GPS and Relativity | How Time Dilation Affects GPS Accuracy | Special and General Relativity
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- Опубликовано: 5 окт 2024
- Did you know that our GPS system serves as a proof of Einstein's theory of relativity? Satellites are moving very fast as viewed by us from the ground. This speed difference causes the very precise clocks on the satellites to appear to us to tick slower! Also, because the satellites are so high up and aren't affected by as strong a force of gravity as we are at the surface, our clocks are slowed down as well. These concepts, special and general relativity, have to be computed into the GPS position, otherwise the errors would be so large as to make the system worthless!
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As an engineer this is one of the most elegant and understandable explanations I've seen of this idea. Very well done, glad you guys go further than what is required!
I have a physics degree and work as a mechanical engineer, and this is the best explanation I have heard of this topic to date. As a private pilot working on my instrument rating, I really appreciate your concise explanations in all of your videos.
My sim flying rabbithole has definitely taken me deep.
Mine too. Sorry..
A perfect explanation; 7micro-s slower and 45micro-s faster due to special and general relativity. Fantastic, thank you.
As an Electrical Engineer and as a pilot, this is one of the best videos created by people who have a 4 dimensional brain and able to narrate it in a simple graphical method. Good job fellow pilots..
As a physics phd and new commercial pilot, I can agree that this is a very elegant explanation and very well presented.
Can't tell you how many times I've seen or heard this explained, but now, thanks to you, I've got a reasonable idea how it works.
Your disclaimer was not necessary. As a commercial pilot/CFI and a high school science teacher, I think you nailed it! This was an awesome explanation, and your infographics were very intuitive. I do think it's hilarious that you apologized, in advance, to the universe. I'm sure that you have been forgiven. It's a merciful universe.
First time I’ve ever felt like I had even the slightest understanding of special and general relativity. Nice job! The simple and straightforward animations were perfect.
This is very relevant to me, because my RV-6 travels at a significant fraction of the speed of light. So these effects matter ;-) Thank you for the explanation - very well done.
ROFL!!! As does my 172… the general relativity impact is immense!
@@arctain1 GR is static (post newtonian)...velocity is special relativity (see: post Minkowski). This stuff matters for interplanetary spacecraft navigation.
As a physicist and a pilot, you nailed it.
Continuing the series, next, tackle RAIM with and without Baro-aiding… 😊
Me too! I’m struggling with this one.
We've got a RAIM video! ruclips.net/video/7ESZcUCKieA/видео.html
@@flightinsight9111 Thanks! You and your team ROCK!
Really well explained, it's difficult for a non-physicist like me to grasp but it makes complete sense after seeing your video. That's the sign of a really well explained video - when noobs like me can understand it now. Gosh, Einstein really must have had a superhuman level of cognition and comprehension to come up with this theory before we had ever sent anything into space - building on existing theories and knowledge without being able to see his ideas demonstrated in person. Godlike. And 100 years later, he's only getting proven right again and again. If only he got to live to see all the discoveries about physics and space that have been made since he died in the 1950s, seeing his theories in action.
I'll pile on. Masters degree in physics, and you did great! Conceptually special relativity is NOT easy to grasp, and your explanation was concise and understandable. Love this channel, BTW. I've learned a ton from you, and wish you'd been around when I was doing ground school.
Very concise. Beautifully explained. Love it
Really nice work. Your aviation videos have always been great and this really cool that you're able to use the same format to explain such a mind bending concept soooo well.
Jesus man, I've been in Physics 12 for like 2 months and only now do I confidently understand special relativity, thank you so much.
As an aerospace engineer and a pilot, bravo. Very well explained!
Thanks for explaining Einstein's theory of relativity. The effects of motion and measurement of light speed.
I believe GPS is a brilliant technological achievement.
🌏🌅
Fantastic explanation! Thank you for putting it together.
My commercial checkride is coming up soon. I'm sure my first question while doing a chandelle will be to explain the special theory or relativity and now I'm all set! I've not studied this since college thanks for the fun review.
