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

Episode Overview

• This episode explores the fascinating intersection of general relativity, mathematical physics, and philosophy, focusing on the fundamental limitations of scientific knowability.
• The discussion challenges the assumption that classical physics is strictly deterministic, revealing that Einstein's equations allow for "pathological" models, such as those permitting time travel or containing un-knowable physical boundaries.
• The conversation introduces key mathematical frameworks used to analyze spacetime structures, including global hyperbolicity, Cauchy surfaces, and Malament-Hogarth spacetimes.
• The narrative shifts to the philosophical concept of underdetermination, proving that even infinite, perfect local empirical data cannot uniquely determine the global topology of our universe.
• The episode concludes by bridging physics and philosophy of mind, comparing the underdetermination of cosmic spacetime to the elusive nature of the "self" in Western empiricism and Zen Buddhism.

Key Concepts

• Undetectability & Underdetermination of Spacetime: The core thesis that local observations and local laws of physics are mathematically insufficient to uniquely determine the global topological and geometric structure of the universe. Even with complete, perfect local data from all points in space and time, multiple distinct, empirically indistinguishable global models (or "nemesis spacetimes") can be constructed.
• The Cauchy Surface & Global Hyperbolicity: To define determinism in general relativity, physicists rely on the concept of global hyperbolicity. A Cauchy surface is a three-dimensional "slice" of spacetime representing an instant of "now" containing all the initial data of the universe. If a spacetime is globally hyperbolic, it possesses a Cauchy surface, allowing the laws of physics to uniquely predict the future or retrodict the past.
• Cauchy Horizons: The boundary of predictability. If a spacetime is not globally hyperbolic, predictability completely breaks down at a certain point because new, uncalculable information can enter the universe from beyond this horizon.
• Spacetime Maximality: The metaphysical idea that the universe is "as big as it can be." Under standard general relativity, any spacetime manifold can be mathematically extended to a maximal limit. However, attempting to eliminate "pathological" models to preserve determinism can destroy the mathematical guarantee that a "maximal" extension exists.
• The Cosmic Censorship Hypothesis: Formulated by Roger Penrose, this hypothesis suggests that physically realistic spacetimes must be globally hyperbolic. It seeks to "censor" unpredictable, naked singularities behind event horizons to preserve determinism for observers outside.
• Earman’s "Time Machine" and Malament-Hogarth Spacetimes: Non-globally hyperbolic spacetimes can be viewed as theoretical "machines." In a Malament-Hogarth spacetime, an observer can experience an infinite amount of time (e.g., a computer running an infinite calculation) within the past light cone of another observer who only experiences a finite amount of proper time, theoretically allowing the finite observer to "know" the result of an infinite computation.
• The Spacetime Hierarchy (Earman's Model): Classical spacetimes are organized hierarchically by the amount of geometric structure they possess. Adding structure (e.g., moving from Leibnizian to Newtonian spacetime) reduces the number of symmetries (allowed transformations) but increases the physical meaningfulness of different types of motion, like absolute velocity.
• Heraclitus Spacetimes: These are maximally asymmetric spacetimes where no two points share the exact same local geometric properties (such as curvature). Because there are no local symmetries, the local structure acts like a unique jigsaw puzzle piece, allowing the global structure to be uniquely determined from local data—temporarily overcoming underdetermination.
• Underdetermination of the Self: In philosophy of mind, the concept of the "self" faces a similar underdetermination problem as cosmic spacetime. Empirical introspection (as noted by David Hume) only reveals passing thoughts, emotions, and perceptions, but never a permanent, stable, observable "self."
• The Zen Buddhist Approach to "Non-Self": Rather than grasping onto "non-self" as a rigid philosophical dogma, Zen Buddhism teaches the practice of letting go of the concept of the self entirely, prioritizing direct experience over intellectualized definitions.

