Information Is Energy: One More Thing

 © 2017 Michael A Hill

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If it is a real thing, then informational energy should “be” someplace, shouldn’t it? Modern standard physics models do not have a place for it though. Information is usually treated as entropy, not energy. Entropy is always a function of energy, however, and not the other way around.  No particular form of energy has ever been named to accompany information entropy, though. What sort of energy should this be? Let’s speculate.

Vacuum Energy

In some places deep in the darkest intergalactic reaches of spacethat contain neither matter nor radiation, nothing else exists but space, time and gravity. Well, it has at least one other thing, and that is an inherent energy, called “vacuum energy.” It may also be named “zero point energy” or “cosmological constant.” Vacuum energy exists not just in intergalactic space, though, it exists everywhere. It’s not very noticeable because it is so small, having an energy density of only 10^-8 ergs/cm³. But wait, there’s more! Because its energy density can be measured, vacuum energy also contains information.

Dark Energy

The universe is expanding, faster and faster. Vacuum energy might be sufficient to explain that, but cosmological equations indicate there should be even more stuff out there. That stuff is “dark energy,” which includes almost 70% of the universe. Nobody realized it was there until about 20 years ago. Sean M. Carroll [2] showed that dark energy should have 10¹²⁰ times the energy density as vacuum energy. That’s a super-inconceivable-huge number, but it is based on the value of Planck’s constant.

Information Content of the Universe

Another super-inconceivable-huge number is the universe’s information content. By considering the universe to be like a giant computer, Seth Lloyd [3] determined that the total number of elementary logical operations that occurred since the universe began equals about 10¹²⁰ bits of information. Since computation requires energy, information therefore contributes to the universal energy budget. A short back-of-the-napkin calculation shows that this corresponds to an energy capacity of approximately 1.78 x 10⁵⁰ ergs/cm³.

Dark Energy = Information?

It’s not a good idea to equate big numbers like these just because they are big. They are approximations that can be off by a few orders of magnitude. Or they might even describe different concepts, like apples and oranges. However, the important thing is that imminent theorists, working separately and using different methods, came to similar conclusions about the total amount of energy in the vast cosmos. One group identified a gap in the universal energy budget, and another group found a way to fill that gap.

Even so, the energy densities still do not add up. It is difficult to compare information with standard energies when no firm theoretical basis linking them has been formulated yet. However, there exists a kernel of a hypothesis here that should be tested: Does information energy comprise the bulk of the universe’s energy budget? Or is there even more stuff out there? More work should be funded. After all, even 1.78 x 10⁵⁰ ergs/cm³ is a whopping chunk of energy to go untapped!

An entertaining way of seeing the information-is-energy concept is by analogy with fictional “L-space” invented by satirical fantasy novelist Terry Pratchett [4]: “The truth is that even big collections of ordinary books distort space…. The relevant equation is: Knowledge = power = energy = matter = mass; a good bookshop is just a genteel Black Hole that knows how to read.”

[2] Carroll, Sean M., “Dark Energy and the Preposterous Universe,” Cornell University Library arXiv Team, 2001, p.3-5.  https://ned.ipac.caltech.edu/level5/March01/Carroll/Carroll1.html

[3] Lloyd, Seth, “The Computational Universe,” Edge, John Brockman, 2002. https://www.edge.org/conversation/seth_lloyd-the-computational-universe

[4] Pratchett, Terry, Guards! Guards! Victor Gollancz Ltd., 1989, p. 8.  http://wiki.lspace.org/mediawiki/L-space

Photo Credit: NASA, ESA S. Beckwith (STScI) and the HUDF Team