argument you are trying to settle. The argument I've been engaged in is really inseparable from the SI Units, because the questions are "What is the role of the number 299,792,458 m/s called the "speed of light" in the SI units?" and "How does this number relate to the fact that light does travel at some speed, regardless of the units you use to describe it?" Brews ohare (talk) 16:36, 13 September 2009 (UTC)

I think to fully understand my argument, it would be helpful to derive all the equations in which c appears, including the correct classical limit of special relativity, starting from the equations in which c has been set to 1. I have done this on another forum, but I made a few small mistakes there. If I have the time, I'll rewrite the correct argment here. I.m.o., this is the only correct derivation of classical mechanics from special relativity, the (simple) derivation given in most textbooks is misleading.

You can then see that the role of c is that of a scaling constant. Given some model, you can study some (singular) limit in which one variable is very small or very large by rescaling the variables in some way. Then, in the limit that the rescaling constant tends to infinity, you can get new independent variables that did not exist (as independent) variables in the original model, because of the singular mature of the limiting case (you lose relations between variables).

Then, in the classical limit, you have independent quantities (e.g. mass and energy, or space and time) that were not independent if c is still finite. But because of the way physics has progressed historically, energy and mass or space and time are still considered to be physically inequivalent quantities, despite the fact that we know that c is not infinite. We take into account the view that the different quantities are physically distict, by assinging different dimensions to the physical quantities, causing c to get dimensions as well. But this means that the SI unit for c is still consistent with

c = 1. Equating 299,792,458 metre/second to 1 yields that one second = 299,792,458 metres. This thus indicates by how much the unit of time is rescaled relative to the unit of space in SI units. Count Iblis (talk) 18:22, 13 September 2009 (UTC)

Note that what I wrote in the last paragraph did not involve the actual SI definition of the metre in terms of the speed of light ad the second. So, if the metre were still defined by the length of some bar stored in Paris, you would still have that one second is speed of light times the length of onemeter. The only difference would be that we would not know precisely the value of the speed of light expressed in these units. Count Iblis (talk) 18:28, 13 September 2009 (UTC)

Count Iblis: I may be a bit dense here (not deliberately so, please). I understand that c t is equivalent to a length in SR, and one could use x₄ = c t just like x₁ x₂ x₃. I don't see how that helps me understand a switch from fringe counts to transit times for length comparisons. They involve different physical measurements, and it is exactly this difference, which is accompanied by different error bars, that led to the 1983 decision. It is this last statement that seems to bring out crazy allegations about fringe science, rewriting history, opposition to all of physics, and so forth. Brews ohare (talk) 17:27, 14 September 2009 (UTC)

Meter defined in terms of the speed of light

The section Meter defined in terms of the speed of light is incorrectly named and contradicts both its contents and the underlying BIPM documents. The BIPM SI Units brochure § 2.1.1.1, p. 112 clearly defines the metre in terms of the transit time of light as the length traversed in 1/299 792 458 of a second. It then says "It follows that the speed of light in 'vacuum' is c₀ = 299 792 458 m/s" (Italics mine).

In short, the value of c₀ does not define the metre, but the reverse is true. In SI units, the metre is the fundamental unit.

Indeed it is not the value of c₀ that defines the metre. It is the physical magnitude of this dimensionfull quantity that defines the metre. Just like it is the physical magnitude of the mass of the international prototype kilo that defines the kilo. It also follows from the definition of the kilo that the mass of the international prototype kilo is exactly 1 kg. Also talking about fundamental units after the 1983 definition the (relevant) fundamental units of the SI are actual the second and the 'metre per second', the metre being derived from these two. (Hopefully putting it this way, you will finally understand.) (TimothyRias (talk) 15:03, 11 September 2009 (UTC))

I have your assertions on this point, but no sources. On the other hand, my statements about transit time as the fundamental measurement are sourced, and appear to contradict your remarks. Can you source your statements?

At a logical level, of course the real physical speed of light determines the metre, inasmuch as the metre is how far light actually travels in 1/299 792 458 s . However, this definition says nothing about what the numerical magnitude of the real physical speed of light might be, and actually it doesn't matter. All that does matter is what transit time you set to decide how big the metre is: it is a transit time issue. Brews ohare (talk) 15:15, 11 September 2009 (UTC)

It's pretty simple math to see that if one metre is the distance traveled by light in 1/299 792 458 s, then the speed of light follows as 299 792 458 m/s.

The key to the 1983 definition is the introduction of transit times as a basis for length comparisons. It is transit times that matter and that is why the transit time 1/299 792 458 s is the basic starting point. It is transit times that can be measured accurately, not the speed of light. See Sydenham "Time measurements are more reproducible (parts in 10 uncertainty) than length (parts in 10 uncertainty)" Of course, the error in length is not reduced all the way down to the error in time because other uncertainties enter, among them the accuracy of realizing the 'vacuum'. Brews ohare (talk) 14:19, 11 September 2009 (UTC)

(edit conflict) You can define the inch as 2.54 cm and the yard as 36 inches, or you can define the yard as 91.44 cm and the inch as 1/36 of a yard. What on Earth would be the difference between the two? --___A. di M. 14:45, 11 September 2009 (UTC)

I believe your point is that if A = 1/B, then B = 1/A? The difference here is that it is transit time that is measured, not speed of light. The number 299 792 458 m/s is a defined, not a measured, value. The metre is the standard that is realized. Brews ohare (talk) 14:49, 11 September 2009 (UTC)

That's right. But it still doesn't mean that c₀ is defined that way, any more than "the temperature of the triple point of water" is defined as "273.16 K"; its numerical value (the number 299,792,458) is defined that way. --___A. di M. 15:03, 11 September 2009 (UTC)

OK, pardon me if I am a bit slow here. I agree that the real physical speed of light has some actual value and that value can be expressed in various units as various actual numerical numbers of those units; e.g. wavelengths/s for some transition. If you choose a different wavelength, or a different second, you get a different speed of light. But I don't think that is what this discussion is about, do you? Brews ohare (talk) 15:21, 11 September 2009 (UTC)

The real question here is, How much of how many people's time can one person waste?'. Martin Hogbin (talk) 20:55, 11 September 2009 (UTC)

Another real question here is whether 'tis nobler to simply opt out of discussions that don't interest you, or to make catcalls that interrupt ongoing discussion between parties that wish to engage? Brews ohare (talk) 15:37, 13 September 2009 (UTC)

Measuring

Some musings based on reading Brews, David's and other's posts:

1) Measurement of a quantity means relating it to something else, but more than that, the definition of a quantity is a comparison with something else. The definition of speed is a relation between distance and time. Measurement of speed means comparing it with a ruler and a clock.

2) The speed of light is postulated to be constant therefore it is assumed to always takes the same time to travel a given distance, or equivalently it always travels the same distance in a given time, therefore an ideal ruler can be defined as the distance traveled by light in a given time.

3) Actual rulers manufactured according to this definition will differ due to the accuracy of the manufacturing equipment and the accuracy of the clock. The numerical value of the speed of light given in these ideal rulers is a defined value but using one of these manufactured rulers to measure the speed of light will give a relation between the speed of light and the manufactured ruler. Since the manufactured ruler will have limited accuracy it may well give a different value than the defined value. This measured value will be a relation between the speed of light and the manufactured ruler. Since the speed of light is postulated to be constant, any discrepancy between the defined value and the measured value will be attributed to the inaccuracy of the ruler, i.e. the difference between the defined value and the measured value will tell you the difference between the ideal ruler and your actual ruler - which is a measurement of the actual ruler in terms of the ideal ruler or equivalently a measurement of the ideal ruler in terms of the actual ruler.

