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"Exact" speed of light???

Defining one meter as 1/299792458 of the distance that light travels in a "vacuum" in one second is perhaps an exact definition of the meter. (Though *not* an exact measurement thereof.)

But this certainly does not mean that 299,792,458 m/sec is the "exact speed of light" -- as the article calls it several times -- because the meaning of one meter has been measured only depending on the accuracy with which the speed of light has been measured.

So: What I am wondering is

a) why is there no mention of how the measurement of the speed of light was improved between 299,792,500 +- 100 m/s to (presumably, before the meter was defined as I cite above) the speed 299,792,458 (and what were the error bounds?)

b) How was this improvement achieved?

And surely, defining the meter in terms of the speed of light has not ended physicists' attempts to measure the speed of light ever more accurately!

c) What about the most recent attempts to measure the speed of light -- their results, and the methods used?Daqu (talk) 18:05, 18 April 2009 (UTC)

See , and more specifically

"In 1983 the international standard for the meter was redefined in terms of the definition of the second and a defined value for the speed of light. The defined value was chosen to be as consistent as possible with the earlier metrological definitions of the meter and the second. Since then it is not possible to measure the speed of light using the current metrological standards, but one can still measure any anisotropy in its speed, or use an earlier definition of the meter if necessary."

DVdm (talk) 21:53, 18 April 2009 (UTC)

Sorry if I was unclear, but it's perfectly obvious that -- as you say -- if the meter is defined in terms of the speed of light, then one cannot improve the accuracy of the figure for the speed of light by using that definition of meter along with the same definition of one second.

But that has nothing to do with the (presumed) continued attempts to improve the accuracy in the measurement of the speed of light!!! The more accurate measurements just need to be cited in terms that used a fixed length unit (as well as a fixed time unit).

My comment opening this section was not requesting references. It was intended to suggest that someone knowledgeable on the subject (which I am not) answer these rather natural questions (a, b, c above) in the article.

In case this is *still* unclear, let me use an analogy. If one defines pi as the ratio of the circumference to the diameter of any perfect circle, that does not end the search for a increasingly exact value of pi.Daqu (talk) 00:01, 26 April 2009 (UTC)

There are no continued attempts to improve the accuracy in the measurement of the speed of light because the speed of light is fixed by definition; there are attempts to improve the precision with which the metre is delineated. Martin Hogbin (talk) 21:43, 4 May 2009 (UTC)

It's crystal clear to me that with the definition of the speed of light as a fixed number (299,792,458) of meters per second -- and the definition of the second fixed (in terms of a fixed number of vibrations of a cesium atom) -- the two endeavors of improving the precision of the meter, and improving the precision of the speed of light are logically equivalent.Daqu (talk) 08:36, 6 May 2009 (UTC)

They are much the same thing, but to go back to your original point, as the speed of light is now fixed by definition and the length of the metre is not, information on experimental improvements in measurement technology after 1983 might be better put in the article on the metre rather than this one. Martin Hogbin (talk) 10:50, 6 May 2009 (UTC)

←This comes down to an equation with three unknowns. One of those unknowns has to be fixed by definition in order to define the system of units; the second (time) can be measured with great accuracy, so its uncertainty doesn't really enter into the experiment. Hence, the measurement uncertainty is concentrated in the third of the variables.

• Before 1983, the length of the metre was fixed by definition, and the uncertainty was expressed in the value of the speed of light: the question being asked was "how long does it take light to travel a given distance?"
• Since 1983, the speed of light is fixed by definition, and the uncertainty is expressed in the length of the metre: the question being asked is "how far does light travel in a given time?"

By fixing the speed of light by definition, it becomes explicit that no measure of length in SI units can be more accurate than the best determinations of the speed of light: all the experiments that, prior to 1983, were determining the speed of light are now determining the length which is equal to one metre. Physchim62 (talk) 13:21, 6 May 2009 (UTC)

no measure of length in any unit -- since, for example, Imperial units are defined in terms of SI. Yes, your point is correct. To put it differently, an experiment that measures the speed of light is in effect an experiment that realizes the meter. And the resulting uncertainty in that realization of the meter will be the uncertainty of the experiment or the uncertainty in the realization of the second -- whichever is larger. (Today, the former will certainly be the larger.) Furthermore, the reason the CGPM adopted the new definition is that this inaccuracy (realization of the meter via speed of light measurement) is now better than the inaccuracy of the previous definition. That, after all, is the basis on which unit definitions are chosen and changed. Paul Koning (talk) 16:51, 6 May 2009 (UTC)

You can actually measure length in astronomical units to a comparable level of accuracy with measures in SI units (within the same order of magnitude of relative uncertainty, that is a few parts in 10, roughly a hair's breadth between New York and Los Angeles), even though the two systems of measurement have very different bases. The stability of atomic clocks, for any single Earth-based experiment, is about 10,000 times greater: hence my comment that the uncertainty in time measurement is negligible. On the other hand, at this level of precision, you have to take account of General Relativity: this teaches us that the measurement of distance and time are not actually independent of one another as one might assume from everyday measurements, and is a huge headache for people devising astronomical units! Physchim62 (talk) 00:10, 7 May 2009 (UTC)

Ok, but AUs are defined in terms of the meter -- exactly as the inch is. An AU is either a measured distance, or an agreed on value; either way, the value is in meters. Paul Koning (talk) 00:51, 8 May 2009 (UTC)

But AUs are not defined in terms of the metre! See Astronomical unit for the actual definition. You can express the value of the AU in metres, of course, and it's instructive in the context of this discussion to see how you do it. Firstly, you measure the time taken for light to be reflected from various astronomical objects (such as the Moon and the inner planets). Then you calculate the positions of these objects using a scale based on astronomical units – you can't do the calculation in SI, because one of the constants (the solar mass) isn't known to sufficient precision in SI, so it is given a conventional value (of unity) in the astronomical system of units. With a measure of time and a calculation of distance, you have a speed: the speed of light in astronomical units! It is usually quoted as a reciprocal speed, that is light time per unit distance, and has a relative uncertainty of 4 parts in 10. If you so wish, you can then calculate the length of the astronomical unit in metres by using the fixed value of the speed of light in the SI. Physchim62 (talk) 06:48, 8 May 2009 (UTC)

I am a bit shocked to see that some folks don't understand the concept of velocity, or of precision. A velocity depends on more than purely a number!!!!! It depends on a number and a unit of length and a unit of time. Basically I am reiterating what I said earlier and (as I understand him) what Physchim62 wrote above.

If the speed of light is said to be "fixed" at "exactly" 299,792,458 meters per second, this velocity is specified only to the extent that the length of a meter and the duration of a second are.

Since the length of a meter is no longer specified (except in the sense that the velocity of light is 299,792,458 meters per second), the speed of light is not specified. Any more than the fact that π = C/D (the circumference of a circle divided by its diameter) is "specified". For we know π only to a certain number of digits. That number of digits can always be increased by further calculation. So, having an exact definition of π is not the same thing as being unable to increase the precision to which we know it.

