Why Some Things Become Facts — and Why That’s Not Optional
We live in a world where things happen. A detector clicks. A measurement gives a result. A memory forms. A record is written. Once these things occur, they don’t quietly “un-happen.” They become facts. Yet much of modern physics is built on mathematical models that are, in principle, perfectly reversible. According to these models, every process could be run backwards if you had enough precision. This creates a deep tension: how can irreversible facts exist in a universe described by reversible laws?
This paper shows that this tension isn’t just philosophical — it reveals a hard structural constraint on reality itself. Throughout, ‘infinite precision’ should be understood operationally as the capacity to retain and recover an unbounded number of physically distinguishable correlations; i.e., infinite recoverable memory.
The Core Result: Infinite Precision Kills Facts
The central result is a no-go theorem:
If physical reality allowed infinitely fine, physically accessible distinctions, then irreversible facts could not exist.
In plain terms, if the universe could always be examined at finer and finer levels — with no fundamental limit to how much detail is physically accessible — then any apparent “loss” of information could always be undone by looking more closely. Measurement outcomes would never truly settle. Records would never be final. Entropy would never genuinely increase. Everything that looks irreversible would, in principle, be reversible.
The existence of facts therefore requires a limit to physical distinguishability. This limit doesn’t have to be discrete mathematics or pixels in space — but it must exist operationally. There must be a finest level beyond which differences are no longer physically recoverable. Without that, nothing ever truly becomes real in the sense we rely on to do science at all.
In an infinite-resolution universe, no event ever truly settles because there is always more physically accessible detail beneath what looks like a finished outcome. Take a bat hitting a ball. At the level we normally describe it, the collision happens and the ball flies away — a clear fact. But if the universe allows unlimited resolution, then every microscopic vibration, deformation, heat flow, sound wave, and field disturbance created during the impact remains, in principle, perfectly trackable. There is no final scale at which alternatives are eliminated. With enough access to these finer details, one could always reconstruct exactly how the contact occurred, distinguish between arbitrarily close alternative impact histories, and in principle reverse the process. What looked like a single, settled event is revealed as a reversible redistribution of information into ever finer structure. In such a universe, the statement “the bat hit the ball in this way” is never final — it is only a provisional description that can always be undone by looking more closely. A true fact requires that, at some point, distinctions stop being physically recoverable. Without that limit, nothing ever fully happens.
When the ball hits the bat, energy and momentum don’t disappear. They spread into many degrees of freedom: vibrations in the bat, deformation of the ball, sound waves in the air, heat, microscopic stresses, electromagnetic fields. In an infinite-resolution universe, every one of those degrees of freedom carries perfectly precise information about the impact. Nothing is rounded off, coarse-grained, or erased.
Because the laws are reversible and the information is fully preserved, the post-impact state uniquely determines the pre-impact state. That means the collision didn’t “destroy” the alternative possibilities — it merely encoded them into finer and finer structure. With complete access to those details, the collision can be mathematically inverted: you could compute exactly how the ball and bat must have been moving before contact.
Crucially, this isn’t about literally grabbing the ball and bat and making them fly backward. It’s about whether the past is still fully present in the physical state of the universe. In an infinite-resolution world, it is. The claim “the bat hit the ball” is therefore not a final fact — it’s a temporary summary of a state that still contains all the information needed to undo it in principle.
A genuine fact requires that, after the collision, some distinctions are no longer physically accessible — that the information about alternative ways the hit could have occurred has been irretrievably lost. Only then does the event become irreversible. Without a limit on resolution, that loss never happens, so the universe never truly commits to the event having occurred in one definite way rather than another.
Why This Is Deeper Than the Measurement Problem
This result doesn’t propose a new interpretation of quantum mechanics, nor does it modify known equations. Instead, it works at a deeper level: admissibility. It asks which kinds of mathematical descriptions are even capable of describing a universe with facts.
That’s why the result applies equally to classical mechanics with infinite precision, fully unitary quantum theories, many-worlds interpretations, and block-universe models. If a framework preserves unlimited recoverability of information within a bounded region, it cannot, on its own, account for irreversible outcomes. Something additional must step in — and whatever that “something” is, it must enforce finite distinguishability.
This reframes long-standing debates. The question is no longer “Which interpretation is right?” but “Which frameworks can possibly host facts at all?”
Connecting Irreversibility, Entropy, and Time
One of the most powerful aspects of the result is that it unifies several puzzles that are usually treated separately. Measurement finality, entropy increase, memory formation, causal order, and the arrow of time all turn out to rely on the same structural requirement: finite distinguishability.
Entropy increases because information is genuinely lost — not merely hidden. Measurements produce outcomes because alternatives are eliminated from physical accessibility. Time has a direction because commitments accumulate and cannot be undone. None of this works if the universe can always be refined without limit.
In this view, entropy is not just disorder or ignorance. It is a ledger of lost possibilities — a record of irreversible commitments that have shaped what comes next.
Why This Matters
This result explains why modern physics already contains hints of fundamental limits: entropy bounds, holographic principles, Landauer’s cost of erasing information, and the apparent discreteness suggested by quantum gravity. These are not arbitrary features or technical curiosities. They are signs of a deeper necessity.
Any universe capable of producing facts must limit how finely reality can be distinguished.
That insight doesn’t tell us exactly where the limit lies — whether it’s at the Planck scale, a holographic boundary, or something else — but it tells us something more important: there must be a limit. Without it, nothing would ever truly happen.
And without things happening, there would be no physics at all.