Re: The most accurate clock ever

[John Clark]

On Sat, Dec 22, 2018 at 2:36 AM Brent Meeker  wrote:

* > I'm not sure why you converted 9" to kilometers instead meters,*
>

Oh that's very easily explained. I was stupid.


> *> but: 2(6.67e-11)112/0.2(9e16) = 8.3e-25*
>

Yes, I get  8.3*10^-25 too. And the square root  of (1 - 8.3^10^-25) is
 0.5850.  In my previous post I claimed it was
 .97 which was dead wrong, and as you correctly say that is
"*Waaay closer to 1.0 than the time dilation due to raising a clock 0.01m
above the Earth's surface*".

So I was entirely wrong and you are entirely correct, thank you for
correcting my careless error.

  > *He *[Cavendish] *claims to have measured the deflection of the smaller
> masses within 0.25mm.*


But in Cavendish's day nobody had a scale sensitive enough to measure or
even detect the difference in gravity caused by the elevation of a meter or
even a kilometer, much less a millimeter as this new clock can. The torsion
balance Cavendish used could only detect forces parallel to the Earth's
surface.

> *Which is not only wrong arithmetically, it is comparing the time
> dilation factor which depends on the potential (goes as 1/r) to the
> acceleration (which goes as 1/r^2).*
>

Yes but that means the difference in gravitational potential and the
resulting time dilation of a clock 6.37* 10^9 mm from the Earth's center
and a clock (6.37* 10^9) +1mm from the center must be really really small
if it changes only linearly with distance and doesn't change according to
the distance squared; and yet this clock could still detect that tiny
change. But you're right, acceleration is not the key factor to
gravitational time dilation, it's escape velocity.

If you were on the surface of a planet that was larger and more massive
than the Earth the surface acceleration could still be at just one g like
on the surface of the Earth if the planet were less dense than the Earth
because then the mass is greater but you're further from the center and
they could cancel out. So although you're still at one g the escape
velocity needed to get free of the planet would be greater and General
Relativity says the gravitational time dilation would be the same as
Special Relativity says it would be if you were moving at the escape
velocity in empty space far from any strong gravitational field.

 John K Clark

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Re: The most accurate clock ever

[Brent Meeker]

On 12/21/2018 7:29 AM, John Clark wrote:
On Thu, Dec 20, 2018 at 11:57 PM Brent Meeker > wrote:


>> The mass of the Earth played no part in Cavendish's
determination of G because he was measuring gravitational
attraction in a direction that was parallel to the Earth's
surface.


/> But in comparing it to the clock precision you have to consider
that the clock is measuring the change over a cm of a very much
greater potential, /


Yes, that makes it even more valuable.

> /while Cavendish is measuring a much smaller change in a much
smaller potential.
/


No, the change Cavendish measured was much larger not smaller.

>> the new clock can detect the difference in time dilation
between 1g and 1.3g, so I'm sure it could detect the
time dilation caused by a 348 pound mass a foot or so away.

/> Could it? /


Yes indeed.

> /The gravitational time dilation factor is tau = sqrt[1 -
2GM/rc^2]. So a clock that can detect a one cm change in height at
the Earth's surface is in fact not accurate enough to to detect
the difference between being adjacent to a 348lbm 18" ball and
being arbitrarily far away from it./


Cavendish could not detect the gravitational field arbitrarily far 
away from an object


I clearly wrote "...to detect /*the difference*/ between being adjacent 
to a 348lbm 18" ball and being arbitrarily far away from it."  But 
Cavendish did more than just detect the difference, he measured it.  He 
claims to have measured the deflection of the smaller masses within 0.25mm.


nor can anybody else because that would take infinite precision, but 
lets calculate what he did do. The gravitational time dilation factor 
is sqrt[1 - 2GM/rc^2]  so if G is 6.67 × 10^-11 m3 kg^-1 s^-2 and c is 
1*10^8 meters/sec then the gravitational time dilation factor caused 
by being 9 inches (.0002 kilometers) away from the center of a 248 
pound (112 kilogram) lead ball is, if I did my arithmetic correctly, 
1-square root of [1- 112 *(13.3 *10^-11) / .0002 *(3*10^8)^2)] = 
1-(2.6*10^-6) = .97.


