It's Not That We Don't Know. It's That We Can't.

• J.B. Manchak’s work reveals that general relativity (GR) is far stranger and more permissive than most physicists acknowledge, and that this permissiveness has deep consequences for what science can ever tell us about the universe.
  • Most physicists treat GR’s “pathological” models — those allowing time travel, indeterminism, or bizarre causal structures — as mathematical artifacts to be dismissed. Manchak proves rigorous theorems about them instead, showing that many common justifications for dismissing these models are question-begging or rely on unstated metaphysical assumptions.
  • His central finding: even with complete knowledge of all local empirical data — everywhere, everywhen, including the future — you still cannot determine the global structure of the universe. This is not a practical limitation but a fundamental, theorem-proven one.
  • He also discovered Heraclitus space-times — radically asymmetric universes where every event is locally unique — which represent the one special case where local data does determine global structure, and which connect to deep questions about symmetry, structure, and knowability.
  • Manchak draws parallels between his unknowability theorems and Buddhist (especially Zen) teachings on non-self, seeing both as responses to a form of underdetermination: just as no amount of introspection reveals a “self,” no amount of empirical data reveals the universe’s global character.

What General Relativity Actually Is

• GR is not a single theory but a vast collection of models, and which questions you can answer depend on which subset of models you’re considering.

  • The standard collection consists of all four-dimensional manifolds equipped with a Lorentzian metric. Einstein’s field equations, without further constraints, are vacuous — any metric can be paired with a matter field that satisfies them by definition.
  • Physicists pare down this collection using energy conditions, causal conditions (like global hyperbolicity), and other restrictions. But there is no consensus on which restrictions are correct, and different choices yield different answers to questions like “Is GR deterministic?”
  • GR is technically indeterministic unless you manually exclude the models that demonstrate indeterminism. This is not a settled physical question but a choice about which models to admit.

• Key technical concepts for understanding the discussion:

  • A Cauchy surface is a spacelike slice of spacetime that every causal curve intersects exactly once — it represents a complete “snapshot” of the universe from which the entire future and past can (in principle) be predicted.
  • A spacetime is globally hyperbolic if it possesses a Cauchy surface. This is the standard assumption that makes GR look deterministic.
  • A Cauchy horizon is a boundary beyond which evolution from a given surface breaks down — it arises when a spacetime can be extended, but only in ways that destroy global hyperbolicity.

Time Travel and Malament-Hogarth Space-Times

• GR genuinely permits time travel in the form of closed timelike curves — worldlines that loop back on themselves so an event can be revisited. This is not science fiction; Kurt Gödel demonstrated it in 1949, and Einstein could not find a physical reason to exclude such models.

  • The time travel allowed in GR does not involve “changing the past” as in movies. A person traveling along a closed timelike curve would return to a previously visited event with all their matter fields in the same state — a periodic structure.
  • Entropy does not “reset” — the matter simply returns to itself in the same configuration.

• Malament-Hogarth (MH) space-times are spacetimes where an observer at a single finite event can, in principle, receive the result of an infinite computation.

  • In an MH spacetime, there exists a point whose past light cone contains the entire infinite worldline of another observer (or computer). This means you could send a computer to run a program of arbitrary length and receive the answer at a finite moment in your own time.
  • MH space-times can solve the halting problem — you could determine whether an arbitrary Turing machine halts by sending it along the right worldline and checking whether a signal arrives.
  • MH space-times are necessarily not globally hyperbolic. They are more causally well-behaved than time travel spacetimes in some respects, and Manchak has constructed models satisfying standard energy conditions and stable causality.
  • A potential objection is blueshift: signals from the infinite worldline get compressed and energetic as they approach the reception point. Manchak has constructed models avoiding blueshift and other unphysical properties, though he acknowledges these constructions are themselves somewhat unphysical (using “cut-and-paste” techniques that create wild topologies).

The Cosmic Censorship Hypothesis and Its Problems

• The strong cosmic censorship hypothesis states that all physically reasonable spacetimes are globally hyperbolic — essentially, that determinism holds in GR.
  • This hypothesis is true or false depending on which collection of models you consider. If you restrict to a small, well-behaved subclass, it’s true by construction. If you allow more models, it can be false.
  • The question is not settled by physics alone — it depends on which models you consider “physically reasonable,” and that judgment is not derivable from the theory itself.
  • Manchak’s work on space-time maximality (the idea that the universe is “as big as it can be”) shows that the standard justifications for excluding extendable spacetimes are Leibnizian metaphysical assumptions, not physical necessities. In some variants of GR, nature may not have the option of building a maximal universe at all.

The Unknowability Theorem

• Manchak’s 2009 theorem proves that the global structure of spacetime is underdetermined by all possible empirical data.

  • Even if you had an “eyeball” at every event in the universe — past, present, and future — and could collect all their observations, you could still construct an entirely different spacetime model that reproduces all that data perfectly.
  • This goes beyond the standard philosophical underdetermination problem (the Matrix, evil demons). It arises from within GR itself, using the theory’s own mathematical structure.
  • The theorem holds even when you constrain the “nemesis” model to share all local properties of the original — same energy conditions, same vacuum structure, same curvature properties locally. The person collecting data is allowed to do any kind of local induction they want. It still isn’t enough.
  • The only way out is to assume global properties from the start — but that’s precisely what’s at issue. You can’t justify global assumptions empirically.

• De Sitter spacetime is a key example: even this highly symmetric, globally hyperbolic, well-behaved model suffers from cosmic underdetermination. An observer in De Sitter space cannot distinguish it from various “unrolled” versions or versions with holes, because the light cone structure limits what any observer can see.

