Gravitational constant.
Brad Eckert
How constant is the gravitational constant?
I once heard of an experiment in which weights of different metals
such as brass, iron, lead, bismuth, etc. were dropped and the travel
time was measured. The result was that some metals fell slightly
faster or slower than others. Does anyone have any information on such
an experiment?
As I recall, this was done over 50 years ago but it could just be an
urban legend. AFAIK, G was determined empirically and if it's safe to
assume F=ma and a=F/m, maybe there's some wiggle room in that F/m
ratio.
What gets interesting is figuring out how to replicate the experiment.
If you want to measure travel time to microsecond resolution then you
have to measure position with something like .001mm accuracy. I
imagine a couple of photoelectric beams could be set up at two points
along the fall path. If the weights are spheres I'd use two parallel
beams at each trigger point. Ideally both beams would break at the
same time, but the ball would probably be a wee bit off center so
having two beams would compensate for this effect.
Or, a mass-spring oscillator could be set up to measure mass. Taking a
reading over many cycles would help remove measurement noise, I think.
Then the computed mass could be compared to what a gravity-based scale
reads.
Any other ideas on how this experiment could be replicated?
[Moderator's note: I think you're talking about the Eotvos experiment;
it's been replicated in many ways, and to the best of our knowledge
it's *not* the case that some metals fall faster than others. - jb]
Uncle Al
Brad Eckert wrote:
>
> Hi all,
>
> How constant is the gravitational constant?
>
> I once heard of an experiment in which weights of different metals
> such as brass, iron, lead, bismuth, etc. were dropped and the travel
> time was measured. The result was that some metals fell slightly
> faster or slower than others. Does anyone have any information on such
> an experiment?
>
> As I recall, this was done over 50 years ago but it could just be an
> urban legend. AFAIK, G was determined empirically and if it's safe to
> assume F=ma and a=F/m, maybe there's some wiggle room in that F/m
> ratio.
You are confusing gravitational constant studies
http://www.phys.lsu.edu/mog/mog22/node9.html
with inertial vs. gravitational mass. You are referring to the Fifth
Force and Ephraim Fischbach building on an apparent trend in Eotvos'
original torsion balance data at the turn of the prior century.
Google
"fifth force" Fischbach 289 hits
All Eotvos balances are now run in Robert Dicke's mode which can be
phase-lock detected, hence Eric Adelberger at U/Washington. There is
no detectable Fifth force. Folks have looked.
http://www.npl.washington.edu/eotwash/
Literally dropping stuff in vacuum is only good to about 10^(-9)
difference/average (James Faller at U/Colorado JILA; Bremen vacuum
drop tower). An ambient temperature Eotvos balance is good to
5x10^(-13) difference/average. Going to 2 K (Riley Newman at U
Cal/Irvine) should improve that by a factor of 10.
All Equivalence Principle (EP) challenges - that gravitational and
inertial masses are rigorously indistinguishable - have been perfect
nulls within experimental error. The only unexamined test mass
variable coupled to an external symmetry is geometric parity,
http://www.mazepath.com/uncleal/eotvos.htm#b21
Properties coupled to internal symmetries do not interact with
rotation or translation by definition. They are default first order
experimental nulls. Gravitoelectric and gravitomagnetic effects
breaking the EP are many orders of magnitude too weak to be
experimentally detectable now or anticipated,
http://arXiv.org/abs/gr-qc/0305094
> What gets interesting is figuring out how to replicate the experiment.
[snip]
It's been done. The current level of sensitivity sees thermal
vibration of the apparatus' constituent atoms as limiting noise.
> [Moderator's note: I think you're talking about the Eotvos experiment;
> it's been replicated in many ways, and to the best of our knowledge
> it's *not* the case that some metals fall faster than others. - jb]
Everything examined falls identically to a half part in a trillion
difference/average experimental accuracy. There remains only one
unexamined quantitative test mass variable, geometric parity. Test
masses of identical chemical composition fashioned from single crystal
alpha-quartz in space group P3(1)21 versus P3(2)21 is a calculated
good parity Eotvos experiment test case.
If the EP is falsified then metric theories of gravitation and
spacetime curvature are no longer valid except as convenient
calculators. Affine/teleparallel theories of gravitation and
spacetime torsion remain valid.
--
Uncle Al
http://www.mazepath.com/uncleal/eotvos.htm
(Somebody should look)
Brad Eckert
> [Moderator's note: I think you're talking about the Eotvos experiment;
> it's been replicated in many ways, and to the best of our knowledge
> it's *not* the case that some metals fall faster than others. - jb]
After some further looking, I found that the Equivalence Principle has
been tested to 10^-13 precision so I won't bother trying to break the
Genreal Theory of Relativity.
Of course, when I'm stuck in traffic fantasizing about anti-gravity
devices the thought does cross my mind.
--
Brad Eckert
Stephen Speicher
> How constant is the gravitational constant?
G is a bit peculiar as compared to the other fundamental
constants, at least as far as the constraints which are placed on
its value. While technology and is concomitant precision has led
to a convergence of measures of most fundamental constants, the
measured values for G have increased in disparity. G is a very
rich constant in that its measure is determined in such a variety
of ways and on such diverse scales -- from micro to cosmological
distances -- perhaps it is not surprising to find such disparity.
But, to provide more context, it is only by reference to the
incredible precision achieved in constraints on the other
fundamental constants that we can think of G as becoming
disparate. In 1998 the CODATA uncertainty for G was increased
from 0.013% to 0.15%, a figure which can only be seen as large,
in relative terms.
For a nice review of the history of the constraints upon G, as
well as the constraints on the other fundamental constants, see
"The fundamental constants and their variation: observational and
theoretical status," Jean-Philippe Uzan, _Reviews of Modern
Physics_, Vol. 75, pp. 403-455, April 2003.
> I once heard of an experiment in which weights of different metals
> such as brass, iron, lead, bismuth, etc. were dropped and the travel
> time was measured. The result was that some metals fell slightly
> faster or slower than others. Does anyone have any information on such
> an experiment?
As moderator jb has already pointed out, it is generally
understood in the physics community that there is no such
variation as you would hint at above. However, if you are
interested in the history of these sort of experiments, along
with voluminous references to the original work, see the book by
one of the most famous experimenters in that field: "The Search
for Non-Newtonian Gravity," Ephraim Fischbach and Carrick L.
Talmadge, _Springer_, 1999.
--
Stephen
s...@speicher.com
Ignorance is just a placeholder for knowledge.
Printed using 100% recycled electrons.
-----------------------------------------------------------
Jacques Fric
"Brad Eckert" <br...@tinyboot.com> a écrit dans le message de
news:4da09e32.03091...@posting.google.com...
1- In some serious theories ( derived from Brans and Dicke relativity
theory for example) , the gravitationnal "constant" is not constant, as to
comply with Mach principle, it depends on location in space time.
Weak equivalence principle is still valid, but strong equivalence principle
is no longer valid. So when performing tests, you have to look carefully
which type of equivalence principle you are testing.
As far as I know Etvos experiment tested the weak principle. For the future
STEP experiment, I don't know.
2- The second issue is the validity of gravitational law for short distance,
let say under the millimeter range . Some of these very accurate
experiments should detect some anomaly in Newton law, for such distances (
extra dimensions theories).
Jacques
colone...@yahoo.com
On 18 Sep 2003, Brad Eckert wrote:
> After some further looking, I found that the Equivalence Principle has
> been tested to 10^-13 precision so I won't bother trying to break the
> Genreal Theory of Relativity.
>
> Of course, when I'm stuck in traffic fantasizing about anti-gravity
> devices the thought does cross my mind.
Well, antigravity devices aren't ruled out as such. Look for, I think,
Robert Forward (amoung others). His involve spinning sets of black holes
though, and if you had a black hole or two handy you might come up with a
quicker solution to your traffic problem.
"In what police decribed as an unusual case of road rage today..."
3ch
Stephen Speicher
> > [Moderator's note: I think you're talking about the Eotvos experiment;
> > it's been replicated in many ways, and to the best of our knowledge
> > it's *not* the case that some metals fall faster than others. - jb]
> After some further looking, I found that the Equivalence Principle has
> been tested to 10^-13 precision so I won't bother trying to break the
> Genreal Theory of Relativity.
You should not feel embarrassed nor reluctant to pursue the
notion of testing the equivalence principle. Some of the most
interesting and technologically advanced methods are currently
being imployed for precisely that purpose -- the newer tests of
the equivalence principle go beyond the standard Eotvos-type
experiments. For a nice short review of this, with a multitude
of references, see "Principles of Equivalence: Their Role in
Gravitation Physics and Experiments That Test Them," M.P. Haugan
and C. Laemmerzahl, pp. 195-212, in the book "Gyros, Clocks,
Interferometers...: Testing Relativistic Gravity in Space,"
Edited by C. Laemmerzahl, et al., _Springer_, 2001.
As an example of one of the new approaches to testing the
equivalence principle, the STEP (Satellite Test of the
Equivalence Principle) project has as its goal the advancement of
the 10^13 accuracy which you mention above, to the level of
10^-18. For a nice in-depth discussion of the STEP project, see
"STEP: A Status Report," N. Lockerbie, et al., pp. 213-247, in
the same book referenced above. Or, for a brief introduction to
STEP online, see <http://einstein.stanford.edu/STEP/>
Stephen Speicher
On Fri, 19 Sep 2003, Jacques Fric wrote:
> 2- The second issue is the validity of gravitational law for short
> distance, let say under the millimeter range . Some of these very
> accurate experiments should detect some anomaly in Newton law, for
> such distances ( extra dimensions theories).
The words "should detect some anomaly" is already a presumption.
Note that some restrictions have already been placed on "extra
dimension theories" based on an actual submillimetre experiment.
