# The light-cone and light-cone variables

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?

## Answers and Replies

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

tom.stoer
Science Advisor
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
Science Advisor
Homework Helper
Gold Member
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).