Boundary Condition

Full Title or Meme

The most common use of the term Boundary Condition is to mark a place or a time where the values for a differential is known and can be used to determine values at other times or places.

In fact, the entire progress of the universe is determined by Boundary Conditions.

Context

Without Boundary Conditions, there would be no structure to the universe.

While physicists have been taught that if all of the conditions of all of the particles, both location and momentum, are known, the the conservation laws can be used to know the condition of the universe at any other time, both past and present. Clearly this assertion could not be determine, so the statement has no value other than the expose the hubris of any team of physicist that believes it. The statement can not be proved either true or false, so it is of no help in the real world.

Given a set the differential equations, it the values of the bulk conditions at any particular boundary are know, then it is possible to know something about the values inside the boundary. However, reality is always intruding and it is clear since the advent of chaos theory and even of the quantum uncertainty principle that our information will always be limited.

Asymmetry of Time

If an asymmetry in time does not arise from the fundamental dynamical laws of physics, it may be found in special Boundary Conditions. The argument normally goes that since thermodynamic Entropy in the past is lower than in the future according to the Second Law of Thermodynamics, then tracing this back to the time around the Big Bang means the universe must have started of in a state of very low thermodynamic Entropy: the Thermodynamic Past Hypothesis. In this paper, we consider another boundary condition that plays a similar role, but for the decoherent arrow of time, i.e. the subsystems of the universe are more mixed in the future than in the past. According to what we call the Entanglement Past Hypothesis, the initial quantum state of the universe had very low entanglement Entropy. We clarify the content of the Entanglement Past Hypothesis, compare it with the Thermodynamic Past Hypothesis, and identify some challenges and open questions for future research.

At the Quantum Level

It seems reasonable that even the progress of the Schrödinger equation that is the basis for all progress in the Universe has two boundaries of interest. When the "particle" is created or "set free" and starts of on the path determined by the Schrodinger equation it must eventually decohere and be constrained by some event. This path may be extreme short, as the motion within a crystal, or span the entirety of space and the time since the universe became transparent approximately 380,000 years after the Big Bang.