I Information is Conserved.
II The fundamental process of Nature must be a Computation Universal process.
III The state of any physical system must have a Digital representation.
IV The only kind of change is that caused by a Digital Informational Process.
Laws III and IV assume that the Finite Nature hypothesis is true.
Conservation of Information is a direct consequence of Reversibility. If the laws of nature are truly and exactly reversible, then in principle, if time were reversed in some physical system, then its evolution would exactly retrace its steps. This is only possible if no information is lost. Information is lost whenever 2 or more distinct states of a system lead to a common successor state, K. In reverse, there would be no basis for choosing which state ought to follow state K. The total number of distinct informational states of any closed reversible system, S, is the same as the total number of states the system will visit before it cycles and starts to repeat itself. The number S always has the same value at any point in time; S is therefore a conserved quantity. Finite irreversible systems must eventually cycle, but the cycle does not include any of the states reached prior to the beginning of the cycle. By having a counter and by saving the initial state, we can make any irreversible system reversible. To get from state t to state t-1, the system restores the initial state and then uses the counter to go forward t-1 steps. A bit expensive, but mathematicians don’t mind. Computers can also be microscopically reversible by building them out of reversible logic gates. Such computers are just as efficient as ordinary computers (in terms of how much hardware and time are needed to do a computation) and they hold the promise of being able to eliminate heat dissipation during computation. The laws of physics make microscopic reversibility an intrinsic part of all microscopic physical processes. We are led to believe that the cost of going forward from some state must be the same as the cost of going backwards from that state. This means that information is microscopically and locally conserved. We postulate that in any volume of space-time, information that is gained or lost from that volume must be lost to or gained from those regions that are space-time neighbors of that volume. In this case, conservation of information is much like conservation of energy.
A system is considered to be Computation Universal if one can demonstrate the possibility of constructing within that system a universal computer. Consider the question “Do the laws of physics allow the construction of Universal Computers?” Of course we know the answer. The fact that we can build computers means that the most fundamental processes in physics must be Computation Universal. If the most fundamental processes were not Computation Universal, then neither life nor computers could possibly exist. There is an amazing consequence in DP of the second Law. In theory, every sufficiently large Computation Universal process can be put into a particular state that is isomorphic [1] with the state of the real universe and would then evolve as to remain isomorphic to the evolving real Universe. This has the bizarre consequence that all questions such as “How many states are there per cell in a true DM model of physics?” have the similar answers: “It is only a matter of esthetics or economy, since we already know that 2 state, 3 state or any larger number of states can all be Universal!” There are well known 2 state, 2 dimensional RUCAs (Reversible Universal Cellular Automata) that are absolutely sufficient to model any and every DM system. We are saved from this tyranny of Universality by the belief that there will be found models that are exactly correct while being so simple and straightforward as compel us to accept them. It is similar to the fact that there are many different possible proofs for every true mathematical proposition, but we happen to favor the simplest and most elegant of these proofs.
III. In physics we often think of a system as being in a particular state. The exact details of the state are often considered unimportant. Consider the difference between the following two statements:
- “The charge state of that ion is –2e (2 extra electrons).”
- “The speed of that ion is 300 meters per second.”
The first statement is clear, precise and unambiguous. The second statement is necessarily approximate and needs more information to make it more definite (a reference frame). It is clear how the information about the 2 extra electrons is represented in the atom. But it is definitely not clear as to how the speed or velocity information is represented in or near the atom. There certainly are areas of contemporary physics that apparently violate the Third Law. Given the Finite Nature hypothesis it must be true that every state has an exact Digital representation. This means that if we could look with a magic magnifying glass we would be able to see and identify the bits that represent the velocity state information. This would then relegate velocity state to the same preciseness as charge state – except that the velocity state of an ion has many more bits of information than does the charge state. The reason all this is true is that there is no other way of representing information given the Finite Nature assumption.
Normally we think of things that simply change. We think that objects move and systems evolve. Given Finite Nature all physical state is represented by digital information. Even information about a dynamic state must be represented by some kind of static digital information. This means that if we examine the state of a system at an instant of time, we must be able to find the static representation of both: the static information and the dynamic information. Any change of the digital information that represents the static state requires a digital process to change that digital information, in accordance with the static representation of the information that represents the dynamic state. For a particle to accelerate, there must be a digital process that changes the dynamic information. All particle decays and interactions are simply digital information processes involving the information that represents the particles and their states. In DP we generalize these observations and claim that there are no other kinds of change.
