Continuum is Real

In the paper's words

For over a century, physics has been defined by an ontological schism. The continuous, deterministic, and local reality described by classical mechanics and general relativity stands in direct opposition to the discrete, probabilistic, and non-local phenomena of quantum mechanics. This division has necessitated a patchwork of competing interpretations, each burdened with paradoxes and philosophical compromises.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. These include the Delft University experiment (Hensen et al., 2015), which used entangled electron spins separated by 1.3 km and measurement settings chosen randomly after the electrons were in flight, closing the locality loophole; NIST experiments (Giustina et al., 2015), which used high-efficiency detectors to close the detection loophole; and the “Cosmic Bell Test” in Vienna, which used light from ancient quasars to choose the measurement settings, closing the freedom-of-choice loophole (Handsteiner et al., 2017).

   from 4.2.2 Consistency

2. At this resolution, the observed waveforms match the predictions from General Relativity’s continuous field equations to a precision better than 0.1%, confirming that spacetime behaves as a smooth, differentiable manifold.

   from 2.1.2 Gravitational Wave

How it is done

1. Planck’s Discovery as an Artifact of Boundary Conditions Planck’s solution to the ultraviolet catastrophe was a mathematical procedure, not an ontological claim.

   from 1.2.1

2. As will be detailed in Section 2.0, the empirical evidence from gravitational wave detection, quantum state tomography, and weak measurements provides direct and overwhelming proof of this underlying continuity.

   from 1.3.1 Pillar I: The Continuum is

3. Statement: The Quantum Sampling Theorem The entire framework is crystallized in a single, verifiable principle, which we term the Quantum Sampling Theorem : “All discrete phenomena are samples of a continuous reality, binned by constraints.

   from 1.4 Thesis

4. The Wigner function is formally defined as: $$ W(x,p) = \frac{1}{\pi\hbar}\int_{-\infty}^{\infty} \psi^*(x+y)\psi(x-y)e^{2ipy/\hbar} dy $$ Its most revealing feature is its capacity to take on negative values, which serves as the “smoking gun” for non-classicality.

   from 2.1.1 Quantum

What would falsify it

1. This success provides a powerful argument against theories of quantum gravity that predict a fundamental granularity for spacetime at observable scales.

   from 2.1.2 Gravitational Wave

2. Experiments using streaking spectroscopy track an electron’s wavepacket during photoionization, revealing a smooth, continuous evolution of its energy and momentum distribution over time, with no observable discontinuities or jumps (Ossiander et al., 2023).

   from 2.1.4 Attosecond Laser

3. The eigenvalues , $E_n$, are the discrete, quantized values of a physical observable (e.g., energy) associated with each stable pattern.

   from 3.1.2

Where the claim stops

1. However, he framed this observation as evidence for “light quanta,” reifying a discrete event into a discrete entity .

   from 1.2.2 Einstein’s

2. The deeper reason for this indivisibility—a fundamental constraint imposed by the compact topology of the U(1) gauge group of electromagnetism—was not yet understood.

   from 1.2.2 Einstein’s

3. Even at this unprecedented temporal resolution, which far exceeds the limits of the energy-time uncertainty principle, no fractional energy absorption is ever detected.

   from 2.1.4 Attosecond Laser

Where to read

1. The37 words · 1 min
2. 1.01,235 words · 5 min
3. 2.0 Pillar I: The Continuum is1,290 words · 6 min
4. 3.0 Pillar II: Binning is902 words · 4 min
5. 4.0 Pillar III: “Quanta” Are938 words · 4 min
6. 5.0 Implications Across543 words · 2 min
7. 6.0599 words · 3 min
8. Appendix A: Scholarly456 words · 2 min
9. Appendix B: Glossary of Key723 words · 3 min