Dear Jonathan,
I did not see your above reply until just now. I revisited your blog to bring to your attention an essay by Tommaso Bolognesi which I thought you might enjoy because it has something of a movie script quality to it.
Now to answer your questions:
"Are you saying that you think light cones should really be depicted as warped images instead of perfect cones?"
No, I am saying that, in my view, the boundaries of lightcones should properly not be considered regions of spacetime. To give a somewhat misleading analogy, a zero-dimensional point cannot be considered a "region of space" because it cannot contain any objects in space.
Where the analogy is misleading is that Euclidean space has only one kind of object that is characterized by the fact that every neighboring point is separated from its center by zero distance: A zero dimensional point; but Minkowski space time has two: A zero-dimensional point and the boundary of a light cone. In this sense, the latter is a second type of "point- like object" for which we, who intuitively perceive ourselves as inhabitants of a 3D Euclidean space have absolutely zero intuition, and this is the reason, I think, that this has not been yet recognized.
If you accept that the boundaries of light cones are not regions of spacetime, then logically things which are constrained to exist only there, like photons, cannot be said to exist in spacetime. That special relativity gives us hints that this is indeed the case, starting from the fact that no spacetime observer can transform to a photon rest frame, was essentially what my vixra paper referenced above was driving at. Again, ultimately I think it will take a mathematical proof that the topology of spacetime really is intrinsically different from the topology of Euclidean space to convince others that this is the case.
"If so, that sort of makes sense in a world where matter warps spacetime... unless the warping of space and time perfectly offset each other so that the light cone looks normal for any object, whether it is near massive bodies or not. (I feel like my understanding is not right, so forgive me if I am off base)"
You are forgiven;) usually what people mean by the "warping" of space and time is that there are coefficients (and sometimes more involved combinations of terms) for the space and time terms different from the constant 1 (in Cartesian coordinates) which modify the metric relations at particular points. Importantly, these metrics are never expressed in such a way that the spacetime interval gains a coefficient different from 1 , because it is the invariant quantity, whereas space and time are separately not invariant. But even if you changed the coefficients of the space and time terms so that it would become equivalent to multiplying the metric interval by a coefficient not equal to 1, which amounts to scaling it, it would still be the case that ds=0 describes the boundary of a lightcone.
"I will try to respond to some of your explanations that you offered on your page to some of my questions, but I do remember thinking that some of it was a little over my head. Oh well, maybe I'll google some stuff and try to understand it a little better."
Well, I appreciate your interest in my ideas, if you have any questions let me know, you can also email me.
Best wishes,
Armin
