6 ms·

"What would be good, though, would be for someone to call us back when the thinking leads to something, anything, that we can see or feel or sense or even under

by gwern 10y ago

"What would be good, though, would be for someone to call us back when the thinking leads to something, anything, that we can see or feel or sense or even understand—because all this astonishingly brilliant thought and science and learning and history, all these amazing stories, as far as I can tell, have no consequences at all. Our commonsense subjective understanding of time is as telling, as tyrannical, as it ever was. A century-plus of fervent speculation and analysis of time and time travel have led to exactly no outcomes. We are as stuck in the present, as irrevocably exiled from both past and future, as ever." Einstein's time dilation has practical consequences: aside from being able to observe the slowdown in atomic clocks taken up in airplanes and the many consequences in astronomy, we also have GPS, which would not work without taking relativity into account. If GPS doesn't count as a 'consequence' or 'outcome' due to a non-traditional understanding of time, nothing does!

dom0 10y ago
This is a relatively common misconception. The location calculation in GPS is independent of any time dilation between the GPS receiver and the satellites (as long as the satellites have roughly equal dilation), because the receiver clock is derived from the satellites' signals. This is also the reason why you need at least four satellites for a 3D fix, and three for a 2D fix - you are always deriving an additional unknown variable, time. (And this is also the reason why a GPS time receiver works with only one satellite: the position is locked when they are set up, after that they can work with 1+ satellites. More satellites will reduce errors, though.) The time dilation is therefore only compensated so that you can use a GPS receiver as a very accurate, absolute clock.
- WJW 10y ago
  Technically the fourth variable that a receiver solves for is the clock error in the receiver, not the actual time (though that then follows easily enough). The system of equations is only solvable because it is assumed that the clock error of the satellietes relative to each other is zero. I'm not convinced though that time dilation is the same for all the satellites, since they are not all in the same orbit. Since the system works by determining signal delay between the satellite and the receiver and the signals move at (rougly) the speed of light, even an nanosecond error in time is already a 30 cm error in position. According to [0] the clock drift due to relativistic effects would be over 45000 nanoseconds per day. So keeping the clocks synchronized for all the satellites is crucial and relativistic corrections are super important for accurate positioning. [0]: http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps....
  - dom0 10y ago
    > According to [0] the clock drift due to relativistic effects would be over 45000 nanoseconds per day. Between an uncorrected satellite and the receiver. This error is already removed through the fourth variable, only the average error of the satellites used for this remains (assuming perfect receiver etc.). So even if the satellites where not corrected the positioning error would not be "XY kilometers per day and climbing", the much smaller difference in time dilation between satellites would remain though.
    - jayisbatman 10y ago
      The location calculation is completely dependent upon relativistic time dilation. The Navistar satellites have an orbital speed of 8,750 MPH (more than 2 miles per second, relative to our earth surface frame), they are subject to a relativistic time dilation adjustment of -7201ns (slower than our earth surface frame). The location calculation cannot ignore that. The GPS signal (radio) takes on average 1 foot per nanosecond (perhaps a slightly bit more, but this is electromag radiation in a non-vacuum). If your receiver didn't account for this you would be more than a mile from your actual location. Relativity and its time dilation are required for any satellite based location system -- unless your satellites are at altitude of zero.

by gwern 10y ago

dom0 10y ago

This is a relatively common misconception. The location calculation in GPS is independent of any time dilation between the GPS receiver and the satellites (as long as the satellites have roughly equal dilation), because the receiver clock is derived from the satellites' signals. This is also the reason why you need at least four satellites for a 3D fix, and three for a 2D fix - you are always deriving an additional unknown variable, time. (And this is also the reason why a GPS time receiver works with only one satellite: the position is locked when they are set up, after that they can work with 1+ satellites. More satellites will reduce errors, though.) The time dilation is therefore only compensated so that you can use a GPS receiver as a very accurate, absolute clock.

WJW 10y ago
Technically the fourth variable that a receiver solves for is the clock error in the receiver, not the actual time (though that then follows easily enough). The system of equations is only solvable because it is assumed that the clock error of the satellietes relative to each other is zero. I'm not convinced though that time dilation is the same for all the satellites, since they are not all in the same orbit. Since the system works by determining signal delay between the satellite and the receiver and the signals move at (rougly) the speed of light, even an nanosecond error in time is already a 30 cm error in position. According to [0] the clock drift due to relativistic effects would be over 45000 nanoseconds per day. So keeping the clocks synchronized for all the satellites is crucial and relativistic corrections are super important for accurate positioning. [0]: http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps....
- dom0 10y ago
  > According to [0] the clock drift due to relativistic effects would be over 45000 nanoseconds per day. Between an uncorrected satellite and the receiver. This error is already removed through the fourth variable, only the average error of the satellites used for this remains (assuming perfect receiver etc.). So even if the satellites where not corrected the positioning error would not be "XY kilometers per day and climbing", the much smaller difference in time dilation between satellites would remain though.
  - jayisbatman 10y ago
    The location calculation is completely dependent upon relativistic time dilation. The Navistar satellites have an orbital speed of 8,750 MPH (more than 2 miles per second, relative to our earth surface frame), they are subject to a relativistic time dilation adjustment of -7201ns (slower than our earth surface frame). The location calculation cannot ignore that. The GPS signal (radio) takes on average 1 foot per nanosecond (perhaps a slightly bit more, but this is electromag radiation in a non-vacuum). If your receiver didn't account for this you would be more than a mile from your actual location. Relativity and its time dilation are required for any satellite based location system -- unless your satellites are at altitude of zero.