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Steve: You ask:

"How can the defined oscillation period of caesium be identified as exactly the same concept as the experimentally measured oscillation period of caesium??" How would you answer that question?

I'd assume that this question is related to the definition of the second

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 cesium 133 atom.

I'd take it that you are suggesting that it is not possible to measure the period of the cesium atom in seconds, because it is defined in terms of the period. Of course that is true.

It also happens that this unit is defined in terms of a physical event that repeats in time, and not in terms of some other property entirely, like a length, or like the speed of light. Naturally, a unit of time can be chosen as the period of any repeated event, like the rotation of the Earth as another old example.

I don't think this example has any bearing upon ε₀, which in the view of CODATA is defined by a formula involving μ₀ and c₀ and is not defined in terms of the permittivity of 'vacuum' or any real medium, as you seem to think. It is defined in terms of μ₀ and c₀ in Table I, p. 1191, and is not related to any physical realization. Brews ohare (talk) 19:06, 26 January 2012 (UTC)[reply]

Maybe I don't have your question clear? The phenomena of the oscillation of cesium can be observed, but to measure it one has to compare it to another periodic phenomenon. If the standard for timing events is the oscillation of cesium, then it cannot be measured. Of course, one could compare a number of different periodic phenomena to see whether they agree over long time intervals, whether one was easier to use, whether one was more precise, and so forth. Those comparisons would decide whether cesium was the best choice.

IMO, this exercise in deciding what is the best unit for time has no parallel in setting up ε₀. Perhaps you disagree? Brews ohare (talk) 18:00, 27 January 2012 (UTC)[reply]

To recap where we seem to be...The two issues we seem to be discussing are (1) You think I must be crazy to think that ε₀ is by definition the same as ε_{EverydayWorld}, (2) I think you are crazy to think that ε₀ is different from ε_{EverydayWorld}. Within (2) is: (2a) If this were true, then the numerical value for ε_EW/ε₀ would be an incredibly important parameter in real life, calculated in many textbooks and papers; however, in the real world, I still have not seen any numerical estimates besides my own rough guess of 1.2. (2b) All the hundreds of thousands of physicists and engineers in the world have "voted with their feet" that ε_EW and ε₀ are equal, by measuring permittivities in a way that references them to "vacuum with quantum fluctuations", rather than "vacuum without quantum fluctuations" (which may be ~20% different).

Out of those two issues, right here we're focused on (1): Am I crazy to think that ε₀ could possibly be the same (by definition) as ε_EW? Well, I thought that your argument was "ε_EW is a kind of real-world thing that has something to do with experimental measurements. On the other hand, CODATA says that ε₀ expressed in SI units is an exact numerical quantity. Therefore ε₀ and ε_EW cannot possibly be the same." I was rebutting this argument by saying that there are real-world things that have something to do with experimental measurements, that are nevertheless exact numerical quantities when expressed in SI units. The oscillation period of caesium is a good example, the mass of the IPK is another, the mass of a mole of carbon-12 is yet another, etc.

It seems your argument was subtler than that. If I understand now, you are saying: "Yes, it is possible for a quantity to have an exact value in SI units, but nevertheless to be experimentally realizable (at least in principle). This funny situation only occurs when the SI unit is defined directly in terms of the quantity. For example, it is possible for the oscillation period of caesium to be an exact fixed number of seconds, because the second is defined as a multiple of the oscillation period of caesium. As another example, it is possible for the mass of the IPK to be an exact fixed number of kilograms, because the kilogram is defined as a multiple of the mass of the IPK."

"But," you say, "ε₀ is not like this, because there is no SI unit defined as a multiple of ε₀ or otherwise in terms of ε₀. Without that trick, it is impossible to think that ε₀ could simultaneously be exact in SI units, and experimentally realizable (at least in principle)."

"Finally," you say, "CODATA says ε₀=1/c₀²μ₀, not approximately equal but exactly equal. If ε₀, c₀, μ₀, were separately defined as three different parameters describing the real-world, experimentally-realizable vacuum (at least in principle), it would be impossible to say with certainty that they satisfy any exact relation."

I will hold off on responding until you can confirm that I am correctly understanding and summarizing your arguments. :-) --Steve (talk) 19:22, 27 January 2012 (UTC)[reply]

Looks largely correct. The definition of ε₀≡1/c₀²μ₀ clearly precludes any measurement of ε₀, because we know its value exactly and no measurement of permittivity can change that. Moreover, ε₀ does not refer to any realizable "unit" of permittivity (say, in terms of the capacitance of some standard capacitor) in the way the period of cesium refers to an actual unit of time.

In the event the logic of the matter is obscure, I appeal to the fact that all models that might apply to real vacuum, such as QED vacuum, demonstrate nonlinearity, dispersion, nonlocality and whatever, while ε₀ shows none of this behavior. Consequently, it seems likely that when experiment rises to the occasion where these things can be demonstrated, ε₀ will not be a candidate to describe any real vacuum. I understand photon-photon scattering has already been observed in real vacuum, showing nonlinearity is an experimental fact as well as a theoretical prediction.

