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Originally Posted by OngBonga
That's a refreshing change of subject, because the previous one was beginning to get overwhelming! I just watched two vids about wave function and I still don't know what it is, other than to say it's a map of the probability of locating a particle. They are complex, both in the literal sense and the numerical sense. And complex numbers are not exactly easy to understand.
That's par for the course. Anyone who says they understand quantum wave functions is going to receive serious doubt from the wider physics community. They're going to have to meet a pretty highly scrutinized standard of proof as they try to explain it to the rest of us. Don't get me wrong, we desperately want to understand wave functions, but the many and various interpretations of QM are ample proof that we're not there, yet.
Slight correction: the wave function encodes everything that can be known about the quantum system, not only its location.
Yeah. Complex to solve, and they are complex valued functions on top of that. Interpreting the imaginary part of the wave is the origin of the pilot wave interpretation of QM. I think you said pilot wave was debunked or something, but it's not. The only thing is that the imaginary portion of the wave cannot be observed, so even if the pilot waves are part of nature, there's no way to measure them, so it's beyond the scope of "predicting the outcomes of measurements," and physics can't really deal with it.
Originally Posted by OngBonga
As for black holes, that's interesting but it begs the question... if spacetime gets exponentially more curved as we approach the singularity, would that not mean the diameter is infinite? The closer you get to the singularity, the more spacetime curves and the further away the singularity gets! Quite the paradox.
I think it would mean the diameter is infinite, if the singularity is indeed an infinitesimal point. Which, I think is what singularity means. But we don't know that there's a singularity, I think; we only know that GR predicts singularities.
The illustration on the slideshow in Kip's presentation had a curved bottom that was not infinitely far down. IDK if that was artistic license, or if that reflects an advancement in GR that I'm not familiar with.
Also, this talk about distances near and inside a black hole requires a lot of explaining in what reference frame you're measuring, since distance is not absolute, but a result of reference frame. Kip was talking about the diameter as seen in the view of a 1-D slice of black hole "from the bulk," as in, from an extra-dimensional perspective that can see the curvature of spacetime.
Originally Posted by OngBonga
I just threw this into google, and I'm reading an article that says black holes are unique for a simple reason... for a "normal" sphere (say, a ball), its mass increases with the cube of its radius, which should come as no surprise. A ball with a radius of 2 has 8 times the mass of a ball with a radius of 1. Of course this only applies when the ball in question isn't massive enough to have significant gravitational pressure, but ignoring this, black holes do not follow this seemingly logical cubic proportion. Instead, their mass increases in direct proportion... a black hole with twice the radius has twice the mass.
I can only assume that the radius we talk of here is the perceived radius as viewed from afar... the circumference / 2pi... ignoring spacetime curvature.
I can affirm that this is the correct reference frame for that radius. I'm not sure if it's talking about the radius of the event horizon or the radius of the apparent size of the black hole, though. My gut would guess the former. It's talking about the radius of the event horizon, and not what an observer would see when looking at the black hole.
The observer sees a bigger black spot than the event horizon because the curvature of spacetime means that when you would be looking just past the side of the event horizon, the light rays are so curved that you're actually looking at the back side of the BH. So the apparent size of the BH is about 2x the size of the event horizon.
Originally Posted by OngBonga
I think the concept of a black hole's radius is quite a challenging on to get your head around. Maybe the interior of a black hole is one dimensional... it is a flat, straight line towards the singularity. Spacetime simply doesn't exist within it, just time. So curvature is zero, rather than infinite. That removes our paradox, and explains our direct proportion relationship between mass and (non-curved) radius.
I wanna say it was PBS Spacetime that told me that the axes of time and space get flipped when you cross an event horizon. So while we're free to move in 3 spacial dimensions, but can only move forward in time at a constant rate... inside a BH, it's flipped. We're free to move about in time however we like, but we are constrained to always move toward the center of the BH.
Don't ask me how there's any sense in that, though. If I'm free to move backward in time, then how does that not change my direction of motion in space?
Bah.
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