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. (01)
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. (02)
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! (03)
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. (04)
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. (05)
Thanks,
-Ed (06)
--
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 (07)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (08)
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