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This explanation somehow was much more intuitive for me when I considered that someone sends a signal from the center of the train to both ends of the train at light speed. Because the train is moving at some speed relative to the platform, the signal will arrive at the back of the train first (because that side is moving towards the light signal) and the signal will arrive at the front of the train second (because that side is moving away from the light signal).
Why do you say they agree on the speed of the train?
George and Gracie know their notion of time is different. They can both agree the train’s length is 210m.
Now George gets on the train and speeds up to 30m/s towards Gracie (who moved some distance away to give the train time to speed up).
Gracie then measures how much time it took for the train to pass her (5.9s), so she concludes the train’s speed is NOT 30m/s like George says, but 210/5.9≈35.6m/s. @mark s
That is a misunderstanding. Gödel’s incompleteness theory does NOT mean we cannot have a unified theory (including quantum gravity). It merely means that in any logic system AS A WHOLE, there are statements that cannot be proven to be correct, even if they are. Those statements are specially crafted statements, and not your ‘normal’ statements. They really have to go hand in hand. Without a theory, you just have empirical insight, but weak extrapolation power. Without experiments, you’ll always be left wondering whether this is simply mathematically possible, but not a reality in our universe.
Personally, I’m more on the side of theory because then you are not bound to limitations of resources. But, I guess I’m in the minority (I would expect 99%+ of the lay persons to be more interested in actually ‘seeing’ it) Physics will be over?!?
Knowing the theory of everything doesn’t do you any good by itself. Presumably 99.9999999999% of the work is in the application of the processes to get things to do what we want them to do. You cannot just point to the equation and tell anyone who wants to put it to practical use to ‘just plug in the numbers’. Actually turning this theory into real world use is where it is at.