Science and spirituality often seem worlds apart: the former devoted to empirical and mathematical rigor, the latter to contemplative or mystical insights. Yet there are striking resonances between these realms. Noether’s theorem—a foundational principle in physics—asserts that whenever a system displays a continuous symmetry, there is a corresponding conservation law (e.g., time-invariance implies conservation of energy). Meanwhile, Buddhist philosophy, particularly as expressed in the Heart Sutra and Nagarjuna’s writings, stresses the interdependence and emptiness (śūnyatā) of phenomena, pointing out how things exist relationally rather than as fixed substances.
This essay explores the phenomenological, first-person dimension of these ideas. By analyzing a single moment of lived experience—such as a breath in meditation—we can see how symmetrical relations and conservation-like principles appear in our own conscious processes. Nagarjuna’s Catuskoti (the “four-cornered” logic) will help us see how claims about existence and non-existence, permanence and impermanence, can be reframed in light of emptiness and dependent origination. The end goal is to highlight an unexpected harmony between the physical insight of symmetries and conservation (Noether’s theorem) and Buddhism’s proclamation that all dharmas (phenomena) are empty of intrinsic essence yet remain functionally effective through interdependence.
Emmy Noether’s theorem (1918) is a cornerstone of theoretical physics. In simplified terms, it states:
Whenever a system’s action (governing equations) remains invariant under a continuous symmetry, a corresponding conservation law arises.
In each case, the “invariance” refers to the idea that the system’s fundamental equations or action do not change when transformed according to a certain symmetry (e.g., shifting the time coordinate or rotating the reference frame).
From a Buddhist standpoint—particularly the Heart Sutra—all phenomena (dharmas) are:
When we overlay these ideas onto Noether’s theorem, we might reinterpret “symmetry” as a form of relational balanceamong empty phenomena. The “conservation laws” are not about locked-in substances persisting through time. Instead, the stability or “conservation” we observe emerges from invariant relational structures—networks of dependent origination that remain functionally consistent under transformations (e.g., time shifts or spatial translations).
In other words, emptiness does not negate phenomena. It reveals that their “conserved” properties (like energy or momentum) exist not as intrinsic possessions but as relational invariants. This parallels the Heart Sutra’s teaching that while all dharmas are empty, they remain “form” in a conventional sense, co-arising in a web of interdependence.
To ground these ideas in direct experience, consider a simple moment of sitting meditation where you focus on the breath. From a Buddhist taxonomical lens, this experience can be broken into the five skandhas (aggregates):
By carefully attending to these five components, you notice that nothing remains static:
Applying the Heart Sutra’s proclamation—“Form is emptiness, emptiness is form”—in meditation reveals that each skandha arises interdependently:
In seeing how none of these aspects hold a permanent essence, the “empty” nature of each skandha becomes experientially tangible, even as they function and interact seamlessly.
Nagarjuna’s Catuskoti lays out four possible stances regarding a proposition (e.g., “the breath exists”):
In a purely logical analysis (the so-called “tetralemma”), these can seem contradictory or puzzling. But for Nagarjuna, the point is to show how conceptual extremes fail to capture the subtlety of dependent origination.
When you see that the breath “both is and is not”—that it arises as an interdependent phenomenon—this reveals a kind of invariance. It consistently behaves in relationship to the body, environment, and consciousness, but that consistency arises relationally rather than from a permanent “something.” This parallels how Noether’s theorem sees conservation laws: they are not rooted in an immutable substance but in invariance principles—the structural “emptiness” or relational “DNA” of the system.
In physics, “conservation laws” state that certain quantities (energy, momentum, etc.) remain constant over time. If we interpret these laws through a Buddhist lens, they become statements about how a system’s relational structure remains stable under transformations. They do not assert a “thing” that eternally exists but reflect how processes continue in an unbroken chain, dependent on symmetrical conditions.
Noether’s theorem can thus be read as a formal corollary of pratītyasamutpāda (dependent origination) in the sense that every “conserved quantity” points to an underlying symmetry in how phenomena relate—i.e., a stable pattern that emerges from cyclical or self-consistent interactions. This pattern is empty of a separate essence, yet it is observableand functionally valid.
Strictly speaking, Noether’s theorem in physics is a mathematical statement requiring Lagrangians, variations of action, and group theory. Nagarjuna’s Catuskoti is a philosophical tool for undermining conceptual extremes and revealing emptiness. How, then, might we talk of “proving” Noether’s theorem in the context of Catuskoti?
Hence, “proving” Noether’s theorem within the Catuskoti amounts to showing the conceptual synergy: the emptiness of phenomena allows symmetrical invariances to become the “locus” for what we call “conservation.” The theorem and the Catuskoti both converge in illustrating that no static essence is required for stability to occur.
By expanding a simple moment of phenomenological analysis—the breath in sitting meditation—through the lens of Buddhist taxonomies (five skandhas, emptiness) and Nagarjuna’s Catuskoti, we see a striking parallel to Noether’s theorem’s principle of symmetry and conservation:
In the meditative moment, we notice the breath’s dynamic nature. It “exists” in a conventional sense, “does not exist” in an ultimate sense, “both exists and doesn’t” as a fusion of form and emptiness, and “neither exists nor doesn’t” when we relinquish all conceptual extremes. These four vantage points mirror how Noether’s theorem demonstrates that conservation laws emerge not from any one ultimate substance but from the self-consistent relational structure of a system.
In short, phenomenological experience and Buddhist emptiness do not undermine the empirical findings of modern physics—rather, they can illuminate why these findings might take the form they do, offering an integrative vision. Both spiritual wisdom and scientific theory uncover invariant patterns in experience and reality, attesting to a shared commitment: that there is no fixed “essence” behind phenomena, yet patterns of stability naturally arise due to the interwoven tapestry of relations.