?? Not even close.  I'm not sure why you converted 9" to kilometers 
instead meters, but:


          2(6.67e-11)112/0.2(9e16) = 8.3e-25

So using sqrt(1-x) ~ 1 - x/2  The time dilation factor is 1-(4.1e-25)  
Waaay closer to 1.0 than the time dilation due to raising a clock 0.01m 
above the Earth's surface, which is given by


    [2(6.67e-11)5.97e24/9e16][1/6.36e6  - 1/(6.36e6 + 0.01)] ~ 
1.39e-9[1  - 1 + 0.01/6.36e6] = 2.19e-18


which gives a time dilation 1-(1.09e-18).



So Cavendish was able to detect a gravitational field that would make 
a time dilation of about 3 parts in a million, but this new clock 
could detect the change in a gravitational field that would make a 
time dilation of about 3 parts in a billion, a thousand fold improvement.


Which is not only wrong arithmetically, it is comparing the time 
dilation factor which depends on the potential (goes as 1/r) to the 
acceleration (which goes as 1/r^2).


Brent



John K Clark


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Re: The most accurate clock ever

[Lawrence Crowell]

The leading term in time difference with radius is the g_{tt} component of 
the Schwarzschild metric


g_{00}(r) = 1 - 2GM/rc^2 


We have 2GM/c^2 = 0.0088m which is the Schwarzschild radius. From R to R' 
we can integrate this 


∫g_{00}(r) dr = R' - R - 2GM/c^2 ln(R'/R).


For R' = R + δr we can approximate this as


∫g_{00}(r) dr = δr - 2GM/c^2 δr/R = g_{00}(r)δr


We take R the radius of the Earth 6.4×10^6m and so we have 


2GM/c^2 δr/R = 1.38×10^{-9}δr


as the difference from δr in a flat space and the curved spacetime result 
from ∫g_{00}(r) dr. For a centimeter this is then 1.38×10^{-11}m. So the 
deviation from a Euclidean space result between R and R' is by this factor. 
Dividing by the speed of light gives a time deviation of 4.6×10^{-18}sec. 


The universe started 13.8 billion years ago and a year is 3.15×10^7sec so 
the universe has been around 4.35×10^{17}sec and so one second deviation 
since the start of the universe would be 2.3×10^{-18}, which is only half 
the result above.


LC

On Thursday, November 29, 2018 at 8:29:12 AM UTC-6, John Clark wrote:
>
> In yesterday's issue of the journal Nature Scientists at the National 
> Institute of Standards and Technology (NIST) reported they have made a new 
> type of clock that is the most accurate ever, it's called a Ytterbium 
> Lattice Clock. It's about 100 times better than any previous clock, if set 
> at the time of the Big Bang 13.8 billion years ago today it would be off by 
> less than one second.
>
> https://www.nature.com/articles/s41586-018-0738-2
>
> It's so good the main source of error is due to General Relativity, if you 
> lift the clock up by just one centimeter the Earth's gravitational field is 
> slightly weaker and so the clock runs noticeably faster, that may be why 
> NIST is now working on a portable version of their Ytterbium Lattice Clock. 
> If GPS satellites had clocks this good they'd know where they were relative 
> to the Earth to within a centimeter and so could tell users on the ground 
> where they were within a centimeter; and that would be more than good 
> enough for jet fighters to automatically land on aircraft carriers without 
> a pilot, even at night in a heavy fog in a bad storm with the deck tossing 
> up and down. It would be by far the best instrument ever made to detect 
> tiny changes in the gravitational field, and that would make it much easier 
> to find things buried deep underground. The Earth just became more 
> transparent. It might even be used to detect Gravitational Waves and Dark 
> Matter.  
>
> John K Clark
>

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Re: The most accurate clock ever

[John Clark]

On Thu, Dec 20, 2018 at 11:57 PM Brent Meeker  wrote:

>> The mass of the Earth played no part in Cavendish's determination of G
>> because he was measuring gravitational attraction in a direction that
>> was parallel to the Earth's surface.
>
>
> * > But in comparing it to the clock precision you have to consider that
> the clock is measuring the change over a cm of a very much greater
> potential, *
>

Yes, that makes it even more valuable.

