The Heisenberg limit at cosmological scales

Abstract

For an observation time {equal to} the universe age, the Heisenberg principle fixes the value of the smallest measurable mass at $m_{\mathrm{H}}=1.35\times 10^{-69}$ kg and prevents to probe the masslessness for any particle using a balance. The corresponding reduced Compton length to $m_{\mathrm{H}}$ is $\lambdabar_{\rm H}$, and represents the length limit beyond which masslessness cannot be proved using a metre ruler. In turns, $\lambdabar_{\rm H}$ is equated to the luminosity distance $d_{\mathrm{H}}$ which corresponds to a red shift $z_{\mathrm{H}}$. When using the Concordance-Model parameters, we get $d_{\mathrm{H}}=8.4$ Gpc and $z_{\mathrm{H}}=1.3$. Remarkably, $d_{\mathrm{H}}$ falls quite short to the radius of the {\it observable} universe. According to this result, tensions in cosmological parameters could be nothing else but due to comparing data inside and beyond $z_{\mathrm{H}}$. Finally, in terms of quantum quantities, the expansion constant $H_0$ reveals to be one order of magnitude above the smallest measurable energy, divided by the Planck constant

A different view on the Hubble tension. To appear in final form on Foundations of Physics by Springer, as follow-on of Capozziello S., Benetti M., Spallicci A.D.A.M., 2020, Found. Phys., 50, 893

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Cited by in corpus (15)

• Seven hints that early-time new physics alone is not sufficient to solve the Hubble tension
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• Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies
• Hubble tension as a guide for refining the early Universe: Cosmologies with explicit local Lorentz and diffeomorphism violation
• Exploiting the Einstein Telescope to solve the Hubble tension
• Questioning the $H_0$ tension via the look-back time
• A critical discussion on the $H_0$ tension
• Investigating dark energy by electromagnetic frequency shifts
• Investigating dark energy by electromagnetic frequency shifts II: the Pantheon+ sample
• Extended Uncertainty Principle: A Deeper Insight into the Hubble Tension?
• Addressing the Hubble tension in Yukawa cosmology?
• Testing the Ampère-Maxwell law on the photon mass and Lorentz-Poincaré symmetry violation with MMS multi-spacecraft data
• Another look on the connections of Hubble tension with the Heisenberg Uncertainty Principle
• Photon frequency variation in non-linear electro-magnetism
• Extended Theories of Electrodynamics in $f(R)$ Gravity