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.

 

[weirdoguy]

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

Well, the loudest people who question GR are crackpots who have no idea about GR whatosever. And they question GR as a whole, in the regime where it has been tested more than they could ever imagine. In general, physicists don't like when non-physicists tell them what they should think, because physicists know perfectly well, that GR, and every single theory in physics, is not complete.

 

[Dale]

TL;DR: All Nobel observations point to discreteness.

No, this is not true. Some do, but not all.

Zero observations anchor continuous spacetime.

On the contrary, every observation which is correctly predicted by a theory which uses continuous spacetime is in actual fact an observation supporting the continuity of spacetime. This is how science works. We make assumptions, build a model based on those assumptions, and then experimentally test the predictions of the model. If the experiment matches the prediction, then the assumptions are justified.

Contrary to your statement, there is not a single measurement that contradicts a continuous spacetime, and spacetime has been experimentally measured to be continuous to every level of precision tested to date. The experimental evidence for continuity is as strong as scientific evidence can possibly be today.

SR gives Δt=0, Δd=0 for photons — a quantum jump, not travel.

This is false. SR does not give that. And besides, SR is a continuous spacetime theory. So it is rather bizarre for you to bring it up. It is an exceptionally well confirmed theory of continuous spacetime

The bottom line is that we use continuous spacetime because it works. We don’t use discrete spacetime because it doesn’t work. Yet.

Physics and physicists often mistake the map for the road, the theories and the mathematics for the physical ontology.

I don’t think this is accurate. I don’t think physicists generally mistake the map for the road. The issue is that neither the math nor the theory nor the evidence actually require any specific ontology. The ontologies don’t match because they don’t need to, scientifically.

 

[martinbn]

You say that there is zero obervational support for continuous space-time, but it is the same for discrete one. You seem to be convinced that it cannot be continuous. Why?

 

[Paul Colby]

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 photoelectric effect demonstrated that light exchanges energy in discrete quanta (E = hν).

Yet, both $\nu$ and $E$ are continuous quantities unless I’ve missed a memo.

 

[PeterDonis]

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

Discreteness of what, though?

Let's take the cases you give:

- 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.

Even leaving aside that there are arguments in the literature against the claim that the photoelectric effect shows that light comes in discrete quanta (the same predictions can be obtained from a model in which light is continuous but matter is discrete), this is still discreteness of light, and matter, not spacetime.

- 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.

There's no discreteness here anywhere.

- 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.

This shows discreteness of energy levels in atoms, not spacetime.

- 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.

This shows discreteness of matter, not spacetime. "Phase space" is an abstraction that we use to model matter; it's not spacetime.

- 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.

$h$ is a property of quantization of matter and energy, not spacetime.

- 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.

This at least is a claim about spacetime, but note that the issue is really with the "local" part, not the "continuous" part. And the claim about spacetime here is certainly not mainstream physics; it's an open area of research.

I am not aware of a single experiment that directly observes concrete evidence for a continuous spacetime.

Since continuity in the mathematical sense requires infinite resolution of measurements, and that's impossible, of course we can never get any positive evidence of a continuum. But, as you yourself note...

Continuity appears to be a mathematical assumption imported from classical differential equations

Yes, because it makes the math much more tractable. And as long as models using continuity continue to make accurate predictions, physicists will continue to use them.

not something forced upon us by empirical data.

Models are never just "forced upon us by empirical data". Models are human tools.

That said, physicists certainly have come up with models that incorporate discreteness, when empirical data requires it. For example, the initial development of quantum mechanics was basically physicists being dragged kicking and screaming to models of matter that incorporated discreteness, particularly for observables like spin, because empirical data forced them to. But none of that empirical data forced them to model spacetime discretely. Indeed, there are important observables in QM even today that have a continuous spectrum: position, momentum, and energy for systems not in bound states. And those are precisely the observables that are most closely tied to spacetime.