See "Upper limits to submillimetre-range forces from extra
space-time dimensions," Joshua C. Long, et al., _Nature_, V. 421,
pp. 922-925, 27 February 2003.
Also see "Short-Range Searches for Non-Newtonian Gravity,"
Michael C. M. Varney, et al., pp. 11-16 in "Matters of Gravity,"
Number 22, Fall 2003. Available online at:
<http://www.phys.lsu.edu/mog/mog22/mog22.html>
John Devers
Silicon joins race to redefine the kilogram
Patrick Van Esch
> Note that some restrictions have already been placed on "extra
> dimension theories" based on an actual submillimetre experiment.
Note also the experimental paper:
http://arxiv.org/PS_cache/hep-ph/pdf/0306/0306198.pdf
There was a follow-up focussing on the restriction of deviations from
Newton's law using this result which was significant, but I don't have
the reference here...
cheers,
Patrick.
robert bristow-johnson
than a year ago, but after learning a new word ("metrology"), and seeing
more and more papers and websites saying stuff like "Gravitational force is
very weak, incomprehensibly weaker than electrostatic force" (from
http://www.phys.ufl.edu/~korytov/phy2049/new_notes/chapter_22.pdf ) when
they are comparing apples to oranges, I wanted to restate some ideas for you
heavyweights out there.
I think Frank Wilczek said it best (June 2001 Physics Today): "We see that
the question it poses is not, 'Why is gravity so feeble?' but rather, 'Why
is the proton's mass so small?' For in Natural (Planck) Units, the strength
of gravity simply is what it is, a primary quantity, while the proton's mass
is the tiny number [1/13 quintillion]."
http://www.physicstoday.org/pt/vol-54/iss-6/p12.html
The strength of gravity is simply what it is and the strength of E&M simply
is what it is (and it operates on a different quantity so it can't be
compared directly to gravity).
Given the commonly accepted definition of G, we have Newton's Eq.:
F = G * (M*m)/r^2
which is the same as
F = (4*pi*G) * (M*m)/(4*pi*r^2)
So the gravitational flux emanating from the mass M is simply M and the the
flux density at distance r is M/(4*pi*r^2). _If_ 4*pi*G was normalized (by
judicious choice of natural units), then to get the force applied to mass m,
you would simply multiply m by the flux density M/(4*pi*r^2). That is why
4*pi*G should be normalized by judicious choice of "Natural Units" rather
than just G as Planck did.
You can, of course do the same song-and-dance with E&M forces and the
Coulomb Force Law and that is what IS commonly done in E&M classes by
defining epsilon0 = 1/(4*pi*k) and using that constant rather than the
Coulomb Force Constant, "k". In both E&M Maxwell's Equations and the GEM
counterparts, the constants you see are epsilon0 and mu0 (or sometimes
epsilon0 and c) and it is those that should be normalized to obtain
definitions of the most natural units. In fact, I think it would be elegant
if Maxwell's Eqs. were expressed in terms of Z0 (the characteristic
impedance of free space) and c rather than epsilon0 and mu0, but in any
case, all of those constants should be normalized to unity by judicious
choice of units.
In my opinion, there are 4 fundamental units to define from which nearly
everything else can be derived. This has been the topic of dispute between
some physics heavyweights: http://xxx.lanl.gov/pdf/physics/0110060 but
none of those guys look at electric charge as being a unique and fundamental
physical quantity whereas I *do*.
Rather than restating all of Maxwell's equations and the GEM counterparts,
to be most concise, I would propose to define a set of units for time [T],
length [L], mass [M], and electric charge [Q] so that the bracketed
constants in the following 4 field equations would take on a numerical value
of one.
E = m * {c^2} {c^2 -> 1}
E = {hbar} * omega {hbar -> 1)
F = {4*pi*G} * (M*m)/(4*pi*r^2) {4*pi*G -> 1}
F = {4*pi*k} * (Q*q)/(4*pi*r^2) {4*pi*k -> 1} or ...
= 1/{epsilon0} * (Q*q)/(4*pi*r^2) {epsilon0 -> 1}
Given common definitions relating force, momentum, energy and the like to
mass, length, and time:
the unit velocity: [V] = [L]/[T] (which should come out to be c)
the unit momentum: [P] = [M]*[V]
the unit force: [F] = [P]/[T]
the unit energy: [E] = [F]*[L]
the unit power: [W] = [E]/[T]
Given all that, you get:
[M]*[L]^2/[T]^2 = [M] * c^2 (same as [L]/[T] = c)
[M]*[L]^2/[T]^2 = hbar * 1/[T]
[M]*[L]/[T]^2 = 4*pi*G * [M]^2/[L]^2
[M]*[L]/[T]^2 = 4*pi*k * [Q]^2/[L]^2
= 1/epsilon0 * [Q]^2/[L]^2
This simply says that:
1. One unit of mass is equivalent to one unit of energy (or
equivalently, the unit velocity is the speed of light).
2. A particle or photon with one unit of radian frequency in its wave
function shall have one unit of energy.
3. The force applied to a unit mass in one unit of gravitational flux
density shall be one unit of force and a single unit of
gravitational flux density shall result from a unit mass
distributed over a unit area.
4. The force applied to a unit charge in one unit of electrostatic flux
density shall be one unit of force and a single unit of
electrostatic flux density shall result from a unit charge
distributed over a unit area.
(Because of the relationship of electromagnetic force and gravitomagnetic
force and special or general relativity, those fundamental constants such as
mu0 are derived and will also come out well normalized in the wash.)
Isn't that the most *natural* way to define these "natural units"? How can
it not be? If you solve for [T], [L], [M], and [Q] you get:
[T] = sqrt( hbar*(4*pi*G)/c^5 )
[L] = sqrt( hbar*(4*pi*G)/c^3 ) = c*[T]
[M] = sqrt( hbar*c/(4*pi*G) )
[Q] = sqrt( hbar*c/(4*pi*k) ) = sqrt( hbar*c*epsilon0 )
= e/sqrt(4*pi*alpha)
And, of course, the derived natural units for [V], [P], [F], [E], and [W]
come out as above.
unit velocity: [V] = [L]/[T] = c
unit momentum: [P] = [M]*[V] = sqrt( hbar*c^3/(4*pi*G) )
unit force: [F] = [P]/[T] = c^4/(4*pi*G)
unit energy: [E] = [F]*[L] = sqrt( hbar*c^5/(4*pi*G) )
unit power: [W] = [E]/[T] = c^5/(4*pi*G)
The natural electrical units come out nicely and, in particular, the natural
unit for resistance,
[Z] = [Voltage Unit]/[Current Unit] = ([E]/[Q]) / ([Q]/[T])
= ([M]*[V]^2*[T]) / [Q]^2
= ([M]*[L]^2) / ([T]*[Q]^2)
= 1/(c*epsilon0) = sqrt(mu0/epsilon0)
= Z0 (the Characteristic Impedance of Free Space)
So, in addition to normalizing the speed of propagation of E&M waves, the
Characteristic Impedance of Free Space of propagation of E&M waves has also
been normalized to unity. (This is more obviously true since both c and
epsilon0 and consequently mu0 have been normalized to unity, so Z0 must also
be. In fact, in any system of units, a satisfying expression of Maxwell's
Equations can leave out epsilon0 and mu0 completely and use c and Z0
instead. When these natural units are used, all four take on a numerical
value of 1.)
Of course, neither the Elementary Charge, e, nor the e/3 in some quarks are
normalized.
e = sqrt(4*pi*alpha) * [Q] = 0.30282212 * [Q]
So it appears that the amount of electric charge (expressed in natural
units) that Nature has bestowed upon the electron is 0.30282212 . This,
rather than 137.03599976 is the number that theoretical physicists should
put up on their walls, in my opinion. The Fine-Structure Constant can be
thought of as being the value that it is because of the amount of charge,
measured in natural units, that electrons, protons, and other charged
particles happen to have been assigned by Nature herself. (An anthropic
principle can probably be applied. If the charge of an electron was
anything different, alpha would be different, and all sorts of physical
manifestations would be different, and we likely wouldn't be around to be
thinking nor talking about it.)
Regarding gravito-electromagnetism ("GEM", whose counterparts to Maxwell's
Equations look identical to Maxwell's if the corresponding symbols are
substituted), if and only if {4*pi*G} is normalized to 1 can you also make
the same claim about the Characteristic Impedance of Free Space of
propagation of GEM radiation being normalized to unity. This is why I wish
Planck had chosen to normalize 4*pi*G rather than just G in his choice of
natural units.
Of course that leaves a "2" in the famous Einstein Equation of General
Relativity:
G = 8*pi*G * T
uv uv
becomes (using natural units)
G = 2 * T
uv uv (monospaced font is needed to view this correctly)
and many have suggested that the 8*pi*G be normalized rather than 4*pi*G,
leaving no "2" in the Einstein Equation. But it seems more important to me
to treat E&M and GEM more identically (as far as metrology is concerned) so
that in *both* E&M and GEM radiation, both the speed of propagation and the
characteristic impedance of radiation in free space should be normalized to
1 with a judicious choice of units. In addition, that "2" doesn't bother me
very much as there is also a 1/2 left in Schrodinger's Eq. even with hbar
normalized to 1.
Of course, not *all* constants in fundamental physical equations go to 1,
but before considering any bodies or particles or "things" in free space, we
should first just consider the equations governing free space with no
*particular* particle in mind, derive a meaningful set of natural units
(that gets rid of, or normalizes, the most basic fundamental constants), and
then see how particles or "things" found in that free space are measured in
those natural units.
r b-j
robert bristow-johnson
i prefer Peter Mohr's and Barry Taylor's proposal:
"The kilogram is the mass of a body at rest whose equivalent energy equals
the energy of a collection of photons whose frequencies sum to 135639274 x
10^42 hertz."
i got it from http://ejde.math.swt.edu/conf-proc/04/m1/mohr.pdf
that number should be c^2/h = 299792458^2/6.62606876e-34 = 1.35639277e50
i dunno why i differ from Mohr in the last digit, but what the hey..
if only we had a really good measurement of G so we could simple define the
meter, kilogram, and second directly in terms of the Planck Units. that
would be nice, IMHO.
r b-j
[Moderator's note: alas, G is the most poorly measured of all
fundamental constants, and it will remain so unless someone gets
a really good new idea, since gravity is so weak. - jb]
Starblade Darksquall
johnd...@iprimus.com.au (John Devers) wrote in message news:<6f838e26.03091...@posting.google.com>...