Likewise, the speed of light can still be determined to increasing precision by more and more careful experiment. (Since by definition, it is equal to 299,792,458 meters per second, this increasing of precision would take the form of increasing the precision of the determination of the length of a meter.)Daqu (talk) 16:49, 13 May 2009 (UTC)

I agree with you that there are legitimate questions on this topic, for example: (1) "the speed of light in astronomical units per second is known to how many decimal places?" and (2) "a meter (with its standard, speed-of-light-based, definition) can be reproduceably created/defined to what precision"? That is, if two labs created two ideal meter-sticks after independently using light and caesium atoms, how close could those meter-sticks be in length? On the other hand, I think (1) isn't very important, and (2) is more a topic for the meter article (as Martin suggested). How reproduceable is a measurement of the speed of light? Moreso than almost any other measurement, which means that the small imprecision has little or no practical consequence, since it's dominated by the larger imprecision of whatever the speed of light is being compared to. --Steve (talk) 22:01, 13 May 2009 (UTC)

The relative uncertainties are 4×10 for (1) and 2×10 for (2). The former is discussed in astronomical unit; the latter should be discussed in metre. I only brought up the example of the AU to demonstrate that the speed of light is only defined with respect to a system of units, even if it is fixed (ie, unchanging) with respect to all observers. You are quite welcome to define the speed of light as 1 unit of speed, and several systems of natural units do exactly that. Physchim62 (talk) 12:01, 16 May 2009 (UTC)

The missing point in all this discussion is that the defined value for the speed of light applies only in free space which is not a realizable medium. (In fact, free space is a medium where c has its defined value, else you don't have an example of free space. Free space also has other defined properties like isotropy, linearity , and frequency independence.) There is zero interest in refining this defined value of c. The experimental interest is in measuring the speed of light in real, obtainable media, such as outer space or ultra-high vacuum as that information tells us something about physical nature of the Universe. Our definitions about the speed of light in free space are really only a matter of convenience in comparing measurements made by different parties on different media in varying circumstances. Brews ohare (talk) 05:33, 16 May 2009 (UTC)

It may be added that the "speed of light" as the maximum speed of transfer of information might be separate from the properties of free space. That is an experimental issue. Brews ohare (talk) 05:45, 16 May 2009 (UTC)

Article Restructuring

I think this article loses focus of its main topic in several sections, and would benefit from a restructuring. Also, the article seems a little too long, which may lead to more confusion as it is being read. I would like to propose that we refactor the article into different sections, then condense those sections, to improve the article. I think sections with titles like: History, The Speed of Light in Scientific Fields, Scientific Uses, Measurements, and Superluminal Experiments, would be appropriate. Although these would result in drastic changes to the article, I think they would result in a much clearer presentation. If anyone has any comments or other suggestions, please leave them here. I'll check back in a few days to see if the community agrees the proposed changes would benefit the article. Pecos Joe (talk) 20:37, 20 April 2009 (UTC)

There is a lot that needs to be cut and some that needs to be added to this article IMO. Personally I don't like either The Speed of Light in Scientific Fields or Scientific Uses. Neither of them say anything useful. (To be fair the current heading are not any better.) I prefer the Faster then light to Superluminal for a heading since those reading the ToC might not know what it means. Also, again IMO, speed of light and causality needs to be a prominent section (just before the Faster than light section. Condensing the History into one section sounds good, though.

Stuff that needs to be cut, IMHO. The michelson morely (check to see if you can merge it with the main article first it looks good it just doesn't belong here). Addition of velocities near the speed of light needs to be drastically shortened or eliminated. It seems silly to me to include an equation just because it has c in it. It would be more appropriate for an article such as List of equations that depend on c. I don't know why the fussion picture is there for the same reason.

Stuff you should consider adding is a section about the different 'speeds of light' in a material. I heard that there are something like 10 different 'speeds of light' that a material can have. Group and phase velocities are the most well known. There is also the wavefront velocity which determines the speed that information travels in the material. These are of course different then the speed of light c which is the limit that any information can travel. (Those are 4 that I am aware of.) TStein (talk) 22:10, 20 April 2009 (UTC)

Agree. This article gets far too involved in abtruse and irrelevant areas, to the point that it barely even defines what the speed of light is. The historical details are relegated to the end of the article, when this page is the most obvious place to put them: instead, the reader is treated to a whole load of tad relativity theory which could be dealt with elsewhere. Faster-than-light phenonema have their own page (justifiably), and so should be treated in summary style (or "See also") here. Physchim62 (talk) 23:40, 20 April 2009 (UTC)

I agree that the article loses focus. I think one of the reasons for the loss of focus is a statement in the initial summary; "When light is traveling in a medium, its speed is less than c and becomes a function of the refractive index of the material.". This statement is really a trap door for the article--because it leads it into explanations to try and justify or explain the apparent contradiction of the earlier statement in the summary; "The speed of light in free space is a physical constant defined as 299,792,458 metres per second.". This gets the article into trying to explain variations, of which there are many, in speed relative to frequency across the electromagnetic spectrum, and material refractivity. It would be better if the summary stated; "Light is simply an electromagnetic wave and the speed of an electromagnetic wave is always constant at 299,792,458 meters per second. Depending on the waves frequency and the medium it is traveling through it can be absorbed and re-emitted resulting in a delay in its propagation. So while the actual speed of an electromagnetic wave never varies, because all mediums contain some free space, its apparent or observed speed propagating through a medium does." Then the article could be linked to separate articles on material refractivity, the electromagnetic spectrum, and other articles that are relevant to the discussion. I think this new summary is what the article is actually saying, just in a very long format. So if the summary was changed to give a more accurate initial understanding and then there were links added to more detailed discussions—this would help to clarify the article to make the restructuring better, and still allow for the detailed discussion to continue under their own heading. Hope this helps. Thanks, for allowing my input.User:68.114.14.80 (talk) 09:05, 21 April 2009 (EST)

You accidentally overwrote the previous discussion of this section. I restored it and indented your paragraph. TStein (talk) 14:04, 21 April 2009 (UTC)

In response to User:68.114.14.80, I think most of us are in agreement that the article needs to be pared down by cutting many sections and paring down other sections with links to the relevant articles. I also agree that the article devolves too quickly into discussing minutia. I am not so comfortable, though, with "Light is simply an electromagnetic wave and the speed of an electromagnetic wave is always constant at 299,792,458 meters per second." While it is true that photons only travel at c it is false to say that electromagnetic waves travel at c.

The real problem is that the term 'speed of light' is used for at least 4 (that I know of) very distinct quantites that are seemingly identical. (1. Maximum speed limit of universe and speed of a photon, 2. phase speed of an electromagnetic wave 3. group speed of a wave pulse. 4. wavefront speed of a wave pulse.) Somehow we need to structure the article to make that distinction apparent as early as possible while keeping the structure simple and organized from simplest material to more complicated material. Further we need to do this while minimizing redundancy and maximizing continuity and readibility.

