Formerly u/CanadaPlus101 on Reddit.

  • 23 Posts
  • 5.29K Comments
Joined 2 years ago
cake
Cake day: June 12th, 2023

help-circle
rss





  • It’s “just” curvature, both through space and time. The Einstein field equation literally has energy and momentum on one side, and a type of curvature measure on the other.

    The trick there is that curved 2D spaces can already be pretty weird, and it gets exponentially crazier in dimensions 3 and 4. This makes it both capable of doing surprisingly a lot, like putting Earth in a fixed, repeating orbit without much local distortion, and difficult to visualise even by analogy. Interestingly, dimensions 5 and higher aren’t any worse, which is actually a pattern that repeats across a lot of geometry.

    In slightly more mathy detail:

    A curved 2D surface can be completely characterised by the Gaussian curvature at each point, which is a single real number (aka a scalar). In dimension 3, you need to use the Ricci curvature, which is a 3x3 matrix/tensor, so 9 scalars, and in dimension 4 it’s the Riemann curvature tensor which is 4x4x4x4. There’s symmetries that you can use to get that down to 6 and 20 scalars respectively, but that’s still a lot more parameters on every point than we’re used to.


    But yes the gravitational waves take is interesting, it burn my mind trying to imagine how to “trap” spacetime in itself.

    There is a bit of nuance there, which is why I said “as I understand it”. Gravitational waves are classically defined in terms of perturbations of flat spacetime, and a black hole is nowhere near close to flat. It’s possible there’s been work showing how to define them in that context, but I’m not a specialist and I couldn’t name it.

    If this were electromagnetism I’d just use the superposition principle, but GR is not linear. In fact, there’s chaotic dynamics that can happen in black holes related to the Mixmaster universe model. It’s also possible (to my limited knowledge) that there isn’t nice propagating waves at all so much as just adjustments to the crazy bending everything is already doing.


  • In this specific case, the gravity of the apple just never went away. It exerts one apple mass before it starts to fall, while it’s falling, and whenever it crosses the event horizon from your point of reference.

    Nothing is actually being “transmitted” per general relativity here. If someone were to jump in with some kind of gravitational wave generating device and send you a secret message from inside, that would be a straighter example. As I understand it that would not work; the waves follow null geodesics (light-type trajectories) and would be trapped with everything else. Which is weird, because spacetime is trapping itself, but deep physics is under no obligation to act normal.

    I clarify my question: beyond the event horizon of a black hole, according to general relativity, the space-time flows faster than the speed of light. If it is the case, then, no information can be transmitted from here.

    It’s a bit of a nitpick, but I’m not sure I’d use “flow” here. That makes it sound like it’s moving, while the Schwarzchild solution is actually static with respect to a properly chosen time coordinate (and without checking, probably the spinning and charged solutions as well). The spacetime is curved in such a way all timelike (c or slower) trajectories go inwards.







  • Mmm, I find it really handy to know that my memories are generated rather than recalled. Sometimes, I remember something that didn’t happen, and I know not to be weird and insistent about it. That hiding things from yourself is a really effective way to manage temptation is also not what I would have expected.

    I’d actually say that by social science standards psychology has an above average number of applications.