4) Suppose you want to measure the speed of light (either because it's hundreds of years ago and you've no idea how fast it is or that it is constant, or you don't really believe it is constant), then you must compare the light with some ruler and some clock and you will get some idea of its speed subject to inaccuracies in your ruler and clock. The act of measuring the speed of light in this way is a different concept from the act of defining the speed of light, i.e. the act of comparing the speed of light to something else is a different concept to the act of not comparing the speed of light to something else. However this doesn't matter because the speed of light is postulated to be constant therefore you use the defined value to define a ruler with which to measure the distances and speeds of everything else - so everything else is ultimately measured in relation to the speed of light.

5) The equation relating c,ε0 and μ0 may have originally been discovered as a result of experiment, but assuming the equation is true then whatever value and units are given for two of the quantities, the third quantity is fully determined. A=B implies B=A so an equation can be read either way, assuming the equation is true, regardless of how the equation was originally discovered. Charvest (talk) 18:14, 12 September 2009 (UTC)

I think there's another point that you miss from your list: that's that nobody is forcing you to use SI units. I'll assume that we're talking about scientific research here and not everyday commerce. Imagine, for example, that you wanted to see if the speed of light varies with frequency. You can't use SI units, because the definition of the SI metre assumes that the speed of light doesn't vary with frequency. That doesn't stop you from using some other length standard, for example an old standard metre bar: you then measure the speed of light at different wavelengths against your chosen length standard, and see if they differ. Similarly if you want to see if the speed of light changes over time: you can't use the SI metre, but you could use some other length standard which you don't think has changed over time, such as some function of the mass of the earth, the Newtonian gravitational constant and a time standard. The way that the metre is defined doesn't stop you from doing these experiments, nor does it mean that they are not physically worthwhile. But it doesn't mean that the speed of light isn't 299,792,458 m/s either. Physchim62 (talk) 19:19, 12 September 2009 (UTC)

As long as the new "perfect" definition results are within the upper and lower limits of the old "perfect " results there is no problem for everybody having to use the result of all these (nonexistent )difficulties.Wdl1961 (talk) 00:46, 13 September 2009 (UTC)

I'd say everybody is a bit right here. For example, Physchim62 points out that you don't need to use SI units. An example might be to go back to the pre-1983 SI units based upon fringe counts of wavelengths. Then you can measure the speed of light in these wavelength-based units, and of course, as with all measurements an error bar of observation will arise (c = 299,792,458 ± 1.2  m/s). Where I think some problems with language show up is in connecting such a measured speed of light with the use of the term "speed of light" to describe the defined value 299,792,458 m/s in today's SI units. These usages are separate. There can be no argument that the speed of light in today's SI units "is" 299,792,458 m/s, but what is its relation to measurement? As the BIPM and others point out, measurement uncertainty has been transferred to the metre itself. Thus, the number 299,792,458 m/s is exact, but the unit m/s is not known. It is the unit that is the experimental quantity now. Brews ohare (talk) 15:52, 13 September 2009 (UTC)

Speed in natural units is expressed as a fraction of lightspeed so:

speed of light = 1 x speed of light

also speed of light = 299,792,458 m/s

therefore 1 = 299,792,458 m/s

or equivalently 1 = 299,792,458 x 1 m/s

i.e. the number 299,792,458 is a conversion factor between natural units and m/s

turning the equation around: 1 m/s = 1/299,792,458 in natural units, that is as a fraction of lightspeed.

The use of the term speed of light for a defined value is basically the same thing as using the term speed of light for the natural unit 1 in which we simply relate the speed of light to itself.

Measuring the speed of light means relating it to something else.

So the different uses of the phrase that you talk about are either 1) relating the speed of light to itself and then relating other speeds to light, or 2) relating it to something else straight away. Charvest (talk) 16:16, 13 September 2009 (UTC)

Brews, what you say is right, but the unit has always been an experimental quantity, not just "now". There's no fundamental difference between using the speed of light, the wavelength of a particular atomic transition, or the distance between two tacks on a particular piece of metal in Paris. In any case, you would know exactly the value of said speed/wavelength/distance in your unit by definition, but you could have uncertainties in the measurement of said speed/wavelength/distance which essentially become uncertainties in the unit. --___A. di M. 16:40, 13 September 2009 (UTC)

Charvest: I agree that today's SI Units use the speed of light as a unit of speed. So for example, the speed of sound can be expressed as a multiple of the speed of light. Moreover, this multiple depends in no way upon knowing the numerical value of the speed of light. So in that sense, the number 299,792,458 m/s is simply an artifact, or as Jespersen says, a defined and arbitrary value. I think we agree about that. Brews ohare (talk) 16:47, 13 September 2009 (UTC)

User:A. di M.: I think your description muddles me. I think I can agree that there is no difference in kind between the metal bar and counting fringes: they both are length measurements. However "the speed of light" is a speed, not a length. It can be related to a length measurement by introducing a transit time, which most probably you would agree. So then, is a transit time measure of length the same in kind as a wavelength determination of length? I'd say not, for this reason: When length is determined using a length measurement and time is determined using a time measurement, then speed can be determined as the ratio of these measurements. However, when length is determined as a time-of-transit measurement and related to length by a defined constant with the dimensions of speed, it no longer is possible to measure speed as length / time, because only the defined conversion factor can result, and it provides no physical information, only the defined value, which is arbitrary. Brews ohare (talk) 16:56, 13 September 2009 (UTC)

So, according to you, when the litre was defined as the volume occupied by one kilogram of water in such-and-such conditions, a measurement of the density of water could "provide no physical information"? --___A. di M. 17:06, 13 September 2009 (UTC)

I am unfamiliar with your example. You seem to suggest, however, that saying the litre = volume occupied by 1 kg. of water → the density of water is 1kg/ litre, appears to be inescapable and of no content. It looks that way. If one measured the dimensions of a litre of water as so many cubic metres, then the density in kg./m would have a meaning. Thus, there appears to be a parallel between time-of-transit length cf. wavelength length compared to density in kg/litre cf. density as kg./m Brews ohare (talk) 17:12, 13 September 2009 (UTC)

So what would you propose as a "non-arbitrary" standard for speed, that would give the "physical information" you're looking for? Physchim62 (talk) 17:30, 13 September 2009 (UTC)

I haven't raised that question, which is a different matter. I simply wished to clarify that the number 299,792,458 m/s has no physical content within the new SI units. It's a hang-over from the pre-1983 units, where it actually was a speed measurement, and was chosen for the new SI Units only to minimize dislocation with prevailing practice. I also wished to point out that the experimental error bar in the new SI Units is now in the unit m/s, having been transferred there by introduction of the now defined value of the speed of light. As the BIPM points out, any advance in the precision of measurement changes the metre, not the number 299,792,458 m/s. Brews ohare (talk) 17:39, 13 September 2009 (UTC)

Erm, no, any advance in the precision of the measurement gives us a more precise metre, which is not the same as changing it. The problem is that we would all really like to believe that you simply don't understand what a unit of measurement is: so, please, give us you proposition for a standard against which to measure the speed of light which would give you the "physical information" you're looking for, instead of just saying that everything is FUBAR since 1983 and nobody else has noticed. Because there, you're making a big claim against pretty much the whole of physics: it might just be that it's you who has the misunderstanding. Physchim62 (talk) 18:00, 13 September 2009 (UTC)

Physchim62: Roger, the metre becomes more precise, and the number 299,792,458 m/s is unaffected, as measurement precision improves. Your summary of my position "saying that everything is FUBAR since 1983 and nobody else has noticed" is an invention of your construction, as I have never said, suggested, or thought anything of this kind. Likewise, "you're making a big claim against pretty much the whole of physics" is completely incorrect: please explain where this crazy notion comes from. Brews ohare (talk) 18:04, 13 September 2009 (UTC)

Charvest, First of all, I'm glad that you have actually acknowledged that the equation relating c,ε0 and μ0 was originally discovered as a result of experiment. I got reported at AN/I for disruptive behaviour for bringing that matter up at WT:PHYS. That equation has got nothing to do with the measured speed of light. It arises exclusively from the ratio between the electromagnetic units of charge and the electrostatic units of charge. That ratio will always exist. There is no system of units that can get rid of that ratio out of Maxwell's equations. If we have a defined speed of light such as in the new SI system, or in the system in which we define 'c' to be equal to 1, we cannot put it into that equation. The only thing that we can do is draw attention to the closeness in value between the defined speed of light and the value that arises from the experimentally measured values in this equation.

