1. As detailed at https://en.wikipedia.org/wiki/No-hiding_theorem , in the quantum world, information cannot be created or destroyed.

  2. The Bekenstein bound limits the amount of information that can be stored within a spherical volume, with the limit equal to the entropy of black hole of that surface area. https://en.wikipedia.org/wiki/Bekenstein_bound

  3. Per the big bang theory, the universe was once smaller than the earth.

  4. The entropy of black hole that is smaller than the earth, is less than the amount of quantum information in the current universe.

In brief, information cannot be created, yet there is more now than there could have been in the past! The conservation of quantum information seems to be incompatible with the big bang theory.

The obvious answer is that an expanding universe is not a closed system; but it is expanding due to quantum effects with no external forces, so the no-hiding theorem should still hold.

My question is this: Which of the statements 1..4 is incorrect, and if none are incorrect, how is quantum mechanics compatible with the big bang theory?

  • $\begingroup$ It has to be 1 that is wrong. When the size of the universe was below that of the size of the Earth, very short after the start of inflation, there had to be a small amount of information. Nice question! $\endgroup$ May 12, 2022 at 5:18
  • $\begingroup$ Coming to think about it, it could also be the Bekenstein entropy that's wrong in that regime! $\endgroup$ May 12, 2022 at 5:20
  • $\begingroup$ This must have been asked before. $\endgroup$
    – Qmechanic
    May 12, 2022 at 10:18
  • $\begingroup$ Perhaps the universe is fully deterministic, and therefore contains 0 bits of information. $\endgroup$
    – user253751
    May 12, 2022 at 11:07
  • $\begingroup$ I agree that it must have been asked before, but I cannot find an answer anywhere and this strikes me as really strange since it is a more severe problem than the black hole information "paradox" - there we just do not know how the information escapes. Here it is being created. $\endgroup$
    – Colin
    Aug 1, 2022 at 18:02

1 Answer 1


This isn't exactly my field of study, but I think that this question is not clearly answerABLE. Why? Because if I stop to think about it, the Big Bang ITSELF is a paradox, since information was actually being created. The law of conservation of energy is also, of course, "defied" by the Big Bang Theory. However, scientists HAVE found evidence of the existence of the Big Bang. (https://www.uwa.edu.au/study/-/media/Faculties/Science/Docs/Evidence-for-the-Big-Bang.pdf). So are we in the wrong here? Well, not exactly. The No Hiding Theorum is of course valid, but the Big Bang is probably an exception since no explanation has been found for the invalidity of the No Hiding theorem or law of conservation of energy in the Big Bang.

  • $\begingroup$ Actually, I believe that the big bang is consistent with the the law of conservation of energy. Gravitational energy is negative and this balances out the energy from bosons and fermions, so the total is zero. It is just information that it apparently being created. $\endgroup$
    – Colin
    May 26, 2022 at 17:52
  • $\begingroup$ Sorry, I suppose I was not being clear. I meant that BEFORE the big bang, there was apparently "no matter" right? So if that is true, where did the energy FOR the big bang come from, if it was not created? $\endgroup$
    – Atri De
    May 29, 2022 at 8:08

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