But in this case you are no longer defining distances but some other arbitrary quantity, like vendors do when they convert a small computer speaker into a rockband PA by using PMPO instead of music power. Herman
-----Original Message----- From: CCP4 bulletin board [mailto:ccp...@jiscmail.ac.uk] On Behalf Of Frank von Delft Sent: Friday, November 20, 2009 1:11 PM To: CCP4BB@JISCMAIL.AC.UK Subject: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] units of the B factor Eh? m and Å are related by the dimensionless quantity 10,000,000,000. Vive la révolution! Marc SCHILTZ wrote: > Frank von Delft wrote: >> Hi Marc >> >> Not at all, one uses units that are convenient. By your reasoning we >> should get rid of Å, atmospheres, AU, light years... They exist not >> to be obnoxious, but because they're handy for a large number of >> people in their specific situations. > > Hi Frank, > > I think that you misunderstood me. Å and atmospheres are units which > really refer to physical quantities of different dimensions. So, of > course, there must be different units for them (by the way: atmosphere > is not an accepted unit in the SI system - not even a tolerated non SI > unit, so a conscientious editor of an IUCr journal would not let it go > through. On the other hand, the Å is a tolerated non SI unit). > > But in the case of B and U, the situation is different. These two > quantities have the same dimension (square of a length). They are > related by the dimensionless factor 8*pi^2. Why would one want to > incorporate this factor into the unit ? What advantage would it have ? > > The physics literature is full of quantities that are related by > multiples of pi. The frequency f of an oscillation (e.g. a sound wave) > can be expressed in s^-1 (or Hz). The same oscillation can also be > charcterized by its angular frequency \omega, which is related to the > former by a factor 2*pi. Yet, no one has ever come up to suggest that > this quantity should be given a new unit. Planck's constant h can be > expressed in J*s. The related (and often more useful) constant h-bar = > h/(2*pi) is also expressed in J*s. No one has ever suggested that this > should be given a different unit. > > The SI system (and other systems as well) has been specially crafted > to avoid the proliferation of units. So I don't think that we can > (should) invent new units whenever it appears "convenient". It would > bring us back to times anterior to the French revolution. > > Please note: I am not saying that the SI system is the definite choice > for every purpose. The nautical system of units (nautical mile, knot, > etc.) is used for navigation on sea and in the air and it works fine > for this purpose. However, within a system of units (whichever is > adopted), the number of different units should be kept reasonably small. > > Cheers > > Marc > > > > > >> >> Sounds familiar... >> phx >> >> >> >> >> Marc SCHILTZ wrote: >>> Hi James, >>> >>> James Holton wrote: >>>> Many textbooks describe the B factor as having units of square >>>> Angstrom (A^2), but then again, so does the mean square atomic >>>> displacement u^2, and B = 8*pi^2*u^2. This can become confusing if >>>> one starts to look at derived units that have started to come out >>>> of the radiation damage field like A^2/MGy, which relates how much >>>> the B factor of a crystal changes after absorbing a given dose. Or >>>> is it the atomic displacement after a given dose? Depends on which >>>> paper you are looking at. >>> >>> There is nothing wrong with this. In the case of derived units, >>> there is almost never a univocal relation between the unit and the >>> physical quantity that it refers to. As an example: from the unit >>> kg/m^3, you can not tell what the physical quantity is that it >>> refers to: it could be the density of a material, but it could also >>> be the mass concentration of a compound in a solution. Therefore, >>> one always has to specify exactly what physical quantity one is >>> talking about, i.e. B/dose or u^2/dose, but this is not something >>> that should be packed into the unit (otherwise, we will need >>> hundreds of different units) >>> >>> It simply has to be made clear by the author of a paper whether the >>> quantity he is referring to is B or u^2. >>> >>> >>>> It seems to me that the units of "B" and "u^2" cannot both be A^2 >>>> any more than 1 radian can be equated to 1 degree. You need a >>>> scale factor. Kind of like trying to express something in terms of >>>> "1/100 cm^2" without the benefit of mm^2. Yes, mm^2 have the >>>> "dimensions" of cm^2, but you can't just say 1 cm^2 when you really >>>> mean 1 mm^2! That would be silly. However, we often say B = 80 >>>> A^2", when we really mean is 1 A^2 of square atomic displacements. >>> >>> This is like claiming that the radius and the circumference of a >>> circle would need different units because they are related by the >>> "scale factor" 2*pi. >>> >>> What matters is the dimension. Both radius and circumference have >>> the dimension of a length, and therefore have the same unit. Both B >>> and u^2 have the dimension of the square of a length and therefoire >>> have the same unit. The scalefactor 8*pi^2 is a dimensionless >>> quantity and does not change the unit. >>> >>> >>>> The "B units", which are ~1/80th of a A^2, do not have a name. So, >>>> I think we have a "new" unit? It is "A^2/(8pi^2)" and it is the >>>> units of the "B factor" that we all know and love. What should we >>>> call it? I nominate the "Born" after Max Born who did so much >>>> fundamental and far-reaching work on the nature of disorder in >>>> crystal lattices. The unit then has the symbol "B", which will >>>> make it easy to say that the B factor was "80 B". This might be >>>> very handy indeed if, say, you had an editor who insists that all >>>> reported values have units? >>>> >>>> Anyone disagree or have a better name? >>> >>> Good luck in submitting your proposal to the General Conference on >>> Weights and Measures. >>> >>> >> >