Heraclitus Space-Times

• A Heraclitus spacetime is one where every pair of distinct events differs in some invariant, locally measurable way — no two points have identical local geometric structure.
  • Named after Heraclitus’s doctrine of radical flux (“you cannot step into the same river twice”), these spacetimes are maximally asymmetric.
  • In a Heraclitus spacetime, local structure uniquely determines global structure. If you cut the universe into tiny puzzle pieces and hand them to someone, there is only one way to reassemble them. This contrasts sharply with, say, Minkowski spacetime, where the same local pieces could be assembled into universes with time travel, holes, or other global pathologies.
  • Most spacetimes are probably Heraclitus — asymmetry is generic. Symmetric spacetimes like FLRW are the special, measure-zero cases. We study symmetric models because they’re tractable, not because they’re typical.
  • Heraclitus spacetimes do not contradict FLRW cosmology. FLRW models are large-scale approximations that average over small-scale curvature variations. The Heraclitus property operates at a fine-grained level; on cosmological scales, approximate symmetries can still emerge.
  • Heraclitus spacetimes rescue knowability — they are the one class of spacetimes where Manchak’s unknowability theorem does not apply. But this rescue comes at the cost of radical asymmetry, which may or may not describe our universe.
  • Constructing explicit Heraclitus metrics is possible in simple settings (2D, conformally flat). Manchak did this by identifying two curvature functions (P and Q) and arranging them so no two points share the same pair of values. Zorn’s Lemma is needed only for maximal Heraclitus spacetimes, not for the basic construction.

Symmetry, Structure, and the Hierarchy of Spacetimes

• Earman’s hierarchy of classical spacetimes illustrates an inverse relationship between structure and symmetry:

  • Leibnizian spacetime: maximum symmetry, minimum structure. You cannot meaningfully talk about acceleration, velocity, or position — all are gauge. Time slices are disconnected except for a temporal metric.
  • Galilean spacetime: less symmetry, more structure. Acceleration is meaningful (Newton’s F=ma works), but absolute velocity is not. You can “boost” the whole universe without changing anything.
  • Newtonian spacetime: even less symmetry. Absolute space is fixed; velocity and position are meaningful. The center of the universe (in Aristotelian spacetime) further reduces symmetry.
  • The general principle: adding structure (identifying a center, fixing absolute space) reduces the symmetry group, making more questions about motion meaningful.

• Heraclitus spacetimes break this pattern. They are maximally asymmetric — you cannot reduce symmetry further — yet you can still add more structure (e.g., marking a “center of the universe”). This “blows up” the symmetry-structure dogma that has dominated philosophy of physics for decades.

  • Manchak and co-author Thomas Barrett are actively investigating the philosophical implications of this breakdown.

Underdetermination of the Self and Zen Buddhism

• Manchak sees a structural parallel between cosmic underdetermination and the problem of self-knowledge.
  • David Hume, as an empiricist, argued that introspection reveals perceptions (love, hate, pain, pleasure) but never reveals a “self” that has those perceptions. The self is underdetermined by the empirical data of inner experience.
  • Buddhist teachings on non-self (anātman) arrive at a similar conclusion from a different direction. But Manchak emphasizes that in Zen, non-self is not a metaphysical claim to be grasped — it is a letting go of the grasping itself.
  • The Western tendency to treat “no-self” as a positive ontological thesis is, from a Zen perspective, a form of attachment — grasping at the negation is still grasping.
  • Zen’s core attitude is skepticism toward words and theories as vehicles for deep truth. Language is “the finger pointing at the moon” — useful for directing attention but easily mistaken for the thing itself. What matters is direct experience.
  • Manchak was drawn to Zen after leaving his Mormon faith in graduate school. He practices zazen (seated meditation) daily with his family and finds in Zen a framework that accommodates his spiritual inclinations without requiring doctrinal belief.

The Hole Argument (Briefly Distinguished)

• The “holes” Manchak discusses in the context of ruling out unphysical spacetimes (e.g., Minkowski space with a point removed) are completely different from the “hole argument” in the philosophy of physics literature (concerning substantivalism vs. relationalism). The terminology is unfortunately identical but the concepts are unrelated.

Manachak’s Method and Style

• Manchak works in the style of David Malament: take a philosophical question, formalize it precisely using the mathematics of GR, then prove a theorem that answers it. The theorem is the philosophy — he avoids flowery prose and lets results speak for themselves.
  • His papers are unusually short (2–3 pages) for philosophy. Every word is necessary.
  • He thinks visually and spatially, working with a clipboard and mechanical pencil, drawing pictures of spacetimes and light cones.
  • He describes himself as a slow thinker — ideas take years or decades to develop. His greatest strength is tenacity: returning to the same problem again and again until he finds a way through.
  • He now collaborates closely with “symmetry buddies” (Thomas Barrett, Jim Weatherall, Hans Halvorson), texting ideas back and forth — a significant shift from his earlier solo work.

Recent Work and Open Problems

• Manchak recently solved a problem posed by Bob Geroch over 50 years ago: Can you construct a spacetime with no time travel such that every extension of it introduces time travel? Working with the Logic Group in Budapest, he showed the answer is yes — by starting with a rolled-up Minkowski spacetime (which has closed timelike curves) and removing a Cantor-set fractal structure that blocks those curves, such that any extension of the fractal necessarily opens a path for time travel.
• He continues to investigate the relationship between symmetry and structure, and the philosophical implications of Heraclitus spacetimes for the symmetry-structure dogma in philosophy of physics.