Black Holes Without Space and Time: I. Beyond Space and Time

We are accustomed to thinking of space and time as the two great dimensions of reality: space provides the arena in which things exist, while time provides the dimension in which things change.

General relativity already unsettles this picture. Space and time are not independent backgrounds. Together they form spacetime, whose geometry changes with the distribution of mass-energy.

But perhaps we can go one step further.

What if space and time are not things at all?

A distance is not a substance existing between two instances. It is a relation between them. A duration is likewise not a substance flowing between two events. It is a relation between them.

From this perspective, spatial extension and temporal duration are different aspects of a relational structure.

Gravity therefore need not be understood as something that distorts space and, separately, dilates time. These are two descriptions of how the same underlying relations change.

Near a concentration of mass-energy, spatial intervals become progressively differentiated from one another. Temporal intervals likewise become progressively differentiated relative to one another. What general relativity expresses as curvature is the geometry of these changing relations.

This gives us a useful reversal of perspective.

We do not begin with a pre-existing space and time, and then ask how gravity distorts them.

We begin with relations, whose changing structure gives us what we describe as spatial and temporal dimensions.

The distinction between space and time therefore becomes less fundamental than it first appears.

And the black hole provides an extraordinary place to test this thought.

Far from the black hole, we can comfortably distinguish spatial distance from temporal duration. As we approach the event horizon, that distinction becomes increasingly dependent upon how we describe the geometry. Inside the horizon, the familiar roles of the radial and temporal coordinates can no longer be maintained in the same way.

Space has not literally turned into time.

Rather, the geometry is telling us that our distinction between the two was never as fundamental as our ordinary language suggests.

The black hole thus invites a deeper question than How is space curved? or How much does time dilate?

It asks:

What kind of relational structure can give rise to both space and time—and what happens when that structure becomes extreme?

That is the question we shall follow into the black hole.