limits on uncertainties

The Heisenberg Uncertainty Principle states that for certain pairs of observable variables, an inverse proportion of uncertainty limits the precision of measuring the two variables.

Two of these variables are momentum (p) and position (x). For these variables:

ΔpΔx ≥ ħ/2,

where ħ is Planck’s constant divided by 2π.

This intrinsic uncertainty is very small, as ħ/2 ≈ 5.27∙10^(-35) kg∙m^(2)/s.

However, assuming that the universe has a finite size, it doesn' t seem reasonable that the uncertainty Δx could exceed its breadth. Thus, the precision of any measurement of momentum might be expected to have a limit imposed by this maximum Δx.

Two other observable variables that relate similarly are energy (E) and time (t):

ΔEΔt ≥ ħ/2.

Likewise, the age of the universe might provide a limit for Δt. These limits would have much greater consequence in the early universe.

Thus, it seems the nature of these intrinsic uncertainties might have changed as the universe has evolved.


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