I believe strongly, that the physics community should not call c 'the speed of light'. (I try to call it simply c.) In most of the cases where it is used the true meaning is something on the order of 'speed limit of the universe'. The fact that c is also the speed at which photons (since they are massless) happen to go at is in most cases irrelevant. Worse it misleads people with respect to cause and effect. That being said, the article needs to, from the very beginning (perhaps the first paragraph), separate the term 'speed of light' into 'speed limit of the universe, c ' and 'speed of light v ' The last term can have many different meanings because no wave moves as a whole. TStein (talk) 14:04, 21 April 2009 (UTC)

I did the reorganizing I mentioned above, taking into consideration everything all of you suggested. The current sections will help identify repetition in the article by grouping some things closer together than they were before, while hopefully still being an improvement on the previous version. I am shying away from adding new information to the article, or doing any substantial rewrite, until the article gets pared down a bit, which will take some time. One section that probably needs to be added is "The speed of light in materials" or something to that effect. Pecos Joe (talk) 18:31, 22 April 2009 (UTC)

In response to User:68.114.14.80, the "defined" speed of light has only an oblique relationship to the physical speed of light because the defined speed applies only in the hypothetical and unrealizable medium of free space. The physical speed of light occurs in real materials, of which vacuum is one, and outer space and ultra-high vacuum are examples. If anything should be dropped from the lead, it is not the "trapdoor" of speed of light in materials, but the undue emphasis upon the "exact" speed of light, which is a red herring. And, as TStein has observed, the speed of photons is distinct (in principle) from the concept of "speed limit" for information transfer, which underlies the notion of spacetime and simultaneity, and is presently under serious scrutiny in the arena of quantum gravity. Brews ohare (talk) 13:11, 16 May 2009 (UTC)

Infinite speed and perception

Copied from the science reference desk. Jay (talk) 09:14, 30 April 2009 (UTC)

I first thought of posting this on the Language ref desk, then changed my mind. Isn't something grammatically wrong with this line from Speed of light: "Francis Bacon argued that the speed of light was not necessarily infinite, since something can travel too fast to be perceived."Jay (talk) 10:43, 20 April 2009 (UTC)

I can't see anything wrong with it. What do you have in mind? Algebraist 11:03, 20 April 2009 (UTC)

The grammar is ok but the logic is questionable because the underlying hypothesis about "something" is not explicit. The OP could bring this up on the article discussion page to see what others think. Would the following sentence be better? "Francis Bacon argued that the speed of light was not necessarily infinite, since it could just be travelling too fast to be perceived."Cuddlyable3 (talk) 11:12, 20 April 2009 (UTC)

Yes, sorry about that. I should have said logically wrong instead of grammatically wrong. Cuddlyable3's version is making sense to me now. The meanings I had in mind were: "Francis Bacon argued that the speed of light was not necessarily infinite, since nothing can travel too fast to be perceived.", and "Francis Bacon argued that the speed of light was not necessarily infinite, since something cannot travel too fast to be perceived.", both meanings are opposite of the original line. Jay (talk) 11:29, 20 April 2009 (UTC)

I think it's vague about what is being perceived; I mean, light is definitely perceived so he can't be referring to that. I assume he's referring to the finite speed being perceived i.e it's really fast and we can't tell the difference between that and infinite speed. How about

"Francis Bacon argued that the speed of light was not necessarily infinite, since it could be travelling at a very large but finite speed which was beyond the scope of contemporary experimental accuracy."

Then again, I could have misinterpreted his point. Martlet1215 (talk) 11:37, 20 April 2009 (UTC)

I think you nailed it. Light is perceived as something instantaneous in all "normal" situations, but that is just an artifact of imperfect observation - and that was the point Bacon was making. --Stephan Schulz (talk) 11:49, 20 April 2009 (UTC)

User:Wile E. Heresiarch who added the line in 2004, has since left Misplaced Pages, and it is hard to confirm the source. This reference however says that Francis Bacon believed the speed of light to be infinite! Jay (talk) 12:25, 20 April 2009 (UTC)

It says that Roger Bacon believed it to be finite, though. Perhaps Heresiarch confused the two. Algebraist 12:29, 20 April 2009 (UTC)

Guys you should take your content discussion to this talk page Cuddlyable3 (talk) 13:30, 20 April 2009 (UTC)

It seems like the original quote implies that Bacon argued that it's possible to imagine a thing that travels imperceptibly fast but not infinitely fast, and that light might be one of those things. User:cuddlyable3's version could be less clear depending on what Bacon actually said. Cuddlyable3's version implies that he specifically theorized that light could travel very fast, but doesn't specify whether Bacon thought this was a special case or whether other items could also attain imperceptible speeds. I have no idea which is correct, but they don't mean exactly the same thing.

This distinction might not matter at all in context. I dunno. APL (talk) 13:46, 20 April 2009 (UTC)

I'd can "can" and replace it with "could". Clarityfiend (talk) 15:53, 20 April 2009 (UTC)

This guy at least included a direct quotation from (Francis) Bacon and a citation: "'Even in sight, whereof the action is most rapid, it appears that there are required certain moments of time for its accomplishment...things which by reason of the velocity of their motion cannot be seen—as when a ball is discharged from a musket' (Philosophical Works of Francis Bacon; J.M. Robertson, Ed.; London, 1905; p. 363)." The ellipsis is awkwardly placed, though, and I don't happen to have a copy of the Philosophical Works lying around in which to examine Bacon's full argument. Deor (talk) 17:01, 20 April 2009 (UTC)

I should have guessed that Google Books would have snapped this up. If one reads the whole chapter, one can say only that Bacon seems to be rather unclear whether he's discussing physics or physiology. Sometimes he seems to be maintaining that light has a finite speed; at other times, he seems to argue that it's our visual impressions that require time for their formation. And I admit to not being able to make much sense of his discussion of the idea that starlight takes time to reach us: he seems to say that he has discarded his initial suspicions that this is so, and now believes that our perception of stars is instantaneous. Deor (talk) 18:00, 20 April 2009 (UTC)

I don't think it's the light that's being not-perceived it's the speed of light. If you have a friend standing on a far distant hilltop with a mirror and you light a candle - the time it takes for the light from the candle to travel to the mirror and back again is too fast to perceive. Bacon argues that the time might not be zero - but merely so short that you can't perceive the delay...smart guy...he turned out to be correct! SteveBaker (talk) 16:58, 20 April 2009 (UTC)

Is anyone interested in getting this article back into shape?

