> the space and time coordinates switch places as you cross the event horizon

I'm sorry but this is blowing my mind. What???

Because it's very misleading. Time and space do not switch places past the event horizon. What happens is that the direction/path between an object and the singularity becomes a timelike dimension, and the direction that plays the role of time outside of the event horizon becomes a spacelike dimension. That is not the same as them swapping or that time becomes space and space becomes time not to mention that space has 3 dimensions and time has only 1 dimension so how could they even swap places.

Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time, specifically the amount of time left before you reach the singularity. It's not so mind blowing when you interpret it that way now is it? You can imagine many things in ordinary life that you use to measure time without claiming that time has literally swapped places with it. On a road trip, the number of kilometres to your exit tells you how long you have left, that's using space as a proxy for time... big deal. The notable difference between a road trip and a black hole is that on a road trip you could stop for a break, you could maybe take a detour, you could decide to go back home... and these would all break your use of space as a proxy for measuring time. Well with a blackhole you can't do any of those things, there is no going back, there is no detour, the relationship between the spatial direction towards the singularity and time is fixed and causal and there's nothing you can do about it.

The phrasing used is used almost certainly to evoke some kind of voodoo mind-blowing mystery that completely disappears when you get down to the more strict formalism.

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pdonis 6 hours ago | parent [-]

> Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time

That's not correct. There is a relationship between the radial coordinate r you are at and the time it will take you, by your clock, to reach the singularity (at least assuming you are freely falling), but that relationship can't be described the way you are describing it.

To put the issue with what you say as starkly as possible: at any event inside the black hole's horizon, there are spacelike curves in every direction from you that will hit the singularity! So "the direction in space between you and the singularity" is not even well-defined.

To be clear, you are right that Susskind's statement is very misleading (I posted my own criticism of it upthread).

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jimberlage 6 hours ago | parent [-]

Am I understanding this right by thinking - if I was walking toward the black hole past the event horizon, and then I turned around, I would still be walking toward the black hole?

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HappMacDonald 6 hours ago | parent | next [-]

Once you pass the event horizon, every direction leads to the singularity in your future. Directions "away" from the singularity may still visibly show what things looked like outside of the event horizon before you fell in, but that is from your past. Heading in that direction will not get you back there anymore, you will only find the singularity along that path in your future.

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pdonis 5 hours ago | parent | prev | next [-]

> if I was walking toward the black hole past the event horizon, and then I turned around

Note that, once you're inside the horizon, you can't "turn around" and go back outside again. You're inside the hole for good.

And once you're inside the hole, yes, no matter which direction in space you move, you're moving "towards" the singularity. But a better way to look at it is that the singularity is a moment of time, not a place in space. You're moving "towards" the singularity in the same sense as you're moving "towards" next Tuesday. You can't stop moving towards next Tuesday by changing which direction in space you move. The same is true for the singularity once you're inside the hole's horizon.

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shepardrtc 4 hours ago | parent | prev | next [-]

You can't turn around though. Everything goes toward the black hole. If you turned around, atoms would be moving away from, or at the least changing their direction in respect to the black hole. And that's not possible. You wouldn't even see anything because all light is going toward the center, and it wouldn't go into your eyes.

Unless you went in butt-first, but the path of the photons would have changed and would now be going toward the black hole, and everything would look probably all smushed together.

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aqfamnzc 6 hours ago | parent | prev [-]

Sounds like that would be true if you were inside any closed surface.

	▲	XorNot 5 hours ago \| parent [-]
		Not quite: inside a closed surface you can't escape, but things can repeat. You can avoid a coordinate, for example by choosing not to go there, or revisit another one repeatedly. A black hole on the other hand doesn't have that: you cannot revisit old locations - attempting to do so moves you closer to the singularity.

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_moof 4 hours ago | parent | prev | next [-]

It's unfortunately misleading shorthand for what actually happens: space becomes timelike. It doesn't become time. All this means is that once you cross the event horizon, you can only ever move toward the center of the black hole, in the same way that outside of a black hole, you can only ever move toward the future. You might not take a direct route to the center, but no matter which way you move, you will be following a track that ends at the center.

The reason this phenomenon has a spooky-sounding name is that it also affects whether two objects can be causally connected. If you can only ever move closer to the center of the black hole, then there are (conceivably) other objects inside the event horizon that you can never have a causal relationship with.

But it doesn't mean that space and time literally switch places.

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MathMonkeyMan 7 hours ago | parent | prev | next [-]

[This video][1] and the one before it on the playlist are a good no nonsense explanation of the topic.

[1]: https://www.youtube.com/watch?v=O_2vnb_eVGE

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7 hours ago | parent | prev | next [-]

[deleted]

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metalliqaz 7 hours ago | parent | prev | next [-]

it might help to think of the singularity as not a point in space but rather a future that cannot be avoided. All possible paths through space and time, no matter what happens, will go towards the singularity.

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lstodd 7 hours ago | parent | prev [-]

Yup. It's that weird.

Also read Nick Gorkavyi: The Oscillating Universe: Einsteinian Cosmology of Black Holes and Gravitational Waves