The light-cone and light-cone variables

[Demon117]

So I've never really understood this idea of a light-cone. I know there is literature, but what are the most important physical concepts/consequences about this light-cone model of special relativity?

Also, could you give a concise explanation of light-cone variables?

 

[Nugatory]

Can you be more specific? Point to some online explanation and tell us exactly where you fell like you're losing understanding?

 

[tom.stoer]

Have a look at http://inspirehep.net/record/324401?ln=fr and references therein.

There are two key-ideas:
- the light-cone frame does is some sense correspond to the infinite momentum frame
- on the light-cone the dispersion relation becomes trivial

However the light-cone frame is singular, and afaik there is no fully consistent quantization.

 

[robphy]

I assume that you have at least consulted http://en.wikipedia.org/wiki/Light_cone .

One of the most important features of the Light Cone of an event is that it invariantly encodes the Causal Relations of that event with other events, which [in my opinion] is the most important feature of Einsteinian relativity (which was first put into this spacetime framework by Minkowski). For example, look at the diagrams on p. 89 of Geroch's "General Relativity from A to B" books.google.com/books?id=rwPDssnbHPEC&lpg=PP1&pg=PA89#v=onepage&q=light-cone&f=false


Light-Cone variables are associated with a non-rectangular coordinate system, where the coordinate axes are along the light cone. In 1+1 spacetime, instead of (t,x), we have instead (u,v) where u=t+x and v=t-x [in my signature convention and my choice of scale-factor (some use, e.g. , (t+x)/2 or (t+x)/sqrt(2) )]. One key feature of these axes is that they are eigenvectors of the Lorentz Boost. The Lorentz Boost looks very simple in Light-Cone variables... it is diagonal... and the two entries (i.e. the eigenvalues) are reciprocals of each other [since the boost has determinant 1]. (The eigenvalues are the Doppler factors.)

The wave-operator in 1+1 spacetime in light-cone variables immediately gives http://mathworld.wolfram.com/dAlembertsSolution.html .

My avatar is a ticking light-clock. The future-light-cone of tick 1 intersects and reflects off the worldtube of a inertial circular light-clock and refocuses back to tick 2 (along the past-light-cone of tick 2).

 

[sardar]

The light-cone model is an important concept in special relativity that helps us understand the relationship between space and time. It represents the path that light travels through space-time and is used to describe the limits of causality, or cause and effect, in the universe.

One of the key physical consequences of the light-cone model is the idea of simultaneity. In special relativity, events that are simultaneous in one frame of reference may not be simultaneous in another frame of reference due to the effects of time dilation and length contraction. The light-cone model helps us understand how these effects affect our perception of time and space.

Another important concept is the idea of causality. The light-cone model shows us that events can only influence each other if they are within each other's light-cones. This means that an event can only be influenced by events in its past light-cone, and it can only influence events in its future light-cone.

Light-cone variables are a set of coordinates used in the light-cone model to describe the position and time of events. They are based on the speed of light, with one axis representing space and the other representing time. These coordinates are used to plot the light-cone and determine the relationship between events in space and time.

In summary, the light-cone model is a crucial concept in special relativity that helps us understand the limits of causality and the effects of time and space on events in the universe. Light-cone variables are a set of coordinates used to describe the position and time of events in this model.