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 not correct, although this wrong claim does sometimes appear in pop science sources. We have had many previous threads on this. The photon's worldline in spacetime between emission and absorption is not a single event; it's a continuum of events along a curve in spacetime, just as for a matter particle. The spacetime interval along that curve is zero for light, but that does not mean the curve collapses to a point. It just means you have to parameterize the curve by something other than arc length. This is well understood in relativity and has been for decades.

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

This is personal speculation and is off limits here, as is your scenario that follows involving light from a quasar. Please be advised.

why is the continuum treated as the default ontological position?

A continuum for spacetime is the easiest mathematical model to use. That's why physicists use it, as explained above. That's not an "ontological position"; it's an obvious practical position to take in order to do physics.

 

[swissgirl1999 Refer]

physical ontology is physics, not phili

Ontology is philosophy, not physics.

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.

physical ontology is physics, not philosophy...

 

[Dale]

physical ontology is physics, not philosophy...

Ontology is philosophy, regardless of whether the philosophy is a philosophy about physical systems or not.

Physics is a science, meaning that it is discovered by the scientific method. Ontology cannot be discovered through the scientific method, as you can always choose between different combinations of ontology and epistemology that are jointly consistent with a given set of experimental data.

 

[swissgirl1999 Refer]

No, this is not true. Some do, but not all.

On the contrary, every observation which is correctly predicted by a theory which uses continuous spacetime is in actual fact an observation supporting the continuity of spacetime. This is how science works. We make assumptions, build a model based on those assumptions, and then experimentally test the predictions of the model. If the experiment matches the prediction, then the assumptions are justified.

Contrary to your statement, there is not a single measurement that contradicts a continuous spacetime, and spacetime has been experimentally measured to be continuous to every level of precision tested to date. The experimental evidence for continuity is as strong as scientific evidence can possibly be today.

This is false. SR does not give that. And besides, SR is a continuous spacetime theory. So it is rather bizarre for you to bring it up. It is an exceptionally well confirmed theory of continuous spacetime

The bottom line is that we use continuous spacetime because it works. We don’t use discrete spacetime because it doesn’t work. Yet.

I don’t think this is accurate. I don’t think physicists generally mistake the map for the road. The issue is that neither the math nor the theory nor the evidence actually require any specific ontology. The ontologies don’t match because they don’t need to, scientifically.

You`re right, I over stated and generalized and it may sound offensive, so I`m sorry for that; however, my point, to be more precise, is — physicists often respond with theories to ontological questions. "We don’t use discrete spacetime because it doesn’t work. Yet" — that's the right attitude and quite rare, to leave openly what is not definitive yet. Nevertheless, your fine answer ultimately doesn' t provide experimental evidence for a continuous spacetime and doesn' t provide any Nobel for it. The conclusion I take from that is that ultimately spacetime is still open for debate; thanks for your honest answer.

 

[PeroK]

physical ontology is physics, not philosophy...

That's what philosophers say!

 

[PeterDonis]

ultimately spacetime is still open for debate

In the sense that physicists, particularly those working on quantum gravity, are considering models that do not treat spacetime as continuous (indeed some of them treat spacetime as not even fundamental, but emerging from something else), this is true, yes.

 

[swissgirl1999 Refer]

Ontology is philosophy, regardless of whether the philosophy is a philosophy about physical systems or not.

You' re right again, but why should it be? Physics (and science) provides the background for physical ontology. So my argument, even though philosophical, doesn' t deviate from the fact of receiving physics' theoretical answers to ontological questions. Correct me if I'm wrong again, but my feeling is that physicists are a little reluctant to leave questions unanswered, preferring closed question in open theories (i.e., uncompleted theories) over opened ontological questions.

 

[swissgirl1999 Refer]

You say that there is zero obervational support for continuous space-time, but it is the same for discrete one. You seem to be convinced that it cannot be continuous. Why?

