The Heisenberg Limit at Cosmological Scales

For an observation time equal to the universe age, the Heisenberg principle fixes the value of the smallest measurable mass at m(H) = 1.35 x 10(-69) kg and prevents to probe the masslessness for any particle using a balance. The corresponding reduced Compton length to m(H) is (lambda) over bar (H), and represents the length limit beyond which masslessness cannot be proved using a metre ruler. In turns, (lambda) over bar (H) is equated to the luminosity distance d(H) which corresponds to a red shift z(H). When using the Concordance-Model parameters, we get d(H) = 8.4 Gpc and z(H) = 1.3. Remarkably, d(H) falls quite short to the radius of the observable universe. According to this result, tensions in cosmological parameters could be nothing else but due to comparing data inside and beyond z(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.

Automated summary

According to the Heisenberg principle, the smallest measurable mass is determined to be m(H) = 1.35 x 10(-69) kg for an observation time equal to the age of the universe, and it is impossible to determine the masslessness of any particle using a balance. Using the Concordance-Model parameters, the red shift distance d(H) and red shift z(H) are calculated to be 8.4 Gpc and 1.3 respectively, which differ significantly from the radius of the observable universe.