This article has now been degraded into a shadow of its former self. Is anyone interested in getting it back into shape? Martin Hogbin (talk) 22:33, 25 May 2009 (UTC)

I have restructured and trimmed the article of much of its extra content recently, because it seemed to me to go into far too much detail about things unrelated to the speed of light. I hope it is not this effort that has made this article into a "shadow of its former self." I have my own ideas about what should be done to make this article better; do you have any specific improvements in mind? Also, see my question in the topic below this one. Thanks, Pecos Joe (talk) 20:50, 27 May 2009 (UTC)

I have many, but it is no use mentioning them all without the consensus to improve the quality of the article. Martin Hogbin (talk) 09:29, 31 May 2009 (UTC)

I don't think anyone here wants to make the article worse, so I'll go first and offer that I think the article could use a lot of effort focused on copy editing: making smooth transitions and clear and grammatically correct prose especially. Perhaps someone will come along and help make the article better, even though I only have one very vague suggestion. Pecos Joe (talk) 20:08, 1 June 2009 (UTC)

I was really talking about the science. It seems to now consist mainly of amateurish interpretations with much of the fundamental and philosophical nature of the subject missing. Martin Hogbin (talk) 22:25, 2 June 2009 (UTC)

I agree that the article is scattered and incoherent. I think we need to organize it into sections, perhaps

• Introduction (non technical, per Misplaced Pages standards)
• Notation (needs to be near the front)
• History
• Use in physics
• Practical impact (should be linked from the intro, since it will be a ways down the article)

I've started with the introduction. What do others think? LouScheffer (talk) 01:28, 3 June 2009 (UTC)

I like the new introduction; it is a better length and covers more of the material properly. I felt I had to undo the organization because it seemed to cause more problems than it helped. Several of the pictures ended up in unrelated sections, which I think would be very confusing for a first-time reader, and one section was just the section heading. As for the suggestions above, I think that the practical impact should be close to the top of the article, while leaving more technical discussions further down. Also, I will note that I think having a section devoted to discussing the speed of light in media (plural of medium) would be good because it would be useful for people trying to understand the concept. Pecos Joe (talk) 21:02, 3 June 2009 (UTC)

Content addition to cosmology section

One of my recent efforts to trim this article down to size was undone recently. I would first like to say I am glad to see it, because it allows specific discussion on the content that should stay in the article. The content that was reinserted was in the section about cosmology, with the reason that it establishes knowledge needed to understand subsequent remarks. I, however, didn't think this was true, and I wonder if someone could explain to me why they think this material should be here.

The material seems to mostly concern the time-dependence of the the speed of light: I think that the treatment here is far too detailed, especially considering the experimental results are not precise enough to differ from 0. Therefore, I thought a mention of the theory (with a link to the page explaining that theory) and a summary of the experimental results was all that should be in this section. Anything more seems to give undue weight to this section. Thanks, Pecos Joe (talk) 20:49, 27 May 2009 (UTC)

The importance of this topic is due to the very fundamental questions raised. At the moment experiment is not much help in settling these questions due to the large errors and the small predicted effects. However, I don't think we can suggest that a topic that interested Dirac, Weyl, Eddington has little importance just because the effect is small. That is how much of physics proceeds - small effects with big logical consequences. Moreover, I suspect that the popular interest in these matters is great, exactly because of the fundamental issues involved. Brews ohare (talk) 05:38, 29 May 2009 (UTC)

I'm mostly with PJ. Yes, it's interesting whether or not physical constants change in time. A general discussion of this should be (and is) in the physical constant article. If that's not enough, you can make a new article, time dependence of physical constants. But no need to go on and on -- particularly in an article with a broad readership. The average reader of this article doesn't care exactly why quantum gravity predicts optical nonlinearities, or how the Planck length is defined, or how the fine-structure constant is defined, etc.

Also, you need to realize that there are loads of physicists who make a career by exploring "what if" scenarios that no one thinks is likely...What if photons have a mass? What if space is anisotropic? What if electrons have quadrupole moments? What if charge quantization isn't exact? Blah blah blah. For every possibility you could dream of: At least one theorist has dreamed up some model where there's an infinitesimal correction; and at least one experimentalist has quantified how small the correction must be. Now, I'm not opposed to this pursuit, but in Misplaced Pages you need to be discriminating...not all these explorations are important, not all deserve to be described in any level of detail (or at all), particularly in less-technical articles like this. Some are extremely important (e.g. "What if there were magnetic monopoles", which is the subject of thousands of articles and textbooks). But a lot more of these (perhaps most?) are not.

I'd say this section should be only 3 sentences:

Some scientists have speculated that the speed of light (and related constants such as the fine-structure constant) may have varied over time in the history of the universe . However, direct measurements, based on either astronomical observation or laboratory experiments, have thus far failed to find any evidence for this hypothesis. For more information, see the article: Time dependence of physical constants.

:-) --Steve (talk) 08:13, 29 May 2009 (UTC)

This denigration of this work as another "blah, blah, blah ... what if" is not supportable. There are many accessible articles cited in the article that refute this view. The questions have a long and very reputable history (also cited), and are under active experimental and theoretical exploration. They are at the heart of such matters as expansion of the universe (a very big problem :-) ) and the testing of relativity's notions of causality and simultaneity on small scales, which is extremely relevant to the speed of light article. They illustrate the way science progresses, and that it is not just parroting odd facts and dusty ideas. I just don't see how a turf war over this paragraph is warranted. Wiki can afford this space, it is not a distraction, and this is the correct place to put it. That is not to say that this section couldn't be shorter. Definitions of fine structure constant and Planck length could be removed at some loss of intelligibility. Some verbiage could be consolidated. But reduction to three sentences and removal of most citations and all historical context is overkill. Brews ohare (talk) 13:57, 29 May 2009 (UTC)

I think we are not too far from agreement here. I agree that historical context would be valuable to this section. Currently, the article states the names of some people who looked at the temporal change; I'd like to see the article say precisely what they did with respect to the change of the speed of light. I think that's probably why I left the experimental results in; it showed a clear result, and I happen to think those specific results should stay in the article. I don't think that naming three or four scientists (whom the general reader may or may not know) without much extra context helps us to understand why the speed of light may change over time.

Much of the material here should be in a different article, though it should still be in Misplaced Pages. An important consideration is 'if I were a reader looking for this information, where would I look for it?', combined with the desire to not have too much duplicate content so that the prose is easier to maintain. The bit about quantum gravity theories should be in the quantum gravity article, as that article doesn't currently mention the word 'light'. The bit about the fine structure constant should probably be in the physical constant article, with links from here and the fine structure constant articles. The bit about photon mass should be in the photon article, and if I remember correctly, it was already there when I removed it from here. Do you agree with those points? Thanks, Pecos Joe (talk) 20:01, 1 June 2009 (UTC)

Consisting of

a light pulse consisting of multiple frequencies - just because it's describable using fourier transforms, does that mean it "consists of" them? 78.86.37.93 (talk) 00:02, 31 May 2009 (UTC)

My answer would be "yes, as long as the transformed pulse has non-negligible width," but there are certainly better ways to word it for the article. I just can't think of one right now. Pecos Joe (talk) 20:11, 1 June 2009 (UTC)

the speed of light can be measured so accurately

The article has a split personality, on the one hand stating the speed is measured and on the other hand that it is defined. These metrology issues have to be resolved. The reference in the Introduction to the "accuracy of measurement" of a defined value for 'c' is beyond comprehension and illustrates a confused mentality. The point really is that the overall error assessment of measurements has led to the view that accuracy is better served when the speed of light is removed from measurement altogether and replaced by measurement of time and wavelength with a defined value for 'c'. Brews ohare (talk) 18:49, 8 June 2009 (UTC)

It makes sense to me - the redefinition of the metre is quite a recent thing in historical terms, but even if it had always been defined that way, we would still need to measure it to work out how long the metre was. CrispMuncher (talk) 19:41, 8 June 2009 (UTC).

