Date: Thu, 29 May 2003 20:20:22 -0400 (EDT)
From: "Keith F. Lynch" <kfl at KeithLynch.net>
To: WSFA members <WSFAlist at KeithLynch.net>
Subject: [WSFA] Re: reference kilogram slowly evaporating, etc.
Reply-To: WSFA members <WSFAlist at keithlynch.net>

ronkean at juno.com wrote:
> ... the wide availability of distilled water, thermometers and
> measuring calipers means that water remains perhaps the most
> accessible standard for casual use.

The water should not only be distilled (free of dissolved solids), but
also free of dissolved gasses.  Then there's the problem that there
are two stable isotopes of hydrogen, and three of oxygen, whose ratios
vary slightly from one sample of water to the next, resulting in "pure
water" having a slightly variable density.

> It might be better to say that 'the kg is defined as the mass of the
> original reference cylinder, as originally made'.

That might be what was intended, but that's not what the definition says.

> In the full length article, it was mentioned that they are
> considering defining the kg as a particular number of atoms of
> silicon, or possibly gold.  Silicon is attractive because it is
> easier to count or estimate the number of atoms in a monocrystal.

Also because science has learned to do detailed work with tiny amounts
of that element.

Unfortunately natural silicon consists of three stable isotopes with
different weights.  The ratio of those isotopes differs slightly
depending on where the silicon was mined and how it was refined and
purified.  Getting all one isotope would be prohibitively expensive.

> Yes, the gravitational constant would be a particularly bad choice
> as the basis for a mass standard, because of the difficulty of
> measuring G precisely.

Unfortunately, it's needed to link astronomical masses to the
kilogram, just as Avogadro's number is needed to link atomic masses to
the kilogram.  In other words, the ratio of the mass of the earth and
the sun is known to much higher precision than the mass of either of
them in kilogram.  Similarly, the ratio of the mass of the electron
and proton is known to much higher precision than the mass of either
of them in kilograms.

> It has been suggested that G might not even be the same at very
> short distances (a few millimeters or less) as it is at astronomical
> distances.

In that case G would simply be redefined as the limiting value at
large distances.  Similarly, it's possible that the photon isn't really
massless, any more than the neutrino was, and that light of different
wavelengths therefore goes at very slightly different speeds.  If so,
C would be redefined as the limiting speed of light.  Not a problem.

> According to a reference chart I found, the SI base units are the
> meter, kilogram, second, ampere, kelvin, mole, and candela.  But
> those are 'base' units because they are conventionally used to
> derive the other units, and not necessarily because they need to
> be at the core of a universal system of units.

Right.  Many alternative systems are possible.  Personally, I think it
would make more sense to regard the coulomb (one ampere per second) as
fundamental, rather than the ampere (one coulomb second).  We don't
make "one kilogram per second" fundamental, and derive the unit of
mass from that, after all.

> For example, the candela is defined for convenience in lighting
> applications and in accord with how the human eye responds to light,
> so it is not really a fundamental physical unit.

The units are designed for people, not for perfectly abstract
entities.  That's also why the units have roughly the sizes they do.
If we wanted a more "natural" system of units, we'd define the speed
of light, Planck's constant, Boltzmann's constant, Avogadro's number,
and the gravitational constant as all equal to one.  Which works just
fine (ignoring the fact that the gravitation constant is only known to
four places) if you don't mind weird numbers.  For instance in that
system my height is 110,000,000,000,000,000,000,000,000,000,000,000,
my weight (mass) is 3,500,000,000, and my age is
27,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

> The candela can be defined as a particular power (watts) of light of
> a particular wavelength, or its equivalent brightness to the human eye.

It is.  Until recently, it was defined in terms of an actual candle.

> The mole depends on the ratio of the mass of a particular type of
> atom to the chosen standard mass, so it's not really fundamental
> either.

It's useful to link the atomic scale to the ordinary scale.
For instance just yesterday someone on the net proposed running
uninsulated power lines on the moon, and it's useful to know that
one einstein (one mole of photons) can knock one faraday (one mole
of electrons) out of a power line in a vacuum.  Especially if you
have a good feel for how large those quantities are.  That makes
it much easier to quickly decide whether it's practical to run
such power lines than if you had to deal with individual electrons
and individual photons, just as you have a better idea how long
it will take you to get somewhere if your speed is expressed in
miles per hour rather than furlongs per fortnight or kiloparsecs
per femtoeon.

> Kelvin can be defined in terms of energy per degree of mechanical
> freedom, ...

It could, but it isn't.  It's defined in terms of the triple point of
water, i.e. the unique temperature at which ice, liquid water, and
water vapor can all coexist.

> The ampere can be defined in terms of the force between two parallel
> wires a certain distance apart carrying current,

Yes, and it is.  This is unfortunate, as it obscures the parallels
between electromagnetism and gravitation.  What's the force between
two one coulomb charges one meter apart?  Not that easy to figure out.
What's the electromagnetic equivalent of the gravitational constant?
What are the gravitational equivalents of epsilon-naught and mu-naught?
It gets hairy, and it doesn't need to be.

> so that's not fundamental, considering that force is derived from
> kilograms and seconds.

Anything can be derived from anything else, via a constant that
connects the two.  That doesn't mean they're the same thing, or that
one is more or less fundamental than the other.

> We are left with the meter, kilogram, and second.  But the meter
> has now been defined in terms of the second and the speed of light,
> which leaves just the kilogram and the second.

We could define the kilogram in terms of the second via any of several
routes.  Most naturally (at least to me) by defining Planck's constant
as some exact value.  Or perhaps the Rydberg constant, which has the
virtue of being known to a very high precision.

> If we woke up one morning, and everything was slightly smaller than
> the day before, by one inch per foot, presumably we would be able to
> detect and measure the change by noticing that the speed of light
> had increased by some 9.09%.

Yes, since the speed of light is constant *by* *definition*.  So we
would conclude that the speed of light was unchanged and everything
had shrunk.  If our units were defined differently, we'd conclude that
everything was the same size, and the speed of light had increased.
There's no fundamental reason to prefer one explanation to the other.
I don't think it means anything to argue about which is really true.

> Santa Cruz - May 28, 2003 - If an asteroid crashes into the Earth,
> it is likely to splash down somewhere in the oceans that cover 70
> percent of the planet's surface.  Huge tsunami waves, spreading out
> from the impact site like the ripples from a rock tossed into a
> pond, would inundate heavily populated coastal areas.

Yes.  This passes for news?

> May 29, 1953: the climbing of Mt. Everest, Edmund Hillary and Tenzing Norgay

Yes.

> May 29, 1453: the fall of Constantinople, Mehmet II and Constantine XI

That's on the Julian calendar.  The actual 550th anniversary of the
fall of "Rome" isn't until June 7th, if you project our calendar
backwards, or June 11th if you project the Julian calendar forward.

The Ottoman empire, which sacked Constantinople, didn't fall until
the 20th century, at the end of WWI.  The past isn't really all that
distant if you look at it right.

Today is also Bob Hope's 100th birthday.
--
Keith F. Lynch - kfl at keithlynch.net - http://keithlynch.net/
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