Sysadmins would know right away.
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My co workers are in Ireland, England, India, Japan and the USA. We’d notice pretty quick
GPS would fail as soon as the first tz ticked over. Internet routing would fail instantly too.
As immediate as the power grid falls apart without constant frequency synchronization, so probably seconds. I do consider North America's Western, Eastern, and Texas power grids as a communication system, because it does convey the precise 60 Hz AC line rate to every part of the continent.
Are you saying they're in sync? And the wavelength is that reliable?
Yes. By necessity. The grid has to be kept in sync within a fairly small frequency range to operate. Every generator that is grid connected, is spinning at the same frequency. It is a small enough window that you can use it as a reliable clock.
Every time the power load changes they have to compensate with increasing or decreasing the power available to balance within the small frequency window. A deviation as small as 0.5 Hz can cause some protective relays to trip and bring down sections of the grid.
This is also one of the major reasons why it takes so long to bring the grid back online after a blackout. They have to balance power output with the load in each section as it is brought online so it doesn't just disconnect itself again immediately from an imbalance.
There was this thing that happened a few years ago. Usually the frequency fluctuates a bit, but averages out to 50hz/60hz. Many appliances are using clocks that use the grids frequency to time them. In one instance the grid frequency averaged slightly below their target over a period of time so clicks would show the wrong time (like a minute or two off). They adjusted the grid to be slightly off in the other direction to compensate and make the clocks catch up to real time.
Here's an article about that: https://www.drax.com/electrification/electricity-causing-clocks-europe-run-slowly/
TIL, thank you!