Can We Able To Escape Big Rip? PART 2: Berkenstein Bound (Quantum / Astronomy / Cosmology)

Previously on “Can We Able to escape big rip? PART 1: Achronal Cosmic Future”, We saw that In 2004, Pedro F. González Diaz obtained that the accretion of dark energy leads to a gradual increase of the wormhole throat radius which eventually overtakes the superaccelerated expansion of the Universe and becomes infinite at a time in the future before the occurrence of the big rip singularity.

After that time, as it continues accreting dark energy, the wormhole becomes an Einstein-Rosen bridge which can, in principle, be used by the future advanced civilizations in their efforts to escape from the big rip. However, in this activity the future civilizations will have to face but another problem: an “extremely stringent information’s bound”.

Guys during 1980’s, Bekenstein proposed a information bound, which is also called as “Berkenstein Bound”, which shows that the total amount of information, which can be stored in region of radius R is I < Im = 2πRE/(hc log 2). Thus,

So, in his paper, he calculated the horizon radius and found that its in the order of Planck scale. Thus, he found the Berkenstein Bound results in,

What it actually mean? Well, it means that, the largest amount of information to be processed and therefore – sent through the Einstein-Rosen bridge is no way greater then 69 bits. Yeah, just 69 bits. As a comparison, the superior limit of amount of information encoded in a human being is about 1045 bits. This value is surely an excess, for any object existing in current universe is encoded far less than any quantum field theory’s constraints, but in any case the amount of 69 bits seems terribly small. For example, the amount of information in a typical book is I ∼ 107 bits, and 1015 bits stands for all books in the Library of Congress. 69 bits is, in fact, slightly higher then the total amount of information that can be coded in the proton, viz. 44 bits!

So, it means you wont be able to leave this universe. The only way to save yourself, is to prevent big rip. And for that, you will need quantum effects.

To be continued in next part..

Reference: Jacob D. Bekenstein, “Energy Cost of Information Transfer”, Phys. Rev. Lett. 46, 623 – Published 9 March 1981. (2) Schiffer M, Bekenstein JD. Proof of the quantum bound on specific entropy for free fields. Phys Rev D Part Fields. 1989 Feb 15;39(4):1109-1115. doi: 10.1103/physrevd.39.1109. PMID: 9959747. (3) Marcelo Schiffer and Jacob D. Bekenstein, “Do zero-frequency modes contribute to the entropy?”, Phys. Rev. D 42, 3598 – Published 15 November 1990.

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