Astronomy - General Relativity (14 of 17) Proof of Theory: Gravitational Time Dialation and GPS
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- Опубліковано 20 вер 2024
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We will learn the proof of the theory of Gravitational Time Dilation and GPS. Both effects do not cancel out completely and must therefore be calculated and the results used in all timing and positioning calculations.
Next video in this series can be seen at:
• Astronomy - General Re...
Perfectly explained, efficient, right to the point and exactly wrong!
The proof is simple, get a USB GPS receiver (Which I have) plug it in.
Now change the time on your computer, it still works. Proving that GPS receiver software does not use GR calculation.
All that GPS receivers do is triangulate, that's why you need a minimum of three satellite signals.
I happen to be an engineer working on GPS and I am very familiar with the code that we use on our receivers. We do use adjustments for GR and SR in our receivers.
Perfectly explained, efficient and right to the point.
Geoids are used to correct for vertical inaccuracies due to differences in gravity. Do you have a video that demonstrates how gravity is affecting the accuracy of the vertical data, and how using a Geoid in processing fixes this error? I am having a very hard time understanding how the error occurs and how using a Geoid fixes it. Thank you for posting this video as it was also very helpful in furthering my understanding.
Your Golden easy minutes briefing hard chapters
Note that in ordered to get the 45 usec number, you have to take the difference between gravity effects at the earth and gravity effects at the satellite. Alternatively, you could use the formula for an orbiting body, sqrt(1-3GM/(rc2)), and get both special and general in one go.
I’m wondering how to derive the equation, t = sqrt(1-3GM/rc^2))?
If we plot time on axis if the receiver is moving slower due to the gravity of the Earth and the satellite is moving faster due to its speed in time, when we do the summation of the special relativity and general relativity does that ever turn to the difference? Where the special relativity is in the positive time axis and the general relativity is in the negative.
I love how he has every color of dry erase marker, my kind of guy!
Always prepared! 🙂
Does gravitational time dilation result from backward motion of time due to decrease in entropy caused by gravity.
There is no indication that time can "travel" backwards.
@@MichelvanBiezenThank you for correcting. I thought forward motion of time was due to increasing Entropy.
The equation for the time dialation on the satellite is NOT correct ! Special Relativity only applies to non accelerating moving objects. Since the gps satellite is in mid earth orbit, it is accelating at 9.8 m/S2, or g. Therefore, SR time dialation equation DO NOT apply !
I am a GPS engineer who worked with the GPS algorithms. I can assure you that the relativistic effects have to be accounted for. (See our GPS videos on this channel).
Hi sir, Omar present..................
What will happen if you go through wormhole???? How time will effect????
Wormholes are theoretical constucts and are presumed to exist at the quantum level, not like they show in movies and we will not be able to travel through them.
But motion itself is relative so for the satellite, it's the earth that's actually revolving from the perspective of the satellite, so shouldn't satellite's point of view be the opposite or am I not understanding something
Yes for both observers the other one will be in motion but that's the beauty of Relativity that it exact tells which properties describe reality. And that's why Tensors are used since they do not change from observers to observers. So the nature of the event and reality is absolute and other measurement are relative
If the clpcks on the satellite and at the Earth's surface change, one wrt to the other, then the receivers would indicate that change .
Is it not true that it is the PERCEPTION that the clocks have changed NOT that they really have changed ?
Only arsking !
They have actually changed. It is not a perception. We must account for these changes in our GPS algorithms or GPS wouldn't work.
I’m just here tryin to figure out how to hit slo-mo irl while playing halo infinite
Nothing on this channel that will help you do that.
“Its probably more than 30 by now”
I believe we have 31 working GPS satellites at the moment.
Sir are you a Professor.if yes then in which University
Loyola Marymount University and El Camino College.
Great!.. can we derive this gravitational time dilation equation using some simple thought experiment, as we did for the time dilation equation in special relativity?
Good question. Let me give that some thought.
Thank teacher
Sir, does the centrifugal force acted on the satellite affect any of the calculations? Since in the 8th video, it is shown experimentally that stronger gravitational field and centrifugal force both has the same time dilation effects
In this case the centripetal force IS the force of gravity.
@@MichelvanBiezen Oh right! For some reason, I thought there was some mysterious rocket boosting it to follow a circular orbit, thanks!
When a person presses A button in A circuit,light is off.When the person presses A button in B circuit,light is on.Why is that?Is it about position of the A button?Sir
prnt.sc/tr7otz
In circuit A, when you push the button, it causes a short so no current will flow to the base of the transistor and does no current will flow through the transistor. In circuit B pushing the button will allow current to flow to the base of the transistor.
This schoolbook computation of relativistic effects in the GPS system 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. 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, base station 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.
Nice summary. Thanks. (For some applications, an error of 10 m is not tolerable, and that is why we adjust for relativistic effects, as well as the ionosphere, etc.)
@@MichelvanBiezen Hi. Ionospheric errors can be adjusted to almost zero during calm solar weathers but increase tremendously during solar storms (15-30m easily). Differential GPS can't correct for that. As for relativistic effects, they account for less than 5m half of the day and between 5 and 10 during the other half, which again is pretty damn low for like 99% of average people applications. If we didn't knew anything about it and did nothing about it, it would still be pretty good. But still we would have noticed it and maybe discovered relativity! On the other hand, in the mean time we could have corrected it by synchronising earth based clocks and satellites by updating orbiting clocks with ground utc time (sending messages). This is still done by the way. So it is still wrong to say that without relativity, we wouldn't have had accurate and functional GPS.
The fact remains that the current system slows the atomic clock to account for relativity. So why do they do it? I have a few thoughts:
1) They wanted to use the system for accurate time-of-day. Note that the error is cumulative in the satellites.
2) They wanted the system to be operational with only 3 satellites visible.
3) They wanted to simplify calculations, so the millions of receivers did not have to work so hard. Remember, this is mid-70's technology.
Any other thoughts?
Sir, is rotational movement of thr earth has an effect in this explanation??
Everything has an effect but in this case it is so minute, we can ignore it.
Good job :)
You're Welcome!
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Please don't say that the clock runs slower.
Instead say that time goes faster.
Please. It twists my mind.
The clock runs slower because time progresses more slowly.
@@MichelvanBiezen that means the clock runs faster ?!
No, that means that everything (including the clock) runs slower.
Geoids are used to correct for vertical inaccuracies due to differences in gravity. Do you have a video that demonstrates how gravity is affecting the accuracy of the vertical data, and how using a Geoid in processing fixes this error? I am having a very hard time understanding how the error occurs and how using a Geoid fixes it. Thank you for posting this video as it was also very helpful in furthering my understanding.
We have posted some GPS videos on this channel that may help in aswering your question.