Does the Uncertainty Principle imply a linear cosmology?

[jcap]

If the uncertainty in the age of the Universe is $\Delta t$ then the Uncertainty Principle implies that it has an uncertainty in its energy $\Delta E$ given by
$$\Delta E \ \Delta t \sim h.\tag{1}$$
If this energy fluctuation excites the zero-point electromagnetic field of the vacuum then a photon is created with energy $\Delta E$ and wavelength $\lambda$ given by
$$\Delta E \sim h \frac{c}{\lambda}.\tag{2}$$
Combining Equations $(1)$ and $(2)$ we find that
$$\lambda \sim c\ \Delta t.\tag{3}$$
Now as this characteristic length $\lambda$ is the wavelength of a photon it is a proper length that expands with the Universal scale factor $a(t)$ so that
$$\lambda \sim a(t).\tag{4}$$
Combining Equations $(3)$ and $(4)$, and taking $\Delta t \sim t$, we arrive at a unique linear cosmology with the normalized scale factor $a$ given by
$$a(t) = \frac{t}{t_0}.$$
where $t_0$ is the current age of the Universe.

 

[phinds]

I'll leave it to more knowledgeable folks to weight in, but what I think is that you have extrapolated the HUP to WAY outside of it's domain of relevance.

 

[PeterDonis]

If the uncertainty in the age of the Universe is $\Delta t$ then the Uncertainty Principle implies that it has an uncertainty in its energy

You can't apply the uncertainty principle to the universe as a whole since there is no way to make an external measurement on it, and the uncertainty principle applies to external measurements.

Also, there is no "energy-time" uncertainty principle as you are using it. See, for example, here:

http://math.ucr.edu/home/baez/uncertainty.html

So your post is based on at least two incorrect premises.

 

[PeterDonis]

If this energy fluctuation excites the zero-point electromagnetic field of the vacuum

Correction, three incorrect premises. The universe as a whole doesn't have "energy fluctuations" in this sense.