Now let's not lose sight of what the main argument is here. The main argument is not even related to what I have just said above. The main argument is about the fact that the measured speed of light is used to define the new metre. It then follows that if we express the speed of light in terms of that new metre that is defined in terms of the speed of light, then we merely end up with an arbitrarily defined number. This defined number is beyond measurement, and it is a different concept to the measured speed of light that was used to define that metre in the first place. In SI units, the speed of light then becomes 299,792,458 times the distance that light travels in 1/299,792,458 seconds, per second. We could have chosen any number. The physical speed of light as a concept cannot therefore be sacrificed in the article for a system of units. The article introduction must clearly explain both concepts. David Tombe (talk) 18:53, 13 September 2009 (UTC)

"The only thing that we can do is draw attention to the closeness in value between the defined speed of light and the value that arises from the experimentally measured values in this equation." – which is all Weber and Kohlrausch could do, until there was sufficient theory to show that the relation will always hold. Some fifty of so years later, the Weber–Kohlrausch experiment had been turned round (new measurements, of course, by Rosa and Dorsey at the U.S. National Bureau of Standards) to provide a measure of the speed of light. These days, it's more likely to be used as a measure of capacitance or as a lab demonstration.

As for the "physical speed of light as a concept" being "sacrificed" for a system of units, the "speed of light an a vacuum" is exactly what it says it is: we could always link speed, light and vacuum if there was any risk of confusion. There should be no apology for quoting its value in the systems of units used by the overwhelming majority of our readers. Or perhaps you believe that the "speed of light" is something completely different? Physchim62 (talk) 19:31, 13 September 2009 (UTC)

Physchim62: As you say: "There should be no apology for quoting its value in the systems of units used by the overwhelming majority of our readers." Undoubtedly so, provided the context is provided explaining the switch from length measurement to time-of-transit measurement, which is a departure from the approach used for many centuries prior to 1983. Brews ohare (talk) 01:22, 14 September 2009 (UTC)

Physchim62: You have not responded to me as to the origin of the ridiculous statements you attribute to me here. Brews ohare (talk) 01:09, 14 September 2009 (UTC)

Physchim62, Nothing has changed as regards the Weber/Kohlrausch experiment. Maxwell's work in 1861 demonstrated a convergence of two measured results. There was the direct measurement of the speed of light by Fizeau and there was the electromagnetic/electrostatic ratio as measured by Weber and Kohlrausch. From that convergence of measured results, Maxwell was able to demonstrate that light is an electromagnetic wave. Nothing has changed to this day. The equation c^2 = 1/(εμ) always has and always will read from right to left. It is the equation which links the speed of light to the measured value of ε. Neither the measured value of the speed of light nor the defined value of the speed of light should be used in that equation. If we use that equation from left to right, we are cooking the books with the benefit of hindsight. In maths, equations may work in both directions, but you as a chemist should know that they don't necessarily work in both directions in chemistry. Likewise in physics. There are issues of cause and effect to be considered as well as the physical scenario that is being described. David Tombe (talk) 05:15, 14 September 2009 (UTC)

When you speak of "cause and effect", you're getting onto philosophical ground about the "nature of science". This is usually described as the "philosophy of science", although some prefer the term "sociology of science" (and, personally, I'd say they're not entirely wrong, but who am I to judge).

That aside, when you say: "The equation c^2 = 1/(εμ) always has and always will read from right to left." you are making a claim that is evidently false. Weber and Kohlrausch suggested it, in reading from right to left. Maxwell proposed a theory (which has been largely supported by experiment, at least in its descriptive value) that the relation will be true whichever way you read it. Rosa and Dorsay (1907) read the equation from left to right to determine the speed of light. Physchim62 (talk) 12:03, 14 September 2009 (UTC)

No Physchim62, That equation links the measured value of electric permittivity to a number that is very close to the measured (or defined) speed of light. That is all there is to it. We can certainly use it in reverse, with the benefit of hindsight, as a lazy way of obtaining a practical working value for electric permittivity. But in doing so, we are cooking the books and working against the spirit of the equation. Where it becomes really ridiculous is when we use the defined value of the speed of light to obtain a defined value of electric permittivity, and then purge the discharging capacitor experiment from the texbooks. David Tombe (talk) 12:14, 14 September 2009 (UTC)

David, when you invoke the discharging capacitor experiment, you also need to explain how you want to define the unit for electric charge and electric potential. Count Iblis (talk) 13:34, 14 September 2009 (UTC)

Count Iblis, When the experiment was originally done in 1856, it involved two distinct units of charge. There was an electromagnetic system of charge and an electrostatic system of charge and the experimental result yielded the ratio of these two units which was related to the measured speed of light. That puts the speed of light firmly into Maxwell's equations, irrespective of what system of units we use. David Tombe (talk) 13:43, 14 September 2009 (UTC)

Clarifying the distinction between the two concepts of the speed of light

This prolonged dispute has come about because of attempts to deny an important point that has been raised by Brews ohare. The matter has now gone to arbitration and the arbitrators will now be watching this page carefully. I think that it's only fair to the arbitrators, most of whom are probably not physicists, to make an attempt to explain to them, and eveybody else here, exactly what the distinction is that Brews has brought to our attention.

Everybody, whether a physicist or not, is familiar with the concept of the speed of light. It is the speed that light travels at, and it is generally known to be extremely fast and unreachable by any existing technology. Now let's imagine that I went unto a stage to give a speech on the speed of light. Imagine that I went unto a stage in front of 10,000 people and said that I am going to tell you all what the speed of light is. And then imagine that I stated "The speed of light is the speed of light". And with the speech ending at that, a loud clapping and stamping of feet erupts and lasts for the next twenty minutes. That sounds like a pretty ridiculous scenario. But in fact it is no more ridiculous than if I went unto the stage and stated the speed of light in modern SI units. If I were to go unto the stage and announce the speed of light in modern SI units, I would be stating "The speed of light is 299,792,458 times the distance that light travels in 1/299,792,458 seconds, every second". I could then expect the twenty minute clapping session to be no less sarcastic for me having just stated the obvious.

Brews has pointed out that it is not satisfactory to state the speed of light in modern SI units without some kind of extended elaboration, because the metre itself is defined in terms of the speed of light. Hence any statement of the speed of light in terms of that metre is merely a statement of the speed of light in terms of itself.

Now if we were to already accept the old classical concepts of length, I could go unto the stage and tell the crowd of 10,000 that I had performed an experiment to measure the speed of light using a Michelson interferometer on top of Mount Wilson, California. I could announce, that after performing some difficult calculations that I have found the speed of light to be in the order of 299,792,458 metres per second with an error bar of 0.04%. That would be news worth hearing. I would have given the audience a useful piece of information that had a physical meaning.

It is this latter measurememnt that Brews and I have been referring to as the physical speed of light that can be measured. It is clearly a different concept from the defined speed of light that I described further up, and which tells us nothing that we don't know already, and which is beyond measurement.

This edit war came about because Martin Hogbin wanted to only include the new SI speed of light in the introduction. His argument was that since the SI system is the internationally established system of units, then it follows that we must exclusively use that system in the introduction. Martin has of course overlooked the fact that in the special case of the speed of light, where one of the staple SI units has itself been defined in terms of the speed of light, then it is not good enough to state the speed of light exclusively in SI units without any kind of elaboration.

