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Kranaryesterday at 7:13 PM1 replyview on HN

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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pdonisyesterday at 7:31 PM

> 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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