A CFI once asked me to explain how a gyroscope works during a flight review. I told him I had 6 years of fundamental science in me and asked him if he still wanted to hear an answer. He said no.
Amazing Explanation! Brilliant in it's simplicity
Did this dude just say that light is a wave of particles? If we had this man sooner we wouldn't have had the need for the wave-particle duality.
Lovely video again, thank you!
Quick question: when you are preparing your videos, do you work with ICAO as a base or also with EASA? Since you are in the USA i guess ICAO is your only source?
You are my favourite youtuber, btw awesome disclaimer at the end!
Q: What's the difference between shining a light on a moving train and the mirror at the far end? Why is the speed of a photon added to the speed of motion in one but not the other?
to add velocity a to b, use c = (a + b) / (1 + ab/c^2) which is a + b for slow speeds.
Really informative, thank you
There are a series of continuously operating reference stations all over the country that correct GPS signals allowing for pinpoint accuracy. For example that is what surveyors use to accurately determine property lines.
you mean differential GPS? where a zero'd in base station takes out the ionosphere, water vapor, and what ever else?
@@DrDeuteron good question.. the ionosphere and moisture content can both affect GPS signals and I know the receivers we use can collect atmospheric data but not sure if that is included in the corrections that are transmitted. The system is primarily used to correct for the 38 microsecond difference between the satellite and fixed ground receiver. The GPS signal is timestamped from the source.
Special Relativity (SR) cannot explain the GPS pseudo-range correction that is included in the algorithm for calculating location by every GPS receiver. The pseudo-range correction is an example of the straight-line one-way Sagnac effect; it is a first order phenomena - a function of v/c where v is due to the rotation of the Earth with respect to the Earth centered inertial reference frame (the ECI) at the latitude of the GPS receiver. SR is a 2nd order transformation - a function of v/c squared. It can only contribute a negligible amount to the pseudo-range correction - less than one millionth of the pseudo-range correction. SR is disproved every day by every cell phone with a GPS receiver.
Well written post. Neil Ashby literally admitted this in his Physics Today article regarding the GPS system. Of course, he didn't mention Sagnac effect debunks relativity, but everyone knows that the Sagnac effect can be derived within 2 lines of highschool alegbra, while relativisits try at to derive the same result using path integrals over Taylor series of a infinitisimal Lorentz transformations. Not to mention the horrendous "derivation" by Paul Langevin in 1921, since Einstein ignored both Sagnac effect and Michelson Gale till the end of his life (42 years in the case of Sagnac) he had to send his minions to attempt answering it.
As an animator, with a BA in Art. I do not have the credentials to post in the comments section here :) Good explanation! There are folks who occasionally don't believe me that satellites are a real world example of relativity theory. "It's just a theory" they say. Can we dedicate some federal funding to re-explaining to the general public what a theory is?
A theory is the origin of the Earth's moon. It can't be truly explained how it became the Earth's moon.
The reason GPS clocks show different times can be easily explained by elementary physics.
FORCE DECREASES WITH DISTANCE TRAVELED. THUS, LESS ACCELERATION.
The inverse square law explains it.
Increasing the separation distance between objects decreases the force of attraction or repulsion between the objects. And decreasing the separation distance between objects increases the force of attraction or repulsion between the objects.
Electrical forces are extremely sensitive to distance.
So why are you using relativity theory from Einstein’s fantasy spacetime universe?
you kinda messed up the intro. In the ball on train experiment, the speed that the ground observer sees the ball moving is:
149.99999999999832 mph < 150 mph.
It's not just for light, it's for everything. It just that the speed difference between Galileo and Einstein in the example is 1 inch per 1000 years.
so our intuitions say that velocities add linearly, c.f. the pitcher on the train, but that is wrong. There is something that does add linearly, and physicists call it "rapidity". It is the inverse hyperbolic tangent^1 of v/c. So for the low velocity case:
atanh(v/c) = v/c * (1 + v^2/3c^2 + ....)
so the correction 1) quadratic in velocity, and less than 10 parts per quadrillion at baseball speeds.
