The information catastrophe

Vopson estimates contemporary annual digital information production at 7.3 × 10²¹ bits, using an IBM daily data-production estimate.

Nb = 7.3 × 1021 bits.

Vopson models cumulative digital information with a constant annual growth factor, estimating that 1% growth reaches roughly as many bits as Earth has atoms after about 6,000 years.

At this rate, we will have ∼1050 bits of information after ∼6000 years from now.

Vopson estimates that bits would equal Earth’s atom count after approximately 1,200, 340, and 150 years at annual growth rates of 5%, 20%, and 50%, respectively.

the total number of bits created will equal the total number of atoms on Earth after ∼1200 years, ∼340 years, and ∼150 years, respectively.

Vopson allows that saturation or reversal of population and technology-access trends could cause accumulated information to saturate instead of following the assumed growth equation.

If any of these other factors are reversed or saturated, the total number of bits of information accumulated on the planet could display saturation at some point in the future, rather than following Eq. (1).

Vopson describes Landauer’s minimum energy cost for erasing a bit and uses a maximum-efficiency, room-temperature model for future digital information production.

Let us assume that our future technological progress will allow writing digital information with maximum efficiency.

Vopson estimates that digital production at 20% annual growth would reach his stated contemporary planetary power benchmark after about 285 years, assuming maximum efficiency.

Similarly, for 5%, 20%, and 50% growth rates, this will occur after ∼1060, ∼285, and ∼130 years from now, respectively.

Vopson states that the mass–energy–information equivalence principle proposed in 2019 still requires experimental verification.

Although this principle still awaits an experimental verification, assuming it is correct, it opens up interesting possibilities

Under his mass-equivalence hypothesis, Vopson assigns a room-temperature digital bit a rest mass of 3.19 × 10⁻³⁸ kilograms.

the rest mass of a digital bit of information at room temperature is mbit = 3.19 × 10−38 kg.

Vopson’s conditional 20%-growth scenario reaches one kilogram of information mass after roughly 188 years and half Earth’s mass after roughly 495 years.

the numbers are ∼188 years and ∼50 years, respectively, for 1 kg of information mass and ∼495 years and ∼225 years for half of the Earth’s mass, respectively.

Vopson concludes that planetary mass remains unchanged under the hypothesis; ordinary matter is redistributed into the proposed information form rather than adding net mass to Earth.

Applying the law of conservation in conjunction with the mass–energy–information equivalence principle, it means that the mass of the planet is unchanged over time.

Vopson identifies Wheeler’s information-based conception of physics as a precursor and discusses the phrase “It from bit.”

Wheeler proposed reformulating the whole physics in terms of the information theory.