The digital universe.

Question

In the theory of digital physics, I need some more understanding.

So what the theory of digital physics says is that everything can be represented as information. The "it from bit" idea.

This rises from the observations of quantum particles. Once we get to looking at the smallest of things we find these indivisible units electrons, neutrinos, up quarks, etc... The particle zoo. At this level there are only a handful of things that describe one of these units. A particle is basically a set of yes or no questions, and yes or no can be modeled by bits. 1 or 0 yes or no. So in theory given the tools we could encode the who universe as a bit string.

So I guess, if the entire universe is a bit string, would time be an operation on that bit string? The laws of physics being the gates that the computation uses; AND gate = arbitrary physical law.

My question: So the universe in the eye of digital physics is just the application of the laws of physics over time to the physical world, or the application of operators to the bit string that represents the universe in its entirety?

So then questions arise, these rules of nature that we alter the universal bit string with, are they to encoded in the bit string, or separate from it?

Answer 1

First I want to point out that digital physics does not necessarily make any claims about the ontology of particles. The only idea universal to digital physics theories is that the Universe is representable as computable information, and that a universal computer can, through some program, simulate the evolution of everything in the Universe.

Some theories only go this far, saying that it's merely possible to encode the Universe as such. Other theories endorse "pancomputationalism", which asserts that the Universe really is some sort of big computer. In either case, your question comes down to whether we can separate "rules" and "things" in the Universe, or whether the rules are themselves things that need to be operated on.

At a relatively high level, I would say that rules are indeed things. This comes from our theories that early on in the Universe, the two "rules" of Electromagnetism and the Weak Nuclear force were actually a single Electroweak force. Thus it seems that if the Universe is computable, this evolution of one of the rules into two separate rules must also be information in that model (otherwise, if the rules were separate from the things, how could this evolution have been computed?).

One would then ask whether at an even more fundamental level, there are "pure" rules for computing the evolution of the rule-things. To the contrary, I think it's perfectly reasonable to have only various things and no pure rules, because even if you have rules that never change, they can still be encoded as rule-things that are immutable but operate on other things.

Sorry that this is not a particularly technical response, but basically my answer is that if the Universe can be encoded as computable information, you should be able to represent it with a string like:

constant rules; mutable rules; simple things

Where the string is not inert like in most languages, but dynamic and self-processing (sort of like a quine), so that it can self-simulate without needing some external compiler and processor. The way I've presented it, the instructions for how to process the string would be in the "constant rules."

Answer 2

Information is a new paradigm to represent the world, as the clockwork universe was in Newtonian Physics.

Bits are great for digital computers but they're nowhere near sophisticated enough for the structures found useful in Modern Physics.

One should note, that chaotic dynamics in Newtonian physics and possible topology change at plank distances when the effect of Heisenbergs uncertainty principle coupled with GR show that information density at those scales are probably uncomputable.

There is however a type-theoretic interpretation of quantum field theory that is an active field of research. Type-theory was originally instigated by Russell & Whitehead which uses classical logic, in its modern incarnation its Martin-Lofs Type Theory which uses intuitionistic logic and is the internal language of a (infinity,1)-Topos. Its also known in another interpretation as Homotopy Type Theory. Interestingly enough this connects to foundational issues in mathematics. Mainstream foundations use Sets as their fundamental structure - and are not geometric, here it is homotopy types that are regarded as fundamental and they are geometric.

Notably, the theorem-provers Coq & Agda are both based on variants of Martin-Lofs Type Theory.

Essentially this is merging logic, computer science, mathematical foundations and physics.

Answer 3

The laws of physics seem to be set up in such a way that any finite physical system can be simulated by a universal quantum computer operating on a finite number of qubits. See for more details and references

http://research.cs.queensu.ca/home/akl/cisc879/papers/SELECTED_PAPERS_FROM_VARIOUS_SOURCES/ItFromQubit.pdf

The laws of physics would then consist of restrictions on the set of operations on those qubits that are instantiated by the real laws of physics. We don't know exactly what those restrictions are and it seems unlikely that all of them can be captured in restrictions on operations that just take place between the simplest kinds of particles. For example, the second law of thermodynamics is often said to apply to macroscopic systems where it is left unclear what macroscopic actually means. You can entangle two particles and increase their entropy and then disentangle them again, which would lead to a decrease in entropy. So there must be some explanation of what kinds of processes the second law restricts and why and it is not going to refer to the simplest possible kinds of interactions. For the same reason I doubt that the laws are directly encoded in the qubits, see section 2.10 of

http://arxiv.org/abs/1210.7439.