Everyday Einstein: GPS & Relativity
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- Опубліковано 17 сер 2020
- The Global Positioning System (GPS) is an everyday technology that incorporates a number of effects from Einstein's theories of general and special relativity.
This video is part of Perimeter Institute's free educational resource Everyday Einstein: GPS & Relativity. Download the teacher's guide, modifiable worksheets, and supporting materials at: resources.perimeterinstitute....
Perimeter's educational outreach programs and resources like these are made possible in part thanks to our donors. Be part of the equation: perimeterinstitute.ca/donate. - Наука та технологія
So thankful for this video. I didn't know that both special and general theory had effect on gps and was confused.
The way Special Relativity is described 100% of the time these days, is to describe it in a fragmented manner. And so people think that it "just is". They have no desire to see the big picture as to what it is that creates the relativistic outcome. "The speed of light is the same in all frames of reference, and so relativity must come into play.". That statement is enough to satisfy almost everyone's mind these days. However, if the absolute cause behind the special relativity(SR) phenomena is revealed in an incredibly simple geometric manner, even a high school dropout could use it to derive the SR mathematical equations, including deriving the Lorentz transformation equations, and do all this in mere minutes. So why is it that schools teach students about SR in a fragmented manner ?
* in all inertial frames of reference
I was just looking for realitivity applications and I suddendly found a sea of knowlege with this video.
Great video. Knowledge is power.
Thanks for finally publishing this video before the heat death of the universe! What else have you been stocking up? :D
The military has higher accuracy GPS than the civilian public. Do they have their own satellites, or do they have a tag in the GPS signal that the receivers look for before reporting their calculations?
They are the same satellites, paid for by the DOD, the military accesses the higher accuracy on a different MHz band.
Is it not it the case that, the cause of any discrepancies between two clocks must be entirely physical rather than temporal and that, such discrepancies, have nothing to do with actual time?
Cool video
The GPS satellites follow 1 of 6 different orbits around the Earth so the satellites have different speeds relative to each other. So why don't the satellite atomic clocks fall out of synchronization with each other if they are adjusted only one time to run more slowly prior to launch? How do they stay synchronized with each other once they are in orbit?
Very good question, apparently the satellites are synced periodically en.wikipedia.org/wiki/Global_Positioning_System#Control_segment
"Then 2 SOPS contacts each GPS satellite regularly with a navigational update using dedicated or shared (AFSCN) ground antennas (GPS dedicated ground antennas are located at Kwajalein, Ascension Island, Diego Garcia, and Cape Canaveral). 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. The updates are created by a Kalman filter that uses inputs from the ground monitoring stations, space weather information, and various other inputs.[96]"
@@iamonhere Yes, and this exactly why, even if we knew nothing about Special/General relativity, we would still be able to have a perfectly functionning GPS system with high accuracy because we would be synchronizing the clocks on a frequent basis by exchanging signals, as we currently actually do.
Nota: special relativistic clock drifts only take into account relative velocity amplitudes of sats wrt to Earth. Since these are roughly the same, the sats clocks are always roughly synchronized between themselves. The signals exchange are needed to essentially correct for other errors which are much more critical than any special relativity based velocity drifts, which are always close to non existent (again due to the sats having identical velocities).
@@pablog4291 " special relativistic clock drifts only take into account relative velocity amplitudes of sats wrt to Earth. Since these are roughly the same, the sats clocks are always roughly synchronized between themselves."
That is not true, it applies between satellites as well. The satellites can have very different orbits and relative velocities between themselves (in some cases even more than a satellite vs ground station). Stop making bad approximations, the satellites are not all in the same inertial frame of reference.
Also as stated in the video, the general relativity effect of time dilation in a gravitation field is much stronger than the special relativity effect due to velocity, so much so that it supersedes it.
"which are always close to non existent (again due to the sats having identical velocities)." This is false as I mentioned above. Velocity is both speed AND direction.
@@iamonhere 'Stop making bad approximations' Says the guy who models gps as a 1 satellite system and computes 11km error per day...
'Velocity is speed and direction'
So much Lorentz factor has vectors all over the place...
Honestly you should not take on subjects you misunderstand so deeply, or at least you could show a bit of humility when you realize you got it all wrong.
Mistakes are human, after all!
Have a nice day!
@@pablog4291 "'Stop making bad approximations' Says the guy who models gps as a 1 satellite system and computes 11km error per day..." I literally never modelled it as that. If you are referring to the equations I put in the previous comments, that was at least 4 equations considering the positions of 4 satellites. If you are referring to the comment about satellite velocity vs ground station that was just considering a small part of a bigger model which is a valid way to simplify the analysis of a complex model.
"Velocity is speed and direction'
So much Lorentz factor has vectors all over the place..." that's not even a proper sentence, just a bunch of words. Adding technical jargon to your sentences does not make an actual argument.
"Honestly you should not take on subjects you misunderstand so deeply, or at least you could show a bit of humility when you realize you got it all wrong."
I am open to criticism, feel free to make an actual argument but you seem content to stay in "I am right and you are wrong" land.
