3 ms·

They are talking about "intervals" in 3+1 dimensional space time. To explain it rigorously, one needs to define a few terms like "metric" or "light cone". One d

They are talking about "intervals" in 3+1 dimensional space time. To explain it rigorously, one needs to define a few terms like "metric" or "light cone". One defining property of the photon is that its space-time interval between any two events in its history is zero. You can think of it as the dual of the fact that a clock moving at the speed of light would be completely stopped.

Filligree 5y ago
Intervals are the square of the distance, so not quite, but… yes. There’s a tendency to treat spacetime intervals as something abstract and possibly metaphysical, because we can’t see or touch them, and they work counterintuitively. They’re actually the opposite. Our normal experience of 3D space is what is unphysical; the (square root of the) spacetime interval is simply distance, measured in meters. Or seconds, of course. The literal, physical distance between an absorption and emission event is always zero. Reality is non-Euclidean. The Manhattan distance is larger than the actual distance, which is usually true anyway. Well, I suspect I just spent a lot of words telling you something you already knew, so I’ll leave off with a book recommendation. Dichronauts, by Greg Egan. Between that and the Clockwork Rocket trilogy, I don’t know a better way to inculcate an intuition for special relativity. One is set in a 2+2 spacetime; the other in 4+0. The differences are instructive.
- krastanov 5y ago
  This made me laugh given that, actually, Greg Egan is by far my favorite author. But I also think you are going way too far by saying that our normal 3D space is what is unphysical. The fact that our everyday reality is the limit of a more interesting reality when some parameter becomes small, does not make it any less real, for any reasonable definition of "real".
  - Filligree 5y ago
    Well, it's certainly consistent. And for the most part you're right; it's just light that gets hard to understand from this perspective. Unfortunately photon behaviour is fairly important...

Filligree 5y ago

Intervals are the square of the distance, so not quite, but… yes. There’s a tendency to treat spacetime intervals as something abstract and possibly metaphysical, because we can’t see or touch them, and they work counterintuitively. They’re actually the opposite. Our normal experience of 3D space is what is unphysical; the (square root of the) spacetime interval is simply distance, measured in meters. Or seconds, of course. The literal, physical distance between an absorption and emission event is always zero. Reality is non-Euclidean. The Manhattan distance is larger than the actual distance, which is usually true anyway. Well, I suspect I just spent a lot of words telling you something you already knew, so I’ll leave off with a book recommendation. Dichronauts, by Greg Egan. Between that and the Clockwork Rocket trilogy, I don’t know a better way to inculcate an intuition for special relativity. One is set in a 2+2 spacetime; the other in 4+0. The differences are instructive.

krastanov 5y ago
This made me laugh given that, actually, Greg Egan is by far my favorite author. But I also think you are going way too far by saying that our normal 3D space is what is unphysical. The fact that our everyday reality is the limit of a more interesting reality when some parameter becomes small, does not make it any less real, for any reasonable definition of "real".
- Filligree 5y ago
  Well, it's certainly consistent. And for the most part you're right; it's just light that gets hard to understand from this perspective. Unfortunately photon behaviour is fairly important...