Re: light cones

On Mar 19, 9:26 pm, Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
ML wrote:
I have a questions about light cones in space-time.
Let's consider 4 events, E1,E2,E3,E4 and take them as origin of 4
light cones.
Then, consider the intersections of these light cones.
My questions is: is there a way to say (and show) a priori if these
intersections are in the past or in the future of the 4 emission
events E1,E2,E3,E4?

In SR, every event in spacetime has a lightcone with a definite future
and past. In addition, the lightcones of any given pair of events always
intersect, and there is non-empty intersection in both the future of
each event and in the past of each event.

The above is not necessarily true in GR (it depends on the topology and
geometry of the manifold and may depend on the specific choice of events).

In both SR and GR, if an event E1 emits a timelike or lightlike signal,
then that signal can be observed by an observer at event E2 only if E1
lies in the past lightcone of E2 (in which case E2 also lies in the
future lightcone of E1).

Timelike, Spacelike or somethinginbetweenlike?
:-)

The emitter looses some EM. The analysist
chooses a convenient balance of temporal and spatial
components. Hopefully one that is not mathematically
absurd.


Note: if you know about complex numbers you will notice
that the space part enters as if it were imaginary

R2 = (ct)2 + (ix)2 + (iy)2 + (iz)2 = (ct)2 + (ir)2

where i^2 = -1 as usual. This turns out to be the essence
of the fabric (or metric) of spacetime geometry
- that space enters in with the imaginary factor i
relative to time.
http://www.nrao.edu/~smyers/courses/astro12/speedoflight.html

"Null Coordinates "
http://www.mathpages.com/rr/s1-09/1-09.htm

Sue...


Tom Roberts

.

Relevant Pages

  • Re: light cones
    ... consider the intersections of these light cones. ... In both SR and GR, if an event E1 emits a timelike or lightlike signal, then that signal can be observed by an observer at event E2 only if E1 lies in the past lightcone of E2. ...
    (sci.physics.relativity)
  • Re: light cones
    ... I have a questions about light cones in space-time. ... consider the intersections of these light cones. ... actually cones but curve inward toward the past due to the universe ...
    (sci.physics)
  • Re: light cones
    ... I have a questions about light cones in space-time. ... consider the intersections of these light cones. ... emission events rather than light arrival events. ...
    (sci.physics)
  • light cones
    ... I have a questions about light cones in space-time. ... consider the intersections of these light cones. ... intersections are in the past or in the future of the 4 emission ...
    (sci.physics.relativity)
  • light cones
    ... I have a questions about light cones in space-time. ... consider the intersections of these light cones. ... intersections are in the past or in the future of the 4 emission ...
    (sci.physics.research)