Will you then be consistent with what you've said in the above post (which I concede as being accurate according to Einstien) and say that if the clock watcher at the top of the mountain came down to visit with the guy at the base of the mountain and asked him how many times the sun has set since they started their experiment that the guy at the base would report one fewer sunsets than the he had?
He won't report one fewer sunsets. They saw the same number. They'll simply disagree on how long each day was (because they are experiencing time differently from each other). Again, this does not mean that the sun should fall out of sync for us. One of us will have
experienced less time in the same period.
Here's a more visual example. Imagine two frames of a movie (showing clocks) running side by side. (Note that I use the term "frame" not to refer to an actual snapshot of the film, but more like two panels of the same film running side by side). One is frame is slowed to half normal speed. So, while one clock ticks off 10 seconds, the other clock in the other frame ticks off five seconds (because the film is actually running slower). Now, imagine a person in each frame who can see out of the frame. Imagine a sun rusing over both frames of the film. They both watch the sun, outside of both frames, rise until midsky. Notice that both frames will
always agree on the position of the sun, but they won't agree on how long it took there. One frame will say "it took 10 hours", but the other frame will say "it took 5 hours". But the sun is in the same position for both frames always. So if the frames could talk to each other, they would always agree on where the sun was, but they wouldn't agree on how much time has passed (and one person would be talking much slower!).
Which brings up a good way to measure this relativistic effect. If we could somehow put people in the situation we could measure how much slower and deeper their voice is to calculate how much time is dilated for that observer. But we can't, so we use light. Imagine you have a lightsource that emits at a known frequency (interval between waves). For example, say you have a lightbulb that emits at 200 Hz, that is 1/200 of a second between each crest of the EM wave. Now whirl that lightbulb around at near the speed of light and measure the frequency of the light from your stationary position. It won't be 200 Hz, because 1/200 of a second at near the speed of light is longer than 1/200 of a second in a relatively stationary frame. So you should measure a
different frequency, after you've accounted for the doppler effect (physicists actually use transverse motion so you don't really need to cancel out the doppler effect). If relativity is correct, then the standard interval should lengthen according to an outside frame stationary relative to the particle. And indeed, the frequency does change (of course, they didn't use a lightbulb).
H.E. Ives and G.R. Stilwell, "An Experimental Study of the Rate of a Moving Atomic Clock", J. Opt. Soc. Am. 28 215-226 (1938); JOSA 31 369-374 (1941).
Yes, that was in
1938. Imagine what they're doing now.
Also notice that using the sun as a timepiece becomes utterly meaningless for communicating time intervals to each other. Because for one frame the sun took 5 hours to reach midsky, while the other frame it took 10 hours. So if we calibrated clocks to the sun, we'd be expressing different intervals depending on our frame. In other words, I couldn't share a recipe with you because my interval is completely different than yours. It's still better to use clocks inside our frames (i.e. our watches) even though they are out of sync. Because if a cake takes five minutes to bake in my frame, it will take five minutes to bake in your frame.
This is a good way to illustrate (though it is not without it's shortcomings) the principle here. Except instead of film frames, physicists use the term inertial frame.
I consider it progress that seemingly everyone is now in agreement on the premise of the hypothetical. Finally!
I have always said that they would see the same sunrise and sunset.
Could you explain how both parties could exist together in the same room at the same time and have a conversation about how one is a full day behind the other?
They are not a "day" behind. One has experienced 24 hours less than the other.
Time "itself" does not exist.
I know that there is no object in the universe we call time, just as there is no object in the universe that we call length. It is a definition. Time is not an object. It is a measurement we have assigned, just like length or height or width. So when we say "Time is relative", we are saying that so-called standard intervals are actually frame-dependent.
standardized set of events (ticks and tocks) by which to compare some other set of events
Truly. But there isn't
really a standard interval. For example, say you define a standard interval as the duration it takes for a particle to decay. You realize that baking a cake takes about 10000 decays. Then you mail me your particles on the top of the mountain. You watch through your telescope and you realize that they're actually decaying a bit faster for me. If you tried to bake a cake by counting 10000 decays of
my particles decaying at the top of a mountain, you'd undercook your cake. However, from my experience at the top of the mountain, they bake a perfect cake. This is another way of saying the same thing I said earlier: using a clock outside of your inertial frame is absurd under extreme relativistic conditions. So it's not accurate to say that using the sun as a clock is better than using an atomic clock.
I dont' think it's any real intrusion on theology either. We don't live under extreme relativistic conditions, and so the sun is, for the most part, fine. Especially for ancient people who don't really know the difference anyways.
But clocks are not actually measuring anything.
They're measuring an interval. We live and die by intervals. What meaning has time if you dissociate it from that which we have defined it as? It has no empirical meaning outside of measurement, as I have said before.
So when we same "time dilates" we mean that standard intervals become shorter or longer from an outside perspective (outside of the object's inertial frame).