# Integrated Information Theory and Cosmology

Information can be broadly defined as the reduction in uncertainty. The reason that the location and momentum of 100 particles in a 1×1 meter box contains less information than either A) the location and momentum of 100 particles in a 10×10 meter box or B) 1,000 particles in a 1×1 meter box is because, in case A, one must specify a greater number of microstates (i.e. there are more possible arrangements of particles) and in case B, there are more particles whose position must be specified. What can we say about cosmology using the integrated information of all particles in existence?

The holographic principle means that there is a limit (the Bekenstein bound) to the amount of information that can exist in a finite space. For black holes, this information limit corresponds to the area of the event horizon surface. This has led some scientists to propose that the same principle – the information of the system being contained on the surface – may apply to our universe as a whole.

If this is true, it puts an upper bound on the accuracy of any measurement. For instance, given that the surface of the particle horizon of our universe is (using Desmos online calculator):

The 46,900,000,000 is the radius of the observable universe in light-years, and so the 1015 is to convert from light-years to meters. The 4πr2 is to calculate the area of the surface of a sphere (the particle horizon around the observable universe).

And the Planck area is:

The 6.626 * 10-34 is the reduced Planck constant, the 6.674 * 10-11 is the gravitational constant, and the 3 * 108 is the speed of light. This quantity is an extremely tiny square and what we are looking for is the number of those squares that make up the surface of the sphere of the particle horizon. To get that, we divide the area of the horizon by the size of one of those tiny squares and we get:

Which is the limit of the amount of information that can be contained on the surface of our particle horizon. This accords with the calculation done by Seth Lloyd on how many elementary operations our universe could have performed by now [by converting all mass into radiation and using the number of polarizations number of particles/antiparticles (1 for bosons or 7/8 for fermions)].

But what happens if we introduce the idea of integrated information? If we say that each causal interaction between particles in the universe is a transfer of information, then the information in the universe is not just the position and momentum of each particle (or the spin/polarization of particles) but also requires all the interactions of particles to be calculated. This can be observed in quantum decoherence: when the particles become entangled, they become integrated.