> >
> *while Cavendish is measuring a much smaller change in a much smaller
> potential.*
>

No, the change Cavendish measured was much larger not smaller.

>> the new clock can detect the difference in time dilation between 1g and
>> 1.3g, so I'm sure it could detect the time dilation caused by a 348
>> pound mass a foot or so away.
>
>

* > Could it? *
>

Yes indeed.


> > *The gravitational time dilation factor is tau = sqrt[1 - 2GM/rc^2]. So
> a clock that can detect a one cm change in height at the Earth's surface is
> in fact not accurate enough to to detect the difference between being
> adjacent to a 348lbm 18" ball and being arbitrarily far away from it.*
>

Cavendish could not detect the gravitational field arbitrarily far away
from an object nor can anybody else because that would take infinite
precision, but lets calculate what he did do. The gravitational time
dilation factor is sqrt[1 - 2GM/rc^2]  so if G is 6.67 × 10^-11 m3 kg^-1
s^-2 and c is 1*10^8 meters/sec then the gravitational time dilation factor
caused by being 9 inches (.0002 kilometers) away from the center of a 248
pound (112 kilogram) lead ball is, if I did my arithmetic correctly,
1-square root of [1- 112 *(13.3 *10^-11) / .0002 *(3*10^8)^2)] =
1-(2.6*10^-6) = .97.

So Cavendish was able to detect a gravitational field that would make a
time dilation of about 3 parts in a million, but this new clock could
detect the change in a gravitational field that would make a time dilation
of about 3 parts in a billion, a thousand fold improvement.

John K Clark

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Re: The most accurate clock ever

[Brent Meeker]

On 12/4/2018 5:35 PM, John Clark wrote:

Brent Meeker wrote:

> / finding the value of G depends on scaling the result by that
ratio of masses (1.37e25 lbm/348 lbm). /


The mass of the Earth played no part in Cavendish's determination of G 
because he was measuring gravitational attraction in a direction that 
was parallel to the Earth's surface.


But in comparing it to the clock precision you have to consider that the 
clock is measuring the change over a cm of a very much greater 
potential, while Cavendish is measuring a much smaller change in a much 
smaller potential.




/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. /


OKlets look at it like that, the new clock can detect the difference 
in time dilation between 1g and 1.3g, so I'm sure it could 
detect the time dilation caused by a 348 pound mass a foot or so away.


Could it?  The gravitational time dilation factor is tau = sqrt[1 - 
2GM/rc^2].  So a clock that can detect a one cm change in height at the 
Earth's surface is in fact not accurate enough to to detect the 
difference between being adjacent to a 348lbm 18" ball and being 
arbitrarily far away from it.


But .3gis so weak a force it would not have caused Cavendish's 
torsion balance to move at all, air resistance and the rigidity of the 
wire holding it up would have prevented it.


The description I read of Cavendish's experiment said the smaller masses 
were 9" from the cannon balls.




/> It's the number I cited, far bigger than the 0.25mm Cavendish
cited as the limit of his measurement./


There is no way Cavendish could have placed the centers of two 
248pound lead balls 0.25mm apart, lead just isn't that dense.


No, 0.25mm is his estimate of the smallest change in deflection he could 
detect.  The weights on his torsion balance were 9" from the cannonballs 
center, which I assume was the radius of his cannon balls since the 
measurement would be most accurate when the torsion weights were nearest 
the cannon balls.


Brent



John K Clark


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Re: The most accurate clock ever

[John Clark]

Brent Meeker wrote:

> * finding the value of G depends on scaling the result by that ratio of
> masses (1.37e25 lbm/348 lbm). *
>

The mass of the Earth played no part in Cavendish's determination of G
because he was measuring gravitational attraction in a direction that
was parallel
to the Earth's surface.


