Re: Gravitational constant

robert bristow-johnson <[EMAIL PROTECTED]> wrote:

please don't cut and paste between posts of different authors.
Reply to each on his own. [Uncle Al snipped]

> In article [EMAIL PROTECTED], J. J. Lodder at
> [EMAIL PROTECTED] wrote on 11/30/2003 12:01:
> 
> > robert bristow-johnson <[EMAIL PROTECTED]> wrote:
> > 

snip

> >> it's a 37 fold
> >> increase in accuracy of G.  if this becomes accepted worldwide , i would
> >> suppose NIST would update their expression for G.
> > 
> > Yeah, just another number in a table.
> > The actual value of G has very little relevance to anything.
> > (with very few exceptions)
> 
> really?!  *very* few??

Name a few.

> > It is only products of an mG that occur in applications.
> > And of course the m's are as inaccurately known as G,
> > while the products mG are known to much greater accuracy.
> 
> this is why i would think knowing G to a high accuracy *is* important.
> assuming M>>m, knowing the radius (or radii if it's elliptical) of an orbit
> of a small satellite tells us something about M, but only to the accuracy
> that G is known.  you're right, M*G is what gets measured directly, but if
> you want to know M, you gotta know G.

Indeed, if you look in a table you'll find that the mass of the earth is
(surprise surprise) known to precisely the same accuracy as G. However,
the mass of the earth (and other bodies) are also just random numbers
for collection into tables.
What matters physically is the density of the earth, since it allows for
testing of stucture models. Unfortunately the accuracy of these is too
small for an improved G value to have an influence.

> suppose the question is "how much does solar wind slow down the earth's
> revolutionary speed around the sun?" 

Not at all, to all forseeable accuracy, and the answer doesn't depend on
any more accurate measurement of G.

> or "how much did ancient asteroid
> impact affect earth's orbit?" or "what is the mass of the moon (assuming we
> accurately know where the common center of mass of moon and earth that both
> revolve around)?"  

G doesn't enter here, only mass ratios matter.

> inertial mass, M, might be an important value and
> assuming that the inertial mass is the same as the gravitational mass, *if*
> we knew G accurately, we could compute M accurately from observation of
> orbits of satellites around the earth.  isn't knowing G important in any
> three-body (or more bodies) gravitational problem?  it's not just M*G.

Ratio of inertial to gravitational mass can be determined -far- more
accurately than G, and there are good resons for assuming that this will
always be the case. 

snip
> > Defining units in terms of fundamental quatities
> > is no aim in itself for metrology.
> 
> i think it is, ultimately.  then these particular fundamental quantities
> (like G, h_bar, c, epsilon_0) become simply "scaling factors" which is what,
> i believe, Nature sees them as.  i really think that we perceive length in
> terms of the Planck Length or time in terms of the Planck Time or mass in
> terms of the Planck Mass and that has as one consequence that we perceive
> speed in terms of c.  i think that the science of metrology ultimately cares
> about the scaling of Nature and, even though i am a sub-enlightened
> electrical engineer, i am pretty sure that the scaling of Nature depends on
> what we like to think as G, h_bar, c, and epsilon_0.

No, Nature doesn't care about our stupidities in describing Her. You
should turn it around: only those aspects of our description of Nature
that do not depend on particular descriptions have physical reality.

> if these theoretical physicists are doing all sorts mathematics with
> c = h_bar = G = 1/(4*pi*epsilon_0) = 1, then if they get any answers, the
> answers will be in terms of Planck Units (with Planck charge being
> e/sqrt(alpha)) and to convert those answers to something we might
> experimentally observe with units like angstroms, conversion factors that
> depend on G (except for charge) must be used.  if our knowledge of G is
> sloppy, then the efficacy of experiments to confirm any of these theoretical
> predictions will be at least half as sloppy ("half" because of the square
> root).   

You have things upside down once more.
Testing theories -experimentally- will (and must) always depend on unit
systems defined experimentally, not on theoretical constructions.


> [[and again, i still think it is better to choose units that
> normalize G to 1/(4*pi) and epsilon_0 to 1 and make all of those 4*pi
> factors go away in Maxwell's Equations and GEM.  that would make the natural
> unit of charge e/sqrt(4*pi*alpha) and a similar change from the other Planck
> values.]]

And once again: it doesn't matter to Nature where you put those 4pi-s.
It is a matter of human convention only. Its merits should be discussed
in terms of saved dead trees, not in terms of descibing Nature.

> is not the science of metrology concerned about that?

No, metrology and the form chosen to write Maxwell's equations in have
no connection. Metrology is about reproducible accuracy.

> > What matters is having units which are as reproducible as possible.
> 
> i agree, but reproducible in the most fundamental of circumstances.
> currently, it makes sense that we measure time in terms of cycles of some
> radiation of Cesium, because we can measure that so well (and currently much
> much better than we can measure G).  but i doubt that the frequency of this
> particular radiation of some radioactive element will have much to do with
> how whatever the TOE views time.  

The existence of an infamous radioactive isotope of Caesium
has nothing to do with it.
In fact the second standard specifies
which (non-radioactive) Ce isotope is to be used.
As Einstein once said "Time is what the clock shows!"
He meant of course that time is the rate at which physical processes go.
Therefore any physical proces whatsoever can serve as a clock.
The choice is again one of realizable stability.

> radioactivity(but what about G, h_bar, and c?  does the
> TOE, whenever humans figure out what it is, care about those fundamental
> constants?)
> 
> > If that happens to require giving some fundamental constant
> > a defined value that's what's done. (as for c, or perhaps Avogadro soon)
> 
> or h (or h_bar)?  i think redefining the kilogram so that h or h_bar is a
> defined constant like c is a far better idea than defining the kg to be
> whatever that piece of iridium in Paris is.  (or was it platinum?  i
> forget.) 

It is no idea at all, for metrology.
All that matters is how accurately
whatever is chosen to represent the kilogram
can be reproduced.

> used to be that the meter was the distance between a couple of
> scratch marks on another piece of metal.  (i know the original definition
> was earth's circumference divided by 40 million.  big deel.)  the definition
> of the meter is far better now.  and so will be the kg when they change it
> to the Mohr and Taylor proposal.  

The propasal will not be 'better' until several independent groups
demonstrate experimentally that the so defined kilogram
is more reproducible than the lump at Sevres,
whatever you may think about the aesthetics.

> so that still leaves the second defined in
> terms of some particular element in the universe instead of a fundamental
> property of the universe itself.

It will always be necessary to fix at least one
length, time, energy, frequncy, or whatever, scale experimentally.
 
Best,

Jan