Not quite tbh. What if we are taking a fast spaceship instead of a photon. Spaceship starts from sun toward me. When it reaches me, I see my watch has ticked for an hour and I see the spaceship watch has ticked for 15 min. But from the spaceship point of view, earth was going toward it. From spaceship point of view, its watch must have ticked for an hour and it sees mine has ticked for 15min.
I realize this is one of the most difficult points to understand about relativity.
The question this paradox comes down to is, when are you comparing your watches? The two observers (the spaceship and you) won't be able to agree on what it means for two events to occur at the same time. Once you take this into account you will realize there is no contradiction and the POVs of the two observers are indeed symmetric as expected from the word "relativity".
For more on this check out e.g. Bernhard Schutz's "A First Course in General Relativity". IMO it's a rather terrible book as far as General Relativity goes but the first chapter, which is about Special Relativity (~25 pages), is fantastic and is was what helped me finally understand SR and, in particular, the paradoxes.
Right. So you see the ship taking an hour to travel from the
Sun to the Earth, and the ship’s clock only counts fifteen minutes. But you turned this round and ask how much time the ship would see our clock tick during its journey? Now if everything is symmetrical then it would see our clock tick 3.75 minutes.
So, the thing the observers disagree in their different reference frames is what “now” means.
I thought A goes toward B at C is undistinguishible from B going toward A at C. So if A sees A:60min and B:15min, therefore B should see B:60min and A:15min. Anything other than that means something was absolute.
Damn its frustrating. Month I ask questions about that. Every time I get: velocity is absolute. Maybe it is, maybe thats the answer to my question, velocity is absolute, meaning the ship is going toward earth in "absolute". But then one could be at rest in the universe and then there is an absolute frame in the universe thats motionless. Therefore we could elect a center.
You’re so close, but missing the important thing. You talk about measuring time with the assumption that all reference frames can agree on whether events are simultaneous.
Let’s turn the problem round. The ship is leaving Earth at some high velocity. In Earth’s frame after 60 minutes have passed the ship’s clock reads as 15 minutes having passed. In the ship’s frame of reference when 60 minutes have passed the clock on Earth will have recorded 15 minutes.
Now this sounds impossible because you think we agree on when events are simultaneous, “A’s clock is at X so B’s must be at Y,” but this is only true when A and B are in the same place, if they aren’t in the same place then you can only say, “A’s clock is at X so in A’s reference frame B’s must be at Y.”
Essential you can divide space time into three regions for a point A. The future is the cone of space time that could be reached from A without exceeding the speed of light. The past is the cone of space time from which an object could reach A without exceeding the speed of light. The third region isn’t the future or the past, and for any point B in this region we can find an inertial reference frame where A and B are simultaneous, or where A happens before B, or where B happens before A.
We can only ever globally agree that points in A’s future cone are after A, and points in its past cobe are before A, and these remain true in every inertial reference frame.
Absolutely wonderful. Great explanation, thank you so so much. Months Im asking questions around.
For a 60 min travel between earth and ship, there is a point where ship reaches earth reading ship:60 and earth:15. And there is a point where earth sees the ship land and read earth:60 and ship:15 resp. Those are not the same points.
So when you travel at high speed in a frame A, you're kind of gonna "experience a different story" than objects traveling in low speed in frame A relative to each other.
Edit: do we know an object with a mass thats traveling at high speed in our frame?
Edit2: Oh but the universe is expanding so we do actually.
If a fast ship leaves earth and comes back. From earth point of view, when it comes back the passenger gonna have outlived us all whereas for the passenger, it only left for an hour.
From earth point of view, when it comes back the passenger has outlived us all whereas from the passenger point of view, when he comes back, he only left for an hour.
Not quite tbh. What if we are taking a fast spaceship instead of a photon. Spaceship starts from sun toward me. When it reaches me, I see my watch has ticked for an hour and I see the spaceship watch has ticked for 15 min. But from the spaceship point of view, earth was going toward it. From spaceship point of view, its watch must have ticked for an hour and it sees mine has ticked for 15min.
If things are relative why isnt it the case?