Learning Light Cones: Seeking Understanding

[d.smith292]

I would like to know how light cones work, Everytime I make a post it gets locked before I can learn something. I obvioulsly didn't understand light cones in my previous post and when someone pointed that out, the post was locked before I could ask questions.

If someone would explain light cones to me I would be very greatful. Thank you.

 

[K^2]

Light cone is a region of space-time from some reference event to which a message traveling at the speed of light can be sent from the reference event.

In flat space-time, the geometry is actually a hyper-cone (hence the name), which is analogue of cone in 4-dimensions. If you look at time-slices, the region is enclosed in a sphere of radius ct, where t is amount of time that has elapsed from reference event, and c is the speed of light.

Does that help at all? If you want to know something more specific, you'll have to ask a more specific question.

 

[d.smith292]

I guess what is throwing me off is the 2D example of light cones. I now understand the reality of it being a sphere. I understand that, for example, when light bounces off an event, E, the sphere grows as it gets further from E. How does the past cone work? Is that just a reflection of the future cone to demonstraight E's past? I guess my question is, How does the past cone play a part in all this? Is there an example of this in a 4D model rather than the diagram of the cones? Can I view this with speres?

 

[K^2]

The projection onto constant-time space is a sphere. It's just like cutting an ordinary cone with a plane and getting a circle in 3-dimensional case.

Past cone contains all of the events from which you can possibly have information. If an event took place outside of your past cone, you cannot possibly know about it yet. And yes, it's just a time-reflection of the future cone.

 

[JesseM]

Imagine a world with only 2 spatial dimensions, like Flatland. Then the past and future light cones would be 3D cones, and the cross-sections of these cones at any moment in time would be circles. In our universe with 3 spatial dimensions, the light cones would be 4-dimensional ones which we three-dimensional beings can't visualize (well maybe a few mathematicians can, but I can't), and every cross-section of the 4D cone at a particular moment in time would be a sphere. Dropping the number of spatial dimensions by one (or two) is just a way to assist in visualizing things.

Here's a good page on spacetime and light cones with a lot of diagrams, including some animated ones:

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/spacetime/index.html

 

[d.smith292]

Thank you for the link, it really helped explain a lot. I appreciate the assistance.