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:[log in to unmask]] On Behalf Of Frank von Delft
Sent: Friday, November 20, 2009 1:11 PM
To: [log in to unmask]
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.
>>>
>>>
>>
>
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