I'm left unsure what it is that makes sense to you: do you believe that it makes sense to "measure" a defined quantity? Bear in mind, a definition has no error bars, while a measurement always is subject to experimental uncertainty or confidence interval. In a perfect vacuum, 'c' = 299 792 458 m/s exactly, regardless of how long a meter is. Brews ohare (talk) 20:00, 8 June 2009 (UTC)

More substantially, the confusion that arises is over the logic behind the definitions. Up to 1983 the metre was defined as "The metre is the length equal to 1 650 763,73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton 86 atom." If c = λ f, 'c' could be calculated using the second.

After 1983 the second became "The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom." "This definition refers to a caesium atom at rest at a temperature of 0 K."

That change in definition of the second does not require any change in the status of the speed of light, which could still have been left a derived quantity. Instead, it was decided to make the meter a derived quantity: λ = c / f. "The meter should be realized by means of the wavelength in vacuum λ of a plane electromagnetic wave of frequency f; this wavelength is obtained from the measured frequency f using the relation λ = c₀/f and the value of the speed of light in vacuum c₀ = 299 792 458 m/s." That is, an additional step was taken: 'c' is not to be measured, but is simply a number.

I do not have the official explanation for this changed status of 'c' from measured to defined quantity. BIPM suggests that "that these various forms, making reference either to the path travelled by light in a specified time interval or to the wavelength of a radiation of measured or specified frequency, have been the object of consultations and deep discussions, have been recognized as being equivalent and that a consensus has emerged in favour of the first form". Some web sites of the government agencies suggest that the change is a consequence of better measurements of the second, but, as I have outlined above, I see no reason why a better second should have this consequence: c = λ f still works with the 1960 definition of the metre (or a revision in terms of some wavelength more stable than the krypton transition). I assume that it is an issue of measurement accuracy, not an issue of theoretical physics or basic principles.

In any event, the context is poorly explained in the article, and various viewpoints are expressed about the present-day stance that are not mutually consistent. Brews ohare (talk) 20:06, 8 June 2009 (UTC)

Yes, measurement is still needed - a definition changes nothing. Indeed, it actually makes precise measurement more critical since it is now the basis of our system of measurement. The speed of light is by definition 299,792,458 ms. In order for us to be able to derive the metre, we need to know how far light travels in one second. Without that we have some mathematical slight of hand that describes a metre, but nothing that tells us how far it is. If we had no knowledge of the speed of light then the unit called a "metre" could be an inch long (if light travelled at 299,792,458" per second) or a mile long (if light travelled at 299,792,458 mi per second). Therefore the accurate measurement is fundamental to to the practicality of using c in our measurement system.

As for your question about where it is defined, I do not see the problem. The very source you cite states:

... that 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)

that a new definition of the metre ...

CrispMuncher (talk) 21:54, 8 June 2009 (UTC).

I'm lost. What do we mean about "how far is a meter?" Apparently it is how far light goes in 1/299,792,458 s in perfect vacuum. The real issue is: how perfect is my vacuum, and how accurate is my clock. Not "how far is a metre?" Redefining the meter as "how far light goes in air in 1s" doesn't change anything, except a massive retooling cost and the need to determine how standardized "air" is to be arranged. Do we agree about that? Brews ohare (talk) 22:19, 8 June 2009 (UTC)

You're still not getting the central point - the difference between definition and using that definition to determine an exact length, which intrinsically requires measurement. Let us consider an artificial unit, the CrispMuncherHour, which is the distance I walk in an hour (we'll assume that my walking speed is constant and it therefore makes sense to use it as a basis of measurement). Now we can tell from the definition how far I will walk in an hour, four years or thirty seconds (1, 35064 or 1/120 CrispMuncherHours). What we can't do from the definition is tell how far those lengths actually are. How can we convert those lengths into another unit? It is actually more fundamental than that, since it is about the physical length itself rather than how it is expressed other units.

So far we have no idea how long the CrispMuncherHour is. We can make educated guesses based on how fast typical people walk but we have no exact measure. To do that we need to measure how fast I walk - say 5.1 miles an hour. Now we know that a CrispMuncherHour is 5.1 miles and we can scale that conversion factor to determine what the other quantities are in terms of actual length. However, until we have an actual measurement the definition does not allow us to say that a CrispMuncherHour is 5.1 miles and not 3 or 10. CrispMuncher (talk) 18:14, 9 June 2009 (UTC)

Sorry, CrispMuncher, I am a bit slow here. Saying a meter is the distance light travels in 1/299,792,458 s seems pretty definite to me, provided I have a vacuum and an accurate clock. Converting to other units seems pretty straightforward, given a definition. For example, if my definition of the unit of length is 1 650 763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton 86 atom, I can find out what time light takes to travel this far and make the conversion to meters. I might have questions as to the accuracy to which I have physically realized the krypton transition (line widths and all that) and how good a vacuum I've got, and there is consequent uncertainty in whether I really have 1 650 763.73 wavelengths to measure, but that doesn't impact the definitions. It impacts the "best good practices" necessary for realization or practical embodiment of the definitions.

None of this seems to bear upon the point that one cannot measure a definition. You can measure a specific object to within some accuracy using the definition of the unit of length, but that cannot impact the definition itself. Brews ohare (talk) 19:14, 9 June 2009 (UTC)

"Best good practices"

I suspect that what you really are driving at is the determination of "best good practices" for embodiment of the standard, which is a significant problem not very well documented by the standards agencies. For example, how do you determine whether you have a "perfect vacuum"? I believe the standards organizations largely focus upon reproducibility: if practical measurements require a certain accuracy, reproducibility of the standard must be better than the measurement requirement. If it isn't, you fiddle about with the "best good practices" until you find what is the perturbing factor you missed - two recent examples: failure to correct for gravitational time dilation and failure to correct for T ≠ 0 K. Sometime in the future, standards will be forced to grapple with the fact that all real vacuums are nonlinear, anisotropic and dichroic. Brews ohare (talk) 16:03, 10 June 2009 (UTC)

All standardized measurements must be made in "vacuum", which is an unobtainable ideal medium. Corrections must be made to measurements done in a real medium to relate them to the "vacuum". One way to handle these corrections for imperfections in the vacuum is simply to define the "vacuum" as the idealized medium where c has a defined numerical value. In other words, defining c in vacuum actually has zero content without a definition of "vacuum". The practical result is to define vacuum as an ideal medium where the speed of light is c, and propose a set of corrections that bring measurements in any real medium back to this ideal. For example, if the lab vacuum has partial pressures of constituents, the contributions of these constituents to the refractive index are estimated and subtracted from the measured results. If the corrections don't work out (e.g. are not reproducible, indicating an unidentified source of variation), then revised corrections are sought. For example, see PE Ciddor (1996). "Refractive index of air: new equations for the visible and near infrared" (PDF). Applied Optics. 35: 1566–1573.. Brews ohare (talk) 18:09, 10 June 2009 (UTC)

Vacuum

I have made some changes in wording that I feel more comfortable with. The modern vacuum is not the same as the classical vacuum, even in principle, and it seems to me that some distance should be placed between the various vacuums: the now archaic "vacuum" of classical electrodynamics, the BIPM official "vacuum", the realizable vacuum of interstellar space, and theoretical vacuums like the QCD vacuum.

