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 ×10^-69 kg and prevents to probe the masslessness for any particle using a balance. The corresponding reduced Compton length to m_H is [inline-graphic not available: see fulltext], and represents the length limit beyond which masslessness cannot be proved using a metre ruler. In turns, [inline-graphic not available: see fulltext] 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 H₀ reveals to be one order of magnitude above the smallest measurable energy, divided by the Planck constant.