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Sorry if the question is not upto the standard of the site but i really can't understand what the following para says.

I am reading the book "A Brief History of Time" by Stephen Hawking and in the second chapter 2 "Space and Time" there is a paragraph about the special theory of relativity which says

If one neglects gravitational effects, for every event in space-time we may construct a light cone (the set of all possible path of light in space-time emitted at that event), and since the seed of light is same at every event in every direction, all the light cones will be identical and point in the same direction. The theory also tells us that nothing can travel faster than light. This means that the path of any object through space and time must be represented by the line that lies within the light cone at each event on it.

well i can't understand the part that says

The theory also tells us that nothing can travel faster than light. This means that the path of any object through space and time must be represented by the line that lies within the light cone at each event on it.

I cant get what it means can anyone explain it in a simpler way.

Thanks

Akash

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  • $\begingroup$ Do you understand the concept of a light cone and don't understand something else or is the concept of a light cone that is confusing? $\endgroup$ – Eiver Feb 14 '14 at 7:08
  • $\begingroup$ i got the concept of the light cone but i am not able to visualize what is being said in the next para (i think that's because the image for that explanation of that para is missing from my pdf ) $\endgroup$ – Dimensionless Feb 14 '14 at 7:12
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    $\begingroup$ Here's an example of a world line that's within a light cone: phy.syr.edu/courses/modules/LIGHTCONE/pics/worldlin.gif $\endgroup$ – BMS Feb 14 '14 at 7:21
  • $\begingroup$ @Akash After seeing the image, do you still need/want clarification on anything? $\endgroup$ – joshphysics Feb 14 '14 at 7:41
  • $\begingroup$ @joshphysics No, the image along with the below answer made it clear thanks for asking $\endgroup$ – Dimensionless Feb 15 '14 at 2:24
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http://en.wikipedia.org/wiki/Light_cone

It simply says that some parts of the space-time are not accessible to us. For example I assume :-) you are on (Earth, Now). No matter what you do (Moon, Now) is not accessible to you. (Moon, Now + 1 second) is also not accessible to you, because the Moon is 1.28 light seconds away from Earth.

Some events from the past are also not accessible to us. For example Andromeda Galaxy is about 2.5 million light years away from us. So:

(Andromeda, Now) is not accessible, it is outside of our light cone of past, there is no way to see what happens inside Andromeda galaxy right now

(Andromeda, Yesterday) is not accessible for the same reason

(Andromeda, 2.5 mln years ago) is accessible but only for something that traveled at the speed of light. It is on the edge of the light cone of past.

(Andromeda, 10 mln years ago) is accessible for something that can travel much slower than the speed of light. It is inside our light cone of past.

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If an object emits light in all directions at the speed of light ( no matter what the velocity of the object is), and the object is moving in the forward direction for instance, light is still emitted in this same direction at the speed of light, thus the object itself can not have been moving any faster than that light. Thus the object is confined in this direction. Thus any motion in any direction leads to this confinement also. Thus we obtain a light cone confinement.

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