Wednesday, May 7, 2014

boundary to quantum cosmology

can you estimate the distance between two points in a FLRW-universe at which the quantum mechanical uncertainty in the velocity measurement is as large as the redshifting effect?

(this fun question is discussed in detail in the paper "the quantum indeterminancy of cosmic systems" by C.J. Hogan)

1 comment:

1. a very rough estimate would assign a momentum $p=mv=mH_0r$ to a body with Hubble recession velocity $v$ at distance $r$, which can be substituted into the uncertainty relation to give $mH_0r^2\simeq\hbar$. numerically, this is $\sim10^5$ meters for a proton and $10^7$ meters for an electron.