Another issue is the introduction by BIPM of the "defined value" of c. This definition is tantamount to a definition of BIPM "vacuum", and is a bit unsatisfactory as there is no theoretical definition of this "vacuum". Rather, it is a moving target that is actually defined in an empirical manner through a library of BIPM corrections that are not completely specified but left up to "standard best practices". About all one can say in its favor is that it is a "reduction to practice" of "vacuum". However, having no theoretical basis outside of this (ever changing) operational definition, it is subject to definition by committee based upon criteria some of which have no physical basis, but are related (ultimately) to convenience, politics, and economics (which is, after all, what metrology is all about) as well as reproducibility and accuracy.

It would be preferable (IMO), to define the speed of light in this article on a physics basis (for example, as the maximum rate of information transfer) and leave its precise value as something that can be measured, whether or not BIPM defines the value. In any case, its value should not be predicated on metrology issues. (An analogy might be the article on matter, where the BIPM definition of the mole is only one way to go.) Perhaps (I'm pretty tentative on this) the entire connection to electromagnetism should be left as a matter for experiment in the sense that (so far) light appears to be the fastest form of information transfer, but the connection is ultimately a matter for experiment. The BIPM defined value is then in the nature of a modern consensus, and not to be confused with some reality of nature. Brews ohare (talk) 18:56, 17 June 2009 (UTC)

Hi! The main purpose of the lead paragraphs is to introduce the topic - see Misplaced Pages:Lead section. In particular, it should avoid jargon and words not obvious to an intelligent but non-specialist reader. I think all readers, within reason, would be familiar with vacuum, but free space is more of a concept for specialists. In fact, I think that anyone who even might distinguish free space from vacuum probably does not need the intro to a Misplaced Pages article. Also note that even the BIPM, sticklers for accuracy that they are, just says "the distance light travels in vacuum", without further specification, as do almost all elementary physics books. So whether or not this is the best possible theory, it's probably the right level of abstraction for a Misplaced Pages introduction. Other's views on this are of course welcome. LouScheffer (talk) 20:05, 17 June 2009 (UTC)

A major obstacle to understanding "the" speed of light is that this term may well be taken differently than is meant due to two confusing aspects: (i) the "vacuum" is not so clear cut as normally might be assumed, corresponding not to the "absence of everything" but rather to at least three or four possible meanings and (ii) the "defined" speed of light is at the least a confusing idea (as this talk page testifies) and leads to the idea that one can "measure" a "defined value" and that "vacuum" is a measurable and attainable medium. In the interest of avoiding these quagmires, a bit more careful introduction than you would like might prove to be very useful. Brews ohare (talk) 21:47, 17 June 2009 (UTC)

One way forward might be to treat c₀ as a limiting value: it's the fastest that information can travel, because it's the fastest that light can travel (and nothing else can travel faster). I agree that c₀ isn't defined as 299792458 m/s: that's getting the definitions the wrong way round! Physchim62 (talk) 00:51, 18 June 2009 (UTC)

Actually, c₀ is defined by NIST and BIPM as 299792458 m/s, and is said to apply in "vacuum" (whatever that may be). I take it that "vacuum" is where the speed of light is c₀; that is, if you measure c and c=c₀, that is a necessary requirement for your sample to be a "vacuum". There are also the requirements of no dispersion, no dichroism, complete linearity and perfect isotropy. Oh yes, and c must have been c₀ forever in the past and forever in the future (that's a bit tougher to substantiate). Brews ohare (talk) 01:16, 18 June 2009 (UTC)

No, the BIPM defines the metre in terms of the speed of light in a vacuum, not the speed of light in a vacuum in terms of the metre: that's what I meant by getting the definitions the wrong way round. The BIPM "vacuum" is self-evidently a practical vacuum, not a theoretical concept, as the SI is a system of practical units. Physchim62 (talk) 01:34, 18 June 2009 (UTC)

Right, the meter is found at metre as the distance traveled by light in "vacuum" in 1 / 299 792 458 s. However, that results in the speed of light being 299 792 458 m/s exactly, as the NIST link says. (It's a tautology.) That is, there is no measurement uncertainty. No measurement uncertainty is possible only if there is no measurement; that is, "vacuum" is a medium that has this property, this c-value. In short, the definition defines "vacuum" by implication as the medium referred to if measurements are corrected using the "standard best practices" corrections. As such the defined value of c₀ never changes, but what we call "vacuum" will change if more or different corrections are added to the list.

Please notice that the definition does not mean that there is no error in measuring any actual physical length, and so we cannot verify a meter was traveled in 1 / 299 792 458 s with zero error. However, this error is not a reflection on the exactitude of the definition itself, only upon its implementation. So for example, our atomic clock has a line width, and we can't know exactly and reproducibly 1 / 299 792 458 s elapsed, and we cannot count fringes to an exact fractional fringe, so we don't know exactly and reproducibly the number of fringes between the arrival and origination points of the light. We also don't know if we have a "vacuum", but we trust the "standard best practices" to fix that. The wavelength of the light is an estimate, its speed is not. Brews ohare (talk) 01:46, 18 June 2009 (UTC)

Imagine you're measuring the wavelength of light of a known frequency (which if how these things are really done). You measure the wavelength at atmospheric pressure, then you pump on your apparatus to take the gas out, taking readings as you go. You will find that the wavelength increases, corresponding to an increase in the speed of light in your medium of study. You wont be able to get to zero pressure, but you can extrapolate your results to deduce what the wavelength would have been a zero pressure using standard statistical procedures: hence you have your practical measure of the speed of light in a vacuum. Under the current definition of the metre, what you're really interested in is the wavelength, which you can then use for optical interference measurements of other objects, but if you have another standard for the unit of length, you will have measured the speed of light in a vacuum for that system of units. Physchim62 (talk) 02:16, 18 June 2009 (UTC)

Then comes the point I think you were making at the start of this section: is this measured speed of light in a vacuum the same as the theoretical speed of light in free space? This is a little bit like the question of inertial mass vs. gravitation mass: we don't know that they're the same, but every experiment we do indicates that they're the same. Physchim62 (talk) 02:31, 18 June 2009 (UTC)

Note that the standard does not define the speed of light, and for good reason. Suppose the speed of light is defined to be X, and you measure and get X'. If only the speed of light is defined, you can fix this by changing the second, the meter, or both, until you get the correct speed. But what the measurement bureaus want is just what they said - the meter is the one that is modified to make this true. LouScheffer (talk) 02:45, 18 June 2009 (UTC)

Indeed. Let's imagine that there was a superbly precise test of Special Relativity that indicated that the speed of light as it appears in relativistic equations is very slightly higher than the measured speed of light in a vacuum. The definition of the metre in terms of the speed of light in a vacuum probably wouldn't change (because that's what we measure practically to use as a length standard), but the speed of light in free space (or at least the tiny correction factor) would become a measured physical constant. Physchim62 (talk) 02:58, 18 June 2009 (UTC)

Speed of light and the defintion of the metre

The statement in the article:

"In modern times, the speed of light can be measured extremely precisely, to the point where the metre is now defined in terms of a known time interval."

does not appear to be consistent with the view of BIPM and NIST that the speed of light has a definite numerical value and not a measured value. (The speed of light is 299 792 458 m/s exactly according to NIST and the BIPM. The measurement uncertainty is zero.)

