The discussion centers on the concept of velocity in relation to light, specifically questioning whether everything else travels at a constant velocity with respect to light. Participants clarify that light does not possess an inertial rest frame, making it meaningless to measure other objects' velocities from light's perspective. They emphasize that all velocities are assessed from an inertial rest frame, and the speed of light remains constant at 'c' regardless of the observer's motion. The conversation also touches on the geometric interpretation of spacetime and the implications of velocity in this context.
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Oh, I don't like that diagram at all! The end of the green line corresponds not to the point where it touches the yellow line but to the end of the yellow line. That is very confusing to me.A.T. said:Which is great because it allows to visualize the age difference geometrically. In a Minkowski diagram you don't see the age difference. In this visualization you see the standard twins paradox in both types of diagrams (space-propertime diagram is called Epstein diagram):
http://www.adamtoons.de/physics/twins.swf
A.T. said:That's true in the sense that Epstein diagram doesn't contain the space like part of the Minkowski diagram. So you can "only" visualize world lines of massive objects and light.
A.T. said:Which is great because it allows to visualize the age difference geometrically. In a Minkowski diagram you don't see the age difference.
I think you misunderstand--I'm not talking about the fact that two observers in a twin paradox situation might not set their proper times to zero at the moment they depart from one another, since as you say we can always imagine resetting their clocks to zero at that moment for convenience. I'm talking about a situation involving multiple worldlines that don't depart from a common point (in Minkowski spacetime) at all, like objects that have been drifting towards each other from infinity until they finally meet, or multiple worldlines that never cross at all, or three worldlines that each cross the others but all three never cross at a single point.A.T. said:I see no problem there. They don't have to start at zero proper time, but it is convenient to use the starting proper times as zero. What you want to visualize, are different rates of proper time. An initial proper time offset is not really relevant.JesseM said:One remaining problem I have with this is that it doesn't really generalize to arbitrary sets of worldlines that may not have set their proper times to zero at a common origin point.
Lets call the guys A and B. Which scenario do you mean:robphy said:A.T.,
How would one draw an Epstein diagram for a radar experiment with light rays?
More specifically, consider two inertial observers with different velocities that met at event O. One observer, after a short [proper-]time interval T1, sends a light-signal to the other. (The ratio of the time-intervals from O is the Doppler Factor.) After a [proper-]time interval T2, the first observer receives the radar echo.
I like this too. It's a bit more complicated tough, and involves an understanding of pseudo Euclidean geometry.robphy said:You can count off the age difference in a Minkowski Diagram:
http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/#twins
and you can relate it to the geometry of Minkowski spacetime.
Ok, but where is the problem in a space-propertime-diagram with this scenarios? You have their spatial position, and proper-time interval since the begin of the observation. You just plot these two in a diagram, for each object.JesseM said:I'm talking about a situation involving multiple worldlines that don't depart from a common point (in Minkowski spacetime) at all, like objects that have been drifting towards each other from infinity until they finally meet, or multiple worldlines that never cross at all, or three worldlines that each cross the others but all three never cross at a single point.
That one.A.T. said:2) T1 after O, B sends signal to A, which A mirrors, so it returns to B T2 after O
Actually it is derived using the standard physics-textbook thought-experiments...A.T. said:I like this too. It's a bit more complicated tough, and involves an understanding of pseudo Euclidean geometry.robphy said:You can count off the age difference in a Minkowski Diagram:
physics.syr.edu/courses/modules/LIGHTCONE/LightClock/#twins[/url]
and you can relate it to the geometry of Minkowski spacetime.
OK, I guess since you're using a particular inertial frame's definition of spatial position for the horizontal axis, you can also use that frame's definition of simultaneity to define the moment that is the "beginning of observation"--I had been thinking about the relativity of simultaneity without realizing that the Epstein diagram already required you to specify which frame you're using.A.T. said:Ok, but where is the problem in a space-propertime-diagram with this scenarios? You have their spatial position, and proper-time interval since the begin of the observation. You just plot these two in a diagram, for each object.
Since objects at c don't experience proper time, their world lines in an Epstein diagram are horizontal. While you could use these diagrams to display a radar experiment, it wouldn't provide much insight, unless you animate them.robphy said:So, T1 and T2 mark off on B's worldline the sending and reception events of the radar experiment performed by B.