[1] this is because velocity changes are hyperbolic rotations in spacetime....it all works out nicely.
Ok, add physics instructor to your list of exceptional talents.
If the DPE askes me about this on my upcoming instrument checkride, and I answer incorrectly, then I will immediately collapse into a singularity.
Was about to comment something similar hahaha
Question: How DOES Special Relativity explain the pseudo-range correction?
Note that an given signal emitted from a GPS satellite takes about one-tenth of a second to reach a receiver. Any time dilation effect due to relative speed or satellite altitude would be negligible
So, I think I got it. Because the satellite is traveling faster, its clock is slower relative to earth (special relativity). But because the earth clock is in a stronger gravitational field, its clock is slower than the satellite by a greater amount (general relativity). Taken together, the earth clock is slower by 38 microseconds. Thanks for the explanation.
Yup that’s it. And now you can safely forget all this and still have a successful flying career!
close. It's not the strength of the gravitational field, it is the difference in gravitational potential. For example, the clock runs slowest at the center of the Earth (I think a few years since creation), but the gravitational field there is ZERO.
Damn amazing. This video is just astronomical.
Thank you
Please tell me that this is not going to be on the instrument knowledge test...
Fact Check needed.
In order to keep how to satellite in orbit you need to turn on and off chemical engine.So errors from that process are million times bigger than clock speed change (according to relativity theory )
Part of GPS is current ephemerides (orbit parameters). Those are constantly updated, and are part of the GPS signal. Now if you have a fixed point base station, you can collected data and correct it after the fact, as better ephemerides are constantly published as they become better known with time. (You can also add atmospheric and ionosphere corrections that are not available in realtime, too).
The biggest error in GPS is the receiver clock (it is not an atomic clock), which is why you need 4 satellites--1 for each spatial dimension and 1 for the receiver clock bias. But 12 are always better than 4.
If the special theory of relativity were correct the time from emission of a radio wave from a GPS satellite to a receiver on the ground would depend only upon the distance from satellite to receiver at the time of emission. However the Earth's rotation during the travel time of the radio wave from satellite to receiver must be taken into account thereby showing that the speed of light relative to the receiver is not c.
So basically light is bizarre because photons always maintain c as its speed hence it slows down in a gps .
what?
Photons move at same speed no matter the speed of the source because once emitted the photon travels in quantum space and it is quantum space that controls the speed not the source.
If you need to adjust SR and GR between the Satellites and the Ground, how do you compensate for the airplanes flying above at the height of 10 km and at the speed of 1,000 km/h?
How about north pole vs equator?
Don't the earth spin at the equator at 1,700 km/h, while the poles are standing still?
Does GPS compensate clock rate for them too?
yes.
@@DrDeuteron LOL
Why doesn't the photon have less distance to travel when going opposite direction of satellite (between mirrors) ? Would that not compensate for when it has to travel a longer distance and them make it even? I mean I know I'm wrong but I don't get it
You're ready to be a physics professor now!
Why didn't you mention the relativistic effects of length contraction in your example?
what does it affect?
@@DrDeuteron I did some relativistic calculations and found that while length contraction would have some effect it would be of second order and thus inconsequential.
How can you assume the speed of light would be same on a train when you can't accurately mesure speed of light in the first place. Than the animation of mirror and light clock which is stupid by the way proves it think about it light travels faster when your moving one way and slower when your moveing the other way just like the baseball, it makes perfect sense it's not time travle it's a faulty clock
Through equations
no, please. just don't. The faulty clock stuff is flat earth on steroids.
If they use traditional clock it will be a time dilation?
So at the same point in space, time dilates and contracts at the same time ? How is this considered a viable explanation, when its obviously a contradiction ?
but it is not. Relativity is a self consistent theory. There are many Special Relativity Paradoxes (twin, pole/barn, Bell's spaceship) that deal with the apparent contradictions for our Galilean minds.
