I read your new page. Difficult since the size of the panels is so small that the font leaves some words illegible. I expanded it to fill the screen, but that doesn't add resolution.
Contents of the page is totally accurate.
uwot wrote:Noax wrote:...they count a different number because it takes time to get to the destination by one route than by another.
I'm sure this was just a slip, but this is not what H-K were testing.
I missed a word there. It takes
more time to get to the destination (the second comparison event) by one route than the other. That is what relativity says, and H-K was testing predictions of relativity. What special relativity doesn't say is that velocity affects the accuracy of a clock. It cannot, because velocity cannot be a property of a thing. This is opposed to the gravity effect. The absolute depth on an object in a gravity well IS a property of a thing, so it is more open to interpretation if gravity alters the accuracy of a clock.
Noax wrote:One cannot accurately read the time of a clock from any distance since the time that it reads 'now' is completely frame dependent.
I don't mean reading the clock, I mean literally, although in practise impossibly, counting the actual vibrations of the atoms.
Reading a clock cannot be done from a distance. The reading that you get is dependent on your arbitrary choice of frame. The atomic clock actually literally counts vibrations, so I'm not contesting that ability. But it is impossible to read (or synchronize) a clock on say Pluto to even the correct hour. Given any arbitrary selection of frame, we have the technology to sync a Pluto clock to within a second. For the same reason, your thing at the pole must assume a frame before it can take those measurements.
Now presumably we would select the frame of the axis itself, in which case it would note that the westbound clock runs fast, and the eastbound clock runs slow, and it all happens at a pretty steady pace assuming the clocks are in reasonably constant motion. Given a different selection of frame, the steady-pace thing goes away, but the results at the end are unaffected.
There is no separation between the hypothetical observer and himself.
He isn't watching himself. You have him watching the aircraft from a distance.
In the unlikely event that he could actually see the atoms of either of the clocks, from the moment it left, to the moment it returned, he would count a different number of vibrations.
It is not unlikely. There was a device counting the vibrations exactly, and they did count a different number of vibrations, and didn't need the axis viewpoint to do it. That has been my point: The axis viewpoint isn't necessary for the result. Arbitrary numbers for intermediate states does not affect the final state, the only one that counts.
A version of the twins paradox, is less cluttered:
There are two synchronised clocks next to each other.
One is flown around the world.
When they are put back next to each other, they are no longer synchronised.
The clocks work by counting vibrations.
Since they are not synchronised, they didn't count the same number of vibrations.
Agree. Don't think I ever said otherwise, but perhaps you interpreted one of my comments as a deviation from this.