tiny-tim

Science Advisor

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## Main Question or Discussion Point

(the story so far … I maintain that, inside an event horizon, there is a useful distinction between "space" and "space-like" dimensions, and that in any realistic coordinate system, time is space-like. JesseM maintains that, in any realistic coordinate system, time must be time-like.

JesseM maintains that, "in a

now read on … )

Hi JesseM!

a thought experiment …

In Schwarzschild coordinates, imagine a free-falling observer inside an event horizon. His path is the axis of two "cylinders" of free-falling particles, following him, but faster.

He can see them until they hit his backward light-cone ("diagonal" light

In your SR-physics local coordinate system, what happens to these "cylinders" when they hit the Schwarzschild light-cone?

Doesn't the Schwarzschild light-cone become a coordinate singularity which swallows them up? And isn't that singularity on the same radius as the observer?

So each "cylinder" converges to an event (possibly "at infinity") whose displacement from him is light-like … and either it is ahead of him, so he

Or is it in his own

(And we can shrink the inside "cylinder", so that that event can be as "close" to the observer as we like.)

And, if the laws of physics are the

And, if the laws of physics are the

JesseM maintains that, "in a

*local*coordinate system constructed out of freefalling rulers and clocks, the laws of physics must look identical to those of SR." I maintain that this is not possible … that inside an event horizon, the laws of physics are the same, but the geometry is different, and therefore the physics*must*look different.now read on … )

**conservation of mass**

a thought experiment …

In Schwarzschild coordinates, imagine a free-falling observer inside an event horizon. His path is the axis of two "cylinders" of free-falling particles, following him, but faster.

He can see them until they hit his backward light-cone ("diagonal" light

*does*go fast enough for that). And the light by which he seems them reaches him at the same time*from both "cylinders".*In your SR-physics local coordinate system, what happens to these "cylinders" when they hit the Schwarzschild light-cone?

Doesn't the Schwarzschild light-cone become a coordinate singularity which swallows them up? And isn't that singularity on the same radius as the observer?

So each "cylinder" converges to an event (possibly "at infinity") whose displacement from him is light-like … and either it is ahead of him, so he

*sees*the particles disappearing*in his own future*… or it is behind him, in which case he literally has a singularity in his wake, and where is there room for the rest of space-time to fit in?Or is it in his own

*present*(as the Schwarzschild system requires)?(And we can shrink the inside "cylinder", so that that event can be as "close" to the observer as we like.)

And, if the laws of physics are the

*same*as in SR, doesn't this coordinate singularity have to be an*actual*singularity … which it obviously isn't?And, if the laws of physics are the

*same*as in SR (and if he can't see infinitely far into the future):**what happened to the mass?**