> You guys might like the latest on using the Avogadro constant to redifine mass.
>
>
>
> Silicon joins race to redefine the kilogram
>
>
> http://physicsweb.org/article/news/7/9/9
See? A kilogram ISN'T some stupid piece of mass located on some
physical place on earth. It is a REAL thing.
Now, all that remains is to eventually define mass in terms of energy,
and set h as a constant. They did that with space, afterall.
Personally, I think it would be an improvement.
(...Starblade Riven Darksquall...)
John Devers
> [Moderator's note: alas, G is the most poorly measured of all
> fundamental constants, and it will remain so unless someone gets
> a really good new idea, since gravity is so weak. - jb]
If you tell me what the wavelenght of gravity waves are I'll have a
think about it;-) Is there a nobel prize in it?
Maybe 2 giant mirrors (yep the mirrors and casimir effect again) if
you get them just the right distance apart they should exclude gravity
waves at a certain point, I'm not sure if that should push or pull the
mirrors apart in this case though?
Ken S. Tucker
Something that has always puzzled me about gravity
constant K, it doesn't seem to be an invariant.
Using basic dimensional analysis from
F = m s / t^2 = K m m / s^2,
and using s =ct , c = invariant light speed =1 gives
K = t/m,
and Plancks's constant h = Et = (mc^2) t = mt =
invariant.=1 so t=1/m.
Thus K transforms like t^2. Spacetime is naturally
represented by contravariant components like dx^u,
meaning the gravitational constant would appear to
require a transformation like K^uv or a tensor density
like K = k*|g^uv| , where k is invariant.
Using the same dimensional reasoning the gravitational
potential K m / s = (t^2) m / s = h/c = invariant.
Is it reasonable for the g-potential to be invariant?
Well I think so because Einsteins G_uv looks to me
like a tensor expression of
Nabla^2 (g-potential), (Nabla = Gradient symbol),
(from Laplace's and Poisson's equations).
which can be treated as a second covariant derivative
like (g-potential);u;v => G_uv
in which case the g-potential is a scalar invariant, as
used in Schwarzschilds solution. Physically, experiment
seems to confirm the invariance of the g-potential, and
gives some credence to the idea that K is a relative
constant.
Could the gravitational constant K be either
1) a 2nd rank tensor like A^uv ?
2) a tensor density of weight -2 ?
I hesitated to question if K is a scalar invariant,
expecting I've made some simple error I can't find,
but if there is a remote chance that K is not a scalar
invariant, then we may need to define an invariant like,
Invariant k = |g_uv| K, or k = g_uv K^uv.
and not expect Newtons Gravitational *constant*
to be a constant. Finally, can we prove K is a
scalar invariant beyond reasonable doubt?
Regards
Ken S. Tucker
Ray Tomes
> How constant is the gravitational constant?
Well if G was varying as much as the meaurements of G it would be pretty =
obvious in the orbits of GPS satellites or planets distances measured by =
radar, unless the timescale of variation was very small. So it is=20
reasonable to assume that the variations are due to some other factor,=20
possibly our incomplete understanding.
> I once heard of an experiment in which weights of different metals
> such as brass, iron, lead, bismuth, etc. were dropped and the travel
> time was measured. The result was that some metals fell slightly
> faster or slower than others. Does anyone have any information on such
> an experiment?
There is an experiment in which the weight of different substances=20
including Gold, Lead, Silver, Bronze, Aluminium and Water are found to=20
vary relative to each other with altitude. All known possible variations =
due to pressure, temperature etc have been eliminated and the effect=20
persists over many years. The weights were not dropped but weighed, but=20
perhaps this is the experiment that you want.
These experiments have been performed by Mario Nanni and several=20
articles relating to them are in Apeiron. I think that these=20
experiments grew out of the earlier suggestive E=F6tv=F6s experiments.
Nanni, M. 1997. "Simple Experiments to Test the Dependence of=20
Gravitational Action on Chemical Composition", Apeiron, vol. 4, no. 1
Nanni, M. 2000, "Dependence of Gravitational Action on Chemical=20
Composition: New Series of Experiments", Apeiron, vol. 7, no. 3 -4
Nanni, M. 2001, "Gravitational Differences of a Chemical Nature"=20
Apeiron, Vol. 8, No. 1, January 2001.
The variations are of the order of several parts in 10^-5 and many times =
larger than the experimental errors. I think the altitude difference is=20
several thousand meters.
It seems to me that if these effects are real then they might also show=20
up in measurements of isotope masses (although these are performed in a=20
different way) if they have been done at different altitudes. The=20
variation in altitude of the isotope mass measuring laboratories is=20
likely to be a lot less than the work done by Nanni, but the accuracy is =
also correspondingly greater. Does anyone know where one might obtain=20
isotope mass measurements listed by different laboratories?
Ray Tomes
Lubos Motl
> If you tell me what the wavelength of gravity waves are I'll have a
> think about it;-)
It is any number between 0 and infinity. Or did you want to ask about
some specific binary stars or supernovae?
> Is there a nobel prize in it?
It is likely. You made a good start to win the prize when you asked the
previous question!
> Maybe 2 giant mirrors (yep the mirrors and casimir effect again) if
> you get them just the right distance apart they should exclude gravity
> waves at a certain point, I'm not sure if that should push or pull the
> mirrors apart in this case though?
Do you know a mirror that reflects gravitational waves?
Concerning the sign of the energy. My guess is that the Casimir energy
does not care about the attractive character of the force, and it just
counts the frequencies of the modes and they are probably similar to the
electromagnetic case. Unless something is very different about the
boundary conditions, the sign of the Casimir force should be the same.
______________________________________________________________________________
E-mail: lu...@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
phone: work: +1-617/496-8199 home: +1-617/868-4487
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Superstring/M-theory is the language in which God wrote the world.
J. J. Lodder
> Something that has always puzzled me about gravity
> constant K, it doesn't seem to be an invariant.
> Using basic dimensional analysis from
> F = m s / t^2 = K m m / s^2,
> and using s =ct , c = invariant light speed =1 gives
>
> K = t/m,
>
> and Plancks's constant h = Et = (mc^2) t = mt =
> invariant.=1 so t=1/m.
snip
> Finally, can we prove K is a
> scalar invariant beyond reasonable doubt?
You are confusing two things:
units and dimensions on one hand,
and transformation character on the other hand.
As for the dimensions: you obtain the result [G] = [T]^2
by putting hbar = 1, [h] = [I] (hbar equals one and is dimensionless)
While this is a valid choice, it is not a necessary one.
You can also define G = 1 [G] = [I] (G equals one and is dimensionless)
hbar then aquires a dimension and a value.
One choice cannot be more right than the other,
it can at best be more convenient.
As for transformation character: G occurs at the most fundamental level
so far in the Einstein equation.
This is an equation between tensors,
with well defined transformation character,
in which G appears as a scalar.
You can put in units and dimensions into the Einstein equation
in any way you want. (while being consistent about it)
The transformation character of G wont be changed by it.
Best,
Jan
robert bristow-johnson
In article BB9A66C7.3EF5%r...@surfglobal.net, robert bristow-johnson at
r...@surfglobal.net wrote on 09/29/2003 13:14:
> if only we had a really good measurement of G so we could simple define the
> meter, kilogram, and second directly in terms of the Planck Units. that
> would be nice, IMHO.
>
> fundamental constants, and it will remain so unless someone gets
> a really good new idea, since gravity is so weak. - jb]
it would be extravagant, but couldn't some experiment be set up in space
with some pretty large and accurately known masses orbiting around each
other at an accurately known set distance? the frequency of revolution
could be precisely measured and that would be a function of G. it might
take a couple of shuttle missions.
r b-j
J. J. Lodder
Starblade Darksquall <Starb...@Yahoo.com> wrote:
> johnd...@iprimus.com.au (John Devers) wrote in message
news:<6f838e26.03091...@posting.google.com>...
> > You guys might like the latest on using the Avogadro constant to
redifine mass.
> >
> >
> >
> > Silicon joins race to redefine the kilogram
> >
> >
> > http://physicsweb.org/article/news/7/9/9
>
> See? A kilogram ISN'T some stupid piece of mass located on some
> physical place on earth. It is a REAL thing.
What could be more real than a piece of platinum? I could hit you with
it, and you would feel the consequences as a nasty bump on the head.
It is the replacement (some e digits on a piece of paper,
or some bits floating around in cyberspace)
which is unreal.
From a fundamental point of view nothing much is going to change.
After all, the kilogram -is- the mass of a fixed number of platinum
atoms, stored in a vault at Sevres. What is going to change is not the
number, but our knowledge about it.
Redefining the kilogram is replacing one arbitrary standard by another.
This has many practical advantages (reproducibility, portability,
stability, etc), but no conceptual ones.
From a metrology point of view what is happening is that the accuracy to
which Avogadro's number can be measured will be limited only by the
accuracy to which the kilogram can be reproduced. Claims of this have
been around for some time, but they are still false. There are
systematic, and as yet unexplained differences between results obtained
by different groups. The kilogram cannot be redefined untill these
problems have been resolved. (Or the errors systematised :-)
Best,
Jan
Ken S. Tucker
nos...@de-ster.demon.nl (J. J. Lodder) wrote in message news:<1g25a15.10o...@de-ster.xs4all.nl>...
