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If the energy of $1 \, \mathrm{bit}$ of information is $k_{\small{\text{B}}}T \ln{2}$, then the energy of that bit increases with the temperature of the system. When I try to calculate how much energy 1 bit of information would have had around the Planck time, when the temperature of the universe was in the ballpark of ${10}^{32}\,\mathrm{K}$ and the diameter was around ${10}^{-33}\,\mathrm{cm}$, then the energy of that $1\,\mathrm{bit}$ of information is suspiciously close to the Bekenstein bound. In fact, the result I got was $1.3719436998375747 ,$ which I think means that the energy of $1\,\mathrm{bit}$ of information at planck time was just a bit less than would have been required to collapse the universe into a black hole before it had even begun (perhaps even before inflation could save it from said fate).

Is it just coincidence that the number I happen to get is so close to the Bekenstein bound? Was the Information (or entropy or negentropy or whatever you want to call it) contained in the big bang really THAT low? I mean, I knew it had to be low, but 1 bit seems to be cutting things a bit fine, doesn't it?

doetoe
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Thor
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1 Answers1

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Was the Information (or entropy or negentropy or whatever you want to call it) contained in the big bang really THAT low?

Yes, the entropy of an observable universe must start low. So, how low?

  1. The history of the universe can be modelled based on just 3 energy density parameters: i) density during inflation, ii) density at radiation – matter equilibrium, and iii) dark energy density at late epochs.

  2. Padmanabhan (2014), using these 3 densities, showed that the cosmological constant problem can be solved within the emergent gravity paradigm if one could attribute a value $4π$ to the measure of degrees of freedom in the universe at the Planck epoch.

TLDR: The above implies that the entropy of the cosmic event horizon of the Universe at the Hot Big Bang (end of inflation) was $4\pi$ nats. So low, yes, but more than 1 bit.

Mr Anderson
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