> * 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. *
>

OK lets look at it like that, the new clock can detect the difference in
time dilation between 1g and 1.3g, so I'm sure it could detect the
time dilation caused by a 348 pound mass a foot or so away. But .3g
is so weak a force it would not have caused Cavendish's torsion balance to
move at all, air resistance and the rigidity of the wire holding it up
would have prevented it.


> *> It's the number I cited, far bigger than the 0.25mm Cavendish cited as
> the limit of his measurement.*
>

There is no way Cavendish could have placed the centers of two 248 pound
lead balls 0.25mm apart, lead just isn't that dense.

John K Clark

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Re: The most accurate clock ever

[Brent Meeker]

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 



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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Re: The most accurate clock ever

[Terren Suydam]

Given the Earth has a liquid core, is there any chance that turbulence in
the core would move the center of gravity around by some minute amount, but
large enough to throw off measurements of such tiny differences?

On Thu, Nov 29, 2018 at 9:29 AM John Clark  wrote:

> In yesterday's issue of the journal Nature Scientists at the National
> Institute of Standards and Technology (NIST) reported they have made a new
> type of clock that is the most accurate ever, it's called a Ytterbium
> Lattice Clock. It's about 100 times better than any previous clock, if set
> at the time of the Big Bang 13.8 billion years ago today it would be off by
> less than one second.
>
> https://www.nature.com/articles/s41586-018-0738-2
>
> It's so good the main source of error is due to General Relativity, if you
> lift the clock up by just one centimeter the Earth's gravitational field is
> slightly weaker and so the clock runs noticeably faster, that may be why
> NIST is now working on a portable version of their Ytterbium Lattice Clock.
> If GPS satellites had clocks this good they'd know where they were relative
> to the Earth to within a centimeter and so could tell users on the ground
> where they were within a centimeter; and that would be more than good
> enough for jet fighters to automatically land on aircraft carriers without
> a pilot, even at night in a heavy fog in a bad storm with the deck tossing
> up and down. It would be by far the best instrument ever made to detect
> tiny changes in the gravitational field, and that would make it much easier
> to find things buried deep underground. The Earth just became more
> transparent. It might even be used to detect Gravitational Waves and Dark
> Matter.
>
> John K Clark
>
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Re: The most accurate clock ever

[John Clark]

 Brent Meeker wrote:

*> 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


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.

John K Clark

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Re: The most accurate clock ever

[Brent Meeker]

On 12/3/2018 5:24 AM, John Clark wrote:
On Sun, Dec 2, 2018 at 11:54 PM Brent Meeker > wrote:


>>If you are on the Earth's surface and you raise a clock by one
centimeter you've increased its distance from the earth's
center by one part in 637,000,000, it is now 1.16
times further away. The intensity of the gravitational field
is proportional to the square of the distance so gravity was
1.31 times stronger before you raised raised the
clock. Cavendish did not have a scale good enough to measure
that, even today the very best (and very expensive) lab weight
scale might be able to measure a change of 1.001 but the
clock can do several hundred times better. 



> He was measuring the change in a much smaller gravitational field.


Cavendish was measuring the displacement of a torsion balance parallel 
to the Earth's surface caused by a weak but constant gravitational 
field, there was no change whatsoever in the gravitational field 
parallel to the Earth's surface at any time during the exparament. If 
he had 2 *PRECISELY* identical cannonballs on the ends of a rod, 
placed a pivot point *PRECISELY*at the center and place one 
cannonball one centimeter higher than the other he would have 
transformed his torsion balance into a weight balance and 
theoretically he could have observed that the balance moved and 
measured the small difference in strength in the large field at 2 
different places, but Cavendish couldn't come close to achieving the 
sort of precision required to do that 220 years ago, we can't even do 
that today.


/> He was measuring the difference between the force on the
torsion balance with the cannon balls present vs absent. /


Cavendishsetup the exparament but nothing moved because the torsion 
balance was held in place by a thread, he then sealed the room and did 
nothing for 2 days to let the air currents settle down. He then 
carefully burned through the thread freeing the torsion balanceand 
observed its movement from far away through a telescope so his own 
movements wouldn't disturb anything. At no time did he measure the 
very small change of strength of 2 very large gravitational fields 
because a torsion balancecan't do that, you'd need either a super good 
weight balance or a super good clock.


