Dear Ed, John and others, (01)
Your idea, building on John's comments, is very interesting. (02)
A common use of a difference scale
----------------------------------
In process engineering, there are:
- absolute pressure - the pressure of a gas with respect to an absolute
zero; and
- gauge pressure - the pressure within a vessel with respect to the
atmospheric pressure outside.
Both can be expressed as bar, psi or Pa. (03)
Hence we have two different instances of kind of quantity, for which the
same unit is used. Pressure is a quantity for which zero is well defined,
and there is no problem in regarding the bar, psi or Pa as firstly a
magnitude of absolute pressure. If it is assumed that there is an addition
operator for the kind of quantity absolute pressure, then the same unit can
be used for the kind of quantity gauge pressure. This assumption is usually
unstated but I believe that it is necessary for the use of the same unit for
both kinds of quantity. (04)
Thinking about the definitions in the BIPM
------------------------------------------
- The unit second appears to be a defined magnitude of temporal separation.
This implies that there is the kind of quantity "time duration" as
separation of instants. For time duration, a zero is defined. There are many
times as experienced by different clocks, but this is not discussed in the
definition of the second. (05)
- The unit metre appears to be a defined magnitude of spatial separation.
This implies that there is the kind of quantity "length" as a separation of
points. For length as separation, a zero is defined. There are many paths
through space along which length can be measured, but this is not discussed
in the definition of the metre. (06)
- The unit kilogram has an abolute definition, which implies that mass is
something absolute rather than a separation. Hence there is an implicit zero. (07)
- The unit "ampere" has an abolute definition, which implies that electric
current is something absolute rather than a separation. Hence there is an
implicit zero. (08)
- The kind of quantity "kelvin" defined as fraction of the separation
between absolute zero for thermodynamic temperature and the triple point of
water. The definition of Kelvin relies upon termodynamic temperature being
something absolute with a zero. (Here I support John rather than Ed. Kelvin
is defined with respect to a theory of temperature which regards it as an
absolute unit like mass.) (09)
A conclusion is that the kinds of quantity for which the BIPM defines a unit
have a zero. Time and position are quite different to time duration and
length and should be considered separately. (010)
Best regards,
David (011)
At 18:32 13/08/2009 -0400, you wrote:
>John F. Sowa wrote:
>> Ed,
>>
>> I agree with Ingvar that there is a fundamental difference between
>> time and temperature: There is a fundamental zero point for
>> temperature, but none for space or time. In that sense, temperature
>> should be compared to mass, which also has a fundamental 0.
>>
>> EB> The absolute zero of time is presumably the Big Bang...
>>
>> As far as we know, there are no physical laws that depend on
>> the time interval between now and the Big Bang. The time of
>> the Big Bang was estimated on the basis of laws that have no
>> fundamental dependence on a zero point for time.
>>
>> But there are many laws that depend on a zero point for temperature:
>> For a gas, pressure times volume is proportional to temperature,
>> as measured from absolute zero.
>>
>> Boltzmann's law states that the amount of energy radiated by an
>> object is proportional to T^4, also measured from absolute zero.
>>
>> The relevance for UoM is that 0 is fundamental for some units,
>> but arbitrary for others.
>>
>> John
>>
>>
>Thank you, John. This is a much clearer description of the issue. (You
>didn't use undefined and badly defined terms from a vocabulary not in
>common use.) And I agree that this is an issue for the ontology.
>
>To be very careful about the last statement, 0 is fundamental for some
>quantity kinds -- the magnitudes are always "absolute" in some sense --
>while it is arbitrary for others -- the magnitudes are always "relative"
>in some sense. I think that is what you meant. That would make
>"temperature difference" a different 'kind of quantity' from
>"temperature", even though they both use the "same?" units.
>
>And then the question is: are the units really the same? Apparently
>not. I model "measurement unit" as a subtype of "quantity magnitude"
>(Q3), so as to talk about ratios. Each measurement unit IS a specific
>magnitude. If the units of absolute measure and difference measure are
>the same, the measurement unit would be always relative in some sense
>and always absolute in some sense. So they can't be the same unit. The
>result of subtracting two absolute quantities is not an absolute
>quantity, but we use the "same" units!
>
>The model I have in my head works the other way around. The unit is
>always a relative magnitude. It acquires an absolute interpretation
>when the quantity _scale_ has a fixed 0. The quantity kinds are still
>distinct and the scales and magnitudes for absolute quantity kinds have
>fixed 0s, while the scales for relative quantity kinds don't. (For a
>relative quantity kind, the zero magnitude always means "no difference"
>in that "dimension".) That allows 45°K to mean "a temperature
>difference of 45 degrees" when the scale is for temperature difference
>and "the temperature whose difference is 45 degrees from zero absolute"
>when the scale is for temperature. The unit -- the Kelvin degree -- is
>always a temperature difference (the degree is defined as a specific
>fraction of the difference between two particular temperatures), but the
>quantity value that uses it may have a more complex interpretation. And
>what I think I am saying is that there is a difference in the concepts:
>'quantity value expresses relative magnitude' and 'quantity value
>expresses absolute magnitude'. In that way, the definition of the unit
>doesn't change, but the relation that denotes the use of the unit changes.
>
>I trust you understand that the above is my first draft at engineering
>the understanding I suddenly acquired by reading your email (and
>integrating it with what David did). I understand that the primary
>meaning of a temperature value is not a temperature difference, but
>ontologically I want to reverse the chicken and egg for temperature so
>that all units are eggs.
>
>Thanks,
>-Ed
>
>--
>Edward J. Barkmeyer Email: edbark@xxxxxxxx
>National Institute of Standards & Technology
>Manufacturing Systems Integration Division
>100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
>Gaithersburg, MD 20899-8263 FAX: +1 301-975-4694
>
>"The opinions expressed above do not reflect consensus of NIST,
> and have not been reviewed by any Government authority."
>
>
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> (012)
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