I remember hearing about this in one of the programs in discovery science. The physicist claimed that the maximum possible information in the universe is $10^{10^{123}}$ whereas the maximum possible information that can be known by man is $10^{10^{90}}$. Can anyone explain to me how can we arrive at such a specific number, and also how can information be represented by only numbers?

  • $\begingroup$ The information in the Universe measured in bits or nats is just $10^{123}$ from the holographic bound; the actual entropy of the known matter except black holes - is about $10^{90+}$ and is dominated by the cosmic microwave background. However, this guess for the entropy is obsolete because most of the entropy we know in the Universe is carried by the black holes, bringing us above $10^{100}$. If you have one more exponentiation, 10 to those large numbers, it doesn't measure the information but the number of possibilities one may distinguish (8 bits = byte distinguish 256 states...). $\endgroup$ – Luboš Motl Sep 9 '12 at 8:11
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    $\begingroup$ is $10^{123}$ bits or qubits? I think the difference is important, since $10^{123}$ classical bits are exhausted with 410 qubits, more or less, and the universe has certainly way more than 410 q-bits $\endgroup$ – lurscher May 29 '13 at 18:21
  • $\begingroup$ unless coherent superposition turns out to break down before arriving at 410 q-bits $\endgroup$ – lurscher May 29 '13 at 18:31
  • $\begingroup$ @lurscher you have misunderstood how qubits work. To send a classical text document reliably using qubits, you need just as many qubits as you would need classical bits (see Holevo bound and HSW theorem). $\endgroup$ – Andrew Steane Dec 17 '18 at 19:32

The number $10^{123}$ emerges as (roughly) the number of Planck areas contained within the boundary of the observable universe. If each Planck area can be (roughly) in two states, a total of $10^{123}$ yes/no questions suffice to describe the boundary of the universe and - via the (still speculative) holographic principle - the whole universe. In other words, if the universe is a hologram, about $10^{123}$ bits of information are needed to describe it.

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    $\begingroup$ Why is the holographic principle "speculative"? It isn't 1990 anymore. $\endgroup$ – Ron Maimon Sep 8 '12 at 15:47
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    $\begingroup$ @RonMaimon It is speculative since it is not experimentally verified. And physics is an experimental science. Speculative is neither incompatible with natural nor synonymous of bizarre. I wonder why you claim it is not speculative. $\endgroup$ – Diego Mazón Sep 8 '12 at 18:39
  • $\begingroup$ If I encode the whole universe from t=0 up to now in a digits sequence, there is more informations contained in this code than if I just encode the whole universe right now, but where in Planck aeras is stored the history of the universe ? $\endgroup$ – Shaktyai Sep 8 '12 at 20:40
  • $\begingroup$ @drake: Physics always involves extrapolation from data, and in this case the extrapolation is relatively safe, since there is no hint of an alternative theoretical construction which even begins to work. When there is only one known possibility, and it is sure to work (although for all we know there is something else which works too, but for the life of me I can't think of what it could be) we generally say it's "established". $\endgroup$ – Ron Maimon Sep 9 '12 at 3:00
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    $\begingroup$ @RonMaimon I agree that physics involves extrapolation from data, but holography (especially some versions or it) requires a change of paradigm as I guess you will agree. It is not just an extension of a previous idea, it is not neutrinos' masses. So, in my opinion, the position you and most of people take is very dogmatic even though holography may be very natural. And dogmatism is very dangerous for a scientific area with lack of experiments/observations. Why not be more open minded? $\endgroup$ – Diego Mazón Sep 9 '12 at 20:45

Also, it is estimated that there are approximately $10^{80}$ protons (or electrons or neutrons) and approximately $10^{90}$ photons in the observable universe. So this is how many "objects" you have to work with. I don't know how to get from this to the maximum amount of information that can be known by man?


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