4 ms·

It's pretty clear GP was using the reference frame of a far-away observer. It's fine to switch to the infalling observer's frame, as you're doing here, but tha

It's pretty clear GP was using the reference frame of a far-away observer. It's fine to switch to the infalling observer's frame, as you're doing here, but that choice isn't objectively any more correct than GP's. For example: > Your acceleration is zero--you're in free fall. That's in the falling observer's frame. It's totally fine to say 'a astronaut in freefall is accelerating towards the earth', explicitly invoking Earth's reference frame. The freedom to choose a frame is literally why it's called 'Relativity'.

pdonis 3y ago
> It's pretty clear GP was using the reference frame of a far-away observer. Even in such a frame (for example, Painleve coordinates), not all of the statements are correct. In those coordinates, the infaller's coordinate acceleration is nonzero, as you say, but their coordinate speed inside the horizon is greater than the speed of light. Their inertial mass is still unchanged. And the coordinate acceleration in this frame is still not "towards" the singularity, since the singularity is still a moment of time, not a place in space. > It's totally fine to say 'a astronaut in freefall is accelerating towards the earth', explicitly invoking Earth's reference frame. In terms of coordinate acceleration, yes. But coordinate acceleration, precisely because it is frame-dependent, is not considered a physically meaningful quantity in relativity. Only invariants can be physically meaningful quantities. Proper acceleration--what an accelerometer attached to the infaller reads--is an invariant, and that is zero for a free-faller.
ithkuil 3y ago
From the point of view of somebody outside the black hole the infaller never reaches the event horizon.
- pdonis 3y ago
  This is not correct. Someone outside will never see the infaller reach the horizon, but that doesn't mean the infaller never reaches the horizon. It just means the outside observer never sees it happen.
  - rocqua 3y ago
    I think the inability of an outsider to detect an event is precisely what it means to say "from the point of view of sn outsider, this event never happens". What happens but can never be observed, may aswell never happen from the p.o.v. of the observer. It has no consequences to say it does, or does not, happen (for if it did, those consequences would make it observable).
    - pdonis 3y ago
      > I think the inability of an outsider to detect an event is precisely what it means to say "from the point of view of sn outsider, this event never happens". No, it isn't. The fact that a particular observer cannot detect an event does not in any way justify the claim that that event never happens. > may aswell never happen from the p.o.v. of the observer Whether or not an event "happens" is not a matter of any particular observer's point of view. At least, not in General Relativity. In GR, an event happening means there is a point in spacetime at which it happens. That point is either there in spacetime or it isn't, independent of what any observer can or cannot detect. You can say an event has no causal effect on a particular observer, but that's not the same as saying the event never happens.

pdonis 3y ago

> It's pretty clear GP was using the reference frame of a far-away observer. Even in such a frame (for example, Painleve coordinates), not all of the statements are correct. In those coordinates, the infaller's coordinate acceleration is nonzero, as you say, but their coordinate speed inside the horizon is greater than the speed of light. Their inertial mass is still unchanged. And the coordinate acceleration in this frame is still not "towards" the singularity, since the singularity is still a moment of time, not a place in space. > It's totally fine to say 'a astronaut in freefall is accelerating towards the earth', explicitly invoking Earth's reference frame. In terms of coordinate acceleration, yes. But coordinate acceleration, precisely because it is frame-dependent, is not considered a physically meaningful quantity in relativity. Only invariants can be physically meaningful quantities. Proper acceleration--what an accelerometer attached to the infaller reads--is an invariant, and that is zero for a free-faller.

ithkuil 3y ago

From the point of view of somebody outside the black hole the infaller never reaches the event horizon.

pdonis 3y ago
This is not correct. Someone outside will never see the infaller reach the horizon, but that doesn't mean the infaller never reaches the horizon. It just means the outside observer never sees it happen.
- rocqua 3y ago
  I think the inability of an outsider to detect an event is precisely what it means to say "from the point of view of sn outsider, this event never happens". What happens but can never be observed, may aswell never happen from the p.o.v. of the observer. It has no consequences to say it does, or does not, happen (for if it did, those consequences would make it observable).
  - pdonis 3y ago
    > I think the inability of an outsider to detect an event is precisely what it means to say "from the point of view of sn outsider, this event never happens". No, it isn't. The fact that a particular observer cannot detect an event does not in any way justify the claim that that event never happens. > may aswell never happen from the p.o.v. of the observer Whether or not an event "happens" is not a matter of any particular observer's point of view. At least, not in General Relativity. In GR, an event happening means there is a point in spacetime at which it happens. That point is either there in spacetime or it isn't, independent of what any observer can or cannot detect. You can say an event has no causal effect on a particular observer, but that's not the same as saying the event never happens.