GPS系统用相对论矫正可能是一个以讹传讹的骗局，请确认。
Global Positioning System (GPS) and Relativity
The Global Positioning System (GPS) is nowadays considered as the prime
example for the everyday importance of Relativity. It is claimed that without
the relativistic corrections (which amount to 38 microseconds/day) the error
in the determination of the position would accumulate quickly to values much
larger then the observed accuracy (Ref.1 , Ref.2).
However, in reality the positions are actually not obtained by comparing the
time signal received from the satellite with the receiver time, but by observing
the difference between the time signals obtained from a number of different
satellites (see the Wikipedia GPS article for details (note that I have
linked this now to an older version of the article, as the latest version
is not as clear in this respect)).
Consider for simplicity a one dimensional problem where the receiver is located
somewhere on the line connecting the two transmitters. In this case the signal
from transmitter 1 reaches the receiver at time
(1) t1 = t0+ x1/c
and the signal from transmitter 2 reaches the receiver at time
(2) t2 = t0+ x2/c ,
where t0 is the time the signal is being sent out (assuming both transmitter
clocks are synchronized), x1 is the distance of the receiver from transmitter
1, x2 the distance of the receiver from transmitter2, and c the speed of light.
Now if one subtracts Eqs.(1) and (2) one gets
(3) x1-x2 = c. [t1-t2].
One knows therefore the position of the receiver just by comparing the time signals
from the two transmitters (the receiver clock is completely irrelevant).
Global Positioning System (GPS) and Relativity
The Global Positioning System (GPS) is nowadays considered as the prime
example for the everyday importance of Relativity. It is claimed that without
the relativistic corrections (which amount to 38 microseconds/day) the error
in the determination of the position would accumulate quickly to values much
larger then the observed accuracy (Ref.1 , Ref.2).
However, in reality the positions are actually not obtained by comparing the
time signal received from the satellite with the receiver time, but by observing
the difference between the time signals obtained from a number of different
satellites (see the Wikipedia GPS article for details (note that I have
linked this now to an older version of the article, as the latest version
is not as clear in this respect)).
Consider for simplicity a one dimensional problem where the receiver is located
somewhere on the line connecting the two transmitters. In this case the signal
from transmitter 1 reaches the receiver at time
(1) t1 = t0+ x1/c
and the signal from transmitter 2 reaches the receiver at time
(2) t2 = t0+ x2/c ,
where t0 is the time the signal is being sent out (assuming both transmitter
clocks are synchronized), x1 is the distance of the receiver from transmitter
1, x2 the distance of the receiver from transmitter2, and c the speed of light.
Now if one subtracts Eqs.(1) and (2) one gets
(3) x1-x2 = c. [t1-t2].
One knows therefore the position of the receiver just by comparing the time signals
from the two transmitters (the receiver clock is completely irrelevant).
