Does GPS use General Relativity?

Question

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?

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: http://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Relativity — 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](http://skeptics.stackexchange.com/posts/20230/revisions) — Sklivvz, Apr 17 '14 at 19:31
Hi, i think that the link to xkcd makes the question loaded with an opinion, which apparently isnt how skeptics.SE questions whould be. also its not my link and is not an attempt by me to put my opinion into the question. I suggest a moderator remove the link. — 497362, May 01 '14 at 07:08
You have not heeded @Sklivvz advice - there is now no longer a notable claim. Putting on hold in accordance with site policy. — Jamiec, May 01 '14 at 12:07
@Jamiec This really should have been locked in the previous version. OP goes in circles trying to prove his point and seem to completely ignore the statements made in the answers by creating a new strawman in almost every single comment. — sashkello, May 01 '14 at 12:42
I was advised by moderators that questions should avoid pre-emting answersm and it is the answers that shoudl contain the notable claims. so i have followed the moderators advice. — 497362, May 01 '14 at 13:34

score 66 · Answer 1 · edited Apr 13 '17 at 12:40

66

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.

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.

edited Apr 13 '17 at 12:40

Community

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answered Apr 13 '14 at 15:00

matt_black

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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 --- ex-moderator kitten Apr 13 '14 at 16:06
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"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..." http://youtu.be/5qlLW60wOjo?t=33m – basic6 Apr 13 '14 at 17:16
GPS signals do not use "triangulation" - that is determining points based on angles. Instead, they use "trilateration" - determining points based on intersecting spheres. – corsiKa Apr 15 '14 at 13:28
Removed thread about ...alternate universes and the meaning of science. Seriously folks - use the comments only to suggest improvement to the answer. – Sklivvz Apr 17 '14 at 11:55
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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
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Stomped on another pointless polemic and accusations of censorship. If you like to debate the finer point of epistemology, use the [chat]. If you need to rant against moderators, contact our community team via [our feedback form](http://skeptics.stackexchange.com/contact). Finally, if you have questions or proposals on our policy, use [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
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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 01:24
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While clearly your answer is correct in that GPS in fact does use GR physics, I think your explanation is wrong. In fact, GPS measures time **differences** between the satellites' signals. Since all satellites experience about the same amount of time shift, your GR corrections would cancel out. Therefore your argument in fact does not show that GR would be neccessary for GPS to work. @sashkello s argument is correct and should be the accepted answer: It's GRs effect on the signal frequency (not the difference to local time) that is crucial. – ilmiacs Aug 21 '14 at 16:21
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@ilmiacs Well, nope. The issue the matters is knowing where the satellites are in space at a given exact time. This means you have to have an almanac of satellite positions that uses the relativistic corrections. Those corrections don't wash out in the calculations. – matt_black Aug 26 '14 at 12:48
@JohnDeters The receiver doesn't need an accurate clock. The signals from the satellites contains information that allows the local clock to be resynchronised to the atomic clocks and then the relevant calculations about where the satellites are in space are done. – matt_black Aug 26 '14 at 12:50
@matt_black, what I said was that the receiver does not carry an accurate source of time, so it cannot directly measure the timing of the signal from one satellite to itself. It can't synchronize to one clock, either, because it doesn't know how far away it is. It can only synchronize the clock after it has determined its position. – John Deters Aug 30 '14 at 03:24
`those milliseconds trump the required accuracy of nanoseconds by factors of thousands` but you speak of microseconds up to that point, not milliseconds. – Federico Jun 27 '15 at 09:31
@Federico well spotted. Now fixed. – matt_black Jun 27 '15 at 11:17
