# Does GPS use General Relativity?

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?

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I've heavily edited the question in order to make it appropriate to the site, removed the obsolete comments and reopened. Please note that further edits on the question may lead to putting it on hold again. –  Sklivvz Apr 17 '14 at 11:52
Example of how relativity is used in GPS: en.wikipedia.org/wiki/… –  Sklivvz Apr 17 '14 at 13:17
@Sklivvz, thanks for your edits of my question. I hope you dont mind that I announce these edits in the question, because the question is so far from the original. i dont want someone to call me out for plagiarism, sometime down the road. –  497362 Apr 17 '14 at 19:24
Please leave the question as is, the history of its edit is clearly visible here –  Sklivvz Apr 17 '14 at 19:31
You have not heeded @Sklivvz advice - there is now no longer a notable claim. Putting on hold in accordance with site policy. –  Jamiec May 1 '14 at 12:07

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 milliseconds 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.

Philosophical note

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.

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It is wort noting that both effects (from relative velocity and from depth of gravitational potential) have been measured very precisely in the laboratory without confounding factors. relative velocity time dilation is measured regularly in the context of unstable particle decay, and gravitational time dilation had been measured directly using Mössbauer spectroscopy. –  dmckee Apr 13 '14 at 16:06
"If you let the clock run on the satellite for one day without compensating it, the clock would be in error by 38 microseconds or so, which would be about 11 km ranging error..." youtu.be/5qlLW60wOjo?t=33m –  basic6 Apr 13 '14 at 17:16
I'd change it to "Crudely, the position of the receiver is calculated by noting the differences between how long the signals take to arrive from each satellite,..." It's the differences that enable the receiver to determine the distance to each. The receiver can't time the signal from one satellite because, unlike the satellite, it has no accurate clock to provide an internal frame of reference. –  John Deters Apr 17 '14 at 19:04
Stomped on another pointless polemic and accusations of censorship. If you like to debate the finer point of epistemology, use the Skeptics Chat. If you need to rant against moderators, contact our community team via our feedback form. Finally, if you have questions or proposals on our policy, use Skeptics Meta. Comments are to constructively suggest improvements to the answer. If you've nothing to offer from that point of view, avoid using them. –  Sklivvz Apr 18 '14 at 19:00
Suggested improvement to answer: back up the claim made in the title. This answer just explains how GPS COULD use GR. It doesnt back up that claim with anything. –  497362 Apr 19 '14 at 1:24

Does GPS use the theory of relativity? Yes.

The information below is quoted from GPS interface specification.

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.

These numbers are explained in detail here.

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 20.3.3.3.3.

...

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 6.2.3.1 In the Autonav mode the Block IIR/IIR-M/IIF SV will maintain normal operations as defined in paragraph 6.2.3.1 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 upload.

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.

This is not only possible, but exactly how it is done at the moment, because there are a lot of factors contributing to the inaccuracies and to calibrate the device you need to know the adjustments exactly.

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

From wikipedia:

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 for both of these.

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Some of the information contained in this post requires additional references. Please edit to add citations to reliable sources that support the assertions made here. Unsourced material may be disputed or deleted.

Please only include paragraphs that you can reference. For example that one can dismiss an atomic clock going slower as "calibration". –  Sklivvz May 1 '14 at 19:25
@Sklivvz I didn't say you can dismiss it. What I said is that any inaccuracy can be accounted for using calibration. This is what is done now, you can't account for all inaccuracies with high enough precision, so satellites get correction data from the Control. Same could happen with relativity correction, it is no different from any other correction, just that it would make coordinates useless within few hours after each re-calibration communication. Knowledge of the source of this inaccuracy is not required. –  sashkello May 1 '14 at 23:06
Please provide a citation that (a) sync can happen with any accuracy with clocks running fast and (b) that the system would not be completely useless without the GR correction or remove the paragraph in question. –  Sklivvz May 2 '14 at 11:58
@Sklivvz I made some edits, hope it helps to understand my point. This part of question is speculative by nature, so all I can do is to show that it might be possible with the exactly same technology as present in modern GPS. –  sashkello May 4 '14 at 1:26