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.
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.
So, here is my idea for cosmology: the reason the universe is expanding is because, on account of all the particles becoming more and more integrated through interactions, more information must be represented on the surface of the universe. The universe has to expand at a rate proportional to Φ Thus, the universe must expand to accomodate all the increasing number of computations being performed.
Perhaps, also, we could think of the universe prior to the big bang as all the energy-momentum density of the universe being independent, i.e. not interacting (except through gravity – more on that in a bit). The big bang occurred when, for some reason or another, all matter in existence began interacting via the other fundamental forces of nature (electromagnetism, the strong and weak nuclear forces), which began integrating the information, resulting in the expansion of the universe.
Gravity, since it is not a force in the same way as other forces, could have existed prior to the big bang. The particles, unable to bump into each other without the other forces, were not integrating as information – the particles were all essentially like dark matter is now, able to interact via gravity but nothing else. Once some of the particles (not all, the leftovers remaining as dark matter) gained some ability to interact with each other via the other three forces, information became integrated and the universe began to expand (i.e. so-called dark energy was born).
Perhaps it may have also been the case that even gravity did not exist until the other forces did. What if gravity, which works because of the bending of spacetime, and mostly due to the slowing down of time when closer to mass (i.e. when you are standing upright, your feet are moving through time slower than your head, and this is what keeps you and the planet being stuck in each others future, in other words, stuck together), occurs because of the integrated information? Where more information is being integrated (where there is more mass and energy there are more operations are being performed), time slows down in order to accommodate all the increased number of operations in the local area around the mass and/or energy. Thus, before the particles began interacting, there was no gravity, since no information was being communicated. Now that such information integration has caused local changes in the speed of time, particles (and dark matter) interact gravitationally as an effect of the differential speed of time between areas of greater and lesser information integration.