Brews on the other hand wanted to make that elaboration for the benefit of the readers. Martin was determined to frustrate Brews in his efforts. A crowd then descended upon the article and tried to accuse Brews of being wrong, and of advocating fringe views and pseudoscience. These allegations against Brews, and also against myself, will simply not stand up even against the mildest standards of probity. David Tombe (talk) 05:42, 14 September 2009 (UTC)

As has been explained to David many times, defining the speed of light as 299,792,458 metres per second is not tautological, since measuring the speed of light is equivalent to measuring a metre (i.e. a recalibration of our instruments). It is analogous to saying that a foot is twelve inches. That doesn't stop us from measuring how long a foot is, which tells us how long an inch is. Similarly, measuring the speed of light tells us how long a metre is. --Michael C. Price 05:58, 14 September 2009 (UTC)

When you say "It is clearly a different concept" and use that to support the POV that there are two different concepts called speed of light, you are aligning yourself with Brews, but not with any source that I have seen cited. The lack of citation to a source supporting the point of view is why it can't stay in the article. The fact that you and Brews push an idiosyncratic point of view is the source of the problem. Brews has at least shown us which sources he thinks are closest to representing the POV he wants to push, and I for one welcome the representation of the points of view expressed in those sources -- but I don't think any of them said anything about there being two different concepts called speed of light. If I got that wrong, just give us the source and the quote that contradicts what I just said. Dicklyon (talk) 06:05, 14 September 2009 (UTC)

Dick: Are we persuading you personally? If so, sourced precepts and a logical argument should suffice. The whole matter is explained with care at User:Brews ohare/Speed of light (Example). Brews ohare (talk) 13:30, 14 September 2009 (UTC)

Dick, Brews provided the sources, and I am backing Brews up on the point that he has made. The arbitrators can decide on whether or not Brews and I have a legitimate point, or whether we need to be topic banned for having advocated this point of view. David Tombe (talk) 06:32, 14 September 2009 (UTC)

David, the sources that Brews cites to justify his POV are typically these: Wheeler; Jespersen; Sydenham. If you want to support him meaningfully, just show where they support the idea of two different concepts of the speed of light. The arbitrators are more like to be swayed by whether you argue with reference to sources than by anything about the physics, which it's not their job to understand. If you keep pushing a POV by insistence, rather than by showing it in sources, you'll just help them see that our complaints about your behavior are well founded. Dicklyon (talk) 07:17, 14 September 2009 (UTC)

But many of the 10,000 people in the audience roughly know how long a metre is (even if they have no idea of how it is officially defined) and how long a second is, in relation with everyday quantities. To such people, telling that the speed of light is 299,792,458 m/s, although tautological for those who do know the definition of the metre, is not useless; they'll know that the light travels roughly 300 million times the distance from their hips to the ground in a time roughly equal to that between two consecutive heartbeats of theirs. And as for the Misplaced Pages article, per WP:MTAA, WP:NOT PAPERS, WP:LEAD and all that, we should not assume that readers will know how the metre is defined, at least not in the lead section. --___A. di M. 09:39, 14 September 2009 (UTC)

Dick, I clicked on Jespersen and the first thing I saw was "One fall out of this new definition of the metre was that the speed of light is now a defined quantity and no longer a measured quantity". What more do you want? David Tombe (talk) 07:40, 14 September 2009 (UTC)

Well, just above, it says "This task has proved to be about as much art as science." This was an art first demonstrated in 1972, and repeated by many laboratories. The value obtained was recommended from 1976, and officially adopted in 1983, after the same procedure had been applied to other light sources and found to give the same result (within experimental error). The fact that the author of an introductory book about the concept of time wishes to distinguish it from science in 1999 (the date of the quoted edition) is of little consequence here. Physchim62 (talk) 12:39, 14 September 2009 (UTC)

Physchim62: This book is written by several scientists at NIST. SO they have some authority. Your denigration of sources is the next step in refusing to engage in this discussion. You are simply running a debate, with the normal rules of debate, which are to obfuscate, distort to score points, and entertain with les bons mots. There is no point holding discussion with those ground rules. Brews ohare (talk) 13:14, 14 September 2009 (UTC)

Physchim62, My argument above stands on its own merits irrespective of sources. Brews has given sources for good measure and you are now trying to belittle one of those sources. David Tombe (talk) 13:31, 14 September 2009 (UTC)

Dear David,

my puny mind needs your mighty intellect's guidance:

Is the kilometre

1. just a defined value?
2. just a measured value?
3. both a defined and a measured value?

Eagerly awaiting your clarification,

--Michael C. Price 10:12, 14 September 2009 (UTC)

Another smart-alecky comment by Michael C. Price, champion debater and master of the snarky remark. Brews ohare (talk) 13:14, 14 September 2009 (UTC)

A question, not a comment. And a question that Brews and David have both avoided answering. I wonder why? --Michael C. Price 14:55, 14 September 2009 (UTC)

A. di M., No. To say that "The speed of light is 299,792,458 times the distance that light travels in 1/299,792,458 seconds, every second" is a meaningless tautology that tells us absolutely nothing about the speed of light. It is no different to saying "The speed of light is k times the distance that light travels in 1/k seconds, every second". The case has been unequivocally proven in Brews's favour along with supporting sources. I suggest that the arbitration committee take note of this and swiftly fold up the case, because there is absolutely nothing more that can be said regarding the dispute. I suggest that Brews ohare is owed a major apology. David Tombe (talk) 12:06, 14 September 2009 (UTC)

Except that many readers won't mentally substitute "the distance that light travels in 1/299,792,458 seconds" for "metre"; most of them have an idea of how long the metre is in relation to everyday stuff (e.g. "slightly more than the width of my bed" or something), but no idea of how it is formally defined. --___A. di M. 12:27, 14 September 2009 (UTC)

Yes, Which is exactly why it is a less informative concept than the measured speed of light. Do you now agree that this matter needs to be elaborated upon in the introduction? You are turning the argument upside down. You are now saying the same thing as me, but doing so in a manner as if you are disagreeing with me. David Tombe (talk) 12:37, 14 September 2009 (UTC)

But what neither Brews nor yourself have been willing to tell us is: "what is this real speed of light?" Can we measure it? The measurement of the speed of light (as we all seem to have agreed on its definition) presents no problem at all, so long as you can provide a length standard that is sufficiently precise. The speed of light is still measured, at inner solar system scales at least, and to admirable precision. All of this after 1983. Physchim62 (talk) 13:00, 14 September 2009 (UTC)

I have attempted real engagement with you on these points time and again. You have many careful explanations above, which you abandon when convergence is approached, and re-open again later. Brews ohare (talk) 13:17, 14 September 2009 (UTC)

Physchim62, Of course we can measure the speed of light. But we have to use a system of units other than the modern SI system, because the defined speed of light in SI units is fixed by definition, and therefore cannot be measured. I've stated the argument clearly above and I intend to take that argument to the arbitration committee. It has now become patently clear that you don't understand this issue, yet you have gone to AN/I and successfully persuaded an administrator to ban me from explaining it to you. David Tombe (talk) 13:37, 14 September 2009 (UTC)

I agree that this explanation has been offered again and again. Dialog only goes so far, and then the questions simply are repeated days later without reference to explanations provided. The fact is, these matters are extremely simple and straightforward, and the resistance cannot be understood as a failure to grasp the issues. An extensive discussion with sources is found at User:Brews ohare/Speed of light (Example). Brews ohare (talk) 15:58, 14 September 2009 (UTC)

