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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?

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    $\begingroup$ I suspect there is some circularity to your calculation: the Planck time is effectively defined as (the ball park) time when the energy density is such that quantum gravity kicks in and the Berkenstein Bound is reached. $\endgroup$
    – isometry
    Oct 13, 2018 at 9:22
  • $\begingroup$ Lol! You might well be right... Still though, any idea how many bits of information would have come with the Big Bang? If the universe had a finite size and a finite volume and a finite temperature, then we should be able to calculate the energy (on that note, I can't believe I didn't do that last night...). What is that figure and how does it compare to the 1 bit = 956992961.692908J I got in my calculation. $\endgroup$
    – Thor
    Oct 13, 2018 at 15:31
  • $\begingroup$ I think you can only study information-of-universe questions from the other end starting with the known observable universe. Check out physics.stackexchange.com/questions/35920/… $\endgroup$
    – isometry
    Oct 13, 2018 at 17:00
  • $\begingroup$ Thanks Bruce, I'll definitely check out that thread. I still think there's something to my question though... Ultimately, all the information that exists in today's universe evolved from the informational content of the universe at the time of the big bang. And, following that, there's the question of how much information will exist at the final moment of the universe? The temperature will be MUCH lower, but will the temperature ever get low enough that once again only 1 bit of information will exist? What does that total information content curve look like? $\endgroup$
    – Thor
    Oct 13, 2018 at 17:07
  • $\begingroup$ Big bang may be not the exact picture. This is to say the expansion of the baby universe is not really an explosion of a certain system, instead it's a expansion just like an empire conquers more countries. I believe the inflation is the process of the establishment of entanglement among qubits just as the scrambling time of black holes, which glues tiny space patches and construct geometry by entangling more qubits just like evolving a product state to an entangled state. $\endgroup$
    – XXDD
    Oct 14, 2018 at 14:09

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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.

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  • $\begingroup$ Holographic equipartition! I love it! But that's 4π nats at the end of inflation, right? I suppose that asking what the entropy/information value would have been at the very first unit of Planck time is actually a pretty silly question now that I think about it... The entropy at the end of inflation is much more relevant to our current predicament. $\endgroup$
    – Thor
    Jul 30, 2021 at 17:20

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