Watches

Unless time.whateverthefuck is running their own cesium clocks, which I doubt. The gshock should be more accurate when synced. 60khz radio waves sent by NIST travel at the speed of light. That is standard em radio propagation. Your computer meanwhile theoretically does, it runs through God knows many nodes, bounced around until it finally gets back to you. I guess they could try to establish your location and correct, but eh....

Now let's talk about why your watch can't transmit. Well it could, but you'd need to carry around a giant antenna and a few kilowatts worth of rms power generation to even be heard over normal background noise at any reasonable distance. The wwvb towers in Denver host an antenna that is electrically one quarter wavelength (1250meters) but obviously not actually that long because that's 10x the towers. They use a series of coils and stretch horizontally to make up for the rest. They power this antenna 24/7 at 70kw. Part of the reason it's in Denver is central location to the country for best average timekeeping. Height above ground also rules when it comes to radio waves.

Im not going to go into the code that's actually transmitted because even as a HAM operator I don't know it all myself, but just know that it uses a system of 1s and 0s by pulsing the carrier wave to tell ever clock that's listening "it will be 2:35pm in... 3...2...1...NOW". Feel free to watch this much less baked youtuber explain.

The reason your watch will always be off by the speed of light at best is the radio station doesn't know where every single person is and can't send out 300,000 signals to tell each one what their specific time is.

Let's gloss over the fact that by the time the light gets from the screen to your eyes, it's TECHNICALLY wrong anyways....

If your interested check out NIST and WWVB website. Thats actually one of the things that got me interested in radio. side note I always wear a radio controlled casio. Sometimes a g. Mostly a field style lcw m100.

…are you serious

The only perfectly accurate watch is a wrist mounted sun dial.

It doesn't account for the time it takes to get the time?

The speed of light is fast, like stupid fast.

Some napkin math puts the travel time from Denver to DC at 1/100 of a second which for a human should be unnoticeable.

I doubt you could tell the difference between two watches with that difference.

To determine how long the signal took to arrive you would need to know the exact distance it traveled and its propagation speed.

To calculate the shortest distance the signal could travel you would need to know the exact locations of the transmitter and the receiver. That, plus some trigonometry, would get you a minimum distance. That seems to be a good enough correction for things like GPS to work.

If you really want to know the exact distance the signal traveled, it gets a lot trickier. Radio waves do not follow the curvature of the earth. To receive a signal that is beyond the range of sight, it needs to bounce off the ionosphere and back down to the surface. It may need to do that multiple times. That doesn't always work, and when it does, it happens at various altitudes that vary based on a multiple factors. Without access to a lot more information, you will never know exactly how far the signal traveled.

Then you need to know how fast the signal was moving over the course of its journey. Radio waves only move at the speed of light in a perfect vacuum. The chemical composition, and even the temperature, of the atmosphere affect how fast it moves. And, of course, those factors will not remain constant from the transmitter to the receiver. So you would need to know the exact route the signal took, as above, and then know the details of the atmosphere at each point over that route. That would require access to even more extremely detailed information. And a lot of computer power to make use of it.

I don't think there is currently any way you could get data about the signal bounce path. I am even more doubtful about getting detailed information about the composition and temperature of the atmosphere along the entire path.

There are probably other considerations that a physicist would bring into this, but I'm just a layman.

What is a sufficiently accurate estimate? That depends on what you need to do with it. There is no universal answer. The uncorrected time signal itself is good enough for nearly all purposes.

Having said all that, I'm actually with you on this. It would make me happy to have the delay-corrected time, even though the difference could not possibly matter to me. I don't need it. But it would be cool.