Thus, this portion of the introduction simply ducks the question: how can the value of the speed of light have a definite value, one that cannot be changed by measurement? Instead, the text suggests incorrectly (albeit indirectly) that 299 792 458 m/s is a measured value when it is not.

One approach to fix this issue is to say

The metre is defined by NIST & BIPM as "The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second."

The correct follow-on statement is:

According to NIST: "Note that the effect of this definition is to fix the speed of light in vacuum at exactly 299 792 458 m/s."

This definition solves the problem about the speed of light, because its value is now a tautological result of the definition of the meter.

This definition of the metre is satisfactory only supposing that the speed of light in "vacuum" is truly a universal constant. If it isn't, then reproducibility of the meter is a flop. As part of this assumption we need to know what "vacuum" is. We know what it is not: it is not the absence of everything, it is not quantum vacuum, it is not ultra-high vacuum, it is not interstellar space. Rather it is a list of corrections to be made to any measurement in any real medium; corrections specific to the chosen medium that will bring the measurement back to the "vacuum". Specifically addressing the "vacuum" the CIPM cautions that:CIPM adopted Recommendation 1 (CI-1983) Appendix 1, p. 77 “provided that the given specifications and accepted good practice are followed; • that in all cases any necessary corrections be applied to take account of actual conditions such as diffraction, gravitation or imperfection in the vacuum; … ”

Less specifically, in regard to the second, the idea of "best practice" is again raised: BIPM suggests in the case of the second:

"It should also be noted that to achieve the uncertainties given here it is not sufficient just to meet the specifications for the listed parameters. In addition, it is necessary to follow the best good practice concerning methods of stabilization as described in numerous scientific and technical publications."

In sum, the statement in the article identified at the beginning of this comment is insufficient. Some of the ground that needs to be covered has been presented elsewhere in the article, but it all has to be drawn into a unified stance. Brews ohare (talk) 11:53, 18 June 2009 (UTC)

Time to reform this article.

From once being a Featured Article this article has now become a rambling essay on different types of vacuum, with much of the important conceptual physical significance of the speed of light being removed.

This was once a good physics article and it is time to get it back that way. Any offers of help? Martin Hogbin (talk) 17:31, 10 July 2009 (UTC)

I agree. I do not wish to be uncivil but the reason for this can be summed up simply: Brews Ohare.

The same thing is happening all over the physics articles. A single disruptive editor attempts to clarify every single point in an article (even the ones that do not need clarifying) with no real understanding of the subject matter. As a result the article loses accuracy and focus and drifts well away from the nominal subject.

Many editors have complained of exactly the same thing but it quickly becomes tiresome when faced with a barrage of ill-considered rapid-fire edits. I recall particular my previous encounter with him above. Despite explaining the situation in terms even a child should understand, he completely missed the point. He then attempted to start exactly the same discussion a few days later completely ignoring what had already been said.

If you feel this article needs pruning personally I will support you and I suspect many other editors will, but it is not an undertaking to be accepted lightly. CrispMuncher (talk) 18:15, 10 July 2009 (UTC)

I suggest we leave the lead section until last as this is meant to be a summary of the article. I have made some changes. Let us see what others think. Martin Hogbin (talk) 20:09, 10 July 2009 (UTC)

I fully support reforming the article, but suggest re-writing the lead section first. I think it's easier to re-write the rest when the outline of ideas to be covered is already in place. Thanks for the effort, LouScheffer (talk) 10:30, 12 July 2009 (UTC)

If we work that way, I suggest that it would be best to prepare a new lead section elsewhere rather than mess up the version here. I have suggested something here, based on the current version and an earlier one. See what you think. Martin Hogbin (talk) 20:50, 12 July 2009 (UTC)

Where to start?

I think that the article main text should start with some kind of description of what the 'speed of light' is. The lead currently says that the 'speed of light' is the actual speed of light in free space. This is fine but we also need to say something along the lines of, 'according to currently accepted and verified theories of physics, the speed of light is believed to be a fundamental physical constant'.

But first, some questions. Do we need to say 'believed to be' and 'according to currently accepted and verified theories of physics'? Is this not normally understood to be the case? Should we just say, as the old lead use to, that the speed of light is a fundamental physical constant. The only problem with the simple statement is that, according to some respectable but speculative theories, the actual speed at which light travels may not be exactly the same as the fundamental constant linking the units of space and time.

Can anyone suggest any good sources on this somewhat philosophical subject. I think it is very important to get this question sorted at the start to avoid the confusion that we currently have in the article between currently accepted theory, experiments designed to verify that theory, and valid theoretical speculation. Martin Hogbin (talk) 10:48, 11 July 2009 (UTC)

If anything, might I suggest Scharnhorst effect ?

69.140.12.180 (talk) 19:03, 11 July 2009 (UTC)Nightvid

I am not sure how that answers the question that I asked. Martin Hogbin (talk) 01:04, 12 July 2009 (UTC)

As no one else has, I have answered my own question. In common with other articles we should just use the wording 'is' rather than 'believed to be' when referring to current, established and verified theories of physics. Martin Hogbin (talk) 16:20, 13 July 2009 (UTC)

Seems reasonable. Tons of super-reliable sources would support the claim that c is a "physical constant". --Steve (talk) 18:56, 13 July 2009 (UTC)

Not sure what you mean here Steve. Martin Hogbin (talk) 21:12, 13 July 2009 (UTC)

Do you want a link such as this ]? and would you like to add that it is a dimensionful constant? Martin Hogbin (talk) 21:27, 13 July 2009 (UTC)

I just meant, "is a physical constant" is a fine and justified thing to say. No need to be ultra-cautious by saying "is believed to be a physical constant". I suppose a reference like that link is good, since the statement is evidently controversial.

I don't think the word "dimensionful" is important or even helpful. The average reader would already think of c as having dimensions...stating something that's so obvious would only be confusing. --Steve (talk) 22:07, 13 July 2009 (UTC)

Fine, I only suggested 'dimensionful' because dimensionless constants are considered more fundamental. Martin Hogbin (talk) 22:29, 13 July 2009 (UTC)

Delbrück scattering

The article says "Quantum electrodynamic theory predicts deviations from a unitary refractive index in the vacuum state for extremely strong electromagnetic fields. To date, there has been no experimental confirmation of that effect." However, this is not quite true, as Delbrück scattering (which is the scattering of gamma rays by the electric field of an atomic nucleus) is experimental evidence that the speed of light is altered (locally). Shouldn't we mention that? 69.140.12.180 (talk) 18:59, 11 July 2009 (UTC)Nightvid

US or Brit spelling?