>Ken S. Tucker <dyna...@vianet.on.ca> wrote:
>> Something that has always puzzled me about gravity
>> constant K, it doesn't seem to be an invariant.
>> Using basic dimensional analysis from
>> F = m s / t^2 = K m m / s^2,
>> and using s =ct , c = invariant light speed =1 gives
>> K = t/m,
>> and Plancks's constant h = Et = (mc^2) t = mt =
>> invariant.=1 so t=1/m.
>snip
>> Finally, can we prove K is a
>> scalar invariant beyond reasonable doubt?
>You are confusing two things:
>units and dimensions on one hand,
>and transformation character on the other hand.
Or was too brief with definitions, hope to improve...
>As for the dimensions: you obtain the result [G] = [T]^2
>by putting hbar = 1, [h] = [I] (hbar equals one and is dimensionless)
>While this is a valid choice, it is not a necessary one.
>You can also define G = 1 [G] = [I] (G equals one and is dimensionless)
>hbar then aquires a dimension and a value.
>One choice cannot be more right than the other,
>it can at best be more convenient.
IMHO...
Generally we cannot make physically measureable
quantities like Length, Time and Mass be invariant,
(although we may transform the measurements to
invariants, like ds^2 = g_uv dx^u dx^v does for
spacetime displacements).
Likewise we can't arbiturarily assign G=1 which
sets G to an invariant.
Invariants are experimentally determined to
be invariant, such as speed of light c, Plancks
constant h and fundamental charge q.
Let me explain what I mean by *invariant*.
Suppose you place 10 Timex watches in a box,
then relative to any Frame of Reference, there is
10 Timex's in the box, so 10 is invariant, because
it is a pure dimensionless number like 1 is.
OTOH the shape of the box, the inertia of the
contents and the time rate of the Timex's are all
relative quantities. The suggestion that we may
arbituarily set G=1 is like suggesting we can make
the length of the box=1, and that would require a
preferred FoR.
For a hard physics example, consider *electrical
potential energy* for a system of two relatively
stationary charges q and Q,
E = q*Q/r,
The invariance of q and Q is established beyond
reasonable doubt, (I won't prove it here) so,
E*r = q*Q = E'*r' and E*r = E'*r',
is required to retain the invariance of q*Q in all
FoR's. (Please note that I specified q and Q to be
at relative rest so magnetic fields do not occur).
If this system is at rest in Coordinate System CS,
but moving relative to CS' then the Energy E' of the
system will have a larger measurement than the
measurement of Energy E relative to CS.
Furthermore, as a consequence of the invariance
of q*Q , r' < r, and is commonly known as Lorentz
contraction.
The box experiment provides a good reason to
equate invariants to pure numbers in relativity,
so I can select units where the physically proven
invariants, c, h, q =1.
>As for transformation character: G occurs at the most fundamental level
>so far in the Einstein equation.
>This is an equation between tensors,
>with well defined transformation character,
>in which G appears as a scalar.
At first I found what you suggest, but then realized
using the *relativity of dimensions* reasoning I've
employed (see my first post to this thread),
that the gravitational potential Phi, is the important
invariant. Effects of General Relativity are predicted
by the Schwarzschild Solution, and SS has as a
primary varible Phi. However this variable, has the
same value when the progression of orbital perihelion
are considered, or when light is deflected, inspite of
the very large differences of velocity.
>You can put in units and dimensions into the Einstein equation
>in any way you want. (while being consistent about it)
>The transformation character of G won't be changed by it.
I've provided my reasoning in a detailed manner, and find
Big G to be relativistic, ie Frame dependant. You seem to
be suggesting it is possible to have units consistent with
c=h=q=1 and G=1?
>Best, Jan
Thanks and the same, hope I improved...
Ken S. Tucker
Uncle Al
>
> Brad Eckert wrote:
> > How constant is the gravitational constant?
[snip]
> There is an experiment in which the weight of different substances
> including Gold, Lead, Silver, Bronze, Aluminium and Water are found to
> vary relative to each other with altitude. All known possible variations
> due to pressure, temperature etc have been eliminated and the effect
> persists over many years. The weights were not dropped but weighed, but
> perhaps this is the experiment that you want.
>
> These experiments have been performed by Mario Nanni and several
> articles relating to them are in Apeiron. I think that these
> experiments grew out of the earlier suggestive E=F6tv=F6s experiments.
>
> Nanni, M. 1997. "Simple Experiments to Test the Dependence of
> Gravitational Action on Chemical Composition", Apeiron, vol. 4, no. 1
>
> Nanni, M. 2000, "Dependence of Gravitational Action on Chemical
> Composition: New Series of Experiments", Apeiron, vol. 7, no. 3 -4
>
> Nanni, M. 2001, "Gravitational Differences of a Chemical Nature"
> Apeiron, Vol. 8, No. 1, January 2001.
>
> The variations are of the order of several parts in 10^-5 and many times
> larger than the experimental errors. I think the altitude difference is
> several thousand meters.
[snip]
A 10^(-5) difference/average with changing altitude or whatever would
be insanely large and have monstrous thermodynamic consequences.
Calculate the temperature difference of a one gram mass changing by 10
micrograms, E=mc^2. It is not a subtle thing. Nanni's experiments are
balderdash. The moon (mostly Al, Si, O with no iron core to speak of)
would be gravitationally different from the Earth (huge iron core
nearly the size of Mars) as they fell around the sun and each other
certainly given measured orbital eccentiricities. This has been
specifically addressed (Nordtvedt effect, etc.) and it isn't there to
be seen to parts per 10^12.
*All* compared masses no matter what variable(s) have been contrasted
are utterly indistinguishable to at least one part in two trillion
weight vector difference/average, 0.5x10^(-12). This is 100%
unaffected by the local environment as demonstrated in Fifth Force
studies (Fleischbach, Newman, and a bunch of others). An Eotvos
balance is a vertically suspended torsion pendulum with two sets of
test masses 180 degrees apart at its periphery. Plane mirrors on the
rotor form one end of a very long optical interferometer. If the
masses do not fall identically as the Earth gravitationally falls
around the sun and inertially spins on its axis, the rotor underges
diurnal rotation torque balanced by fiber torque. The otherwise
nulled interferometer gives a 24-hr sinusoidal signal. It has never
happened.
Actually dropping lumps in vacuum, Dr. Faller in Colorado more than a
mile above sea level, gives invariant inertial vs. gravitational mass
to several parts per billion.
Nanni's experiments are balderdash. Composition appears in no theory
of gravitation. Any observable coupled to an internal symmetry by
Noether's theorem cannot interact with rotation or translation by the
definition of internal symmetry,
http://www.mazepath.com/uncleal/eotvos.htm#b21
There is only one external symmetry-coupled test mass observable that
has never been quantitatively examined. All gravitation theories are
either symmetric (e.g., metric theories) or antisymmetric (e.g., some
affine and then teleparallel theories) to parity transformation. Test
mass quantitative parity divergence arises from atom coordinates
alone, measured on a normalized scale of CHI=0 (achiral) to CHI=1
(perfect parity divergence). Parity eotvos experiments in unmodified
apparatus contrasting chemically and dimensionally identical
alpha-quartz single crystal test masses in crystallographic space
groups P3(1)21 and P3(2)21 are proposed. Both explicit calculation of
a 3.34x10^14 atom model and a pure geometric model yield CHI >
1-(1.48x10^(-16)). It is shown that parity Eotvos experiment
Equivalence Principle violation is >520 times that allowed for
composition experiments, suggesting empirically measurable failure of
the weakest general relativity founding postulate.
If Nanni's results had any reality about them at all, there would be
riots in the streets (or at least at APS meetings).
(Do something naughty to physics)
Uncle Al
Perturbations would destroy you - even light pressure, certainly solar
wind. Large masses are measurable to ppm. They won't get you
anything. The solar sytem is dirty with gravitational perturbations -
all that mass moving as planets and such. The kilogram is the only SI
fundamental quantity that has no first principles standard. Mass
*cannot* be measured more accurately than the Paris kilogram.
http://www.phys.lsu.edu/mog/mog13/node11.html
Not so good.
www.physics.uci.edu/gravity/papers/LondonGPaper.pdf
Better.
http://www.phys.lsu.edu/mog/mog16/node8.html
http://www.npl.washington.edu/eotwash/gconst.html
http://www.npl.washington.edu/eotwash/pdf/prl85-2869.pdf
Much better.
Science 288(5468) 944 (2000)
Phys. Rev. Lett. 89 161102 (2002)
The two citations together are definitive because they cook the same
number from two wildly different kinds of measurements. If you want a
short route to a believable better value of Big G, then you improve
upon the U/Wash apparatus in terms of function and isolation.
robert bristow-johnson
Uncle Al <Uncl...@hate.spam.net> wrote in message news:<3F7E0C1C...@hate.spam.net>...
> robert bristow-johnson wrote:
> >
> > In article BB9A66C7.3EF5%r...@surfglobal.net, robert bristow-johnson at
> > r...@surfglobal.net wrote on 09/29/2003 13:14:
> >
> > > if only we had a really good measurement of G so we could simple define the
> > > meter, kilogram, and second directly in terms of the Planck Units. that
> > > would be nice, IMHO.
> > >
> > > [Moderator's note: alas, G is the most poorly measured of all
> > > fundamental constants, and it will remain so unless someone gets
> > > a really good new idea, since gravity is so weak. - jb]
> >
> > it would be extravagant, but couldn't some experiment be set up in space
> > with some pretty large and accurately known masses orbiting around each
> > other at an accurately known set distance? the frequency of revolution
> > could be precisely measured and that would be a function of G. it might
> > take a couple of shuttle missions.
