4 ms·

What I don’t understand is why we would ever assume two clocks in two different places could be compared in a non approximate way. Your clock, your observations

What I don’t understand is why we would ever assume two clocks in two different places could be compared in a non approximate way. Your clock, your observations of the world state, are always situated in a local context. In the best of all possible cases, the reasons why your clock and time reports from other clocks differ are well understood.

pavel_lishin 2y ago
camera cuts across to Newton, seething on his side of the desk, his knuckles white as the table visibly starts to crack under his grip
ses1984 2y ago
I think something like the small angle approximation applies. There are plenty of applications where you can assume clocks are basically in the same frame of reference because relativistic effects are orders of magnitude smaller than your uncertainty.
christina97 2y ago
The approximation error is so small that you can often ignore it. Hence the concept of exact time. Eg in most computing contexts, you can synchronize clocks close enough to ignore a few nanos difference.
- Asraelite 2y ago
  How? Unless you have an atomic clock nearby, they will very quickly drift apart by many nanoseconds again. It's also impossible to synchronize to that level of precision across a network.
  - AlotOfReading 2y ago
    It's not only possible, you can demonstrate it on your phone. Check the GPS error on your device in a clear area. 1 ft of spatial error is roughly 1ns timing error on the signal (assuming other error sources are zero). Alternatively, you can just look at the published clock errors: http://navigationservices.agi.com/GNSSWeb/PAFPSFViewer.aspx http://navigationservices.agi.com/GNSSWeb/PAFPSFViewer.aspx All the satellites in all of the GNSS constellations are synchronized to each other and every device tracking them to within a few tens of nanoseconds. Yes, atomic clocks are involved, but none of them are corrected locally and they're running at a significantly different rate than "true" time here on earth.
    - Asraelite 2y ago
      That's true, but it's not really the situation I'm thinking of. Your phone is comparing the differences between the timestamps of multiple incoming GNSS signals at a given instant, not using them to set its local clock for future reference. A better analogy to practical networked computing scenarios would be this: receive a timestamp from a GNSS signal, set your local clock to that, wait a few minutes, then receive a GNSS timestamp again and compare it to your local clock. Use the difference to measure how far you've travelled in those few minutes. If you did that without a local atomic clock then I don't think it would be very accurate.
      - AlotOfReading 2y ago
        That's a common way of doing high precision time sync, yes. It's slightly out of phone budget/form factor, but that's what a GPSDO does. The receiver in your phone also needs pretty good short term stability to track the signal for all of the higher processing. It'd be absolutely fine to depend on PPS output with seconds or minutes between measurements.
      - wat10000 2y ago
        Basic hardware gets you a precise GNSS time once per second. Your local clock won’t drift that much in that time, and you can track and compensate for the drift. If you’re in a position to get the signal and have the hardware, then you can have very accurate clocks in your system.
        tucnak 2y ago
        Until somebody start spoofing GPS like they do in Ukraine, and you look embarrassing.
        AlotOfReading 2y ago
        So use Galileo's OSNMA instead. That'll work until they spend $100 on a jammer.
  - mgaunard 2y ago
    WhiteRabbit achieves sub-nanosecond time synchronization over a network.
    - Asraelite 2y ago
      Oh wow, that's impressive. Is that over a standard internet connection? Do they need special hardware?
      - mgaunard 2y ago
        It does require a special switch yes.
  - prerok 2y ago
    The Precision Time Protocol is intended to solve this problem: https://en.m.wikipedia.org/wiki/Precision_Time_Protocol https://en.m.wikipedia.org/wiki/Precision_Time_Protocol It does require hardware support, though.
vpaulus 2y ago
I believe it has some advantages that while you are waiting at the train station your clock shows exactly the same time as the train conductor’s several miles away from you.
- sevensor 2y ago
  Surely not! We could be a whole minute off and I’d still be standing on the platform when the train arrived.
  - dibujaron 2y ago
    in the US or parts of Europe you could wait there for 10m past the scheduled time and barely notice. In Japan if the train clock disagreed with the station clock by 30s, causing the train to arrive 30s late, they'd have to write all of the passengers excuse notes for why they were late to work.
wat10000 2y ago
GPS depends on widely separated (several times the diameter of Earth) clocks agreeing with each other down to the nanosecond.
- withinboredom 2y ago
  and moving at such high speeds that relativity factors into the equations.
  - wat10000 2y ago
    Speeds and altitude both! I believe time dilation from gravity is more significant but both are big enough to need compensation.