Neither does a cesium clock measure the change in strength of 2 large 
gravitational fields.  It measures the difference in gravitational 
potential.  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

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Re: The most accurate clock ever

[John Clark]

On Sun, Dec 2, 2018 at 11:54 PM Brent Meeker  wrote:

>>If you are on the Earth's surface and you raise a clock by one centimeter
>> you've increased its distance from the earth's center by one part in
>> 637,000,000, it is now 1.16 times further away. The intensity of
>> the gravitational field is proportional to the square of the distance so
>> gravity was 1.31 times stronger before you raised raised the clock.
>> Cavendish did not have a scale good enough to measure that, even today the
>> very best (and very expensive) lab weight scale might be able to measure a
>> change of 1.001 but the clock can do several hundred times better.
>
>
> > He was measuring the change in a much smaller gravitational field.
>

Cavendish was measuring the displacement of a torsion balance parallel to
the Earth's surface caused by a weak but constant gravitational field,
there was no change whatsoever in the gravitational field parallel to the
Earth's surface at any time during the exparament. If he had 2
*PRECISELY* identical
cannonballs on the ends of a rod, placed a pivot point *PRECISELY* at the
center and place one cannonball one centimeter higher than the other he
would have transformed his torsion balance into a weight balance and
theoretically he could have observed that the balance moved and measured
the small difference in strength in the large field at 2 different places,
but Cavendish couldn't come close to achieving the sort of precision
required to do that 220 years ago, we can't even do that today.


> * > He was measuring the difference between the force on the torsion
> balance with the cannon balls present vs absent.  *
>

 Cavendish setup the exparament but nothing moved because the torsion
balance was held in place by a thread, he then sealed the room and did
nothing for 2 days to let the air currents settle down. He then carefully
burned through the thread freeing the torsion balance and observed its
movement from far away through a telescope so his own movements wouldn't
disturb anything. At no time did he measure the very small change of
strength of 2 very large gravitational fields because a torsion balance can't
do that, you'd need either a super good weight balance or a super good
clock.

 John K Clark

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Re: The most accurate clock ever

[Brent Meeker]

On 12/2/2018 7:04 PM, John Clark wrote:
On Sun, Dec 2, 2018 at 4:29 PM Brent Meeker > wrote:


/> The Earth is 3.9e22 times heavier than Cavendishes cannon ball. /


The mass of the earth is irrelevant because we're talking about 
measuring the difference in the strength of gravity as distance 
increases not its absolute value.


>> In 1798 technology was good enough for Cavendish to measure
the gravitational attraction between 2 cannonballs a few
inches apart (andby doing so determine the value of the
Gravitational Constant) but until a few months ago no
technology was good enough to measure the difference in
strength of a gravitational field that was 637,000,000
centimeters from the center of the Earth and one that was
637,000,001 centimeters from the center of the Earth. But the
technology is good enough now thanks to this new clock. 



> /N//o.  The potential difference measured by the cesium clock when
raised 1cm relative to the Earth was 2.03e9 times bigger than the
smallest difference measured by Cavendish (assuming he could
measure 0.00025m deflection).  The Earth is 3.9e22 times heavier
than Cavendishes cannon ball.     So 300yrs ago Cavendishes
technology was good enough;/


If you are on the Earth's surface and you raise a clock by one 
centimeter you've increased its distance from the earth's center by 
one part in 637,000,000, it is now 1.16 times further away. 
The intensity of the gravitational field is proportional to the square 
of the distance so gravity was 1.31 times stronger before you 
raised raised the clock. Cavendish did not have a scale good enough to 
measure that, even today the very best (and very expensive) lab weight 
scale might be able to measure a change of 1.001 but the clock can 
do several hundred times better.


He was measuring the change in a much smaller gravitational field.



> (assuming he could measure 0.00025m deflection).