The schoolbook computation of relativistic effects in the GPS system as presented in the video does not correspond to how the GPS really works ( GPS is not made of 1 receiver and 1 satellite but is made of a constellation of satellites in order to always have 4 over any point on earth surface). The schoolbook derivations for the 1 satellite-1 receiver system yields something around 11km inaccuracy shift in position per day ( -7us for the Special Relativity time dilation due to the velocity of the satellite and + 45us for the General Relativity gravitational time dilation due to the high altitude of the satellite resulting in 38us overall time drift which multiplied by the speed of light gives the 11 km figure). Is this the real expected time drift due to relativistic effects? No, it is not. The reason is that they are always 4 satellites over any point on Earth and all satellites have, in first approximation, same velocities and same altitudes: their clocks are thus synchronized ( they do not drift with respect to each other). This means than when a receiver receives 4 satellites navigation messages with their positions and times, it doesn’t matter how shifted their clocks are with respect to the receiver: 4 equations with 3 unknowns ( receiver x,y,z) allows to eliminate receiver t and compute x, y, z. Now the question is does the satellites always have same velocities and altitudes? the answer is again no, as satellites can slightly jump in their excentricities. But the shifts are small and introduce a small inaccuracy in position which varies between 0 and 10m within a period of 12h. Without knowing relativistic effects, the resulting GPS inaccuracy would be 10 m at max, 0-5m 12 h per day and 5-10 m during the other 12h. Is that a big deal ? Not at all. For instance, ionospheric errors are up to several ten of meters during bad solar weather days. Moreover, ground stations based on Earth regularly send signals to the satellites that contains their UTC time, allowing for synchronisation between their clocks times. Conclusion: Are there relativistic effects at play in the GPS? Yes. Is it of primordial importance to take them into account to have a working accuracy on a GPS system: not at all, as 10 m accuracy is better than good for most everyday use cases. As a leading institute promoting the advancement of knowledge and science, It would be desirable that you update the video with an appropriate erratum explaining why the 11km gps inaccuracy you present and that you supposedly attribute to relativistic clock drifts is not the correct one.
Hi Pablo, do you have a reference about this? than you
"in first approximation, same velocities and same altitudes: their clocks are thus synchronized ( they do not drift with respect to each other)." This is a bad approximation. The satellites can be in entirely different orbits, velocity is not merely speed but also direction.
"4 equations with 3 unknowns ( receiver x,y,z) allows to eliminate receiver t and compute x, y, z." Even granting the bad approximation above this statement is still wrong, even if there is no time dilation between the satellites, there is still a significant amount of time dilation between the satellites and the receiver on Earth which cannot be ignored when solving those equations.
The equation of a sphere centered at the satellite at (x_0, y_0, z_0), you get a message that was sent at t_s0 (according to satellite clock) and you receive it at t_e0 (according to your clock on earth)
(x - x_0^2) + (y - y_0^2) + (z - z_0^2) = r^2
(x - x_0^2) + (y - y_0^2) + (z - z_0^2) = c^2*(t_e0 - t_s0)^2 (where c is the speed of light in vacuum)
and you have 3 more equations like that for the other 3 satellites.
It's very clear that if the clocks that measure t_e0 and t_s0 are out of sync by a large amount then the time difference (t_e0 - t_s0) will also be off by a large amount and the distance squared r^2 will be off by a very large amount. So your final position (x, y, z) will be off by a lot (may not even be on the surface of the Earth anymore depending on how out of sync the clocks get).
Clearly you cannot ignore the time dilation between satellites and Earth even if you ignore time dilation between satellites.
"For instance, ionospheric errors are up to several ten of meters during bad solar weather days." Those are temporary vs the gravitational time dilation is an accumulative error. Even your overly conservative estimate of "10 m at max, 0-5m 12 h per day" is a very big deal when the error accumulates.
"Moreover, ground stations based on Earth regularly send signals to the satellites that contains their UTC time, allowing for synchronisation between their clocks times." That's literally to correct for gravitational time dilation among a whole host of other errors. en.wikipedia.org/wiki/Global_Positioning_System
"In 1955, Friedwardt Winterberg proposed a test of general relativity-detecting time slowing in a strong gravitational field using accurate atomic clocks placed in orbit inside artificial satellites. Special and general relativity predicted that the clocks on GPS satellites, as observed by those on Earth, run 38 microseconds faster per day than those on the Earth. The design of GPS corrects for this difference; because without doing so, GPS calculated positions would accumulate errors of up to 10 kilometers per day (6 mi/d).[21]"
"as 10 m accuracy is better than good for most everyday use cases." Whose use case? 10m is the difference between 2 different streets in a lot of places which leads to a lot of frustration for every day delivery drivers. Not to mention the whole reason GPS was developed in the first place was for military applications which require sub 1m accuracy.
The information is the video is a simplified version of the GPS system meant for a general audience. It is accurate to a first approximation.
