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Comment by pkolaczk | Hacker News Reader

Thank you, this is very useful. But I have some more doubts. What is that space-time actually? Is there a global single space-time or does everyone has its own? Let's assume the starting point of my travel have coordinates (x: 0, y: 0, z: 0, t: 0). Then I go at near the speed of an light to the center of the Galaxy and come back to the same point a second later (as measured by my local clock). So I arrive at coordinates (0,0,0,1). But for the ones who stayed on Earth this point has a different coordinate (0,0,0,<very large number>). So it looks like it is not a single spacetime and this analogy kinda breaks :(

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There is only one space-time, and everybody agrees on it.

Time in space-time is not measured by your clock. It's measured by all clocks that are at rest with respect to each other.

Everybody sees you arriving at that point (0,0,0,<very large number>), including yourself. That's the number on the clock at your destination when you arrived. You took a different route through space-time to arrive there, which is why your wristwatch reads 1.

(We're assuming that the earth clock and the center-of-the-galaxy clock are not moving relative to each other, which isn't quite true but close enough to avoid introducing those complications.)

Since you are the one accelerating and decelerating, you're the one whose wristwatch cannot be trusted. That's the half-assed solution to the twin paradox. A better solution to the twin paradox involves watching the "boosts" from one frame to another and doing the math to calculate what happens. But you do know that the non-moving clock at the origin is always going to the longest route in time, and anything moving relative to it will be moving more in space (and thus less in time).

There is an interesting analogy which came to my mind. Let's say we have $100 each and both decided to buy stock, only I bought e.g. Microsoft shares, and you bought Facebook. Who has more money (i.e. cash)? Hard to tell until we both sell and compare. Similar things happen with inertial frames of references. You can only compare time when you are at the same point in space and have zero relative speed (reminds me of Back To The Future moment when Doc Brown compared watches). E.g. time on the ISS is ticking slower. Really? How do we know that? We put one clock on the ISS (i.e. launch it there), wait some time and bring it back. Yes, it shows less ticks. Is it because ISS is moving? Not really, ISS is following its world line and is roughly an inertial system, so its time is proper. And proper time is always the shortest. We on Earth on the other hand are constantly crossing world lines (unless falling down with 1g of acceleration). Why is it in reverse then? Because we need to accelerate to get there and decelerate returning back. Now imagine that somebody from ISS sends one of their clocks down to the Earth then gets it back. Which clock has less ticks? You guessed it, the one that traveled to Earth and back, because it's our time that is dilated, not their.

One correction: "moving" has nothing to do with it, crossing world lines does. Space ship flying at the speed of light (well, close to it) is also following its world line, so its clock is not "worse" or "better" than the one on the Earth. They both show "proper" time (https://en.wikipedia.org/wiki/Proper_time). When the ship starts to accelerate that's when its time becomes skewed. Also times at two different points of space are not comparable as there is no way to synchronize them, it depends on observer's speed. So "all clocks that are at rest" _always_ show different time if they are not at the same spot (well, they may show "the same" time like a stopped clock shows correct time two times a day).

Thank you. That makes sense!

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