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In a recent lecture on Conformal Cyclic Cosmology by Roger Penrose this equation was displayed

$$\nu= m \frac{{c^2}}{h}$$

derived by substituting Einstein's equation on the equivalence of mass/energy and Planck's equation.

His point was the relationship between mass and time (frequency) and that as the mass of the universe decays (if it decays) then so does time. But I'm having a hard time interpreting more detail surrounding this connection.

First I thought this derived equation relates to particles (only baryon's?) but don't see how Penrose connects it to a cosmological wholeness.

Can someone help me interpret the meaning in a cosmological context, if any?

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  • $\begingroup$ Sounds like a case of unit analysis used as a gross estimate, to me. $\endgroup$
    – Sean E. Lake
    Commented Jan 22, 2018 at 21:11
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    $\begingroup$ I wish I could read some lecture notes to see why $mc^2/h$ is more relevant to him than, say, $mc^2/\hbar$. Incidentally, $mc^2/h$ is the maximum bitrate of a mass-$m$ computer's computations: en.wikipedia.org/wiki/Bremermann%27s_limit $\endgroup$
    – J.G.
    Commented Oct 28, 2018 at 21:48

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In de Broglie's hypothesis, the momentum of a particle with mass $m$ can be associated with a wavelength. Penrose's equation takes that to the extreme; if the entire mass, $m$, is converted into energy, its frequency is given by $\nu$, on the left side of his equation.

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  • $\begingroup$ So was Penrose using this equality in a loose manner? The wavelength in this case would be way shorter than gamma rays. $\endgroup$
    – docscience
    Commented Oct 30, 2018 at 0:03

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