The "ridiculous distraction" is actually the whole point of the claim. The xkcd comic claims that general relativity is used to make money from GPS, and if the phenomenon of general relativity didn't exist, then GPS wouldn't exist. And _that_ is wrong. All that GPS needs is a highly precise clock, a high but not too high speed of light, and of course good knowledge of physics. Without relativity we'd have to compensate for speed of light changing as the light comes from moving satellites, but there's no reason why GPS wouldn't work. – gnasher729 Jun 29 '15 at 19:36
Umm, satellites have to be about 2 times faster than you wrote https://en.wikipedia.org/wiki/Orbital_speed – Mithoron Jul 29 '15 at 22:29
@Mithoron Not according to that table at the bottom of that wiki article. I think you are looking at the orbital speed of the earth round the sun. – matt_black Jul 30 '15 at 08:23
No, I thought they're on low orbit instead of high :( – Mithoron Jul 30 '15 at 11:29
@Mithoron Well Molniya orbits range from about 5,000km/hr to >30,000km/hr according to the Wikipedia entry and that seems to cover the range quoted for GPS satellites (btw they are not geostationary). – matt_black Jul 30 '15 at 19:09
I checked, Molniya orbits are elliptic - v varies, GPS has intermediate circular orbit v=20.2*3.14/12=10.6 (thousands of km/h). – Mithoron Jul 31 '15 at 00:16
The answer is wrong, GPS does not *require* relativity. The correction is just a constant factor that is explained by relativistic effect, but obeservable and applicable without knowledge of relativity. https://space.stackexchange.com/questions/40330/when-was-newton-not-good-enough-for-spaceflight-first-use-and-first-absolute/40372#40372 and https://physics.stackexchange.com/questions/390400/how-are-gps-corrected-for-special-general-relativity – May 27 '21 at 22:10
@a_donda A nitpicking semantic argument. The corrections required for a GPS system to work are precisely those *predicted* 50 years earlier by general and special relativity. Similarly, we didn't need a Newtonian theory of gravity to land men on the moon, we could have used empirical observations. We'd have needed a lot more observations. But we had the theory and it worked. Same with GPS. – matt_black May 27 '21 at 23:21
"The corrections required for a GPS system to work are precisely those predicted 50 years earlier" citation needed, and deeper knowledge. They are indeed 2 magnitudes higher. The other answer got it right, relativity is *not* needed (that's where you're wrong), they would simply have corrected a constant factor they observed (that's actually what they did in the first batch of satellites literally, by adjusting the clock's frequencies), and of course afterwards searched for an explanation. Read the two olinks I posted, and the Arbery (or so) paper ... – May 27 '21 at 23:29
@a_donda "two magnitude" (100 times) higher" ? *That* needs a citation. I already provided sources. If you want to argue that the observed corrections that match the theory mean that GPS doesn't *use* the theory, you should be on philosophy.SE not here. – matt_black May 28 '21 at 00:36
@matt_black You need to source your claim, which you haven't. Even the 50 years are incorrect. And again, if you care to read: contrary to your claim and as stated by others, the GPS systems works perfectly without an understanding relativity, by applying a 'factory offset'. – May 28 '21 at 01:01
@a_donda I quoted my sources and I'm not making a strong claim about 50 years that was just a colloquialism. Your claim that relativity isn't "needed" is a philosophical and semantic quibble not a scientific objection. Are you also claiming that we didn't need Newtonian gravity to fly to the moon? The logic is the same. – matt_black May 28 '21 at 01:02
I'm not playing whataboutism. Your answer is wrong, the other one (and those on physics and space se) got it right. – May 28 '21 at 01:17
@a_donda Do you mean the right answer to the one titled “Does GPS use the theory of relativity? Yes”? If so I struggle to see your point as it essentially agrees with my answer. – matt_black May 28 '21 at 01:23

sashkello · Answer 2 · 2014-05-04T01:25:42.373

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.

Please only include paragraphs that you can reference. For example that one can dismiss an atomic clock going slower as "calibration". — Sklivvz, May 01 '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 01 '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 02 '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 04 '14 at 01:26
I'm just surprised about the minor frequency correction. Actually, the same change in frequency would be induced by Doppler effect if sender and receiver move at about 14 cm/s. While this may raise doubt that the *frequency* needs to be tuned so precisely it also tells us that forgetting relativistic correction would be somewhat like the satellites drifting away form their supposed orbit at 14 cm/s, which sooner or later makes the trilateration inexact — Hagen von Eitzen, Jun 27 '15 at 22:33

Does GPS use General Relativity?

2 Answers2