>
> Perturbations would destroy you - even light pressure, certainly solar
> wind. Large masses are measurable to ppm. They won't get you
> anything. The solar sytem is dirty with gravitational perturbations -
> all that mass moving as planets and such.
why is it then that the Earth has orbitted so stably around the Sun
for so long that life could evolve and not get burned up or frozen
solid from the perturbations accumulating (as in the "Drunk's Walk"
random process) and the orbit changing sufficiently (eventually, as in
many million years)?
> The kilogram is the only SI
> fundamental quantity that has no first principles standard.
sure it can. isn't that what Mohr at NIST has proposed to do
(redefine the kilogram in terms of hbar and c in a similar way to how
the meter was redefined)?
> Mass *cannot* be measured more accurately than the Paris kilogram.
>
...
> http://www.phys.lsu.edu/mog/mog16/node8.html
...
> If you want a
> short route to a believable better value of Big G, then you improve
> upon the U/Wash apparatus in terms of function and isolation.
i haven't looked at all of the references nor can claim that i
understand the detail of this one, but i have 2 questions. Does NIST
agree with the results and validity of the U/Wash experiment? if so,
i would expect them to change their value or at least cite a pending
(and possibly provisional) update. And, if more significant digits get
into G than the number of atoms in the Paris kilogram, wouldn't that
contradict your assertion?
i dunno.
r b-j
Uncle Al
Orbits tend to be equilibrium processes. Random perturbations
cancel. When things aren't random you get resonant orbital locking to
planet ejection. Look up digital orrerys. No projection can be
accurate because no degree of accuracy is sufficient given positive
feedback. One runs a sheaf of models and learnedly goes "hmmmm" in
the literature.
The Earth is nowhere near stable! Compare the Carboniferous Period to
the Ice Ages, the Maunder Minimum to contemporary climate. If you
were a Canadian earthworm you went extinct when big ice arrived, ditto
Jamestown and a blip. Look at how Enviro-whiners howl about the
normal evolution of an interglacial period. The Garden of Eden is
returning - warm and wet. Live with it.
> > The kilogram is the only SI
> > fundamental quantity that has no first principles standard.
>
> sure it can. isn't that what Mohr at NIST has proposed to do
> (redefine the kilogram in terms of hbar and c in a similar way to how
> the meter was redefined)?
Push come to shove, a standard must be measurable and reproducible at
will. Atomic clocks are easy. There is no evidence that even hints a
fundamental kilogram is in the works. There is something wrong with
mass. It never appears in the Standard Model except as a jury rig.
Gravitation theory of whatever ilk is remarkably coy about mass.
Given reduction to practice, a kilogram is too bloody big. A gram is
reasonable.
> i haven't looked at all of the references nor can claim that i
> understand the detail of this one, but i have 2 questions. Does NIST
> agree with the results and validity of the U/Wash experiment? if so,
> i would expect them to change their value or at least cite a pending
> (and possibly provisional) update. And, if more significant digits get
> into G than the number of atoms in the Paris kilogram, wouldn't that
> contradict your assertion?
Science 288(5468) 944 (2000)
Phys. Rev. Lett. 89 161102 (2002)
Taken together, these two results are more credible than all that have
gone before. The measurement modalities are wholly disparate. One
could be naughty and say that local values of G can be (unknowlingly -
aside from tides, sprinklers, and rush hours) influenced in far
decimal places... but my vote goes to subtle errors in apparatus or
software.
Suppose it were spacetime torsion rather than spacetime curvature and
the Equivalence Principle was facile coincidence rather than dictum.
Deviations around 1000 parts-per-trillion difference vs. average would
still be astonishing and 100 ppt amazing - and all subject to time of
day (phase angle between Earth's gravitational free fall around the
sun and inertial spin of the Earth about its axis). You'd see diurnal
modulation in the data collection.
> And, if more significant digits get
> into G than the number of atoms in the Paris kilogram, wouldn't that
> contradict your assertion?
3x10^24 significant digits? Learn more chemistry and physics before
you pronounce judgement on either. Yours was an unforgivable
statement.
Starblade Darksquall
> On Wed, 1 Oct 2003, John Devers wrote:
>
> > If you tell me what the wavelength of gravity waves are I'll have a
> > think about it;-)
>
> It is any number between 0 and infinity. Or did you want to ask about
> some specific binary stars or supernovae?
>
Really though, Lubos is right, there is no particular wavelength that
all gravity waves must exhibit.
> > Is there a nobel prize in it?
>
> It is likely. You made a good start to win the prize when you asked the
> previous question!
>
> > Maybe 2 giant mirrors (yep the mirrors and casimir effect again) if
> > you get them just the right distance apart they should exclude gravity
> > waves at a certain point, I'm not sure if that should push or pull the
> > mirrors apart in this case though?
>
> Do you know a mirror that reflects gravitational waves?
>
Wait... at first I thought you were saying that mirrors DID reflect
gravitational waves.
I'm not sure if such a mirror could be constructed... gravity goes
right through everything. The only thing it doesn't go through are
black holes, but it does goes around them.
> Concerning the sign of the energy. My guess is that the Casimir energy
> does not care about the attractive character of the force, and it just
> counts the frequencies of the modes and they are probably similar to the
> electromagnetic case. Unless something is very different about the
> boundary conditions, the sign of the Casimir force should be the same.
>
There is something fundamentally different between gravity waves and
most other kinds of waves. Given that we don't have a quantum theory
of gravity, I doubt any questions, including those concerning Casimir
forces with gravity, can be properly answered.
______________________________________________________________________________
> E-mail: lu...@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
> phone: work: +1-617/496-8199 home: +1-617/868-4487
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> Superstring/M-theory is the language in which God wrote the world.
(...Starblade Riven Darksquall...)
Starblade Darksquall
> >
> > In article BB9A66C7.3EF5%r...@surfglobal.net, robert bristow-johnson at
> > r...@surfglobal.net wrote on 09/29/2003 13:14:
> >
> > > if only we had a really good measurement of G so we could simple define the
> > > meter, kilogram, and second directly in terms of the Planck Units. that
> > > would be nice, IMHO.
> > >
> > > [Moderator's note: alas, G is the most poorly measured of all
> > > fundamental constants, and it will remain so unless someone gets
> > > a really good new idea, since gravity is so weak. - jb]
> >
> > it would be extravagant, but couldn't some experiment be set up in space
> > with some pretty large and accurately known masses orbiting around each
> > other at an accurately known set distance? the frequency of revolution
> > could be precisely measured and that would be a function of G. it might
> > take a couple of shuttle missions.
>
> Perturbations would destroy you - even light pressure, certainly solar
> wind. Large masses are measurable to ppm. They won't get you
> anything. The solar sytem is dirty with gravitational perturbations -
> all that mass moving as planets and such. The kilogram is the only SI
> fundamental quantity that has no first principles standard. Mass
> *cannot* be measured more accurately than the Paris kilogram.
>
I don't see why you're so against this. It's much better to define the
kilogram in terms of something more easily accessible than the Paris
kilogram.
Personally, I agree with the method outlined in the article cited at
the beginning with this thread.
> http://www.phys.lsu.edu/mog/mog13/node11.html
> Not so good.
> www.physics.uci.edu/gravity/papers/LondonGPaper.pdf
> Better.
> http://www.phys.lsu.edu/mog/mog16/node8.html
> http://www.npl.washington.edu/eotwash/gconst.html
> http://www.npl.washington.edu/eotwash/pdf/prl85-2869.pdf
> Much better.
>
> Science 288(5468) 944 (2000)
> Phys. Rev. Lett. 89 161102 (2002)
>
> The two citations together are definitive because they cook the same
> number from two wildly different kinds of measurements. If you want a
> short route to a believable better value of Big G, then you improve
> upon the U/Wash apparatus in terms of function and isolation.
Would such an apparatus be more accurate in space, where it's further
from Earth's gravitational influence and the potential for seismic,
atmospheric, and other kinds of influence? Or would that just make
things more difficult?
(...Starblade Riven Darksquall...)
Oliver Jennrich
> robert bristow-johnson wrote:
>>
>> In article BB9A66C7.3EF5%r...@surfglobal.net, robert bristow-johnson at
>> r...@surfglobal.net wrote on 09/29/2003 13:14:
>>
>> > if only we had a really good measurement of G so we could simple define the
>> > meter, kilogram, and second directly in terms of the Planck Units. that
>> > would be nice, IMHO.
>> >
>> > [Moderator's note: alas, G is the most poorly measured of all
>> > fundamental constants, and it will remain so unless someone gets
>> > a really good new idea, since gravity is so weak. - jb]
>>
>> it would be extravagant, but couldn't some experiment be set up in space
>> with some pretty large and accurately known masses orbiting around each
>> other at an accurately known set distance? the frequency of revolution
>> could be precisely measured and that would be a function of G. it might
>> take a couple of shuttle missions.
> Perturbations would destroy you - even light pressure, certainly solar
> wind.
Not necessarily so. There are ways to deal with non-gravitational
pertubations up to a point where people hope to fly missions with
residual accelerations of the level of 10^{-16} g/sqrt(Hz). However,
in the Heavens and on Earth, problems are not that different.
Lack of knowlegde of the multipole moments of your mass and the local
gravity and gravity gradients due to your surroundings (you'll need a
spacecraft, after all) will hamber you pretty much the same way as it
does on ground. The only advantage: you don't have to counteract 1g.
> Large masses are measurable to ppm. They won't get you anything.
> The solar sytem is dirty with gravitational perturbations - all that
> mass moving as planets and such.
Indeed. However, having two test masses close enough togehter might
allow you to have them 'jointly free falling' - their geodesics
(ignoring their mutual gravity) can be made almost identical - all
what changes their distance then has to be due to the mutual gravity.
That said, I still have to see a proposal for a mission to measure G
in interplanetray space that has a decent chance to survive the
selection process.
