Part of a series of articles about
Quantum mechanics
${\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }$ Schrödinger equation
Introduction Glossary History
Background Classical mechanics Old quantum theory Bra–ket notation Hamiltonian Interference
Fundamentals Complementarity Decoherence Entanglement Energy level Measurement Nonlocality Quantum number State Superposition Symmetry Tunnelling Uncertainty Wave function Collapse
Experiments Bell's inequality Davisson–Germer Double-slit Elitzur–Vaidman Franck–Hertz Leggett–Garg inequality Mach–Zehnder Popper Quantum eraser Delayed-choice Schrödinger's cat Stern–Gerlach Wheeler's delayed-choice
Formulations Overview Heisenberg Interaction Matrix Phase-space Schrödinger Sum-over-histories (path integral)
Equations Dirac Klein–Gordon Pauli Rydberg Schrödinger
Interpretations Bayesian Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Local Superdeterminism Many-worlds Objective collapse Quantum logic Relational Transactional Von Neumann–Wigner
Advanced topics Relativistic quantum mechanics Quantum field theory Quantum information science Quantum computing Quantum chaos EPR paradox Density matrix Scattering theory Quantum statistical mechanics Quantum machine learning
Scientists Aharonov Bell Bethe Blackett Bloch Bohm Bohr Born Bose de Broglie Compton Dirac Davisson Debye Ehrenfest Einstein Everett Fock Fermi Feynman Glauber Gutzwiller Heisenberg Hilbert Jordan Kramers Pauli Lamb Landau Laue Moseley Millikan Onnes Planck Rabi Raman Rydberg Schrödinger Simmons Sommerfeld von Neumann Weyl Wien Wigner Zeeman Zeilinger

The Calogero conjecture^[1] is a minority interpretation of quantum mechanics. It is a quantization explanation involving quantum mechanics, originally stipulated in 1997 and further republished in 2004^[2][3] by Francesco Calogero that suggests the classical stochastic background field to which Edward Nelson attributes quantum mechanical behavior in his theory of stochastic quantization is a fluctuating space-time, and that there are further mathematical relations between the involved quantities.

The hypothesis itself suggests that if the angular momentum associated with a stochastic tremor^[3] with spatial coherence provides an action purported by that motion within the order of magnitude of Planck's constant^[3] then the order of magnitude of the associated angular momentum has the same value.^[3] Calogero himself suggests^[3] that these findings, originally based on the simplified model of the universe^[3] "are affected (and essentially, unaffected) by the possible presence in the mass of the Universe of a large component made up of particles much lighter than nucleons".^[3]

Essentially, the relation explained by Calogero can be expressed with the formulas:

${\displaystyle h\approx \alpha G^{1/2}m^{3/2}[R(t)]^{1/2}.}$

Furthermore:

${\displaystyle h\equiv h(t)=A{\sqrt {R(t)}}=h_{0}{\sqrt {a(t)}}}$ Const G,m

Where:

${\displaystyle G}$ represents the gravitational constant

${\displaystyle m}$ represents the mass of a hydrogen atom.

${\displaystyle R(t)}$ represents the radius of the universe accessible by gravitational interactions in time, t.

${\displaystyle A}$ is a dimensional constant.

Despite its common description, it has been noted that the conjecture is not entirely defined within the realms of Nelson's stochastic mechanics, but can also be thought of as a means of inquiring into the statistical effects of interaction with distant masses in the universe and was expected by Calogero himself^[1] to be within the same order of magnitude as quantum mechanical effects.^[1]

Analysis

References

• Gaeta, Giuseppe (2000). "Calogero Conjecture and Hubble Law". International Journal of Theoretical Physics. Springer Science and Business Media LLC. 39 (5): 1339–1350. doi:10.1023/a:1003647122051. ISSN 0020-7748. S2CID 118571985.