# [ExI] The most accurate clock ever

John Clark johnkclark at gmail.com
Sat Dec 1 15:53:31 UTC 2018

```On Thu, Nov 29, 2018 at 11:57 AM <spike at rainier66.com> wrote:

*> John just a coupla comments please.  The time error measurement is (as I
> recall) a consequence of Special Relativity rather than General Relativity*
>

Actually in this case General Relativity makes a larger contribution than
Special Relativity, it's one of the few examples where it does something
practical. The GPS satellite is moving very fast so due to Special
Relativity the satellite's clock will LOSE  7210 nanoseconds a day, but the
satellite's clock is more distant from the Earth's center so it's in a
weaker gravitational field than the clock on the ground, so due to General
Relativity the clock will GAIN 45,850 nanoseconds a day. Taking these 2
factors into account the satellite's clocks gains 45,850 −7,210 = 38,640
nanoseconds a day relative to a clock on the ground. If this were not taken
into account the GPS system would drift off by 6 miles each day every day
and soon become useless.

> *We already know of gravitational anomalies big enough to be noticed by
> satellites,*
>

The position and intensity of those gravitational anomalies are well known
and stable and thus could easily be taken into account.  As for the local
conditions caused by the waves, 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.

>*variation in magnetic field also produces time dilation.  Reasoning:
> Maxwell’s equations tell us a varying magnetic field induces a magnetic
> field, which is an energy transfer (ja?) and Special Relativity gives us
> the tools to deal with that, so we take that c^2 factor (also in that E17
> range) and if this new atomic clock can measure stuff down there, we might
> have a new magnetic field anomaly detector better than what we had before.*
>

I think that huge c^2 factor would work against you in this case, even a
gigantic amount of magnetic energy would correspond to a tiny amount of
mass and a corresponding super small change in gravity, so small a change
that even this clock probably couldn't detect it.

John K Clark

*> Is this a cool time to be living or what?*

Indeed it is!

John K Clark
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