On 12/4/2018 6:28 AM, John Clark wrote:
Brent Meekerwrote:
/> Neither does a cesium clock measure the change in strength of 2
large gravitational fields. It measures the difference in
gravitational potential. /
Same thing, a gravitational field describes the gravitational
potential at every point.
/> //So I compared the change in gravitational potential when
moving the clock up 1cm to the change in potential when
Cavendish's torsion balance moved the sensing weights the smallest
change in distance he said he could measure 0.25mm with the
weights 9" (0.23m) from the cannon balls. The ratio of these two
potentials is the product of three terms: The ratio of masses
(1.37e25 lbm/348 lbm) The ratio distances squared
(0.23m/6.4e6m)^2. The ratio of smallest measurable changes
(0.01m/0.00025m). Work it out yourself./
Brent, Cavendish's torsion balance was only sensitive enough to
measure the Gravitational constant to one part in 100, and even today
with the newest and best torsion balance money can buy you can only
get 11.6 parts per MILLION.
New Torsion Balance
<https://www.nature.com/articles/s41586-018-0431-5.epdf?referrer_access_token=AvVGTXPKzx5IZ2BvbCeXZ9RgN0jAjWel9jnR3ZoTv0PGEE1clqTcXObDifjS0tqXqs3lxGXdPvbEAM8ynqscFj7fcELZiKCXKxoMnqb4-xBubiNDE73FY1mUm1mWsbpfug1i5cdw_J3iXDOJ6CG_hQg59N-6UoqggryzeBZ1jILTd2UVJhLbcIpBoaPFTFLJXW65I-Y-nAHw_1_tws_V9pImRR24QlUj8zMpiN3wmRcARzfzszmxgsUFN-4wm9nmteg2BM7LRMlz5O1FuE0_ehqjn0w0YyWray5ZATt04iM%3D&tracking_referrer=physicsworld.com>
To measure the difference in Earth's gravity at 2 points one
centimeter higher from the surface than the other you'd need to do
better than 3 parts per BILLION. This new clock can do that, 3,900
times better than the best modern torsion balance.
But that's because finding the value of G depends on scaling the result
by that ratio of masses (1.37e25 lbm/348 lbm). The way you are looking
at consider how far you would have to move the cesium clock from the
surface of the 348lbm cannon ball in order to detect the change in
gravitational time dilation affecting the clock. It's the number I
cited, far bigger than the 0.25mm Cavendish cited as the limit of his
measurement.
Brent
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