Re: Perfect clocks

On 5/4/2024 11:46 AM, Tom Roberts wrote:

On 5/1/24 12:06 PM, Maciej Wozniak wrote:

sane people, as anyone can check at GPS, keep assuming the second to be  9 192 631 770 on Earth,

 This is not an "assumption", this is the definition of the second --
that's what these words mean.
 

but 9 192 631 774 on a GPS satellite.

 This is not true. NOBODY thinks that (except some deranged idiots around
here).
 On a GPS satellite, the usual definition of the second applies. But in
order for the SIGNALS from GPS satellites to be received on earth at the
correct frequencies, the time-base on the satellite must tick about 4
parts in 10^10 more slowly than a corresponding time-base on earth's
geoid (mean sea level).

Perhaps it may be easier to understand if it is compared to the Doppler effect of a train horn.
Consider a train whose horn sounds at exactly 440 Hz (musical tone A4).
What note did the train engineer and passengers hear the horn sound? Assume they had perfect pitch.
Now the train is parked at a station and it sounds its horn. What note would a passenger on the platform (with perfect pitch) hear the train horn sound?
Now the train approaches the station at 134.796 km/hr. What note do the passengers on the train sound? And...what note would the passenger on the platform hear the horn sound? He would hear it sound at 493.883 Hz, better known as "B" or B4. Why?
Another train approaches at 134.796 km/hr. The passenger on the platform hears its horn at 440 Hz or A4. But the passengers aboard the train insist it sounds at 391.995 Hz, better known to musicians as G or G4.
The signal from the GPS birds is much like this (frequency shifted but for a different reason), but its master frequency is set so that the signal is received at the correct frequency. Much like the second train.