Mathematical model vs Experimental observations

One way of looking at this argument is to say that physics as a whole is a mathematical model of reality consisting of various constants, various variables and various equations relating the constants and variables. The model is deemed useful if it corresponds closely to experimental observations. There is an element of the model called c. The model relates c to various other elements of the model, and experiments can try to invalidate the model by measuring the real world counterparts of elements of the model and seeing whether within statistical error bounds the model reflects the real world. In this respect, the difference between c as part of the model, and real world measurements of the speed of light, is no different from how every part of the model can be contrasted with real world measurements. Does that mean every article about a concept in physics should explain the difference between a model and the real world in the lead paragraph ? There's no reason why the speed of light should be singled out for such treatment. Charvest (talk) 17:16, 14 September 2009 (UTC)

Your discussion of model equations involving c is fine. However, it is not related directly to the question of the status of the number 299,792,458 m/s. In the pre-1983 system of units, measurements of the c you talk about were made with the result c = 299,792,458 ± 1.2 m/s. In the post-1983 a speed called the "speed of light" and given by c₀ = 299,792,458 m/s exactly is introduced. The connection between c and c₀ is the subject of discussion. Because of the switch to times-of-transit for length comparisons, a means to convert such times to lengths was needed. For that conversion the number c₀ = 299,792,458 m/s exactly was selected. Possibly, if the number 500,000,000 m/s exactly had been chosen instead it woudl have avoided the confusion between c = 299,792,458 ± 1.2 m/s and c₀ = 500,000,000 m/s exactly and made more clear the arbitrary nature of this number. It is the distinction between c = 299,792,458 ± 1.2 m/s with its error bar and c₀ = 299,792,458 m/s exactly that I would like to see clearly explained in the article. Brews ohare (talk) 17:43, 14 September 2009 (UTC)

And my point is that "299,792,458 exactly" is part of today's model, but 299,792,458 ± 1.2 m/s was a real world measurement based on the then-used units. This part of the model was chosen to reflect that real world measurement, just as all parts of the model should closely reflect the real world measurements. Charvest (talk) 17:54, 14 September 2009 (UTC)

Why do you say that the exact value is part of a model. There is no physics in the fact that the speed of light is exact when expressed in SI units. It is just a choice of units. Martin Hogbin (talk) 18:03, 14 September 2009 (UTC)

I'm simply allowing the possibility of having a model which also models units. You One might say that there is no interesting physics in including units but it seems to me that a numerically complete model should allow for the modelling of units. Charvest (talk) 18:07, 14 September 2009 (UTC) (modified Charvest (talk) 05:26, 15 September 2009 (UTC))

I see what you are saying but I do not think it has anything to do with the Brews' perceived problem. Martin Hogbin (talk) 09:43, 15 September 2009 (UTC)

I think it does. It is my take on how to deal with the issue of defined values vs measured values. Charvest (talk) 05:47, 16 September 2009 (UTC)

I agree with Charvest's argument about the physical world being equivalent to a model in which c appears. However, it then has to be recognized that there exists a one parameter family of equivalent models that is obtained by rescaling the time variable relative to the spatial variables. This rescaling constant can then be absorbed into c, so the set of equivalent models is parametrized by c. Count Iblis (talk) 18:16, 14 September 2009 (UTC)

To Count Iblis:I didn't say the model was "equivalent" to reality though. I would say the model has been built up to reflect reality to the best of our abilities at building models. But the model known as physics isn't complete or even necessarily as accurate as we might one day make it. But anyway, you mention that we have different models parametrized by c which are equivalent to each other. What is the conclusion that you want us to draw from that statement? Charvest (talk) 18:50, 14 September 2009 (UTC)

The conclusion is that c has the same status as the constant 1.609344 kilometers/mile :) Count Iblis (talk) 23:21, 16 September 2009 (UTC)

my point is that "299,792,458 exactly" is part of today's model is not true if one means somehow that this particular number is a demand that must be met if the model is to fit nature. The measurement c = 299,792,458 ± 1.2 m/s was an evaluation of a model parameter. The number "299,792,458 exactly" is part of a definition and contains no physical information. It happens to be that a different choice, say c₀ = 500,000,000 m/s would result in a 1983 metre so different from the previous metre as to cause great dislocation during its adoption, but of course, one could elect to do that if, for example, one were really hung up on easy arithmetic and didn't care about scrapping all exiting metre sticks. Brews ohare (talk) 18:36, 14 September 2009 (UTC)

To Brews ohare: I don't mean that nature demands it. I mean that it is a defined value therefore it is part of what I consider to be a model which includes numerical values and units. Charvest (talk) 18:50, 14 September 2009 (UTC)

Charvest: A model, like SR, does not require a specific value for c. But to fit nature using the pre-1983 SI units, one value of c will be optimal. However, whatever that value is, it's got nothing to do with the number 299,792,458 m/s in the modern SI Units. That number may be chosen arbitrarily to be any real number whatsoever without affecting in any way how SR fits nature. Brews ohare (talk) 20:02, 14 September 2009 (UTC)

Of course we don't have to put the particular number 299,792,458 in our model, but if we write down a model that includes all the units and numerical values then one way of doing this is to use 299,792,458. I don't see how you can say with a straight face that 299,792,458 has nothing to do with 299,792,458 ± 1.2 Charvest (talk) 04:56, 15 September 2009 (UTC)

Of course 299,792,458 ± 1.2 was an evaluation of a model parameter. But that parameter was 1,650,763.73/9,192,631,770 times the ratio between a particular transition of the krypton-86 atom and another particular transition of the caesium-133 atom. Hardly a fundamental parameter. --___A. di M. 19:22, 14 September 2009 (UTC)

I have not said it was fundamental. Brews ohare (talk) 20:02, 14 September 2009 (UTC)

Alternative (mainstream) view

Just in case the arbitrators are interested in the content of the page and none of them happen to be physicists I have written my version of what I believe to be the standard view of this subject in my user space. Please do not edit this page, it is my personal opinion. The views of other physicists and experts in metrology are welcome on the associated talk page. Martin Hogbin (talk) 17:31, 14 September 2009 (UTC)

Just in the same case, the Usenet Physics FAQ contain a very decent explanation of those issues. --___A. di M. 19:31, 14 September 2009 (UTC)

I've also produced a rather more flippant reply to the idea that a fixed speed of light has no physical significance… Physchim62 (talk) 09:10, 16 September 2009 (UTC)

Brilliant. You should be debunking crackpots on Usenet ;-) - DVdm (talk) 11:35, 16 September 2009 (UTC)

I'm old enough (in RL) to have cut my teeth on Usenet, that much is true ;) — Physchim62 (talk) 12:43, 16 September 2009 (UTC)

Two different concepts of the "speed limit"

I think I've figured this out. If you asked "what is the speed limit?" you could answer "the speed faster than which it is illegal to drive". Or else you could answer "65 miles per hour". Just like the answer to "what is the speed of light?" could be "the speed at which light travels in a vaccum, a fundamental physical constant" or else "299,792,458 m/s". The word "speed" is ambiguous. To say that there are two distinct concepts is misleading, though, since in each case both have to be true about the same thing.