Quotes

• At 0:02:18 - "You can collect evidence—all the evidence you want, you can collect evidence forever... and the idea of that not being enough to pin down what the universe is like, that's something that naturally pops up in theories of space and time." - JB Manchak explaining that the underdetermination of spacetime is a mathematical property of space and time itself, not a limitation of our instruments.
• At 0:03:47 - "A philosopher like me... is going to want to really think about this deeply and ask: 'Why exactly is this particular model physically unreasonable?' And it turns out that a lot of the usual justifications... when you really analyze them, they are kind of pithy." - Highlighting the tension between pragmatic physics, which discards inconvenient solutions, and philosophy, which demands logical rigor.
• At 0:05:08 - "Why would nature stop when nature could keep building? So she has to keep building." - Explaining the metaphysical, Leibnizian origin of the "maximal spacetime" assumption in physics.
• At 0:07:55 - "General Relativity is not deterministic unless you kind of get rid of all those pathological models... [and] you can say GR is deterministic if you kick out all the models that show it's indeterministic." - Exposing the circular logic sometimes used to claim classical physics is deterministic.
• At 0:11:35 - "What you do find in GR are models that have a peculiar causal structure in the sense that you'll have worldlines of particles... that can go forward in time, but the structure of the spacetime allows that curve to wrap back on itself, and so the event can be revisited." - Explaining how closed timelike curves (CTCs) represent time travel within Einstein's field equations.
• At 0:12:14 - "Einstein's response was... 'That's very interesting, we'll have to see if there are physical reasons to exclude such a model.' And here we are, many decades later... we're still looking for physical reasons." - Showing that Kurt Gödel's 1949 proof of a time-traveling universe remains an open challenge to physics.
• At 0:27:08 - "The way to think about these things first is to not call it a Cauchy surface, just call it a surface... you put some data on this surface, and then you evolve it... if we do so and we find ourselves in a situation where we've evolved it as far as we can—that's a globally hyperbolic spacetime." - Explaining how determinism and global hyperbolicity are defined through mathematical evolution.
• At 0:28:16 - "If [the Cosmic Censorship Hypothesis] is false, then what that means is you've evolved it as far as you can go, but that doesn't mean that it's necessarily a maximal spacetime. You may be able to extend it further, it's just that any extension will ruin the global hyperbolicity property." - Highlighting the breakdown of determinism when spacetime can be extended beyond the reach of a Cauchy surface's predictive power.
• At 0:29:59 - "What if we could show somehow that all of the extensions, every last one of them, satisfies some property—either they have time travel in them, or they have the Malament-Hogarth property?" - Introducing John Earman’s philosophical approach to classifying non-unique, non-deterministic extensions of spacetime.
• At 0:31:07 - "In the past light cone, you have an observer with an infinite future... so for you, you're making an observation at a particular finite point in space and time, but part of what you're observing is an infinite future of some other observer." - Explaining the bizarre causal structure of Malament-Hogarth spacetimes.
• At 0:33:37 - "What happens with the infinite blueshift situation is when the computer is sending signals back to that point, they can start to bunch up... the wavelength will go towards the blue side of things... some people have said this really isn't physically reasonable." - Discussing the primary physical objection to Malament-Hogarth "supertask" machines: the infinite energy buildup of incoming signals.
• At 1:03:12 - "It doesn't matter where in the universe one finds oneself... suppose that you give me all of that data. Suppose that you have an eyeball everywhere in the universe... I'm going to go back in my workshop and I'm going to come up with a model that's going to reproduce all of that data, but it's going to be completely different." - Illustrating the robust nature of the underdetermination thesis.
• At 1:05:47 - "The theorem goes through even under those additional constraints... It shuts down a common response... which is, 'Of course deductively you can't prove it, but science works on induction.' ... I'm telling you to give me all of your data, and I'm allowing you to do any kind of local induction that you want; you're still not going to be able to pin down what the universe is like." - Clarifying that underdetermination persists even when local inductive reasoning is permitted.
• At 1:07:04 - "The only way to wiggle out of this is to do a global induction... but that's precisely what's at issue here... It's not coming from any empirical data... it's just an assumption about the way that you want the universe to be." - Highlighting that assuming global properties (like simplicity) is a metaphysical choice rather than an empirical conclusion.
• At 1:11:51 - "In philosophy of physics, there is a long tradition of saying the symmetries of an object tell you how much structure it has. If it's got tons of symmetries, it doesn't have very much structure. If it has few symmetries, it's got tons of structure." - Defining the inverse relationship between symmetry and structure in physics.
• At 1:12:58 - "At some point, you get to the stage where your asymmetries max out—you can't be any more asymmetric than a Heraclitus spacetime—but your structure doesn't max out... you can pile on structure, but that's not going to decrease the asymmetries." - Explaining a key limitation of the traditional "symmetry-structure" dogma when dealing with maximally asymmetric systems.
• At 1:21:19 - "Newton thought there was an absolute space... that's a lot of structure. If you are pointing to a certain point in the universe and saying 'this is the center,' that's an extra structure, and what that's going to do is limit the type of symmetries that are going to be allowed." - Providing a historical example of how adding physical features breaks symmetry.
• At 1:23:44 - "Even in principle, there are things that science just isn't going to be able to help us better understand. And in this case, one of those things is the big structure of the universe that we're living in." - Encapsulating the inherent boundaries of empirical science regarding global cosmic structure.
• At 1:35:33 - "If there's symmetries around, like in Minkowski spacetime, the local structure just does not determine the global structure... But in Heraclitus spacetime there's just one way to put the pieces together." - Explaining how a lack of symmetry makes the global structure of a universe mathematically knowable from its local parts.
• At 1:37:39 - "You don't get to see very much of the universe in a de Sitter spacetime... You have no way of knowing if you're in de Sitter, or some other unrolled de Sitter, or some de Sitter with holes in it." - Showing how the geometry of our actual universe might prevent us from ever knowing its true global shape.
• At 1:39:35 - "One can use science to show that science has limits. And that's what I'm trying to do here... Even in principle, there are things that science just isn't going to be able to help us better understand." - Emphasizing that limits of knowledge are mathematically proven discoveries of science.
• At 1:51:24 - "When I try to observe what I am... I find that I don't have any observation of myself. I see love in me, I see hate, I see pleasure, I see pain... but I never see 'me'." - Connecting David Hume’s empiricist skepticism of the self to the scientific problem of local observation.
• At 1:53:45 - "The idea of non-self is not... grasping onto an idea of non-self. It's a letting go of the idea of self... Whenever you're grasping on anything, you're not doing the Zen thing." - Clarifying the psychological and spiritual practice of Zen regarding the illusion of identity.
• At 1:57:05 - "Where some people might give up on an idea, I just don't give up. I'm relentless... Things don't come very quickly to me, but I can tenaciously come back to the same idea again and again." - Reflecting on the academic and personal virtue of slow, persistent, and deep thinking.

