Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?« on: 26/01/2023 17:59:06 »
Ok, I understand.I am not sure I am following. An event is just a point.Prove what?
Let me try to "prove" it to you geometrically.QuoteImagine a 2d spacetime diagram (as you know time is the y axis, and x is the spatial axis)x and t (ct techmically) axis since y is traditionally another spatial axis.QuoteHow can any 2 points horizontal with each other (in other words have the same time) have differential aging without a curve or bend?Points in spacetime (events) don't age. If they did, they be a different point since they'd have a different t coordinate. Furthermore, two events at the same time are space-like separated. It is impossible to travel from one to the other since it would require you to do it in no time. All events at the beginning and end of scenarios like the twins scenario are time-like separated, meaning their coordinates differ more by ct than they do by x. So if the two events (ct, x) are at (0, 0) and (2, 1), something can travel between those if it moves at 0.5c. If the second event is at (2, 0) then the thing can stay stationary and get there, path length t = 2. The path length to the (2, 1) event is √(2² - 1²) = √3, shorter than the path to the (0,0) event.QuoteYes I understand. But we can say that cause should be the same for all observers as time passes (of course except in extreme cases in GR).Sorry, but still have no idea what you mean by 'cause'. Differential aging is about geometry, not causation. Causation is not the same for everybody. I like vanilla for the flavor, the other guy picks it because he thinks the drips will not be as easily seen on his shirt. Same effect, different causes. This has nothing to do with Minkowskian geometry, where the mathematics accurately describes (doesn't cause) the ages the the twins at the reunion.
After thinking about all of this for the past few days, I think I know why this topic is so unclear (at least for me).
In physics, we observe a quality of something, for example; mass, redness, or gravity. Then we try to quantify, relate, reduce them down to their simplest forms, predict, formulize, etc. Well with this situation, a velocity and a "turnaround" seems to be the necessary, and I think the minimum, that makes differential aging happen. The turnaround by itself (without acceleration if that even makes any sense) is not really quantifiable, so I don't think it can be a function of anything.
I am really trying to figure this out, but it seems like this is a different kind of physics problem than we are used to.
What do you think is minimally necessary for a twin to have differential aging, without gravity?