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Comment by ninkendo | Hacker News Reader

Nope, you're in an inertial reference frame when in free-fall. Ignoring air resistance, if you were to take an apple out of your pocket and place it next to you in mid-air, it would be motionless relative to yourself. Put a box around you with no windows and you'll have no idea whether you're floating through space in the absence of gravity, or if you're free-falling inside a gravity well.

This is the main difference between general relativity and the newtonian notion of gravity: GR says gravity is just spacetime curvature, and by following an inertial (geodesic) path through spacetime, it appears to be acceleration to certain observers, but is in fact inertial. Newtonian mechanics says instead that gravity is a force and you're indeed accelerating, but it's a view that breaks down at high mass/speed, and GR makes correct predictions where Newtonian mechanics does not, so we generally prefer the GR interpretation.

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> you're in an inertial reference frame when in free-fall.

But the falling person's frame isn't the only one available. Someone on the ground would rightfully describe the falling person as accelerating towards the ground (or them) (at least until they reach terminal velocity).

The most important lesson of relativity is that no reference frame is privileged. That means both descriptions are valid, provided you attach the reference frame to the description.

> The most important lesson of relativity is that no reference frame is privileged.

No, the most important lesson of relativity is that only invariants are physically meaningful. IIRC Einstein once commented that he wished his theory had been called the "theory of invariants" since that would have been a better description of its most important feature.

The second most important lesson of relativity is that yes, you can use whatever frame you wish, because invariants are the same no matter what frame you use to calculate them. So you will come up with the same physically meaningful quantities no matter what frame you choose.

all this talk of GR and invariants, not to confuse a mathematical singularity with a gravitational one, at which point GR itself breaks down per the need for a quantum mechanical description. the truth is we don't know what happens within a black hole, and probably never will

> GR itself breaks down per the need for a quantum mechanical description

This is the current predominant belief among physicists, yes, but that doesn't mean it's established fact.

> the truth is we don't know what happens within a black hole, and probably never will

This is way too pessimistic. The predictions of GR for this regime are precise and unequivocal. Even if you believe GR breaks down when spacetime curvatures reach the Planck scale (which is the current predominant belief, as I said above), that still leaves most of the black hole's interior within GR's domain of validity.

> that still leaves most of the black hole's interior within GR's domain of validity.

Thanks, that's what I (as a layman) supposed: that inside the event horizon isn't some space that you can't think about; it's qualitatively not distinguishable from outide.

Upthread, someone mentioned that the singularity wasn't a place in space, it was a location in time. That made me think; the mass of a BH isn't the mass of a volume of space, it's the mass of the "singularity", which (presumably?) is located at the center of the space described by the event horizon. So there must be a place where the singularity is located, and there must be a direction towards it.

Someone else suggested there are two things: a mathematical singularity and a gravitational singularity, and that they aren't the same. That hadn't crossed my mind.

> someone mentioned that the singularity wasn't a place in space, it was a location in time.

That was me.

> That made me think; the mass of a BH isn't the mass of a volume of space, it's the mass of the "singularity"

This is not correct. The mass of the hole is not somehow "concentrated" at the singularity. There is no matter anywhere inside a black hole. The "mass" of the hole is a global property of its spacetime geometry.

> "singularity", which (presumably?) is located at the center of the space described by the event horizon.

Your presumption is wrong. There is no "center" of the black hole in the ordinary sense. Its spacetime geometry simply doesn't work that way; it is not like the spacetime geometry inside an ordinary spherical object.

> So there must be a place where the singularity is located

Wrong. See above.

> and there must be a direction towards it.

There is such a spacetime direction, but it's a timelike direction--towards the future--not a spacelike direction.

> Someone else suggested there are two things: a mathematical singularity and a gravitational singularity, and that they aren't the same.

That is not correct.

but if most of the interior is concentrated into an infinite mass, i.e. impossible, that kinda invalidates its validity

So is it correct to say that Newtonian mechanics is "just" an approximation (based on our observations) for all practical purposes? (EDIT: Spelling)

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