To Brews and David, I gather, the SI's "speed of light" is a number. The number itself, since it is "defined", doesn't depend on c, although a measured value would. Drawing a distinction between the number and the physical constant sounds like a claim that c!=299,792,458 m/s. But that isn't what Brews and David are saying. This is not a dispute over a fringe theory; it's just a matter of semantics. 140.247.103.158 (talk) 14:17, 16 September 2009 (UTC)

140.247.103.158, That's pretty well it. It's got nothing to do with fringe science. It's a simple case of pointing out that the speed of light, when expressed in terms of a metre that is itself defined in terms of the speed of light, is merely an uninformative tautology that should not be confused with the actual physical speed of light itself. And those who haven't grasped this point are making malice out of what Brews and I have been saying, because what we are saying can sound superficially ridiculous to those who haven't grasped the subtlety of the argument. Imagine we defined a new unit of length as being the height of the Eiffel Tower and that we called it an 'Eiffel Tower'. Then imagine somebody asking what height is the Eiffel Tower, and the reply comes that it is one 'Eiffel Tower' high. The person then asks "how high is an 'Eiffel Tower'?" The reply comes that an 'Eiffel Tower' is the height of the Eiffel Tower. So does the person now know how high the Eiffel Tower is? This would be no more ridiculous than stating the speed of light in modern SI units. David Tombe (talk) 01:44, 17 September 2009 (UTC)

It's not a tautology at all, it's a point on a scale. On your hypothetical scale, the Washington Monument is 0.523 Et and the Empire State Building is 1.176 Et. Are you trying to claim that there's no information in those relations? The answer to your question "How high is the Eiffel Tower?" could very well be "Just under twice as high as the Washington Monument." or "Not quite as high at the Empire State Building, but nearly." Physchim62 (talk) 10:36, 17 September 2009 (UTC)

To IP 140.247.103.158: Not quite. Speed is the distance traveled in a unit of time. The units of distance and time are invented by people based on standards that people choose to define the units. Speed is a real phenomenon, and you can use any units of distance and time that you choose to measure it; the number will be different, but the speed won't be. With modern technology, scientists can measure the speed of light very accurately (but, of course, not perfectly). Because the speed of light in a vacuum is constant, and because it is relatively easy to measure the speed of light very accurately in a laboratory, in 1983 the organizations that define units of measurements decided to redefine the metre (the basic unit of length in the International System of Units, abbreviated SI), based on the speed of light, as the distance light travels in 1/299,792,458 of a second. This conformed to the speed of light as measured with the pre-1983 metres, within narrow limits of accuracy. Everyone here agrees on what I have said up to this point, I believe. However, David and Brews contend that using the speed of light as the standard to define the unit of length caused big problems. I hesitate to describe their positions (which are similar in many ways but not identical), because David and Brews seem to object to everyone else's attempts to summarize succinctly what they say, but I'll try to do the best I can with some of the key points. They both contend that it changed the speed of light from something that real that can be be measured into something that is merely a "convention" (without real physical meaning) or a "tautology". David argues that this 26-year-old definition of the metre undermined part of the foundation of physics. Brews contends that the "real, physical speed of light" is now decoupled from any statement of its value (or at least from the statement of its value in SI metres). Professional physicists, which David and Brews admittedly are not, don't agree, and the professional literature on the subject doesn't support these views (although David and Brews, unlike the professional physicists here, contend that some passages in the professional literature do support them). That is the essence of the dispute, as I understand it. —Finell (Talk) 16:50, 16 September 2009 (UTC)

Well put. That is the problem as I understand it too. Martin Hogbin (talk) 10:42, 17 September 2009 (UTC)

There are many aspects to answering "what is X?"; and we should give them all. But that's not the same as saying that "X is really two different concepts"; if no source says that, then neither should we. Dicklyon (talk) 18:23, 16 September 2009 (UTC)

Has it been considered that - from our limited view amid the process of incomplete Universe - the structure of space extends more rapidly with distance, carrying its contents with it at the same faster rate, that space conducts light in the same way that a cable conducts electricity, and that therefore, by bodies travelling away from us, distant light is emitted at velocities relatively different from that in our position in space? Those bodies would apparently be static in their position in receding space, so light there would be conducted by the space there 'at the speed of light', and at all the positions between here and there, and also as it passes us here, but the light is simply increasingly 'red-shifted'. Your comments are welcome.Absolutelyamazin (talk) 07:51, 19 September 2009 (UTC)

Many things have been considered by many people but this page is about physics that has a sound theoretical basis and which has been experimentally verified. Martin Hogbin (talk) 08:01, 19 September 2009 (UTC)

Ah. Then would you be so kind as to explain how the proposal is 'theoretically unsound'? Absolutelyamazin (talk) 09:21, 20 September 2009 (UTC)

Light in vacuum appears to travel always at the same speed, regardless of the relative motion of the source and the observer. See Introduction to special relativity. --___A. di M. 09:33, 20 September 2009 (UTC)

Yes, I agree. And where a block of space at a distance of ten billion light years is moving away from us now at, say, half the speed of light, a galaxy it carries within it will emit light there 'at the speed of light' into its local space which is immobile relative to the galaxy itself. That light, being conducted 'at the speed of light' by space now in an outward direction through space accelerating away from us will be travelling at faster than the speed of light relative to us here and now. No? Absolutelyamazin (talk) 18:54, 20 September 2009 (UTC)

No indeed. Abtract (talk) 19:47, 20 September 2009 (UTC)

If the light is travelling away from us, we wouldn't be able to "know" anything about it until it is reflected back towards us. In principle, say if there's a random variation in the intensity of the galaxy, we can measure the distance between the galaxy and whatever is doing the reflecting by measuring the time lag between the signals (attention: this is just a thought experiment, it isn't anything that's practically feasible and the distances you're talking about). What we would see – in our frame of reference – is the reflecting object at a distance x. If we were in the galaxy itself, travelling away from the Earth at half the speed of light, we would see the giant reflecting object at a distance 3x/2. It is an example of Lorentz contraction.

But, you say, surely that means that the light being emitted away from us is travelling away from us at 3c/2? Well, you can imagine that if you like, but special relativity (which is a pretty well-tested theory) says that you will never be able to to an experiment to measure a speed of light that is different from c. Special relativity doesn't put a limit on your imagination, simply what you're able to observe. Warp factor 5, Scotty! Physchim62 (talk) 09:48, 21 September 2009 (UTC)

We do understand, don't we, that the Universe is already complete, that it already contains both its 'beginnings' and its 'end', whatever both may be. Only, it makes a difference if you appreciate this, as you will understand that 'time' as such does not exist, but only the relative position in the process, of which we are simply a part, and our observation gives us the impression of an incomplete Universe which is in action and with the perception of 'time'. Absolutelyamazin (talk) 17:00, 22 September 2009 (UTC)

Er . . . Hello? - I have just seen the following on 'the expansion of space' - "While special relativity constrains objects in the universe from moving faster than the speed of light with respect to each other, there is no such theoretical constraint when space itself is expanding. It is thus possible for two very distant objects to be moving away from each other at a speed greater than the speed of light (meaning that one cannot be observed from the other)."

Right, that is what I am saying here, and have been saying for fifty years, except that the objects are not constrained by anything except the nature of the Universe rather than by any 'theory' or its associated mathematical formula. I am only describing what Universe does, and if you have reservations, perhaps you should take the matter up with the 'expansion of space' page - Or, indeed, with Universe itself.Absolutelyamazin (talk) 10:08, 23 September 2009 (UTC)

So suppose you say that light travels at c through a vacuum of uniform space, but where space is distorted by extension or compression, this velocity may vary.Absolutelyamazin (talk) 05:32, 24 September 2009 (UTC)

We don't make stuff up here; show us a source. Dicklyon (talk) 06:20, 24 September 2009 (UTC)

Neither do I. Just write 'extension of space' in Misplaced Pages, and read the second paragraph.213.60.135.75 (talk) 14:15, 24 September 2009 (UTC) Sorry, that should have been 'expansion of space'. It's still there. And, by the way, I am a source. But you still have to see it said by 'someone else'? Brother.

