Question

Does the Uncertainty Principle imply a linear cosmology?

Answer 1

If the uncertainty in the age of the Universe is ΔtΔt then the Uncertainty Principle implies that it has an uncertainty in its energy ΔEΔE given by

ΔE Δt∼h.(1)(1)ΔE Δt∼h.

If this energy fluctuation excites the zero-point electromagnetic field of the vacuum then a photon is created with energy ΔEΔE and wavelength λλgiven by

ΔE∼hcλ.(2)(2)ΔE∼hcλ.

Combining Equations (1)(1) and (2)(2) we find that

λ∼c Δt.(3)(3)λ∼c Δt.

Now as this characteristic length λλ is the wavelength of a photon it is a proper length that expands with the Universal scale factor a(t)a(t) so that

λ∼a(t).(4)(4)λ∼a(t).

Combining Equations (3)(3) and (4)(4), and taking Δt∼tΔt∼t, we arrive at a unique linear cosmology with the normalized scale factor aa given by

a(t)=tt0.a(t)=tt0.

where t0t0 is the current age of the Universe.