Black Holes Without Space and Time: II. Where Space Becomes Time

There is a strange fact about a black hole.

Outside its event horizon, we can distinguish rather comfortably between moving through space and moving through time. Inside the horizon, that distinction becomes radically altered.

In the Schwarzschild description, the radial coordinate (r) takes on the character of a timelike direction, while the coordinate (t) takes on the character of a spacelike one.

This is sometimes described, rather loosely, as space becoming time.

But nothing has literally changed one kind of substance into another.

The deeper lesson is that the distinction between space and time is not fundamental in the way our everyday experience suggests.

What matters physically is the structure of the possible paths through spacetime—the causal relations between events.

Outside the horizon, an object can move inward or outward while its proper time carries it toward the future. At the horizon, the geometry changes the relation between these possibilities. Inside, every future-directed causal path leads toward decreasing (r).

The object is not being forced through space toward the centre by some invisible hand.

Rather, the geometry has made decreasing radius part of its future.

This is why the familiar picture of falling into a black hole can mislead us. We imagine an object travelling through an already existing space, with time flowing alongside it.

But the relational picture suggests something different.

Space and time are not two containers through which the object travels. They are aspects of the relations between events, and those relations determine what trajectories are possible.

The horizon is therefore not the place where space suddenly turns into time.

It is the place where the geometry makes visible something that was true all along:

space and time are not independent ingredients of reality.

They are differentiated aspects of a single relational structure.

Inside the horizon, that structure becomes so strongly directional that what we ordinarily call a spatial direction becomes inseparable from the future-directed character of an event.

And this gives the black hole its peculiar temporal character.

The centre is not simply a place to which the falling object is travelling.

It lies in its future.

The question is therefore no longer merely Where will the object go?

It becomes:

What kind of geometry makes a particular direction part of the future itself?

To follow that question all the way inward is to encounter the strangest feature of the black hole of all.

At the centre, it is not merely our distinction between space and time that reaches its limit.

The geometry itself does.

That is where becoming begins to matter.