--
Space - the final frontier
Oliver Jennrich
Starblade Darksquall writes:
>Some poor uncited soul wrote:
>> Science 288(5468) 944 (2000)
>> Phys. Rev. Lett. 89 161102 (2002)
>>
>> The two citations together are definitive because they cook the same
>> number from two wildly different kinds of measurements. If you want a
>> short route to a believable better value of Big G, then you improve
>> upon the U/Wash apparatus in terms of function and isolation.
> Would such an apparatus be more accurate in space, where it's further
> from Earth's gravitational influence and the potential for seismic,
> atmospheric, and other kinds of influence? Or would that just make
> things more difficult?
Both. And don't forget 'more expensive'. Space offers a uniquely quiet
environment when it comes to low frequency disturbances. Unfortunately
it offers you unique possibilities for spectacular failure as well.
But to the question: You would not need a torsion balance in space, as
you would not have to counteract Earth's gravity.
robert bristow-johnson
Uncl...@hate.spam.net wrote on 10/16/2003 19:54:
> robert bristow-johnson wrote:
>> And, if more significant digits get
>> into G than the number of atoms in the Paris kilogram, wouldn't that
>> contradict your assertion?
> 3x10^24 significant digits? Learn more chemistry and physics before
> you pronounce judgement on either. Yours was an unforgivable
> statement.
i guess particularly for an engineer. after hitting the "post"
button, i immediately saw the mistake. of course i didn't mean 10^24
significant digits, but i meant the number of significant digits in
the known number of atoms in the Paris kilogram (which is, i presume,
a measure of accuracy on it as a standard of mass). in fact, it is
possible to parse the sentence to mean that (if more significant
digits get into G than [significant digits that get into] the number
of atoms in the Paris kilogram).
anyway, the Mohr redefinition of the kg depends not on G but on c and
hbar which are both known to 9 digits. since the meter was redefined,
c is now an exact constant, and all this kg redefinition would do is
make hbar an exact constant virtually equal to the accepted value
today.
still, if G (or hbar) is ever measured as accurately as we know the
Paris kg, then i still wonder why "Mass *cannot* be measured more
accurately than the Paris kilogram" ?
now to atone for my unforgivable statement.
r b-j
John Devers
> Lubos Motl <mo...@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.03100...@feynman.harvard.edu>...
> > On Wed, 1 Oct 2003, John Devers wrote:
> >
> > > If you tell me what the wavelength of gravity waves are I'll have a
> > > think about it;-)
> >
> > It is any number between 0 and infinity. Or did you want to ask about
> > some specific binary stars or supernovae?
> >
> Maybe the wavelength is h/p? :P
>
> Really though, Lubos is right, there is no particular wavelength that
> all gravity waves must exhibit.
>
Yep sorry, Lubos explained to me via email that,
>>However, photons and gravitons are massless, and the corresponding
>>wavelength would be infinite. There is no preferred distance scale
>>associated with photons.
Ok I believe you:-) so what's the deal with many sites saying the
wavelength of the graviton is theorized to be 4.0507625(38) x 10^-35
m?
http://www.boardbot.com/boards/Archaeologica/925.html
>>In the Casimir effect, the energy in the space in between comes from
all
>>"standing waves" whose wavelengths are divisors of the separation of
the
>>two metallic walls.
Is the Compton wavelength a standing wave that can be a divisor?
>>Wavelength is related - by quantum mechanics - to momentum, and
energy is
>>related to frequency (E=hf), and energy and momentum are constrained
by
>>the conservation laws. So it is not true that you can always create
>>anything with any parameters, but in different experiments you can
create
>>photons of different wavelengths. Atoms emit radiation of some
frequency -
>>some special discrete "spectral lines" are associated with every
elements
>>- and there are also radio waves, X-rays, gamma-rays etc. There are
many
>>possible frequencies that are interesting here or there, but none is
truly
>>relevant for the Casimir effect. The Casimir effect is also "scale
>>invariant" - if you change the separation of the domain walls, all
>>energies will rescale in some way. Very easy, no special points, no
>>discontinuities.
-----------------------------------------------------------------------
PS. Is there any way to prove the casimir force/effect is virtual EMF
and not exclusion of gravity waves?
Michael Petri
"John Devers" <johnd...@iprimus.com.au> schrieb im Newsbeitrag
news:6f838e26.03101...@posting.google.com...
> Ok I believe you:-) so what's the deal with many sites saying the
> wavelength of the graviton is theorized to be 4.0507625(38) x 10^-35
> m?
>
> http://www.boardbot.com/boards/Archaeologica/925.html
4.05 x 10^-35 m is roughly 2.5 times the Planck-Length. However, I don't
know where this factor 2.5 should orginate from. I didn't look at the page
you cited, though (I wouldn't make the effort to look up a page, that makes
the above claim).
Most physicists agree that at the Planck length gravitational effects become
as "strong" as the other - hopefully unified - interactions
(electromagnetic, weak, strong). Probably the author of the above page
confused the scale, where gravity becomes "important" with respect to the
other interactions, with the wavelength of the graviton, which is something
quite different.
In fact, the concept of the graviton as a messenger particle for the
gravitational interaction is basically a low-energy construct. For low
energies it is quite safe to talk about gravitons, but at the Planck energy?
I'm not sure whether this makes much sense. I assume we would need a
non-perturbative description of the graviton at these energies.
But even if we postpone the question, whether the graviton really exists,
what we know so far is, that the graviton - if it exists - must be a spin-2
particle (due to the attractive nature - and the tensor character - of the
gravitational interaction) and it must be a massless particle (due to the
infinite range of the gravitational "interaction"). Therefore its wavelength
depends on its energy. It makes no sense to talk about *the* wavelength of
the graviton.
There is something else, which is quite obscure about the above quoted
numerical value. Obviously the value is somehow related to (or derived from)
the Planck length. But the Planck length depends on the squareroot of the
gravitational constant G, which isn't known very accurately. According to
CODATA 1998 we have:
G = 6.673(10) x 10^-11 m^3 kg^-1 s^-2
meaning that G is known to roughly 0.1 %, i.e. three significant digits.
Taking the square-root halves the relative error, so that the Planck-length
is known to roughly 0.05 %, i.e. 3,5 significant digits. The value quoted
above is far too accurate (7 significant digits).
Best regards, Mike
J. J. Lodder
Uncle Al <Uncl...@hate.spam.net> wrote:
> The kilogram is the only SI
> fundamental quantity that has no first principles standard. Mass
> *cannot* be measured more accurately than the Paris kilogram.
True of course, at present, but untrue in the long term.
But what is relevant is not how accurately the standard can be defined,
or how stable it is, but how accurately it can be reproduced.
And in that respect the Paris kilogram
will lose out soon to a newer standard,
based on a defined value of Avogadro's number.
In more detail: the Paris kg is possibly the most stable,
and best defined standard known.
Its stability is limited only
by the evaporation or oxidation rates of the platinum alloy used.
From a metrology point of view this is nice to know, but irrelevant,
given that this stability is much better than the reproducibility.
What matters is how accurately the standard can be reproduced.
Given the standard kg
(actually a copy, the primary one is never used)
one may make copies of it, by the usual methods. ('equal' armed balance etc)
The copies will have slightly different masses,
caused by the unavoidable errors in the measurement proces.
The magnitude of this spread is known,
and it is the relevant quantity for the 'stability' of the standard,
not its 'real' change of mass.
Measuring Avogadro's number in principle has the potential
of setting a mass standard more reproducibly than the Paris kg.
Or, saying the same thing in other words:
With the increase of the realizable accuracy of measurement
the errors in reproducing the kg will soon be, one hopes,
the dominant source of error in the experimental determination
of Avogadro's number.
And that also is why it hasn't happened yet:
systematic and as yet unexplained differences
between results obtained in different laboratories,
using different methods, still cast doubt on the claim
that the required reproducibility has indeed been reached.
For practical purposes very little wil change,
beyond some letters in the textbooks.
Ordinary mortals (outside a few highly specicialized standard laboratories)
will still have secondary, tertiary, ... etc practical kg standards,
represented by various lumps of metal.
Only the certification that these lumps really are (to a given accuracy)
one kg by mass will change.
Best,
Jan
Starblade Darksquall
(Snip)
(Not like I don't agree with what you said, I do... but that's why
there's no point for me to keep it on here.)
> There is something else, which is quite obscure about the above quoted
> numerical value. Obviously the value is somehow related to (or derived from)
> the Planck length. But the Planck length depends on the squareroot of the
> gravitational constant G, which isn't known very accurately. According to
> CODATA 1998 we have:
>
> G = 6.673(10) x 10^-11 m^3 kg^-1 s^-2
>
> meaning that G is known to roughly 0.1 %, i.e. three significant digits.
> Taking the square-root halves the relative error, so that the Planck-length
> is known to roughly 0.05 %, i.e. 3,5 significant digits. The value quoted
> above is far too accurate (7 significant digits).
>
> Best regards, Mike
Actually, I'd like to point out that they HAVE obtained more accurate
measurements of G recently. It's difficult for me to find any pages on
google because this would require me to look over several undesired
pages to sort through the ones I'm looking for, but I know there was
an article on it.
(...Starblade Riven Darksquall...)
Michael Petri
"Starblade Darksquall" <Starb...@Yahoo.com> wrote in
news:4aa861fb.03102...@posting.google.com...
> Actually, I'd like to point out that they HAVE obtained more accurate
> measurements of G recently. It's difficult for me to find any pages on
> google because this would require me to look over several undesired
> pages to sort through the ones I'm looking for, but I know there was
> an article on it.
I also remember vaguely a new more accurate measurement of G. I didn't
really pay too much attention to it, because before CODATA 1998 we also had
a much more accurate value of G (at least by one significant digit!), which
had to be revised, because the subsequent measurements differed widely.
