What empirical observation supports the axiom of continuous spacetime?

[swissgirl1999 Refer]

TL;DR

All Nobel observations point to discreteness. Zero observations anchor continuous spacetime. SR gives Δt=0, Δd=0 for photons — a quantum jump, not travel. Same jump from orbitals to quasars. What empirical basis supports the continuum axiom?

The Nobel Prize-winning experiments that form the observational foundation of Modern Physics consistently point toward discreteness rather than continuity.

I did not find an equivalent (or any at all) body of direct observation supporting the continuity axiom.

Here is a non-exhaustive list of observations that suggest fundamental discreteness:

- Einstein (1905) — "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt"* (On a Heuristic Viewpoint Concerning the Production and Transformation of Light). The photoelectric effect demonstrated that light exchanges energy in discrete quanta (E = hν). Nobel Prize in Physics 1921.

- Einstein (1905) — "Zur Elektrodynamik bewegter Körper" (On the Electrodynamics of Moving Bodies). Special Relativity establishes the relativity of simultaneity and, when applied to lightlike intervals, yields Δt = 0 and Δd = 0 for the photon. Also part of the 1921 Nobel citation, though the prize specifically referenced the photoelectric effect.

- Bohr (1913) — On the Constitution of Atoms and Molecules. The Bohr model introduced discrete energy levels and quantum jumps between stationary states. Electrons do not transition continuously; they jump. Nobel Prize in Physics 1922.

- Heisenberg (1927) — "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik" (On the Perceptual Content of Quantum Theoretical Kinematics and Mechanics). The uncertainty principle establishes an ontological limit: there is no simultaneous definition of complementary variables. Nature itself is granular in phase space. **Nobel Prize in Physics 1932.

- Planck (1900) — "Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum" (On the Theory of the Energy Distribution Law of the Normal Spectrum). The quantization of action (h) introduced a fundamental granularity into physics. Nobel Prize in Physics 1918.

- Aspect, Clauser, and Zeilinger (2022) — For experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science. Their work empirically demonstrates non-locality, which is difficult to reconcile with a local, continuous spacetime manifold. Nobel Prize in Physics 2022.

In contrast, I am not aware of a single experiment that directly observes concrete evidence for a continuous spacetime.
Continuity appears to be a mathematical assumption imported from classical differential equations, not something forced upon us by empirical data.

There is also a straightforward consequence of Special Relativity that point in the same direction, yet is rarely taken at face value ontologically.

For a photon traveling from emission to absorption, the relativistic interval is:
Δs² = c²Δt² - Δd² = 0.

For massless particles, the proper time and proper distance between emission and absorption are both zero:
Δt = 0, Δd = 0.

The mathematics of SR itself tells us that, from the photon's perspective — or more precisely, along the lightlike worldline —emission and absorption are not separated by space or time. They coincide.

This is often dismissed as a "mathematical curiosity" or "not a valid reference frame."

But why should we ignore what the mathematics is telling us? If Δt = 0 and Δd = 0, then the only way something can "travel" without traversing distance and without time passing is that it does not travel at all. It connects. It jumps.

This is exactly the same ontological structure as the electron's quantum jump between atomic orbitals: discrete, direct, no continuous trajectory through intervening space.

Now consider a photon emitted by a quasar 8 billion light-years away — one of the very photons used in the Bell-Aspect-Zeilinger experiments — absorbed here on Earth.

The empirical evidence (Nobel Prize 2022) shows non-local correlation. The photon's emission-absorption is a single event with Δt = 0, Δd = 0.

No one delivered a memorandum to the photon explaining that quantum jumps are "only allowed" at the atomic scale and forbidden at cosmological scales.

The photon does not calculate the macroscopic reference frames between emission and absorption and conclude: "Sorry, that jump is too large; I am not authorized."

If the laws of physics are the same at all scales — and we have no observation suggesting otherwise —, then the same quantum jump that connects electron orbitals is the same quantum jump that connects a quasar to a telescope. The scale is different for us, the massive observers. For the photon, there is no scale. There is only the connection.

So, given that the empirical evidence consistently reveals a discrete, granular, connection-based structure — from Planck's quanta, to Bohr's jumps, to Heisenberg's uncertainty, to Bell's non-locality, to the SR prediction of Δt = Δd = 0 — what empirical observation anchors the axiom of a continuous spacetime manifold?

If no such observations exist, why is the continuum treated as the default ontological position?

 

[PeroK]

Because it makes the mathematics easier.

 

[swissgirl1999 Refer]

At the cost of making physical ontology incompatible with theories that claim that the universe has fundamental laws that differ according to scale; who tells the photon how far it can jump?

If the space inside the atom is non-continuous, why should it be continuous between molecules, and so on, and so far?

At which scale does the nothingness of the vacuum suddenly become something?

If all Nobel points towards discreetness, why is it the discrete that is a “heterodox theory” and the continuous is axiomatic?

 

[PeroK]

If all Nobel points towards discreetness, why is it the discrete that is a “heterodox theory” and the continuous is axiomatic?

It isn't. No one has found a way to make a discrete theory work. The continuum is simpler mathematically and thereby the default.

Moreover, the current theory of spacetime is not fundamental. The question is more relevant for a more fundamental theory (i.e. quantum gravity), where spacetime (discrete or continuous) may emerge from a yet more fundamental concept.

It's not enough to suspect that ultimately spacetime may be discrete. That by itself doesn't invalidate a continuum model in its current scope of applicability. Everyone knows that ultimately spacetime might be discrete, but you shouldn't let that stop you using a differentiable manifold.

PS even if someone produced a fundamental theory of discrete spacetime, most cosmology wouild continue to use continuous manifolds. Because, the discrete model must approximate to a continuous manifold in any case. You can use integration on a macroscopic object (like a baseball bat) despite knowing that it is ultimately not a continuous distribution of matter, but a large number of molecules, atoms and elementary particles.

 

[PeroK]

PPS you can use calculus on population studies, for example, even though an animal or human population is ultimately discrete. You don't have to throw away calculus just because a continuum model is an approximation.

 

[swissgirl1999 Refer]

It isn't. No one has found a way to make a discrete theory work. The continuum is simpler mathematically and thereby the default.

Moreover, the current theory of spacetime is not fundamental. The question is more relevant for a more fundamental theory (i.e. quantum gravity), where spacetime (discrete or continuous) may emerge from a yet more fundamental concept.

It's not enough to suspect that ultimately spacetime may be discrete. That by itself doesn't invalidate a continuum model in its current scope of applicability. Everyone knows that ultimately spacetime might be discrete, but you shouldn't let that stop you using a differentiable manifold.

PS even if someone produced a fundamental theory of discrete spacetime, most cosmology wouild continue to use continuous manifolds. Because, the discrete model must approximate to a continuous manifold in any case. You can use integration on a macroscopic object (like a baseball bat) despite knowing that it is ultimately not a continuous distribution of matter, but a large number of molecules, atoms and elementary particles.

I totally agree with you, nevertheless, my point is about ontology and not engineering... Cosmology or QM may always use continuous models 'cause they really work; I'm not also claiming spacetime must be discrete, I'm just asking why both models don't have the same approach on ontology? Continuous spacetime is axiomatic but it's not demonstrated, however, to quention GR is considered an act of heresy by many... Physics and physicists often mistake the map for the road, the theories and the mathematics for the physical ontology.

 

[PeroK]

Ontology is philosophy, not physics.

however, to quention GR is considered an act of heresy by many...

No it's not. Everyone knows GR can't be the whole story. There's an explicit singularity in the spacetime of a black hole. So, the theory fails for that reason alone.