The case of the speed of light is an interesting one. Choosing c₀ as the unit of speed might refer to a real speed as entertained by relativity, and if so, it does make it unobservable in SI units, just like the second makes the period of Cesium unobservable. And like that case, this speed can be compared to other speeds to decide what is the best choice for a standard. The experiments supporting relativity indicate it has some undisputed advantages in reproducibility etc., although in practice people will use the speed of light in air or in helium-filled chambers and correct for the medium using c₀/n

In an exactly similar fashion to realizing the standard speed in air, it may turn out that the refractive index of no real vacuum has identically n≡1. In which case choosing the speed of light as a constant independent of frequency, wavelength, polarization, intensity, etc. makes this choice a convenient fiction, which nonetheless can be used here as well to refer to the speed of light in real vacuum as c₀/n. Brews ohare (talk) 21:20, 27 January 2012 (UTC)[reply]

Hi Steve: Have you decided we are at an impasse at this point, or have you decided that in fact we are on the same page? Brews ohare (talk) 14:06, 31 January 2012 (UTC)[reply]

I've been busy, sorry.

• YOUR ARGUMENT 1: "all models that might apply to real vacuum, such as QED vacuum, demonstrate nonlinearity, dispersion, nonlocality and whatever, while ε₀ shows none of this behavior."
• MY BELITTLING REPHRASE 1: "There are some people--not CODATA but other people--who use the term "vacuum permittivity" for the quantity ε₀. They do not call it "vacuum permittivity in the limit of weak fields", they just call it "vacuum permittivity". Therefore we must require that ε₀ is the permittivity of "vacuum" (whatever that is) at any field whatsoever, no matter how high. This proves that "vacuum" cannot be "real-world vacuum", because the permittivity of a real-world vacuum changes at extremely intense fields."
• MY RESPONSE 1: I think that ε₀ is the permittivity of the real-world vacuum in the limit of very weak fields but not in the limit of extremely intense fields. I don't see any reason to be bothered by that or any suggestion that SI authorities think differently.
• YOUR ARGUMENT 2 (as rephrased by me): "CODATA says ε₀=1/c₀²μ₀, not approximately equal but exactly equal. If ε₀, c₀, μ₀, were separately defined as three different parameters describing the real-world, experimentally-realizable vacuum (at least in principle), it would be impossible to say with certainty that they satisfy any exact relation."
• MY RESPONSE 2: OK, fine, we can take ε₀≡1/c₀²μ₀ to be a definition. (It is certainly the definition in the CODATA paper.) Then I would say μ₀=μ_{EverydayWorld} by definition, c₀=c_{EverydayWorld} by definition, and ε₀≈ε_{EverydayWorld} insofar as Maxwell's equations hold in the EverydayWorld limit, which is probably "they hold exactly in this limit", and certainly "they hold within parts-per-billion in this limit", and definitely not "they are 20% wrong in this limit". [Again, EverydayWorld means the real-world vacuum in the limit of weak fields, long distances, removal of every last particle, etc.] We can shift the debate, therefore, to whether μ₀=μ_{EverydayWorld} exactly by definition (which I believe), or whether μ₀=μ_{EverydayWorld}*1.2 (which is the value you would get based on the QED calculation of vacuum fluctuations; "the QED vacuum is diamagnetic, with relative magnetic permeability < 1", as you put it.)

So I'm sorry about the unnecessary diversion into ε₀. You can now please try to explain to me why "Steve, you would have to be crazy to believe that μ₀=μ_{EverydayWorld} exactly by definition!" and also why "There is nothing at all implausible or troubling in my belief that μ₀=μ_{EverydayWorld}*1.2." Again, for the latter, there is (1) the fact that all the engineers of the world have "voted with their feet" that μ₀ and μ_EW are not 20% different; (2) the fact that CODATA has explicitly endorsed measurements in the literature that use the assumption μ₀=μ_EW; (3) the fact that no one on earth has ever given a numerical estimate for the extremely-important ratio μ₀/μ_{EverydayWorld} except for my own estimate of 1.2 right here; etc. --Steve (talk) 21:33, 15 March 2012 (UTC)[reply]

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Steve: I wondered if you noticed this exchange. It would seem that this issue is not clear from the present intro, and is not understood even by Blackburne, who says the "exact value" is a consequence of advanced concepts from special relativity. Could it be that there is no English language formulation possible, or could it be that the climate on this page is so tempestuous that no agreement can be found? Brews ohare (talk) 18:05, 14 February 2012 (UTC)[reply]

I stopped watching that page a long time ago...was getting too time-consuming...maybe I'll look. I owe you a response on this page too but I've hit a very busy patch at work....well, that hasn't quite totally stopped me from procrastinating via wikipedia, but still, I'm trying to minimize it :-) --Steve (talk) 18:10, 14 February 2012 (UTC)[reply]

on the WikiProject Physics talk page on March 15th, the new subsection

5.1 - {{template:Physics equations navbox}} "here to stay just because of user:F=q(E+v^B)"????