It’s all perception though, it doesn’t speed up or slow down time itself. In other words, if both started at point a, and 3,2,1 go, if we pressed pause, looked at the time, one would not and could not be at a time that hasn’t happens yet, time dilation is only relevant because of latency. I bring this up in regard to the idea of time travel, by moving at speed of light in one direction then turning around and being told you would have traveled into the future basically. I
If you got up to speed at a “higher” space time and then dropped all your mass would you suddenly fly off at a higher speed?
no.
But is this is just an analogy for space-time warping, yes? These GPS clocks don't actually work by counting the rate of reflecting photons, do they? I am not a scientist. I am easily confused!
they are atomic clocks, which measure the cycles of an atomic transition in cesium (133-Cs). Note that per quantum mechanics, all 133-Cs atoms are not just identical (we can't tell them apart), they are indistinguishable (God can't tell them apart--this is why we have quantum entanglement). Anyway, they are all the same, and in the time it takes to count 9,192,631,770 oscillations, one seconds has passed. No matter where you are, or how you are moving.
The light clock example is used because it is easy to understand in a thought experiment. Keyword: thought. You don't need to build it.
The atomic clock aboard an aircraft moves slower than one on the ground, but the atomic clock onboard a gps satellite moves faster than the one on board the airplane. Has anyone tried to explain why? The satellite is traveling faster than the airplane. Any answers or are my facts incorrect?
Do you have your XC Nav Log in PDF? u like your layout better
Yes! You can check that out here: www.flight-insight.com/post/use-this-excel-vfr-navlog-to-organize-your-cross-country-flights
Actually... that's not true. Yes, I'm a repair guy youtub'r... but I have a physics degree. We actually look for a "Red Shift" in stars to know if they are traveling away from us. This is a doppler shift in the speed of light. With that said... I never thought about a time shift in the GPS system. Thanks for the early morning brain exercise.
I am still baffled by the fact we say time is relative, without showing it is.
All i see is that math just gets altered in this way so that equasions fit the errors we introduce by the limit of lightspeed.
but it is, and relativity is required in many applications.
@@DrDeuteron
I still say the clock on the satelite is not mesuring time, but distance.
GPS does not need relativity to work and also does NOT use it. The clocks that are sent into space are given a delay of 39 microseconds, so that when they reach their destination the clocks on ground and satellite are synchronized but that is not even a necessity as only the satellite clocks should run in synch and those are kept in synch. This continual drift due to hypothetical relativity is not taken into account. Also according to relativity, depending on the frame taken, the satellite clocks should either tick slower and faster at the same time. It is the same absurdity with the twin paradox. Also taken into account the effect of relativity or not, only makes a difference of 8 millimeters in pinpointing the location of the receiver. So get the facts straight instead of listening to popular media outlets copying the same false claims from everyone else.
You should add an apology to the universe at the end of every video
I don't believe in time dilation, change my mind.
Who cares what you think.
@@sissyfus6181 Ronald Hatch.
@@DavidJohnAr that guy is so wrong. It's pathetic.
why not? It is experimentally observed. Why don't you prove that the Galilean view of time is correct. Change meh mind.
Start with Maxwell's Eqs. for radiation from a moving dipole.
Please provide a self consistent answer here:________________________
ps: that is rhetorical, because you can't.
😂time dilation😂
I know, right!!!!
You're gonna need a bigger boat!!!
foolishness...
Special relativity is a special case of general relativity, and only applies to non accelerating objects outside of gravitational fields. You simply cannot apply special relativity in this situation where the GPS satellite is in a gravitational field and has a circular or centripetal acceleration. You can only apply general relativity.
Furthermore, if you apply both SR and GR you get time dilation from the first (from higher speed) and a time contraction from the latter (from weaker gravity). Which leads to a paradox, of time dilating and contracting at the same time.
Ron Hatch, one of the inventors of GPS, states that GPS actually proves relativity WRONG. See his disertation in the video 'Relativity in light of GPS'.
Ron Hatch's video are garbage.