What exactly is meant when people say that a Light Cone is "tilting"?

[Benjamin113]

I understand the general idea of a light cone when it comes to how it's used to represent light particles. However, I do not understand what is meant when one states that in Relativity, "Light cones cannot be tilted so that they are parallel."


Would anyone care to explain this to me?

[Fredrik]

"Light cones cannot be tilted so that they are parallel."

That sentence doesn't make any sense to me either. Is that an exact quote from a book?

Do you understand what it means to say that a Lorentz transformation "tilts" the time axis or a simultaneity line?

[Benjamin113]

Thank you for your response!

Yes, and that does make more sense. I believe now that the term "tilting" was meant to have a more...figurative...meaning than the light cone literally tilting.

[JesseM]

Yes, and that does make more sense. I believe now that the term "tilting" was meant to have a more...figurative...meaning than the light cone literally tilting.
In coordinate systems in general relativity, light cones in a diagram using these coordinates may be tilted...for example, here is a diagram showing worldlines of particles and photons near the event horizon of a black hole in Eddington-Finkelstein coordinates (the diagram is from the textbook Gravitation by Misner/Thorne/Wheeler), you can see that if we draw in the future light cones of various events on these worldlines, they look more tilted as you approach the horizon (the grey column, the vertical axis being time):

http://www.valdostamuseum.org/hamsmith/DFblackIn.gif

this page (http://www.etsu.edu/physics/plntrm/relat/blackhl.htm) has some similar diagrams at the bottom, one showing more clearly how for an event exactly on the horizon, the light cone has tilted over enough so it becomes impossible for anything in the future light cone to be outside the horizon:

http://www.etsu.edu/physics/plntrm/relat/eventho2.gif

Still, I don't understand what it would mean to say light cones "cannot be tilted so that they are parallel". Can you give some more context for that statement? Were they talking about general relativity or special relativity, for example?

[Benjamin113]

Yes, it was actually an internet (or, to be more precise, Wikipedia) article on light cones.
Here is the link:
http://en.wikipedia.org/wiki/Light_cone

[Benjamin113]

By the way, thanks for the diagrams.

[JesseM]

OK, so the full paragraph of the wikipedia article is:
In a curved spacetime, the light-cones cannot all be tilted so that they are 'parallel'; this reflects the fact that the spacetime is curved and is essentially different from Minkowski space. In vacuum regions (those points of spacetime free of matter), this inability to tilt all the light-cones so that they are all parallel is reflected in the non-vanishing of the Weyl tensor.
Does this reference to the Weyl tensor make sense to people well-versed in GR? The article doesn't cite a source...