No White Holes Theorem

In a finite, static space of informational configurations. “Time” is the ordered experience produced when an observer is instantiated across neighboring, record-compatible configurations.

Let $x$ run from the singularity-like configuration to the event-horizon-like configuration:

$$ x=0 ;; \text{singularity}, \qquad x=x_H ;; \text{event horizon}. $$

Let $R(x)$ be the amount—or multiplicity—of observer-supporting raw material. It has a hump shape, with a maximum at $x=x_*$:

$$ R'(x)>0 \quad \text{for }x<x_*, $$

$$ R'(x)<0 \quad \text{for }x>x_*. $$

An observer “falls” in the direction of increasing (R). That is not a force acting in time. It is the statistical asymmetry among possible observer-compatible continuations:

$$ \text{experienced direction} \propto \nabla R. $$

So “down” simply means:

$$ \text{more configurations containing the material needed for the observer’s continuation}. $$

The compression factor plays a separate role. It biases where observers are found:

$$ P_{\mathrm{obs}}(x)\propto C(x)R(x), $$

where (C(x)) favors the more compressible, lower-entropy side. Therefore the typical observer is displaced onto the singularity side of the raw-material peak:

$$ x_{\mathrm{obs}}<x_*. $$

From there,

$$ R'(x_{\mathrm{obs}})>0, $$

so the observer’s walk points toward larger $x$: toward larger-scale, higher-entropy, horizon-like configurations. That experienced ordering is what we call an expanding universe.

On the other side of the hump,

$$ x>x_*, $$

the direction of increasing raw-material support is toward smaller $x$, so the experienced ordering is toward the singularity. That appears as collapse or a black-hole interior.

The entire structure is therefore:

$$ \text{singularity} ;\longrightarrow; \boxed{\text{maximum observer-support}} ;\longleftarrow; \text{event-horizon side}. $$

Both experiential arrows point down the probability landscape toward the hump maximum. They do not point away from it.

A white hole would require the missing orientation:

$$ \text{observer walk away from greater support}, $$

or mathematically,

$$ \frac{dx}{d\tau},R'(x)<0, $$

where $\tau$ is only a label for the observer’s experienced ordering, not fundamental time. It would mean observers systematically walking “uphill,” toward configurations containing fewer compatible continuations and less supporting raw material.

So no-white-hole result is:

With a single-peaked raw-material measure and observer walks directed toward greater conditional multiplicity, the experiential flow converges toward the peak from both sides. A white hole would require a divergent, anti-gradient branch, which the informational landscape does not contain.

This is also why simply “reversing time” cannot generate a white hole. There is no external time variable to reverse. Reversing a drawn sequence of configurations does not make it an observer-experienced sequence, because the reversed sequence points against the conditional probability gradient and its internal records would not support that ordering.