Since that happened, I sort of always have my "warning bells ringing", when
reading about some new mesurement of G. I know, it is a prejudice. However,
with limited time to spare you have to keep at least some prejudices around
you, so that the information flow remains manageable.
So is this the time to through one of my prejudices away and actually locate
that paper(s) you are referring to?
Help me!
Best, Mike
Ralph Hartley
> Lubos Motl <mo...@feynman.harvard.edu> wrote:
>>Do you know a mirror that reflects gravitational waves?
...
> I'm not sure if such a mirror could be constructed... gravity goes
> right through everything. The only thing it doesn't go through are
> black holes, but it does goes around them.
I would be surprised if the surface of any real material did not reflect
gravitational waves to some extent.
Gravitational waves should cause a vibration that would emit a
"reflected" wave.
Does anyone know the formula for the gravitational refractive index of
a solid? I would expect it to depend on the density and the elastic
moduli. Outside of a neutron star I expect most materials have a
density close enough to zero not to matter.
In any case, such a reflection would be *exceedingly* faint.
Puzzle: what is the polarization of the reflected wave as a function
of angle?
>>Concerning the sign of the energy. My guess is that the Casimir energy
>>does not care about the attractive character of the force, and it just
>>counts the frequencies of the modes and they are probably similar to the
>>electromagnetic case. Unless something is very different about the
>>boundary conditions, the sign of the Casimir force should be the same.
But the magnitude should be *very* much weaker. At least with real (only
slightly reflective) mirrors.
Ralph Hartley
Oliver Jennrich
> So is this the time to through one of my prejudices away and actually locate
> that paper(s) you are referring to?
Does this one help?
http://www.npl.washington.edu/eotwash/pdf/prl85-2869.pdf
George Wilkie
johnd...@iprimus.com.au (John Devers) wrote in message news:<6f838e26.03093...@posting.google.com>...
> If you tell me what the wavelenght of gravity waves are I'll have a
> think about it;-) Is there a nobel prize in it?
>
> Maybe 2 giant mirrors (yep the mirrors and casimir effect again) if
> you get them just the right distance apart they should exclude gravity
> waves at a certain point, I'm not sure if that should push or pull the
> mirrors apart in this case though?
If gravitational waves behave like GR says they do, gravitational
waves are not distorted, reflected, refracted or scattered by any
material. The only thing that affects GWs is the curvature of
space-time itself. So to reflect a gravitational wave, you'd have to
make sure it passes sufficiently close to the event horizon of a black
hole. Not an easy experiment.
Oliver Jennrich
* George Wilkie writes:
> johnd...@iprimus.com.au (John Devers) wrote in message news:<6f838e26.03093...@posting.google.com>...
>> If you tell me what the wavelenght of gravity waves are I'll have a
>> think about it;-) Is there a nobel prize in it?
>>
>> Maybe 2 giant mirrors (yep the mirrors and casimir effect again) if
>> you get them just the right distance apart they should exclude gravity
>> waves at a certain point, I'm not sure if that should push or pull the
>> mirrors apart in this case though?
> If gravitational waves behave like GR says they do, gravitational
> waves are not distorted, reflected, refracted or scattered by any
> material.
I beg to differ. GRT predicts the possibility of detecting GW by
observing the energy deposited in bulk material (resonant bar
detectors).
Consider two masses attached to a spring. A passing GW will cause this
ensemble to oscillate and emit, however weak, GW itself. As long as
the amplitudes of the GW are small enough we can consider them to
follow linear equations - hence the GW *will* be scattered by matter.
Put together enough of these simple oscillators and you will be able
to observe all of the effects of classical optics - refraction,
reflection, scattering and so on.
Oliver Jennrich
>>
>> [Moderator's note: alas, G is the most poorly measured of all
>> fundamental constants, and it will remain so unless someone gets
>> a really good new idea, since gravity is so weak. - jb]
> If you tell me what the wavelenght of gravity waves are I'll have a
> think about it;-) Is there a nobel prize in it?
The frequencies of GW are spanning a range from at least 10^-4 Hz to a
couple of kilohertz.
> Maybe 2 giant mirrors (yep the mirrors and casimir effect again) if
> you get them just the right distance apart they should exclude gravity
> waves at a certain point, I'm not sure if that should push or pull the
> mirrors apart in this case though?
Neither. Free falling objects remain free falling objects under the
(linearily approximatated) action of GW. The distance between these
mirrors would be changing periodiacally, however.
Building a mirror for GW is a challenging task, though.
John Devers
> >> [Moderator's note: alas, G is the most poorly measured of all
> >> fundamental constants, and it will remain so unless someone gets
> >> a really good new idea, since gravity is so weak. - jb]
>
Some news just in, a new value has been measured for G, it's,
G = 6.673 87(0.000 27)×10^-11 m^3 kg^-1 s^-2
New Measurements of G Using the Measurement Standards Laboratory Torsion Balance
robert bristow-johnson
johnd...@iprimus.com.au wrote on 11/25/2003 02:27:
>
>>>> [Moderator's note: alas, G is the most poorly measured of all
>>>> fundamental constants, and it will remain so unless someone gets
>>>> a really good new idea, since gravity is so weak. - jb]
>>
>
> Some news just in, a new value has been measured for G, it's,
>
> G = 6.67387(0.00027) X 10^-11 m^3 kg^-1 s^-2
>
> New Measurements of G Using the Measurement Standards Laboratory Torsion
> Balance
>
> http://link.aps.org/abstract/PRL/v91/e201101
maybe it's just me, but this should be pretty exciting. it's a 37 fold
increase in accuracy of G. if this becomes accepted worldwide , i would
suppost NIST would update their expression for G.
a couple more passes at this (each with another increase in precision of 37
times) might make it so that people could redefine the meter, kg, and second
directly in terms of the Planck Units. i suppose that would be wishful
thinking.
r b-j
Uncle Al
G = 6.67422x10^(-11)
http://www.npl.washington.edu/eotwash/pdf/prl85-2869.pdf
Phys. Rev. Lett. 85(14) 2869 (2000)
Science 288(5468) 944 (2000)
G = 6.67407x10^-11)
Phys. Rev. Lett. 89 161102 (2002)
G = G = 6.67387 X 10^(-11)
Your reference.
Your reference is rather off two very good independent measurements.
The U/Wash quadrupole torsion pendulum in particular is an
extraordinarily good experiment that is amazingly resistant to outside
influences - unlike Cavendish balances.
http://www.iop.org/EJ/abstract/0957-0233/10/6/001
http://www.npl.washington.edu/eotwash/gconst.html
http://www.phys.lsu.edu/mog/mog16/node8.html
And if you want to dance...
http://arxiv.org/abs/gr-qc/0311084
http://arxiv.org/abs/astro-ph/0310699
The U/Wash experiment used a Pyrex plate of nominal density 2.23
g/cm^3 and stainless steel attractors of nominal density 7.98 g/cm^3.
One could imagine obtaining tighter bounds using a precision machined
much stiffer (and therefore thinner) single crystal alumina plate,
d=3.965, and precision machined HIPed tungsten attractors of nominal
density 19.35 g/cm^3.
G is a particularly nasty measurement for the weakness of the
interaction and the impossiblity of shielding external gravitational
noise (tides, rain, passersby). Additional "two passes of 37-fold
improvement" are not within extrapolatable technology.
--
Uncle Al
http://www.mazepath.com/uncleal/qz.pdf
J. J. Lodder
> In article 6f838e26.03112...@posting.google.com, John Devers at
> johnd...@iprimus.com.au wrote on 11/25/2003 02:27:
>
> >
> >>>> [Moderator's note: alas, G is the most poorly measured of all
> >>>> fundamental constants, and it will remain so unless someone gets
> >>>> a really good new idea, since gravity is so weak. - jb]
> >>
> >
> > Some news just in, a new value has been measured for G, it's,
> >
> > G = 6.67387(0.00027) X 10^-11 m^3 kg^-1 s^-2
> >
> > New Measurements of G Using the Measurement Standards Laboratory Torsion
> > Balance
> >
> > http://link.aps.org/abstract/PRL/v91/e201101
>
> maybe it's just me, but this should be pretty exciting.
You exite easily.
> it's a 37 fold
> increase in accuracy of G. if this becomes accepted worldwide , i would
> suppost 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)
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.
> a couple more passes at this (each with another increase in precision of 37
> times) might make it so that people could redefine the meter, kg, and second
> directly in terms of the Planck Units. i suppose that would be wishful
> thinking.
No. merely irrelevant.
Defining units in terms of fundamental quatities
is no aim in itself for metrology.
What matters is having units which are as reproducible as possible.
If that happens to require giving some fundamental constant
a defined value that's what's done. (as for c, or perhaps Avogadro soon)
If not, we'll just keep an extra unit.
Best,
Jan
robert bristow-johnson
wrote on 11/30/2003 12:01:
> G = 6.67422x10^(-11)
> http://www.npl.washington.edu/eotwash/pdf/prl85-2869.pdf
> Phys. Rev. Lett. 85(14) 2869 (2000)
> Science 288(5468) 944 (2000)
> G = 6.67407x10^-11)
> Phys. Rev. Lett. 89 161102 (2002)
> G = G = 6.67387 X 10^(-11)
> Your reference.
>
> Your reference is rather off two very good independent measurements.
it ain't my reference, i was just quoting someone else.
> G is a particularly nasty measurement for the weakness of the
> interaction and the impossibility of shielding external gravitational
> noise (tides, rain, passersby).
it seems to me that the big qualitative difference between gravitation and
E&M is that there is no "negative" masses (that repel a positive mass) that
some kind of shielding could be made out of. would not some expensive
shuttle missions (maybe a permanent station in orbit) be useful to get away
from that terrestrial noise? (there would still be the E.T. noise, but we
know when the moon swings by, can't some of that be accounted for?)