When Cavendish measured a deflection he was measuring the strength of 
the attraction between 2 canon balls, he was not measuring the 
difference in the gravitational field at 2 points. Cavendish used a 
torsion balanceand its very good at measuring weak forces but it can't 
measure the super small difference between 2 strong forces, to do that 
he'd need a weight scale, or a super accurate clock.


He was measuring the difference between the force on the torsion balance 
with the cannon balls present vs absent.


Brent

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Re: The most accurate clock ever

[John Clark]

On Sun, Dec 2, 2018 at 4:29 PM Brent Meeker  wrote:


> *> The Earth is 3.9e22 times heavier than Cavendishes cannon ball. *
>

The mass of the earth is irrelevant because we're talking about measuring the
difference in the strength of gravity as distance increases not its
absolute value.

>> In 1798 technology was good enough for Cavendish to measure the
>> gravitational attraction between 2 cannonballs a few inches apart (andby
>> doing so determine the value of the Gravitational Constant) but until a
>> few months ago no technology was good enough to measure the difference in
>> strength of a gravitational field that was 637,000,000 centimeters from the
>> center of the Earth and one that was 637,000,001 centimeters from the
>> center of the Earth. But the technology is good enough now thanks to
>> this new clock.
>
>
> > *N**o.  The potential difference measured by the cesium clock when
> raised 1cm relative to the Earth was 2.03e9 times bigger than the smallest
> difference measured by Cavendish (assuming he could measure 0.00025m
> deflection).  The Earth is 3.9e22 times heavier than Cavendishes cannon
> ball. So 300yrs ago Cavendishes technology was good enough;*


If you are on the Earth's surface and you raise a clock by one centimeter
you've increased its distance from the earth's center by one part in
637,000,000, it is now 1.16 times further away. The intensity of
the gravitational field is proportional to the square of the distance so
gravity was 1.31 times stronger before you raised raised the clock.
Cavendish did not have a scale good enough to measure that, even today the
very best (and very expensive) lab weight scale might be able to measure a
change of 1.001 but the clock can do several hundred times better.


> > (assuming he could measure 0.00025m deflection).
>

When Cavendish measured a deflection he was measuring the strength of the
attraction between 2 canon balls, he was not measuring the difference in
the gravitational field at 2 points. Cavendish used a torsion balance and
its very good at measuring weak forces but it can't measure the super small
difference between 2 strong forces, to do that he'd need a weight scale, or
a super accurate clock.

John K Clark
>
>
>
>

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Re: The most accurate clock ever

[Brent Meeker]

On 12/2/2018 6:22 AM, John Clark wrote:
On Sat, Dec 1, 2018 at 6:59 PM Brent Meeker > wrote:


> /But an ocean wave many feet high would change the gravitational
field less than would moving a centimeter relative to the Earth's
center of mass./


Not so. In 1798 technology was good enough for Cavendish to measure 
the gravitational attraction between 2 cannonballs a few inches apart 
(and by doing so determine the value of the Gravitational Constant) 
but until a few months ago no technology was good enough to measure 
the difference in strength of a gravitational field that was 
637,000,000 centimeters from the center of the Earth and one that was 
637,000,001 centimeters from the center of the Earth. But the 
technology is good enough nowthanks to this new clock. And this isn't 
the end of the line for clock technology, nobody has made one yet but 
a Thorium Nuclear Clock would be even more accurate.


No.  The potential difference measured by the cesium clock when raised 
1cm relative to the Earth was 2.03e9 times bigger than the smallest 
difference measured by Cavendish (assuming he could measure 0.00025m 
deflection).  The Earth is 3.9e22 times heavier than Cavendishes cannon 
ball.     So 300yrs ago Cavendishes technology was good enough; it's 
just hard to hang two Earth masses in a big box.