sparked an argument and then settled down, concerning the pointless {{template:physics equations navbox}}. I also find no use with the template. Just thought I'd let you know. Keep up the good + hard work, cheers, Maschen (talk) 17:54, 1 April 2012 (UTC)[reply]

... but Frank Wilczek used the term "Natural (Planck) units", for example. I don't like that particle physics uses that general term, particularly when their unit voltage is the SI volt, hardly a natural quantity to reference. A natural unit system is one that requires some definitive meaning: it should be possible for the aliens on the planet Zog can come up with the same system. There is no possibility that the Zoglings will come up with the eV for their unit energy. Planck units do have a special claim to "naturalness", moreso than the eV-based "natural units" of particle physics. And the article mentions that, but I also don't think it should be "a.k.a. Natural units". 71.169.179.168 (talk) 03:13, 25 April 2012 (UTC)[reply]

Glad you agree with the edit. Whether or not the particle-physics community is justified in calling something "natural units" when it has eV's is an unrelated issue. The more relevant issue here is that Zoglings may not be using exactly Planck units. Maybe they set h=1 instead of hbar=1, to take just one example. The Frank Wilczek quote is interesting, but I do think he's using "natural" as a describing adjective, rather than as a specific terminology...notwithsanding the capitalization. :-) --Steve (talk) 04:05, 25 April 2012 (UTC)[reply]

I consider it quite salient that particle-physics community calls the eV a "natural unit" of energy. It just isn't, and the name they attach to that system of units is not appropriate. Nonetheless, they use it.

So I'll emphasize a word A natural unit system is one that requires some definitive meaning: it should be possible for the aliens on the planet Zog to come up with the same system. Zoglings could choose to normalize ħ (or they could h), but they cannot choose to normalize the eV as the unit of energy. So whether it's ħ or h, it's a "natural" system. But it's not if it's the volt. BTW, I think that if the Zoglings come to a similar understanding of the laws of nature, they will be thinking about the ħ vs. h issue and will likely choose ħ. And I think they would normalize 4πG rather than G. But that, of course, is idle speculation. 71.169.179.168 (talk) 15:01, 26 April 2012 (UTC)[reply]

I don't think you'll find anyone who says "the eV is THE unit of energy in natural units". Once you set ${\displaystyle \hbar =c=1}$, then everything is expressed in powers of a single unit, but the phrase "natural units" does not speak to what that single unit is. Usually it is eV or keV or MeV etc. But if a particle physicist said

The particle's energy is 20 nanometers^-1 (by the way, I'm obviously using natural units here).

then I think he or she would be understood quite clearly and would not be saying anything unusual or incorrect. Again, I think the phrase "natural units", as it is used in particle physics, just refers to ${\displaystyle \hbar =c=1}$ and nothing else. eV is merely a common and conventional choice of unit that supplements "natural units", rather than being one of the natural units.

If you agree that "natural units" means ${\displaystyle \hbar =c=1}$ and nothing else, then I think your objection is based on the word "units" rather than the word "natural". Maybe you think it should be called "some natural units" so that it does not imply a complete system of units? :-) --Steve (talk) 15:25, 26 April 2012 (UTC)[reply]

I think any system of units must be complete in that any quantity can be expressed with that system. As best as I can tell, that means you don't need any mole or candela as long as you have length, time, mass, electric charge, and temperature or some other independent combination. Like you can eliminate either length, time, or mass from the list if you include energy or momentum in its stead (or like SI, you can use electric current instead of charge as a base unit). Temperature is largely considered a scaling factor applied to energy per particle.

So a system of natural units must define more than ħ and c as natural units. It must pick another universal quantity in nature (perhaps the mass or rest energy of an elementary particle if not G) just to get to the mechanical units, and it must pick up something regarding the EM interaction (perhaps e or ϵ₀) to define a natural unit of charge. And I cannot think of any other constant, other than the Boltzmann constant, k_B, to use for a natural definition of a temperature unit. If there is any unit defined by an anthropocentric physical quantity, the system that uses that unit is not a "natural system of units". 71.169.179.168 (talk) 17:11, 26 April 2012 (UTC)[reply]

Yea, I think that's why people usually say "natural units" rather than "natural system of units". There are exceptions. (Incidentally, this is an example where it is stated very clearly that the extra unit is not part of the phrase "natural units", and also an example of eV not being used.) here's another example where the word "system" is used like you say. But again, 90% of the time or more, the word "system" is not used. I agree with you that the word "system" should not be used. "System" implies "Complete system". :-) --Steve (talk) 17:37, 26 April 2012 (UTC)[reply]

My draft is now available at http://en.wikipedia.org/wiki/User:Petergans/sandbox Please feel free to comment, amend etc. Watch out for typos, there may be lots of them which I don't see! Petergans (talk) 13:05, 2 May 2012 (UTC)[reply]

See User_talk:Petergans/sandbox :-) --Steve (talk) 13:54, 2 May 2012 (UTC)[reply]