Statements on Misplaced Pages must be supported by what our policies and guidelines define as Misplaced Pages:Reliable sources. Finell (Talk) 21:47, 24 September 2009 (UTC)

In terms of expanding space, you need to think of the tiny distance that light travels in an "instant", that is dx/dt in differential calculus. That speed stays constant, according to mainstream physics, although there is a minority view that things might have been different in the early Universe. Physchim62 (talk) 21:56, 24 September 2009 (UTC)

Planck units" some phycisist use length/time dimension

It seems that if we do not use "Planck units" some phycisist use length/time dimension. Rather than an edit war can we get an educational discussion about this? (see art. history).Wdl1961 (talk) 15:40, 23 September 2009 (UTC)

I think this deserves a separate section in the article. I'm ok with removing "dimesionless" in the table (not mentioning this doesn't mean the opposite POV is taken). If I have time I'll start the new section later today. Count Iblis (talk) 15:49, 23 September 2009 (UTC)

Fair enough, I'll wait and see what you propose ;) I agree that the "spacetime dimensionality" needs to be mentioned somewhere, but I would also put my voice towards the opposite site, which is that most readers won't care about spacetime, and will only want to know about the classical approximation. For me that means something a brief as possible while remaining correct, and good links to other articles. How does that sound to you? Physchim62 (talk) 21:41, 24 September 2009 (UTC)

Assuming that "'spacetime dimensionality needs to be mentioned somewhere", is it clear that it needs to be mentioned in this article? Finell (Talk) 21:50, 24 September 2009 (UTC)

What I mean is dimensions in the context of unit systems. Count Iblis (talk) 14:23, 28 September 2009 (UTC)

Let's make sure we're not talking at cross-purposes

Is anyone who disagree on any of the following points? My hunch says that some of the disagreements around here might actually be misunderstanding.

1. "A physical quantity is expressed as the product of a numerical value (i.e., a pure number) and a unit". (From the IUPAP Red Book.) For example, in m_e = 9.10938215(45) kg, m_e is a physical quantity, 9.10938215(45) is a numerical value and the kilogram is a unit.
2. The numerical value of a physical quantity normally depends on the unit used, even if the physical quantity normally doesn't. For example, my choice of the unit I use to measure height has no effect on how tall I am, but the numerical value of my height is about 1.87 if I use the metre, and about 187 if I use the centimetre. In other words, the same physical quantity can be expressed with different units, but the numerical values will be different, too. For this reason, numerical values of dimensionful quantities are artefacts of the choice of units.
3. Any dimensionful unit of measurement must be defined in terms of a physical quantity of the same dimension; such physical quantity can be expressed as the product of one or more physical quantities and pure numbers. For example, for the kilogram it is the mass of a piece of metal in France, and for the kelvin it is the product of the triple point temperature of water (with a certain isotopic composition) by the pure number 1/273.16.
4. You can never directly measure a dimensionful physical quantity: any such measurement is inherently a measurement of a pure number, the ratio of the quantity being measured and a quantity of the same kind being used as a reference standard. For example, what I measure when I put my ruler along a line on a piece of paper is the dimensionless ratio between the length of the line and the distance between consecutive ticks on the ruler. For this reason, if two measurements of the same quantity yield different values, there's no way to determine whether the quantity has changed, the reference standard has changed, or both; to do that, we have to measure the quantity and the reference standard with respect to some other reference standard which is assumed to be constant.
5. Once you have measured such a ratio, you convert it into the form "numerical value times unit" by multiplying it by the reference standard. Then there are two kinds of uncertainties in the numerical value you get: the one in determining the ratio and the one with which you know the numerical value of the reference standard; but in practice, usually one of these two kinds of error will largely dominate. For example, if I measure a time around 10 seconds with my digital stopwatch, the first kind of error (due to my reflex times when pressing the start and stop buttons) will be significant, whereas the second won't, because I can trust the time between two consecutive updates of the display to be 0.01 s to a very great accuracy. On the other hand, if I measured a time around two months, the error in the number of clock ticks in the period being measured would be negligible, but I could not be sure that the clock isn't too fast or too slow.
6. When the reference standard is the unit itself, or an exact number of times the unit itself, the second kind of error is zero. For example, if I had a caesium-133 atomic clock at 0 K, I'd be sure that 9,192,631,770 of its ticks are one second exactly.
7. When the quantity being measured is the unit itself, the ratio which is measured can be inverted to get the numerical value of the reference standard in the unit used, to use it for subsequent usages; this is called calibrating the measurement apparatus. For example, if I weighed the piece of metal used to define the kilogram and I got 1.024 kg, it'd mean that my scale's reference value is not 1 kg but 0.9765625 kg, to within the error with which the ratio was measured. I can now multiply all subsequent measurements by this value, and the second kind of error in these measurements will be the first kind of error in the calibration. Another way of stating this is that it is pointless to measure the numerical value of the IPK mass in kilograms, as it is exactly 1 by definition; but it still makes sense to measure the ratio of that mass and other masses, for example to use the latter as reference standards, or (assuming that we can somehow be sure that the latter mass stays constant) to determine whether the IPK mass has changed.
8. In some cases, the ratio between two physical quantities can be determined to within much greater accuracy than the numerical value of either of them in a particular unit; this usually happens when the physical quantity used to define the unit is such that it's hard to precisely measure the ratio between it and other quantities, and so the second type of errors will be large. For example, I can determine the ratio between the lengths of two sheets of paper on my desk to be 1.000±0.001; but I can't determine the numerical values of those lengths in ancient Egyptian cubits with any decent accuracy, because I can't determine the ratio between any reference standard I could use and an ancient Egyptian cubic with any decent accuracy.
9. To minimize the second kind of errors, one should use units of measurement which can be accurately compared with other reference standards. That's why the meridian definition of the metre didn't last long, and why they are thinking of replacing the International Prototype Kilogram with another definition: for example, we are able to measure the ratio of the electron mass and the IPK mass to within 50 parts per billion, and the ratio of the electron mass and the carbon-12 atom mass to within 0.42 ppb; ditto for many other subatomic particles. So, defining (for example) the unit of mass in terms of the carbon-12 atom rather than the IPK would allow for errors of the second kind about 120 times as small. Also, for the reason given at the end of point 4. above, it's useful to use reference standards with are assumed to be unable to change with time or circumstances.
10. According to special relativity, which is by far the most widespread accepted description of kinematics in absence of gravity among the scientific community and is backed up by very solid experimental evidence, the speed of light in vacuum is a universal constant; also, ratios of lengths to the path traveled by light in one second can be determined to within excellent precision, better than any other reference standard.
11. Everyone is free to call things whatever the f*** they want; for example, if I want to call t the quantity you call ct, E the quantity you call E/c, v the quantity you call v/c, and so on, I am perfectly free to do so, as long as it's clear what I am doing; since in SR quantities like v/c show up far more often than quantities like v, it makes perfectly sense to use the shorter symbol for the more common quantity. This is colloquially referred to "using units in which c = 1". The philosophical reason why one would do that are irrelevant, and different people could do that having different ideas (or no ideas at all) in their mind of the philosophical reason why they do that. --___A. di M. 10:49, 28 September 2009 (UTC)

I agree with all of that and always have done. I have stopped discussion of the subject and editing the article here until we get a response from the arbitrators. I am hoping that the arbitrators' response will let us get on with discussing the subject and article rationally without the madcap contributions and arguments we have had here in the past. Martin Hogbin (talk) 12:36, 28 September 2009 (UTC)

I only really disagree on one point that is minor (probably completely irrelevant) for this article, of which a quick summary in a second (however you define it). I also think there are a couple of "basic principles" point that you hint at but don't mention explicitly.

PC1. Every measurement is based on some theory. For example, if we measure length relative to the length of a given metal bar, we assume that the length of the metal bar (under given conditions of storage and measurement) is constant. If we measure length relative to the distance travelled by light in a vacuum in a given time, we assume that the speed of light is constant. The current definition of the metre also assumes that the speed of light is independent of frequency.

PC2. We can usually make different measurements based on different aspects of physical theory, although rarely to the same precision at any given moment. If one of the underlying theories is "wrong" (to within the precision of the measurements), the measurements won't agree. A priori, we don't know which of the theories is at fault, but we can then test them independently against other measurements: the one that is only an approximation will always be simply an approximation. In practice, the constancy of length of metal bars was held to be an approximation.

