4 ms·
Actually no, the parent comment is correct: When you undergo an acceleration, it corresponds to a hyperbolic rotation of the spacetime around you (from your fr
by Diggsey 5y ago
Actually no, the parent comment is correct:
When you undergo an acceleration, it corresponds to a hyperbolic rotation of the spacetime around you (from your frame of reference). When the acceleration is small, the rotation is also very, very small; however at very large distances, even a small rotation can have a large effect.
In the example, that "large effect" is the alien debate moving in time forward or backwards a day (again, from the accelerated reference frame).
This has nothing to do with the observation delay, it's just an artefact of what it means for two far apart events to happen "simultaneously": simultaneity is a relative property, so two things that happen simultaneously in one reference frame might not happen simultaneously in another.
The reason this doesn't introduce a paradox is because without a specific reference frame, events only have a partial order: when you compare two events, there are three possible results:
1) Event A is in the past light-cone of event B.
2) Event B is in the past light-cone of event A.
3) Neither event is in the past light-cone of the other.
For 1+2 this means that the time between the events is greater than the distance between the events, whereas for 3 it means the reverse. For 1+2, the ordering of the events is the same for any reference frame. For 3, there will always be some frame of reference where both events appear to happen at exactly the same time, so nothing can be said about their order without choosing a reference frame.
- awb 5y agoI don’t think the interpretation you describe is widely held. Check out the criticisms of the paradox: https://en.m.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument#Criticisms https://en.m.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argu...
- Diggsey 5y agoThat it has critics does not imply it's not widely held. Regardless, that's just a dispute about terminology: sure we could say that we should only talk about events being "simultaneous" if they happen in exactly the same place - but in that case it's not a particularly useful term anymore. It's just an argument about how we apply words derived from newtonian intuitions to a relativistic context. Mathematically, for a given reference frame we can draw a space-time diagram, and certain events will be above the horizontal line. We can draw the same space-time diagram for a different reference frame and have those same events be below the horizontal line. Whether that horizontal line has any actual physical relevance doesn't really matter IMO, the maths says that events move in relation to the line when the frame of reference accelerates, and that's what the "paradox" is illustrating. Having said that, if the "one way speed of light" exists (https://en.wikipedia.org/wiki/One-way_speed_of_light https://en.wikipedia.org/wiki/One-way_speed_of_light) and even if it's not the same in all directions, then this "plane of simultaneity" is definitely a physical thing, since you can send a beam of light to a target, measure how long it takes to return, and using the speed of light in that direction you can work out exactly when that beam hit the target in your local time - ie. you've found two events to be simultaneous from your frame of reference, that are not in the same location.