> Additional "two passes of 37-fold
> improvement" are not within extrapolatable technology.
only time will tell. maybe something like "Moore's Law" (but with a slower
exponent) might apply and they just get better and better at machining
precision monster masses and torsion bars that don't break and instruments
that measure minute deflections. i dunno, but i wouldn't have imagined the
speed and density of today's silicon chips two decades ago.
In article 1g58blh.pj8...@de-ster.xs4all.nl, J. J. Lodder at
nos...@de-ster.demon.nl wrote on 11/30/2003 12:01:
> robert bristow-johnson <r...@surfglobal.net> wrote:
>
>> In article 6f838e26.03112...@posting.google.com, John Devers at
>> johnd...@iprimus.com.au wrote on 11/25/2003 02:27:
>>
>>>
>>>>>> [Moderator's note: alas, G is the most poorly measured of all
>>>>>> fundamental constants, and it will remain so unless someone gets
>>>>>> a really good new idea, since gravity is so weak. - jb]
>>>>
>>>
>>> Some news just in, a new value has been measured for G, it's,
>>>
>>> G = 6.67387(0.00027) X 10^-11 m^3 kg^-1 s^-2
..
>> 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??
> 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.
suppose the question is "how much does solar wind slow down the earth's
revolutionary speed around the sun?" 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)?" 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.
>> a couple more passes at this (each with another increase in precision of 37
>> times) might make it so that people could redefine the meter, kg, and second
>> directly in terms of the Planck Units. i suppose that would be wishful
>> thinking.
>
> No. merely irrelevant.
who says my wishful thinking can't be irrelevant! :-)
> 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.
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). [[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.]]
is not the science of metrology concerned about that?
> 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. (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.) 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. 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.
> If not, we'll just keep an extra unit.
which is what seems to me to be less than elegant.
> Best,
and also to you.
r b-j
Oliver Jennrich
> The U/Wash experiment used a Pyrex plate of nominal density 2.23
> g/cm^3 and stainless steel attractors of nominal density 7.98 g/cm^3.
> One could imagine obtaining tighter bounds using a precision machined
> much stiffer (and therefore thinner) single crystal alumina plate,
> d=3.965, and precision machined HIPed tungsten attractors of nominal
> density 19.35 g/cm^3.
The keyword is 'nominal'. The problem with attractor masses is that it
takes some care to manufacture them to the required homogeneity and
precision machining therefor is only half of the story.
> G is a particularly nasty measurement for the weakness of the
> interaction and the impossiblity of shielding external gravitational
> noise (tides, rain, passersby).
Indeed.
Uncle Al
I'm not part of the group, and obviously the reduction to practice is
more than meets the eye. However, according to their publications
one major dynamic variable is the pendulum plate. It must be massive
while being "infintesimally" thin, homogeneous, and perfectly flat and
proportioned. Pyrex was a mediocre material choice. Pyrex is rather
floppy in large thin sections. Its compositional and strain
homogeneity is variable.
Single crystal alumina (white sapphire) from directional
solidification boules or edge-defined growth, then fabricated with
standard optical techniques, would have been better. It is immensely
stiff and 180% as dense as Pyrex, allowing a very thin but robust
plate. There are a large number of dense single crystals grown big
for nuclear detector and laser host purposes. A single crystal is
homogeneous by definition.
Much higher densities in hard stiff materials would be sintered
tungsten, binderless tungsten carbide (no magnetic cobalt!), tantalum
carbide... Those surfaces are routinely worked to fractional
wavelength smoothness and flatness, as in Johnny blocks. Given a
homogeneous mass, grinding and polishing perfect ball bearings is well
in hand (gyroscopes). The problem is making big ones. Given a
density 220% that of stainless steel, a smaller attractor ball will
get you to the same place with better precision and accuracy.
The U/Wash group has pioneered an exceptional way to accurately
measure Big G. Elegant physics is degraded by mediocre engineering.
Few race cars have automatic transmissions.
John Devers
nos...@de-ster.demon.nl (J. J. Lodder) wrote in message news:<1g58blh.pj8...@de-ster.xs4all.nl>...
> a defined value that's what's done. (as for c, or perhaps Avogadro soon)
> If not, we'll just keep an extra unit.
>
I'll just throw in this link now as the last one inspired so much
debate;-)
Silicon joins race to redefine the kilogram
http://physicsweb.org/article/news/7/9/9
"Then they calculated the Avogadro constant by dividing the molar
volume - the ratio of the mean molar mass of silicon to the density of
the crystal - by the atomic volume."
J. J. Lodder
please don't cut and paste between posts of different authors.
Reply to each on his own. [Uncle Al snipped]
> In article 1g58blh.pj8...@de-ster.xs4all.nl, J. J. Lodder at
> nos...@de-ster.demon.nl wrote on 11/30/2003 12:01:
>
> > robert bristow-johnson <r...@surfglobal.net> 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
Uncle Al
robert bristow-johnson wrote:
>
> In article 3FC91E8...@hate.spam.net, Uncle Al at Uncl...@hate.spam.net
> wrote on 11/30/2003 12:01:
>
> > G = 6.67422x10^(-11)
> > http://www.npl.washington.edu/eotwash/pdf/prl85-2869.pdf
> > Phys. Rev. Lett. 85(14) 2869 (2000)
> > Science 288(5468) 944 (2000)
> > G = 6.67407x10^-11)
> > Phys. Rev. Lett. 89 161102 (2002)
> > G = G = 6.67387 X 10^(-11)
> > Your reference.
> >
> > Your reference is rather off two very good independent measurements.
>
> it ain't my reference, i was just quoting someone else.
That makes it your reference. If you cite it, then you must defend
your choice (though not its content - certainly not in a seminar!).
> > G is a particularly nasty measurement for the weakness of the
> > interaction and the impossibility of shielding external gravitational
> > noise (tides, rain, passersby).
>
> it seems to me that the big qualitative difference between gravitation and
> E&M is that there is no "negative" masses (that repel a positive mass) that
> some kind of shielding could be made out of. would not some expensive
> shuttle missions (maybe a permanent station in orbit) be useful to get away
> from that terrestrial noise? (there would still be the E.T. noise, but we
> know when the moon swings by, can't some of that be accounted for?)
Read my sentence. That is the whole of it. Orbiting in space you
have orbital parameters and the moon, plus astronauts moving about,
propellant sloshing... It's a mess. One functional answer is to
create an experiment that is insensitive to minor perturbations, which
is what the U/Wash group has done. One could stick it a mile deep in
a mine and then everybody leaves, to dampen local fluctuations, and
upgrade its pendulum and net gravitating masses as I have suggested.
They are currently redesigning to use higher multipoles with better
noise rejection.
> > Additional "two passes of 37-fold
> > improvement" are not within extrapolatable technology.
>
> only time will tell. maybe something like "Moore's Law" (but with a slower
> exponent) might apply and they just get better and better at machining
> precision monster masses and torsion bars that don't break and instruments
> that measure minute deflections. i dunno, but i wouldn't have imagined the
> speed and density of today's silicon chips two decades ago.
Apples and oranges. Measuring Big G is not an engineering problem, it
is a physics problem. You cannot "Moore's law" the strength of the
interaction nor can you wait for gravitational shielding to be
discovered. Atoms won't change size.
U/Wash runs their torsion balances at room temp. Newman at UC/Irvine
runs his at ~2 K in an abandoned missile bunker in Washington State.
One can do a straightforward set of calculations to show that Newman
can cakewalk to 10X the sensitivity of U/Wash, since atomic thermal
jitter is the limiting noise and the torsion fiber is way better when
cryogenic. In the real world, cryogenic rigs are no better than
ambient temp rigs to date, the added overhead being parasitic upon the
paper imrovement. In Eotvos experiments the properties being tested
are less than 0.002 difference/average of total test mass. One could
easily get a 100-fold improvement in sensitivity by being more clever
*with the test masses* not the apparatus. Measurement of Big G is not
amenable to that sort of thing. It is already running 100% flat out.
> In article 1g58blh.pj8...@de-ster.xs4all.nl, J. J. Lodder at
> nos...@de-ster.demon.nl wrote on 11/30/2003 12:01:
>
> > robert bristow-johnson <r...@surfglobal.net> wrote:
> >
> >> In article 6f838e26.03112...@posting.google.com, John Devers at
> >> johnd...@iprimus.com.au wrote on 11/25/2003 02:27:
[snip]
> > 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.
>
> suppose the question is "how much does solar wind slow down the earth's
> revolutionary speed around the sun?" 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)?" 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.
Do more reading. mG is important, Big G as such doesn't figure in
much of anything but homework problems. Inertial and gravitational
mass indistinguishability, the Equivalence Principle, is unrelated to
Big G. Similarly, lightspeed as such is irrelevant. Lorentz
transformation merely requires that there be a universal finite speed
limit. The value as such can be normalized away.
[snip]
> 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). [[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.]]
Given any two irrational numbers 'x' and 'y' it is always possible to
find integers j, k, m, n such that |(j)(x^m) - (k)(y^n)| < epsilon,
where "epsilon" is arbitrarily small. One should not be impressed by
such a relationship since one could find an arbitrarily large number
of relationships as good or better by picking any other irrational
number, like the Napierian base 'e', Euler's constant gamma, the
Golden Ratio, any irrational square root, etc.
Proximity is not causality.
> 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.) used to be that the meter was the distance between a couple of
> scratch marks on another piece of metal.
1) One is only allowed so many independent variables.
2) Measurement is not valid absent a real world standard for
comparison to the required number of significant figures.
Mass does not even appear in the Standard model. It is artificially
inserted after the fact via the Higgs mechanism and 20 fudge factors.
That is execrable curve fitting. Mass barely appears in gravitation
theories, and then it is at most an abstract distortion. One might
argue that mass is not a valid variable at all, and then merely
substitute something that is. The Devil lays in the details.