Animated Spacetime Diagram

See more at http://www.spoonfedrelativity.com

Category:

Education

Tags:

• special relativity
• rindler
• rindler horizon
• spacetime
• space-time
• space time
• Lorentz transformation
• software tutorial

[good4usoul]

Sorry I did not respond sooner. I think you've worked it out. I definitely agree with Example (2). There's really four; no eight parabaloids left, up, down, right. four centered on the observer, and four centered on the little point in space-time where all the objects appear to be colliding. (even though nothing is really happening to them at all.) I think that's what you mean by Example (3). It's neat to watch paths of events around that event; they follow little parobolic arcs.

[ScalarPhotonZ]

@good4usoul In reference to the animated spacetime diagram, would I be right in saying that the paths of these events along the diagram, more accurately, are hyperbolae, whose asymptotes are lightlike lines which intersect at the event on the Rindler horizon?

[good4usoul]

@ScalarPhotonZ

Yes. Exactly. Also, I have put a new website up, at spoonfedrelativity. The exact link is up above in the description of the video.

[ScalarPhotonZ]

@good4usoul Are we thinking the same thing here? I'm NOT referring to e.g. a paraboloid of revolution on a 3D spacetime diagram with 2 spatial and 1 temporal dimension. In a spatially 3D universe with 1 time dimension, this is a paraboloid within 3D space, in the reference frame of a uniformly accelerating observer. My discussion is about the world as seen through the observer's telescope.

[ScalarPhotonZ]

Continued...

Examples:

(1)Events appearing on the observer's side of the paraboloid would have physically occured finitely long ago according to the Rindler frame, but no moment in time, in the Rindler frame, can be pin-pointed for events appearing on the opposite side

(2)I believe objects cannot ever appear to move from the observer's side to the other side, but vice versa is possible

(3)I believe the apparent position of any inertial object will tend to a point on the paraboloid

Comments?

[ScalarPhotonZ]

Continued . . .

Then in this "apparent world", the "special surface" here, I believe I've worked out, is the paraboloid of revolution with focus at the position of the observer, and directirx plane coinciding with the plane of the Rindler horizon. Time does not appear completely frozen on this paraboloid, but this paraboloid very neatly partitions 3D space in this "apparent world", over a variety of features.

Continue . . .

[ScalarPhotonZ]

Physically, in the accelerating observer's Rindler frame, the Rindler horizon is a plane, on which time is effectively frozen. But consider the world of what appears to the observer, given that light must travel from event to observer. Assume light travels from object to observer at the full speed of light, and the spatial position at which an event appears to occur is the position at which it would have physically occured according to the instantaneous inertial frame.

Continue . . .