As for the slight point of disagreement, your example in point 9 will only work for the electron at our current level of theory, and your statement assumes that E = mc is correct (I don't dispute that it's correct, but it's an additional assumption to those inherent in the definition of the metre). Also, we cannot practically redefine the kilogram in terms of a number of carbon atom-masses, nor even with more amenable nuclides, because of the problems of accurately measuring the number of atoms: several groups are spending huge amounts of money to try overcome these problems at the present time, but they're not there yet! Physchim62 (talk) 13:11, 28 September 2009 (UTC)

What I meant is that currently (i.e. as of CODATA 2006), the value of the electron mass in kilograms is known with a relative standard uncertainty of 5.0×10 and the value of the electron mass in amu is known with a r.s.u. of 4.2×10. BTW, that was intended to be an example, so the fact that the latter measurement assumes that E = mc is only marginally relevant.

A slight clarification, particularly on point 3, is needed I think. The problem here is that different systems of units do not have to be dimensionally compatible. E.g. the cgs system is not compatible with the SI system as far as elecromagnetism is concerned. In SI units the electric charge is assigned an independent dimension but in cgs units it can be expressed in Length, Time and Mass.

So, the problem with point 3 is that the whole notion if "dimensions" is not well defined. Point 3 must actually be understood in reverse. I.e. different quantities were originally assigned different dimensions simply because when they were first measured there was no known universal way to compare the different quantities. Then, in the SI system of units, one introduced extra dimensionful quantities for metrological reasons. Even if you can do with only a few independent physical standards, that may not be the most accurate way to perform measurements. Count Iblis (talk) 14:17, 28 September 2009 (UTC)

Indeed that was part of the follow-up I was going to post after everyone said "yes, all of those points are valid". These are two points which in my mind are logical extensions of the ones above, but for some unfathomable reason appear to be more controversial; I wrote them shortly after posting the list above, and before reading your replies.

1. The numerical value of the speed of light in vacuum in metres per second is fixed by definition as 299,792,458 and so it's pointless to measure it. Nevertheless, you can measure the ratio of the speed of light in vacuum to any other reference standard for speeds; but if you found such a ratio to have changed, you couldn't say whether it's the speed of light which changed, your reference standard which changed, or both, short of comparing them both to another reference standard you assume to be unable to change. In the framework of special relativity, the speed of light in vacuum is a constant, so it'd be your reference standard for speeds which changed; in another framework, you could find another reference standard constant in that framework and compare both the speed of light and your reference standard.
2. If you know on theoretical grounds that two quantities are always proportional, Whether they have the same or different dimensions depends on the system of units used, and hence is partly arbitrary. For example, assuming that the first law of thermodynamics holds, you may consider heat to have the dimensions of an energy, and then the first law of thermodynamics is dU = δQ − δW ; or you may consider them to have a different dimension, and the law is dU = kδQ − δW , where k is the mechanical equivalent of heat, a constant with the dimension of energy/heat equal to 4184 J/kcal_th. Assuming that Newton's first law holds, you may consider force to have the dimension of a mass times an acceleration, and then Newton's first law is F = ma; or you may consider it to have a different dimension, and then it's g_nF = ma, where g_n is a constant of the dimension of mass×acceleration/force equal to 9.80665 kg m/(s kgf). Likewise, assuming that special relativity holds, you can consider time to have the dimension of a length, and then the metric in Minkowski spacetime is ds = dt − dx − dy − dz, or to have a different dimension, and it's ds = cdt − dx − dy − dz, where c is a constant of the dimension of length/time equal to 299,792,458 m/s. This may be viewed as the former person calling Q, F, and t the quantities the latter person calls kQ, g_nF and ct.

Let's see whether Tombe and Ohare can find a way to claim it makes sense to agree with the points I posted earlier but not with these last two. --___A. di M. 14:28, 28 September 2009 (UTC)

A. di M, with these additions, I now fully agree. I think the "unfathomable reason" is this: If something has been treated in a certain way, this tends to stick. In high school, people are still taught that the dimensions of the unit system corresponds to a fundamental physical incompatibility. But this is not something that can be supported from within physics itself. Duff writes in the Trialogue article that he himself was taughed to believe this and only later did he realize that there isn't a shed of evidence to support this view. Count Iblis (talk) 15:20, 28 September 2009 (UTC)

Subsection: Meter defined in terms of the speed of light

In the light of these facts:

1. The CGPM defines the metre as The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. I don't see speed of light mentioned in this definition. I see a time-of-transit.
2. Morevover, the CGPM says that wavelengths determined from frequency measurements and a given value for the speed of light have a reproducibility superior to that which can be obtained by comparison with the wavelength of the standard radiation of krypton 86 and this superior reproducibility of frequency measurement compared to comparison of lengths is one reason for the change in definition of the metre to refer to time of transit. Again, no mention of speed of light.
3. Finally, the choice of a time interval of 1/299 792 458 s is arbitrary and has been selected at this value because there is an advantage, notably for astronomy and geodesy, in maintaining unchanged the value of the speed of light recommended in 1975 by the 15th CGPM in its Resolution 2 (c = 299 792 458 m/s). Here is where the "speed of light" crops up: as a matter of convenience, not necessity.

Given these points, the above sub-section title appears inappropriate. Shouldn't it be replaced with something like

Meter defined in terms of time of transit,

or, because this is a speed-of-light article,

Speed of light set by definition of the metre.

This last title seems to put the burden of explanation upon the metre, where it belongs. Brews ohare (talk) 19:08, 28 September 2009 (UTC)

Here we go again! Martin Hogbin (talk) 20:14, 28 September 2009 (UTC)

Brews, #1 defines the metre in terms of the distance that light travels in a certain time a.k.a. the speed of light. How hard can this be to understand.(TimothyRias (talk) 21:46, 28 September 2009 (UTC))

It's the numerical value of the speed of light that is set by definition of the metre, not the speed of light itself. They are not the same concept. See point 1. at the top of the section above for the distinction between the two. ___A. di M. 22:46, 28 September 2009 (UTC)

In response to Martin Hogbin: Catcalls aimed simply at interruption don't aid discussion. They should be severely dealt with, but so far have not been. Brews ohare (talk) 23:53, 28 September 2009 (UTC)

In response to TimothyRias: Rhetoric ("How hard can this be to understand") doesn't aid discussion, and is inflammatory. It should be severely dealt with, but so far has not been. In my mind and contrary to your point, #1 defines the metre in terms of a transit time. That is, I believe, simply a straightforward read of the exact wording of the definition, and therefore beyond controversy. The value chosen 1/299… s is an artifact of compatibility with the earlier definition of the metre, and this arbitrary choice of value is, as a matter of reasoning, logically separate from the notion of using a transit time. With that in mind, do you now agree that the title of this subsection should be changed? Brews ohare (talk) 23:53, 28 September 2009 (UTC)

In response to A. di M.: I agree with this remark. Do you support a change in title, or not? Brews ohare (talk) 23:53, 28 September 2009 (UTC)

"Metre defined in terms of the speed of light" (I just conformed the spelling of metre to the rest of the article) is an accurate statement and an accurate heading for the section. The section explains the consequence of this definition of the metre to the value of the speed of light. Further, the heading accurately reflects the significance of the definition of the metre to the speed of light, which is the topic of the article. Plus, the documentation of the definition explains that the value chosen for the metre was not "arbitrary", as you keep insisting, but was chosen based on the measurement of the speed of light. Finell (Talk) 02:35, 29 September 2009 (UTC)

Meter defined in terms of the speed of light :Agree Wdl1961 (talk) 03:05, 29 September 2009 (UTC)

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