Only there was no "fix". GPS weren't adjusted for time dilation. The engineers who made this stuff said it was too insignificant a number for them to bother with so, although they knew the theory, they hadn't actually implemented it. They responded to this very question directly on their own forums. GPS does not take any account for time dilation. It's an Urban Myth. Like the discovery of the gay gene and teleportation. Or how CERN will make black holes. A good hook to get you interested in what is ultimately a very dull subject. Physics. So while I might be willing to dispute the conclusions of the time dilation experiment with the two atomic clocks and the aeroplane, I prefer it as scientific evidence of time dilation since I do actually believe it happened. Unlike that GPS story, which is just a good story Brian Cox comes out with on TV get you listening.
Google Tennis? Seems like a dull game, https://books.google.co.uk/books?id=3qIACAAAQBAJ&pg=PA24&lpg=PA24&dq=navstar++time+dilation&source=bl&ots=5Sz6IYE_gK&sig=tai9jwhqV1AvHmXs0S5TjYxyK6I&hl=en&sa=X&ved=0ahUKEwj55IuxlpDYAhUmCMAKHWUAD7cQ6AEIMTAC#v=onepage&q=navstar time dilation&f=false Believe what you will please. As will I.
The very first SENTENCE in your post confirms what I said! The rest goes on to discuss other time dilation issues that also are notable if you're interested in accuracy.
"Google Tennis?" Could be used in GPS as opposed to "is" used in GPS. The subtle difference between theory and practice. So the use of time dilation in GPS is a theoretical example and not a practical one because in practice, they don't. Theoretical science vs applied science. I think Einstein was 15 years old when he came out with this one. Not really his finest work. Makes for a lot of good sci fi plots however, like the poster above's spaceship encounters.
No, it then goes on to say how they remove the time dilation affects of the fact that the GPS satellites are in a slightly egg shaped orbit. In other words, they identify ANOTHER time dilation factor that must be considered. Notice that they say that ground GPS units know the altitude of the satellites at any given time and thus can correct for the difference in time passage between being slightly below or above the nominal altitude of the assumed perfect orbit that the clocks are set for. Dude - it explains this right in YOUR cite.
Yes, yes, the two time dilation effects cancel each other out. That's your theory? Rather a convenient theory that one. Very neat. My key point being, in practise they don't bother applying it because it makes no difference to GPS. And you can theorise that it does, and that they do. but in practise, they don't because it doesn't. The practical example you offered me of time dilation theory being used was incorrect. Was a practical example of time dilation theory not being used. Because it made no difference whatsoever whether they applied the theory to the satellite or not. None. Same result either way. So they don't bother. Fart gas dressed up as science.
Each observer is at rest in their own frame of reference. There is no such a thing as an absolutely motionless observer - there is no absolute state rest. It is all relative. So each observer measures the other's clocks running more slowly - each observer sees the other in a state of motion relative to them.
You couldn't be more wrong except for your correction in the final paragraph; respect. The military has to take GRAVITY into account so they do adjust time and hence accuracy in regards to our GPS. Don't believe me but look for yourself. That is not germane exactly to the topic of speed I'll concede. But one can infer that if gravity changes time then it is likely speed does as well since it is part of the equation. Does time slow or speed up differently in a strong gravity field relative to one not as strong? Consider black holes and time as a start although there are plenty of other ways to explore that topic.
Which works well at the atomic level and above but not so much at the subatomic level. Not sure that it is possible for both ships to record the other ships clocks as running slower. Why is velocity left out of the equation?
I worked on NAVSTAR many years ago and I can assure you that we had to take account of time dilation effects though, unless I remember wrongly, we corrected the difference using look up ROM and not using a different clock speed. This was in very early stages of Navstar and accuracy was not as is now. I think that there has been some confusion in posts above stating that different clock speeds are used - what is actually done is the number of ticks used in the clock is adjusted depending on location of transmitter and receiver
You are forgetting that the observers are on the rockets. Their relative velocity is the same hence each observer will measure the same time dilation.
The thing is, there is no "really" about it. Your "really" implies an absolute frame of reference from which you can decide what is "really" going on.
If you think the frame of reference is arbitrary, then it is just as valid to say the sun orbits the earth as it is to say the earth orbits the sun.
Here's a better paradox. A man on a unicycle is traveling at relativistic speeds towards a grate set in the road. The man on the unicyle sees the slits on the grate become narrower so he can easily traverse the grate, A man standing beside the grate sees the unicyclist and his unicycle become narrower so he is certain to fall through the slits of the grate. What really happens?
Nope. The earth undergoes centripetal acceleration by orbiting. This is not a constant velocity so the choice is no longer arbitrary. When you consider velocity you have to consider the vector form, which includes both speed and direction. The direction is constantly changing so the velocity vector is not a constant.
He falls through because in the defined fixed frame of reference, the man standing beside the grate, his length is contracted. There is an introductory problem sometimes used in physics - how fast do you have to be going to fit a 10 foot car in a 5 foot garage? Same problem. Whoops, I misread that... I need to think for a moment. My answer is correct but I'm not sure how to resolve the apparent paradox. Good one. I need to think... or maybe I'm just rusty!
But not in their own frame. Each observer sees the other's clocks running slowly compared to their own frame of reference.
So what? One can formulate a perfectly fine physics in an accelerating frame of reference. Which is a good thing, because all we have are accelerating frames of reference.
Special Relativity is only valid when the velocity vectors are constant. General Relativity is required for non-inertial frames. Basically SR assumes you are in deep space and free off any gravitational forces and accelerations. I remember reading that when Relativity was checked using jets and atomic clocks, the correction for time dilation due to gravity was more significant than due to the speed of the jets. The clocks on the jets ran faster than earth clocks because of the reduced gravity at altitude.
