2024/06/12 by Kévin Cahill, Cahill, Kevin
Medicine · Physics and Astronomy · #Biofield Effects and Biophysics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Physics (physics.gen-ph) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2406.09448
openalex publication_date 2024/06/12 · openalex created_date 2024/06/18 · openalex updated_date 2026/07/28
Since Einstein's equations Gij = 8π G Tij / c4 relate the metric gij of spacetime to the energy-momentum tensor Tij which is a quantum field, the metric gij must be a quantum field. And since the metric gij(x) is the dot product gij(x) = ∂i pα(x) ∂j pα(x) of the derivatives of the points p(x) of spacetime, spacetime must be a quantum field. Its points have average values ⟨ p(x) ⟩ that obey general relativity and fluctuations q(x) = p(x) - ⟨ p(x) ⟩ that obey quantum mechanics. It is suggested that the fields of quantum field theory be regarded not as functions ϕ(x) of their classical coordinates x but as functions ϕ(p(x)) of their quantum coordinates p(x). In empty flat spacetime where p(x) = x + q(x) and x = (t, \boldsymbol x), the Fourier exponentials exp(i k(x+q(x)) averaged over normally distributed fluctuations q(x) are gaussians exp(i kx -ℓ2 \boldsymbol k2 - ℓ2 m2/2). These gaussians make Feynman diagrams finite. The zero-point energy density of the vacuum also is finite -- but negative and too large to explain dark energy unless new bosons exist.