pavel_lishin 2y ago

camera cuts across to Newton, seething on his side of the desk, his knuckles white as the table visibly starts to crack under his grip

ses1984 2y ago

I think something like the small angle approximation applies. There are plenty of applications where you can assume clocks are basically in the same frame of reference because relativistic effects are orders of magnitude smaller than your uncertainty.

christina97 2y ago

The approximation error is so small that you can often ignore it. Hence the concept of exact time. Eg in most computing contexts, you can synchronize clocks close enough to ignore a few nanos difference.

Asraelite 2y ago
How? Unless you have an atomic clock nearby, they will very quickly drift apart by many nanoseconds again. It's also impossible to synchronize to that level of precision across a network.
- AlotOfReading 2y ago
  It's not only possible, you can demonstrate it on your phone. Check the GPS error on your device in a clear area. 1 ft of spatial error is roughly 1ns timing error on the signal (assuming other error sources are zero). Alternatively, you can just look at the published clock errors: http://navigationservices.agi.com/GNSSWeb/PAFPSFViewer.aspx http://navigationservices.agi.com/GNSSWeb/PAFPSFViewer.aspx All the satellites in all of the GNSS constellations are synchronized to each other and every device tracking them to within a few tens of nanoseconds. Yes, atomic clocks are involved, but none of them are corrected locally and they're running at a significantly different rate than "true" time here on earth.
  - Asraelite 2y ago
    That's true, but it's not really the situation I'm thinking of. Your phone is comparing the differences between the timestamps of multiple incoming GNSS signals at a given instant, not using them to set its local clock for future reference. A better analogy to practical networked computing scenarios would be this: receive a timestamp from a GNSS signal, set your local clock to that, wait a few minutes, then receive a GNSS timestamp again and compare it to your local clock. Use the difference to measure how far you've travelled in those few minutes. If you did that without a local atomic clock then I don't think it would be very accurate.
    - AlotOfReading 2y ago
      That's a common way of doing high precision time sync, yes. It's slightly out of phone budget/form factor, but that's what a GPSDO does. The receiver in your phone also needs pretty good short term stability to track the signal for all of the higher processing. It'd be absolutely fine to depend on PPS output with seconds or minutes between measurements.
    - wat10000 2y ago
      Basic hardware gets you a precise GNSS time once per second. Your local clock won’t drift that much in that time, and you can track and compensate for the drift. If you’re in a position to get the signal and have the hardware, then you can have very accurate clocks in your system.
      - tucnak 2y ago
        Until somebody start spoofing GPS like they do in Ukraine, and you look embarrassing.
        AlotOfReading 2y ago
        So use Galileo's OSNMA instead. That'll work until they spend $100 on a jammer.
- mgaunard 2y ago
  WhiteRabbit achieves sub-nanosecond time synchronization over a network.
  - Asraelite 2y ago
    Oh wow, that's impressive. Is that over a standard internet connection? Do they need special hardware?
    - mgaunard 2y ago
      It does require a special switch yes.
- prerok 2y ago
  The Precision Time Protocol is intended to solve this problem: https://en.m.wikipedia.org/wiki/Precision_Time_Protocol https://en.m.wikipedia.org/wiki/Precision_Time_Protocol It does require hardware support, though.

vpaulus 2y ago

I believe it has some advantages that while you are waiting at the train station your clock shows exactly the same time as the train conductor’s several miles away from you.

sevensor 2y ago
Surely not! We could be a whole minute off and I’d still be standing on the platform when the train arrived.
- dibujaron 2y ago
  in the US or parts of Europe you could wait there for 10m past the scheduled time and barely notice. In Japan if the train clock disagreed with the station clock by 30s, causing the train to arrive 30s late, they'd have to write all of the passengers excuse notes for why they were late to work.

wat10000 2y ago

GPS depends on widely separated (several times the diameter of Earth) clocks agreeing with each other down to the nanosecond.

withinboredom 2y ago
and moving at such high speeds that relativity factors into the equations.
- wat10000 2y ago
  Speeds and altitude both! I believe time dilation from gravity is more significant but both are big enough to need compensation.