Takeaways

• Recognize Metaphysical Assumptions in Science: Be aware that what physicists classify as "physically reasonable" often relies on aesthetic or philosophical preferences (like determinism or homogeneity) rather than empirical proof.
• Deconstruct Classical Determinism: Understand that classical general relativity is not strictly deterministic unless we actively filter out valid, non-deterministic mathematical solutions (like closed timelike curves).
• Acknowledge the Limits of Observation: Accept that because we can only observe our local "past light cone," we are fundamentally blind to the global topology of the universe.
• Use Mathematical Counterexamples Productively: Leverage "unphysical" models (like Malament-Hogarth spacetimes) as valuable stress-tests to map the logical boundaries of physical theories.
• Distinguish Local and Global Induction: Realize that assuming the laws of physics are uniform locally (local induction) does not logically justify making sweeping assumptions about the global structure of the cosmos (global induction).
• Understand the Blue-Shift Barrier: Recognize the physical limitation of "supertask" spacetimes, where the infinite energy buildup of incoming signals (infinite blueshift) threatens to destroy the observer.
• Re-evaluate Symmetry and Structure: Shift your perspective to see that while high symmetry is often equated with order, it actually creates observational ambiguity, whereas zero symmetry (asymmetry) allows for unique global reconstruction.
• Appreciate "Science Proving Its Own Limits": View the mathematical boundaries of what we can know (such as observational horizons in de Sitter spacetime) not as failures of science, but as rigorous scientific discoveries.
• Apply Underdetermination to Identity: Draw a parallel between the cosmos and the mind; understand that just as we cannot observe global spacetime, we cannot observe a permanent, static "self" through local thoughts and sensations.
• Practice Zen "Non-Grasping": Adopt the Zen approach to identity by actively letting go of the conceptual "self" rather than dogmatically clinging to a rigid definition of "non-self."
• Embrace the Value of Slow Thinking: Cultivate intellectual tenacity and deep, visual problem-solving, returning persistently to the foundations of a problem over years rather than chasing quick academic victories.
• Remain Humble in the Quest for Knowledge: Let the mathematical reality of underdetermination foster scientific and intellectual humility regarding our ability to achieve a complete "Theory of Everything."