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Light Cones ----> what for?
Name: wildman jackson
Status: N/a
Age: N/A
Location: N/A
Country: N/A
Date: Around 1993
Question:
Can someone explain to me the concept of light cones? What are
these cones actually "used for?
Replies:
Nothing very practical! The light cone is just one of many tools
used by physicists as a way of seeing how certain things have to be true, or
how certain things might work. First of all, a light cone is 4-dimensional,
so visualizing the cone itself is a little tricky. Think of a 3-dimensional
cone first though. If you place the mouth of the cone down on the floor, with
the point of the cone on top some of the properties of the cone should be
clear. For example, the cone touches the floor in a circle, and any
horizontal slice through the cone makes a circle, up to the top where there is
just a single point. Similarly, a light cone starts at a point (say a place
in space and time where a flash of light was emitted) and then at any later
time the surface of the cone forms a sphere (the sphere in space where the
light has reached by that particular time). If we take a vertical slice
through our cone on the floor - say by just looking at its profile from some
horizontal distance away, then we notice that the sides are straight lines
coming from the point. Similarly, the edges of the light cone are formed by
individual rays of light leaving the central flash - each ray moves out at a
constant speed (the speed of light) and that means that the relation between
position and time is linear - the edges are "straight" in space-time. Also,
the slope of our 3-dimensional cone can be anything - it can be wide and
short, or tall and slender. However, the slope of the light-cone is fixed -
it is simply the speed of light! (Remember speed is a ratio of distance over
time, and slope is a ratio of one axis over the other). Ok, so it really is
like a cone, except in four dimensions, and the slope can only have one value.
What does it mean? Well, if nothing can travel faster than the speed of
light, that means that somebody watching at a particular point in space can
not know anything about this light flash actually having occurred until that
time when the sphere of light has expanded to include where the observer is
waiting. At earlier times, those points in space-time were OUTSIDE the light
cone, and could have had no communication from the light flash. At later
times, the corresponding sequence of points in space-time is INSIDE the light
cone, and there has been communication from the light flash. In essence, the
light-cone is a surface that divides space-- time into two pieces - one piece
that can never have yet known about the flash, and a second piece that can
know. If the light flash is supposed to set in motion some other events
elsewhere in space (to "cause" things to happen) then those other events can
only be INSIDE the light cone. The light flash cannot cause anything to
happen OUTSIDE. This is pretty fundamental stuff. The light cone is also
often extended back in time, because there is an exact reversal there - going
backwards the things OUTSIDE cannot have caused the light flash, whereas the
things INSIDE could have. Of course, this does not have anything to do with a
spherical shell of light expanding backwards in time! It is just another way
of dividing space-time into 2 fundamentally distinct regions, from the point
of view of the light-flash. In fact, allowing things to be moving at any
speed relative to one another (as is usually supposed in discussions of
relativity) we cannot say whether the light flash happened first, or one of
the OUTSIDE events happened first - in some frames of references any event in
the OUTSIDE happens at exactly the same moment as the light flash. But all
the events in the INSIDE of the original light cone (going forward in time)
must happen after the light flash, and all the events in the INSIDE of the
backwards light cone must have happened before the light flash, so there IS a
meaning to sequence in time for those events.
Arthur Smith
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Update: June 2012
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