It's been a while since I last made a post here, but as usual any input from those with the appropiate knowledge would be greatly appreciated. 1) Does all the information within the universe run under the guiding principle that it should follow the path of least resistance, I think this is also referred to as Energy Conservation. If YES 1b) Does this principle also apply at the quantum level 'quantum foam', or is this a principal which is generated from interactions occurring at this level, and which apply to the subatomic and greater? OR 1C) If it does also apply to the quantum foam level, what is governing the enforcement of this principle?
Energy and information are different things. Natural processes usually tend towards a state of lowest energy, with "excess" energy eventually converted to heat. "Least resistance" is a somewhat hazy concept, in my opinion. The law of conservation of energy applies at every level. The laws of thermodynamics were originally derived at the classical level, but later applied to the quantum level. If you're talking about "quantum foam", quantum thermodynamics explains the energy fluctuations of the quantum foam. The quantum foam is (probably) in the lowest possible energy state, but that is often a non-zero energy state in quantum physics. Moreover, the state can fluctuate randomly. In the quantum foam case, these fluctuations lead to a constant appearance and disappearance of "virtual particles".
First off, energy conservation has nothing to do with resistance. Let's say that you drain 1kW of power through a 50 Ohm resistor and then you drain 1kW of power through a 500 Ohm resistor. If the resistor is in a calorimeter you will measure 1kW of heat dissapation each time, energy is conserved regardless of the resistance. Second, the "path of least resistance" idea is generally wrong. Let's say that you had the 50 and 500 Ohm resistors rigged in parallel. Then the 50 Ohm resistor would be the path of least resistance and, according to the "path of least resistance" idea, the current should all flow there and not in the larger resistor. In reality, the current flows through both paths. More flows through the path of least resistance, but some flows through the path of most resistance. In this case, if 1kW were flowing through the path of least resistance then 100W would also be flowing through the path of most resistance. -Dale
Information generally has to do with the number of possible ways of arranging things. For example, if you flip a coin, and it can land either heads or tails, the coin is said, in that sense, to contain one bit of information. One bit gives two possibilities. Energy, on the other hand, is defined as the ability to do work, where work is given a specific physical definition.
Here is a slightly analogous situation. Imagine that you have two holes in the bottom of a large tank of water. One hole is 1cm in diameter and the other hole is 1mm in diameter. The 1cm diameter hole is the "path of least resistance". Does that mean that no water will go through the 1mm hole? No, it simply means that more water will go through the 1cm hole than through the 1mm hole, but some will go through each. Why does it do that? I don't know. I just know that it does. -Dale
Does this not imply that the 1mm hole becomes the 'next' path of least resistance, since the 1cm hole will only allow a given amount of water to pass (dependent on water pressure) at any one time?
I suppose you could describe it that way if you wanted. However, I don't know what the "next path of least resistance" is supposed to imply. Given a fixed water pressure the amount of water that flows through a 1 cm hole is completely independent of whether or not there are other holes present. In sense there is no importance to being the path of most resistance, of least resistance, or of some intermediate resistance. The same principle applies for electrical circuits, just replace pressure with voltage and water flow with current. -Dale