I do not care much which we decide on but we should choose one and stick to it. We currently have both 'color' and 'colour' and 'travelling' has just been changed to 'traveling'. Martin Hogbin (talk) 18:54, 12 July 2009 (UTC)

Fundamental importance in physics

I have attempted to collect all the information about the fundamental importance of the speed of light in physics into one section. The article in its current state seemed to miss much of this information. The material has mainly come from the current article and earlier versions. Martin Hogbin (talk) 11:54, 13 July 2009 (UTC)

My recent changes

I have recently made quite a few changes to the article and no one has reverted any of them or commented here. Do I take that as tacit approval or is it just that no one cares or is watching this page? Martin Hogbin (talk) 21:48, 14 July 2009 (UTC)

Well Martin, as is your wont, you are confusing defined behavior in unrealizable free space with actual observation on real media. You are proposing that definition is confirmable by experimental observation, while all that can be done is to confirm models approximate reality. Please get these differences straight in the article. Brews ohare (talk) 11:20, 15 July 2009 (UTC)

This distinction is made quite clear in the article, but only once. Martin Hogbin (talk) 11:34, 15 July 2009 (UTC)

Actually, it is still mentioned twice; that is plenty. Please do not keep adding references to this distinction throughout the article. I agree that it is an important point that needs to be made, but it is made. To many people it is a detail that does not need to be mentioned at every opportunity. Martin Hogbin (talk) 11:41, 15 July 2009 (UTC)

A statement of principle does not compensate for misstatements that contradict the principle elsewhere in the article. Brews ohare (talk) 12:11, 15 July 2009 (UTC)

I have changed to wording to use 'verify'. This is standard terminology. As I am sure you know, an experiment can never prove a theory or model. The model in question predicts that the velocity of EM radiation in (the hypothetical) free space does not depend on frequency. The actual experiment, which took place in (the real medium of) interstellar space does not produce evidence contrary to the model. The model, or theory, is therefore said to be verified by the experiment. Martin Hogbin (talk) 12:17, 15 July 2009 (UTC)

Martin: you cannot "verify" or "confirm" a definition. You statement is " According to classical electromagnetism, the speed of electromagnetic radiation in free space is the same for all frequencies. This has been verified to a high degree of accuracy by experiment." Apparently you are unaware that "free space" is not a real medium and is not measurable. Therefore, one cannot "verify" its properties: they are given. One can measure outer space however, and establish to within some accuracy that it behaves like free space. Hence the difference in meaning. The test is the comparison between the model and reality, which establishes that reality behaves like the model. One does not test to see if free space is dispersionless (it is, by definition), but whether outer space is dispersionless. Brews ohare (talk) 12:20, 15 July 2009 (UTC)

Brews. This is how physics works. You develop a theory, in this case classical electromagnetism, which predicts no dispersion in (hypothetical) free space. You then do experiments to test the theory. In this case an experiment in (the real medium of) interstellar space. You then ask yourself if the results of the experiment are contrary to the predictions of your theory. If this is not the case the experiment is said to verify the theory. I can explain in more detail if you like.

Please also note the actual title wording of two of the quoted sources: 'Severe limits on variations of the speed of light with frequency' and 'Probing the Speed of Light with Radio Waves at Extremely Low Frequencies'. They both just say 'speed of light'. Martin Hogbin (talk) 12:31, 15 July 2009 (UTC)

Martin: Here's the statement: "According to classical electromagnetism, the speed of electromagnetic radiation in free space is the same for all frequencies. This has been verified to a high degree of accuracy by experiment." I understand this to mean that experiment has verified that a property of free space is that the speed of light is the same for all frequencies. That is simply not correct, neither in fact nor in principle. This is not a question about experimental method. The simple fact is that the statement that free space is dispersionless is true independent of any experimental test whatsoever. Do you understand that? Brews ohare (talk) 12:40, 15 July 2009 (UTC)

As for the sources saying "speed of light", that has nothing to do with the question of whether they measured "free space". Of course, they did not. Brews ohare (talk) 12:42, 15 July 2009 (UTC)

Experimental results are always the product of lots of assumptions. An assumption here is that real vacuums behave like the hypothetical free space *to the accuracy needed by the experiment*. The general scientific concensus is that this assumption is true, and the exceptions where it may be expected to fail (super high fields, tiny scales, etc) are well known. Of course it is philosphically possible that the speed of light *does* vary with frequency, but the dispersion of 'real vacuum' cancels it out in these specific measurements, but in general the simplest (and only accepted) explanation is that *both* the speed of light is constant with frequency, *and* real vacuums behave like free space to the accuracy of the measurement. So in practice the experiments verify *both* assumptions. Since the article is about the speed of light, saying the speed of light is verified seems reasonable. At the very most, a footnote saying something like "Technically, this also assumes interstellar vacuum can be modelled to sufficient accuracy as free space, but this is widely accepted." could be added. LouScheffer (talk) 12:53, 15 July 2009 (UTC)

Why aren't the imperial units listed as exact values ?

miles per second = 186282.39705122

miles per hour = 670616629.384395

Computations: 1/.0254/12/5280*299792458

1/.0254/12/5280*299792458*3600

Seriously this is a scientific article, values should be exact not approximated. — Preceding unsigned comment added by 69.232.221.200 (talk • contribs) 19:08, 14 July 2009 (UTC)

1. Those aren't exact values. It's a repeating decimal, for example 186282.3970512208701185079137835043346854370476417720512208701185079137835043346854370476417720512209...

2. Who would ever want to know the speed of light in miles per hour to more than 0.1% accuracy? No one. Almost no one ever wants better than 0.1% accuracy for anything. Those who do are professional scientists who are capable of calculating it themselves, and moreover wouldn't do so in imperial units.

3. It clutters and distracts. If I look for 0.1 seconds at the number 186282.39705122, it's a meaningless mess of digits. If I look for 0.1 seconds at the number 186,000, I can understand it immediately. Plus, the extra digits add to the width of the whole table. --Steve (talk) 00:36, 15 July 2009 (UTC)

"Measuring" free space

From the article:

"According to classical electromagnetism, the speed of electromagnetic radiation in free space is the same for all frequencies. This has been verified to a high degree of accuracy by experiment."

The statement that free space is dispersion free is a defined property of the unrealizable, ideal medium of free space. To claim that this defined property is experimentally verified is a logical error, as one cannot measure a defined property: its value is what the definition says it is. All that experiment can do is confirm wheedler some realizable medium, like outer space say, has this property. Such confirmation serves to support the notion that "free space" is a useful model, but it cannot change the model. It can only support its utility. These statements in the article should be replaced with something like:

"According to classical electromagnetism, the speed of electromagnetic radiation in free space is the same for all frequencies. This behavior has been verified by experiment to a high degree of accuracy for media such as outer space or ultra-high vacuum, showing that in this respect these media are good approximations to free space."

Brews ohare (talk) 13:02, 15 July 2009 (UTC)

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