Brent

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Re: The most accurate clock ever

[John Clark]

On Sat, Dec 1, 2018 at 6:59 PM Brent Meeker  wrote:

> *But an ocean wave many feet high would change the gravitational field
> less than would moving a centimeter relative to the Earth's center of mass.*


Not so. In 1798 technology was good enough for Cavendish to measure the
gravitational attraction between 2 cannonballs a few inches apart (and by
doing so determine the value of the Gravitational Constant) but until a few
months ago no technology was good enough to measure the difference in
strength of a gravitational field that was 637,000,000 centimeters from the
center of the Earth and one that was 637,000,001 centimeters from the
center of the Earth. But the technology is good enough now thanks to this
new clock. And this isn't the end of the line for clock technology, nobody
has made one yet but a Thorium Nuclear Clock would be even more accurate.

John K Clark

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Re: The most accurate clock ever

[Brent Meeker]

On 12/1/2018 7:06 AM, John Clark wrote:


On Thu, Nov 29, 2018 at 6:34 PM Brent Meeker > wrote:


>> good enough for jet fighters to automatically land on
aircraft carriers without a pilot, even at night in a heavy
fog in a bad storm with the deck tossing up and down.

/> Unfortunately for that idea, the surface of the Earth, and
especially the ocean, varies by a lot more than a centimeter. /


If the ocean fluctuates up and down the intensity of the Earth's 
gravitational field will fluctuate too and with exactly the same 
rhythm, the change in gravity will be very very small but a clock this 
good could detect it. In a practical system in wartime conditions the 
error would probably be a few inches rather than a centimeter but that 
would be good enough; even the best human fighter pilot only knows 
where the deck of his aircraft carrier is within a foot or two when he 
lands.


But an ocean wave many feet high would change the gravitational field 
less than would moving a centimeter relative to the Earth's center of mass.


Brent

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Re: The most accurate clock ever

[John Clark]

On Thu, Nov 29, 2018 at 6:34 PM Brent Meeker  wrote:

 >> good enough for jet fighters to automatically land on aircraft carriers
>> without a pilot, even at night in a heavy fog in a bad storm with the deck
>> tossing up and down.
>
>

* > Unfortunately for that idea, the surface of the Earth, and especially
> the ocean, varies by a lot more than a centimeter. *
>

If the ocean fluctuates up and down the intensity of the Earth's
gravitational field will fluctuate too and with exactly the same rhythm,
the change in gravity will be very very small but a clock this good could
detect it. In a practical system in wartime conditions the error would
probably be a few inches rather than a centimeter but that would be good
enough; even the best human fighter pilot only knows where the deck of his
aircraft carrier is within a foot or two when he lands.

 John K Clark

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Re: The most accurate clock ever

[Brent Meeker]

On 11/29/2018 6:28 AM, John Clark wrote:
In yesterday's issue of the journal Nature Scientists at the National 
Institute of Standards and Technology (NIST) reported they have made a 
new type of clock that is the most accurate ever, it's called a 
Ytterbium Lattice Clock. It's about 100 times better than any previous 
clock, if set at the time of the Big Bang 13.8 billion years ago today 
it would be off by less than one second.


https://www.nature.com/articles/s41586-018-0738-2

It's so good the main source of error is due to General Relativity, if 
you lift the clock up by just one centimeter the Earth's gravitational 
field is slightly weaker and so the clock runs noticeably faster, that 
may be why NIST is now working on a portable version of their 
Ytterbium Lattice Clock. If GPS satellites had clocks this good they'd 
know where they were relative to the Earth to within a centimeter and 
so could tell users on the ground where they were within a centimeter; 
and that would be more than good enough for jet fighters to 
automatically land on aircraft carriers without a pilot, even at night 
in a heavy fog in a bad storm with the deck tossing up and down.


Unfortunately for that idea, the surface of the Earth, and especially 
the ocean, varies by a lot more than a centimeter.  Off the coast of CA 
where the Pacific Missile range is, the "Earth's surface" as defined in 
WGS84 is a few meters underwater.  That's why one must us local 
corrections for GPS altitude.  But the local correction is still only an 
average over tidal cycles, etc.


Brent

It would be by far the best instrument ever made to detect tiny 
changes in the gravitational field, and that would make it much easier 
to find things buried deep underground. The Earth just became more 
transparent. It might even be used to detect Gravitational Waves and 
Dark Matter.


John K Clark
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