Information Capacity of the Universe

Please help with a follow up to my question about the Computational Capacity of the Universe. According to Seth Lloyd's calculation, the capacity in bits is proportional to the age of the universe. But in your answer: http://van.physics.illinois.edu/qa/listing.php?id=24045 you explain that quantum information is neither created nor destroyed. So can the information capacity increase with time? Thank you.
- Bill Hibbard (age 66)
Madison, WI, USA

That's a great question, pretty near the limits of our competence.

Seth Lloyd's calculation involves not just information storage but also the performance of computational operations. Those take some time, so that the number of operations performed over time grows even if the net information capacity doesn't change. The calculation also is based on something different than a fixed set of stuff called a "universe". It concerns instead the number of operations that could have an effect on things at some particular place at some time. That involves communication with a larger and larger set of things as the horizon for light-speed communication expands over time.  So this accessible universe isn't really an isolated system since it keeps including more stuff. (Lloyd used a simple model that did not include the current weak inflation of the universe.)

The conservation of information theorem assumes that there are no cosmic horizons over which information can flow in or out, just an isolated quantum system evolving by its own internal rules. In our old answers, , we worried only about the horizons at black holes, but we should have also mentioned the cosmic horizons. I'll go back and add a note.

Mike W.

(published on 06/07/2014)

Thanks Mike, great answer. I've seen references to the idea that total energy or information is for the "observable universe" and that as time goes on more of the universe becomes observable. But doesn't the big bang imply a finite total amount of energy, observable or not? If the total energy is infinite and energy density is finite, then the spatial extents of energy must be infinite and hence velocities of some energy away from the big bang must have been infinite. Thanks for any help.
- Bill Hibbard (age 66)
Madison, WI, USA

Hi Bill-  Let me steer you towards one of our old answers for starters:  .

More specifically, we really don't know if our universe is finite or infinite. WHichever it is, it's been that way since the Big Bang. We know it's substantially bigger than the content of our horizons. 

Assigning relative velocities to distant points is a little arbitrary, since there are a variety of valid coordinate systems. Your basic point, however, is right. There's no finite limit on those velocities if you try to make a description of the universe extending beyond the horizon. The speed limit applies to objects whizzing past close to you.

Mike W.

(published on 06/17/2014)