@@iamonhere I'll answer your remarks:
"The satellites can be in entirely different orbits, velocity is not merely speed but also direction." Only the amplitude of the velocity vector affects Einsteinian relativity 'time dilation'. If the satellites have same velocities on their orbits (which they have in first approximation), then their direction is unrelevant. My first approximation is still valid: there is no clock drifts between different satelites clocks since their clocks are all affected same way, they remain synchronized.
"Even granting the bad approximation above this statement is still wrong, even if there is no time dilation between the satellites, there is still a significant amount of time dilation between the satellites and the receiver on Earth which cannot be ignored when solving those equations."
Let's simplify this: In 1D positionning, if I want to get my x coordinate along a line, we need 2 satellites in order to achieve that regardless of the synchronisation of receiver clock with emitter, assuming there is no clock drift between the satellites. Why? let's assume I receive t1=t2 (the times sat1 and sat2 emitted their GPS signals), this means I am in an equidistant position from both satellites, no need to use my receiver clocks, I'm able to compute my position given the knowledge of sat positions (ephemerides). if I receive t1>t2, I know I am closer to the second satelite and the ratio t1/t2 is enough to figure out about how much and compute the position. Reasoning goes the same for t2>t1. Then you can generalize to 2D (with 3 satellites), and 3D (with 4 satellites). This is exacltly why GPS requires at least 4 sats in view, because this way we eliminate the need for receiver's clock data, hence receiver's clock plays absolutely NO role in modern GPS positioning. Having more than 4 sats in view (usual), further improves accuracy.
"Clearly you cannot ignore the time dilation between satellites and Earth even if you ignore time dilation between satellites." Clearly GPS was designed in a such a way we can do that all the time (no pun intended) as demonstrated in my previous reply.
"Those are temporary vs the gravitational time dilation is an accumulative error. Even your overly conservative estimate of "10 m at max, 0-5m 12 h per day" is a very big deal when the error accumulates."
Excentricity errors don't accumulate. That's the whole point why they are not a big deal. During a day, error is ~10 meters maximum, twice per day, with sinusoidal variations in between. That's the only significant error due to clock drifts.
"That's literally to correct for gravitational time dilation among a whole host of other errors."
Nope, that's to correct essentially the whole host of other errors since they are much more significant that the relativistic clock drifts which "only" leads to the excentricity error (the ~10m one). Even if we knew strictly nothing about Special Relativity/General Relativity, the cyclical excentricity drift would have been corrected with a simple analytical fit. But the key here is that other errors are much, much worse and more difficult to fully model a priori, so we need to regularly update the parameters of a polynomial fit to update clock data onboard sats, and we do it through signal exchange because it is practical.
"The design of GPS corrects for this difference; because without doing so, GPS calculated positions would accumulate errors of up to 10 kilometers per day (6 mi/d).[21]"
This statement is obviously wrong. The 10km accumulative error is pure urban legend with no scientific grounds whatsoever. I think we should stop trying to impress general public with relativity by propagating false ideas about what is really going on in the GPS system and false claims about how relativity plays a role in it. That's bad popular science and bad science practice overall. There never was any sort of accumulative 10km error predicted by any valid study of the GPS system. The 10km accumulative error is solely derived from a series of wrong assumptions about how the GPS system really works. I insist: it is a shame to keep pushing for this BS to the public, science does not deserve that. The public deserves to have better popular science education that is accurate and that develop its critical thinking abilities. Wrong dumb down popular science can't be the way, it hurts science a lot.
"Whose use case? 10m is the difference between 2 different streets in a lot of places which leads to a lot of frustration for every day delivery drivers. Not to mention the whole reason GPS was developed in the first place was for military applications which require sub 1m accuracy."
To reach those accuracies you build very sophisticated algos to correct for the more important sources of errors which are not relativity related. And again, the 10 m error is only twice per day, it is lower than that most of the time. But we correct for those too easily, as explained in my previous remarks.
"The information is the video is a simplified version of the GPS system meant for a general audience. It is accurate to a first approximation."
We profoundly disagree on that one. it is not "simplified", it is just WRONG. We should really stop to propagate the 10 km accumulative error urban legend, it hurts science. The general public deserves much better popular science approaches that works towards developing their critical thinking and above all, gives accurate information about what is really going on. None of that is done here. It is pretty sad a major institution dedicated to scientific research at top level patronizes such content. I think that it is OK to start with the 10 km approach, but then it is mandatory to go further to explain to teh public why such simplified picture DOES NOT correspond to the reality of teh inner workings of the GPS sytstem. That's how you develop genuine general scientific knowledge by calling to critical thinking and reasoning.
Thanks for your replies tho, they were constructive overall.
Thank you. I always thought relativity was nothing more than fiction. Just plain hogwash. Newtonian physics ftw baby.
"It could be" v Theoretical Physics.
The phones and GPS handhelds in this video are all 10+ years old.
Update: the final lines on the end credits: "(C) 2010"
Yup.
Doesn't mean the information is out of date :)
@@yrebrac Well, it doesn't mention WAAS or LAAS ground stations.
@@yrebrac
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Looks like a flat erf derp hit the dislike button already 🤣
Another video on GPS and relativity?
Must be nothing new to report on.
Wrong!! no relativity is required for GPS