I think that humans are intelligent beings, so, if, for more than a century, cosmology and QM don' t speak the same language, i.e., the discrete ontology of Nobel award physicists (including Einstein himself) does not fit with cosmological observations, if GR and QM are incompatible, if nobody ever found quantum gravity, or dark matter and dark energy, it' s not because of lack in intelligence, so I tend towards the empirical observations rather than theoretical ones; don' t get me wrong, Einstein was a genius, in my opinion he deserved 3 Nobel (SR and e=mc2), and his annus mirabilis works fine with QM, but I don' t see strong pursue in connecting Einstein' s 1905 physics with QM as in trying to joint GR with QM. In my opinion, GR is a brilliant engineering toll that fails as ontological truth, thus the need for dark energy and dark matter; GR fails at the minimum scale and at the maximum scale and works perfect for our technological reality. In my view, spacetime would not be thing at all, it would be the continuous update of discrete interactions at Planck scale.

 

[Nugatory]

physical ontology is physics, not philosophy.....

The claim that quantum mechanics requires any ontology is a philosophical claim, not a physical one. All the physics is in the probabilities of measurement results following an initial state preparation, and that comes from the mathematical statement of the theory without assuming anything "real" behind it.

"We don’t use discrete spacetime because it doesn’t work. Yet" — that's the right attitude and quite rare.

Not as rare as you may be thinking. I'd expect that most serious practitioners would agree but also find the discussion, starting with neither a candidate theory nor an accurate understanding of the current evidence, to be futile at best... and after endless attempts to relitigate it, annoying.

 

[PeterDonis]

the discrete ontology of Nobel award physicists (including Einstein himself) does not fit with cosmological observations

This is not correct. I have already pointed out how your examples only show certain kinds of discreteness. None of those kinds are incompatible with cosmological observations.

In my opinion, GR is a brilliant engineering toll that fails as ontological truth, thus the need for dark energy and dark matter

Dark energy and dark matter are not failures of GR. GR accommodates them just fine.

Dark matter, if you want to call it a failure of anything, is a failure of the Standard Model of fundamental particles (actually quantum fields), since none of them can account for it. That's why the various proposed explanations all involve new fields that aren't included in the Standard Model.

Dark energy points to some kind of failure, or at least incomplete understanding, in quantum field theory, since the naive QFT prediction of its magnitude is at least 120 orders of magnitude larger than observations.

Neither of those things have anything to do with a failure of GR.

In my view, spacetime would not be thing at all, it would be the continuous update of discrete interactions at Planck scale.

This is personal speculation and is off limits here.

 

[Dale]

your fine answer ultimately doesn' t provide experimental evidence for a continuous spacetime

It seems you missed the statement:

Contrary to your statement, there is not a single measurement that contradicts a continuous spacetime, and spacetime has been experimentally measured to be continuous to every level of precision tested to date. The experimental evidence for continuity is as strong as scientific evidence can possibly be today.

This includes the Nobel-related evidence that you cited.

The conclusion I take from that is that ultimately spacetime is still open for debate; thanks for your honest answer.

Everything is still open to future evidence. But currently there is no evidence supporting discrete spacetime. And current discrete spacetime theories struggle with self-consistency, consistency with existing experimental evidence, reduced predictive power, or some combination of all three.

discrete ontology of Nobel award physicists (including Einstein himself)

This is simply a blatant misrepresentation of the actual evidence. Not a single one of the sources you cited actually supports discrete spacetime. Each one of them is predicted by theories with continuous spacetime and the data is consistent with those theories.

Simply name-dropping a bunch of famous scientists does not strengthen your argument. And making false claims about what their papers say destroys your own credibility. Particularly when you misrepresent them to an audience that actually knows those papers and their content in detail.

I tend towards the empirical observations rather than theoretical ones

If so, you do not show it here. Your argument in this thread is pure philosophy with neither supporting empirical evidence nor any reference to an actual scientific theory.

 

[PeterDonis]

The title question of the thread has been addressed and the thread is now closed. Thanks to all who participated.