Sources on the internet claim that the GPS system requires Relativity to work (xkcd). I've searched information about the GPS system, how it works and how it was set up, reading information from many sources including the US military who maintain the GPS system. I also looked at the equations used to calculate position.
I couldn't find any dependence on relativity anywhere.
All I could find is a minor claim that the satellite clocks initial setting were CONSISTENT with relativity, but that claim didn't come from the US military websites.
Does GPS use Einstein's General Relativity in order to work accurately?
Yes, GPS requires both general and special relativity to work
[Note this is simplified account based on this and this (MS word download)]
We can understand why by looking at how GPS actually determines where you are. The system relies on a number of satellites transmitting signals and your GPS device receiving those signals (see wikipedia). There are about 32 GPS satellites and each transmits a signal that contains the exact time based on very accurate atomic clocks on the satellite and position information about where the satellite is. A typical GPS receiver can "see" a handful of satellites from any given position on the earth's surface. Crudely, the position of the receiver is calculated by noting how long the signal takes to arrive from each satellite, using this to calculate the distance to the satellite and then, by trilateration (the 3D equivalent of triangulation), deriving the receiver's position from the distances from several satellites whose positions are known.
Civilian GPS is typically quoted as having an accuracy of about +/- 15m though there are ways to do better. Military GPS can go below +/- 1m precision. Since the speed of light (the speed of the radio signals from the satellites) is about 300 million m/s this means we need to be able to account for time in accurate units of a handful of nano seconds to get that degree of precision for distance.
This is where relativity comes in. Clocks are affected by both gravity and motion. High speeds make clocks run slower according to special relativity and higher gravity also slows them according to general relativity. Since GPS satellites travel at about 14,000km/hr their clocks will be slow relative to the earth's surface by about 7 microseconds (7,000 nano seconds) per day. Because the earth's surface has gravity about 4 times higher than a GPS satellite the satellite clocks run about 45 microseconds faster than one on the ground. This gives a net difference of about 38 microseconds relative to the surface per day. If we ignored relativity and failed to correct for this, GPS positions would be out by about a dozen kilometres per day (those microseconds trump the required accuracy of nanoseconds by factors of thousands).
To summarise the issue. We need to keep accurate account of time for GPS to work. But GPS clocks are affected by relativistic effects that alter their clocks relative to the earth's surface. We can retain accurate times if we adjust for the known differences and so we can retain an ability to accurately find the position of a GPS receiver.
So relativity, both special and general, is required or the system would be useless.
The comments here have suggested that there is some obfuscation and confusion on the conclusion here.
It is true, as some have pointed out, that absolute proof is not possible in science (at least if you take a Popperian view of verification). Facts can show a theory is wrong, but they can't prove it is correct. While true this isn't a strong objection to the answer here. Perhaps it would be clearer if we said "provides extremely strong evidence in favour of" rather than "proves" but in practice the difference is small.
In the case of GPS we have a scientific theory (or two related theories) that predicted precise effects more than 50 years before the GPS system was deployed. That is pretty much the strongest sort of scientific verification that is possible. Arguing that it isn't "proof" in a mathematical sense is merely nit-picking.
And arguing that the relativistic corrections would be irrelevant in a Newtonian universe is just a ridiculous distraction based on an irrelevant philosophical though experiment. The question is about this universe and this universe is accurately modeled by relativity.
SV here is Space Vehicle. This is how the frequency of the clock set:
The nominal frequency of this source - as it appears to an observer
on the ground - is 10.23 MHz. The SV carrier frequency and clock
rates - as they would appear to an observer located in the SV - are
offset to compensate for relativistic effects. The clock rates are
offset by ∆f/f = -4.4647E-10, equivalent to a change in the P-code
chipping rate of 10.23 MHz offset by a ∆f = -4.5674E-3 Hz. This is
equal to 10.22999999543 MHz.
This is not the only clock correction, there are many effects discussed in the paper, and so:
[SV message] ... contain the parameters needed by the users for apparent SV clock correction
(toc, af2, af1, af0). The related algorithm is given in paragraph
The algorithms defined below (a)
allow all users to correct the code phase time received from the SV
with respect to both SV code phase offset and relativistic effects
SV basically keeps track of its clock's error which is calculated by the communication with the Control Segment (CS):
The NAV data contains the requisite data for relating GPS time to UTC.
The accuracy of this data during the transmission interval shall be
such that it shall relate GPS time (maintained by the MCS of the CS)
to UTC (USNO) within 90 nanoseconds (one sigma).
Also, it is outlined how the user should calculate the relativistic shifts given the data from SV:
the user's equipment must determine the requisite relativistic
correction. Accordingly, the offset given below includes a term to
perform this function...
There is a list of different generations of GPS blocks which have different periods in which they can function independently from Control Segment. If no data (including time correction) has been uploaded to the satellite within this period, it's health is considered "bad" and it is no longer used (until revived).
Each Block IIR/IIR-M/IIF SV in the constellation determines its
own ephemeris and clock correction parameters via SV-to-SV ranging,
communication of data, and on-board data processing which updates data
uploaded by the CS. In the Autonav mode the Block IIR/IIR-M/IIF SV
will maintain normal operations as defined in paragraph 220.127.116.11 In
the Autonav mode the Block IIR/IIR-M/IIF SV will maintain normal
operations as defined in paragraph 18.104.22.168 precision. If the CS is
unable to upload the SVs, the Block IIR/IIR-M/IIF SVs will maintain
normal operations for period of at least 60 days after the last
The document is huge and there's lots of interesting information in there. One of the things to derive from it is that the newer generations of GPS devices take into account more time correction effects with higher precision and thus require less frequent calibration from Control Segment.
Does GPS require the knowledge of relativity? No.
The GR correction can be done without the knowledge of where it comes from. The signal frequency received from a satellite is different from the frequency originally emitted, and this shift can be measured experimentally. Knowing this shift, then one can proceed with the whole procedure described above, and all the other minor relativistic corrections would be included in on-line calibration, exactly as such hard-to-estimate or random effects are included now, as described here:
These updates synchronize the atomic clocks on board the satellites to
within a few nanoseconds of each other, and adjust the ephemeris of
each satellite's internal orbital model.
So, would it be possible to create GPS system without the knowledge of Theory of Relativity? Yes, as described above, using experimental results, calibration and trial and error method. However, it would suggest the presence of unexplained phenomenon(a), because the frequency shift would not be explainable by the known phenomena. It likely will not work very well as it will require more frequent clock correction (I would not speculate further because it is too hard to guess what "would be" in such case).
Does GPS prove Relativity (General and/or Special)? Yes and no.
All I could find is a minor claim that the satellite clocks initial
setting were CONSISTENT with relativity
A scientific theory is a well-substantiated explanation of some aspect
of the natural world that is acquired through the scientific method,
and repeatedly confirmed through observation and experimentation.
There is no other way to confirm a theory but by observation. A consistent confirmation of a theory through observation constitutes a proof of a theory. The emitted frequency from the satellite is different from the frequency observed by the receiver, and the difference closely matches the GR time shift. In this instance, the theory matches (and successfully predicts) the observation. Of course, GPS alone is not a proof (in the aforementioned sense) of GR and SR, no serious scientific resource claims this. This is just one of the many demonstrations of the predictive power of these theories and there are certainly multiple other experiments and observations which provide a much more elaborate proof forboth of these.