Sunday, September 2, 2012

Quantum algebra and axiomatic physics

Since the 1930s, quantum mechanics was viewed as one of the two foundations of physics, more fundamental than the classical physics. Seemingly, without adding “quantum” in front of a physics theory, it cannot be a viable theory.  Yet, besides all those quantum-theories, what is the ontological essence about “quantum”?

In general, the Uncertainty Principle can be interpreted in two descriptions.

One --- In the article “Ball on a Spring (Classic vs. Quantum physics),”, it wrote, “A is the amplitude of oscillation (which we are free to choose to be as large or small as we want). 
In quantum mechanics, things change.  At first glance (and that’s the only glance we need, really, …) there’s really only one thing that changes, and that is the statement that ‘we are free to choose [the amplitude] to be as large or small as we want.’  It turns out this isn’t true.  And correspondingly, the energy stored in the oscillation cannot be chosen arbitrarily.
A single quantum of oscillation wouldn’t even make the ball move by a distance of an atomic nucleus! No wonder we can’t observe this quantization!!  If the ball moves an amount that we can see, it has an enormous number of quanta of oscillation — and for such large values of n, we can make A be anything we want, as far as we can tell; see Figure 2. We can’t measure A nearly well enough to notice such fine restrictions on its precise value.”

In this description, although the quantum is the foundation, it becomes insignificant at the large scale which is ruled by determinism. That is, there is no conflict or contradiction between quantum facts as a foundation in a small region and the rule of determinism which rules the large scale.  

It says again, “… Even when there are no quanta of oscillation in the oscillator at all — when n = 0 — there’s still some amount of energy in the oscillator.  This is called zero-point energy, and it is due to a basic jitter, a basic unpredictability, that is at the heart of quantum mechanics.”

This shows that the “quantum zero” is seemingly significantly different from the mathematics zero which is a “static zero, the foundation of determinism”. In the quantum region, zero cannot be defined at a specific space-time point, and it can only be defined by averaging out a range of space-time points. The larger this range is, the closer the quantum zero approaches to the mathematics zero. The largest space-time range is this physical universe, and the quantum zero for it is the Cosmology constant, which is the best known measured “Physical zero”.  And, it is almost identical to the mathematics zero.  Again, there is no conflict or contradiction between the quantum zero and the determinism (the mathematics zero). Furthermore, no any kind of quantum dancing is able to help the quantum zero escaping from the confinement of the deterministic zero.

Two --- It can be stated with the following statement.
Statement A --- Quantum mechanics doesn't allow us to predict anything else than probabilities. So there's always some uncertainty about the answer to the question.”

If statement A is absolute, then it itself is a statement of determinism. If we add a statement B,

Statement B --- The validity of statement A depends on a probability.

Then, is the system of “statement A + statement B” absolute?

In fact, regardless of how many statements are added to the above, there is no way of any kind (even by God) to construct a Quantum-system to escape from the grip of the determinism at the end. Is the recently discovered Higgs-like particle a quantum particle? Are we positively determined that we have caught its tail?  I call this “quantum-ness paradox”.

With the two points above, it is clear that the important-ness of quantum-ness was overhyped in the past 80 years. I can show this more with the following three points.

A. Quantum algebra:
In mathematics,  sugar + sugar = more sugar, and one apple + one apple = two apples (not two oranges). But, in quantum algebra, there is a significantly different rule.
               Quantum + quantum = deterministic, such as,
       Quantum particle + quantum particle = deterministic particle, for examples,
                   Proton + electron = hydrogen atom
                  Hydrogen atom + hydrogen atom = hydrogen molecule
                   Two hydrogen molecules + one oxygen atom = water (wholly deterministic).
In fact, any kind of quantum dancing (fields, operators, etc.) will eventually lead to the determinism, and there is no way escape from it. It does not take too many steps to erase the quantum-ness.

B. All important quantum parameters can be derived from the axiomatic physics deterministically.
The most important quantum parameters for the construction of this universe are the Cabibbo angle, the Weinberg angle and the Fine structure constant (Alpha).  And, they can all be derived deterministically in the axiomatic physics. Please read the article “Axiomatic physics, the revolutionary physics epistemology,” for details.

C. Both proton and neutron must be Turing computers in order to give rise to a biologic universe. Please read the article “Quantum behavior vs. the Cellular Automaton determinism,” for details.

With the five points above, I have concluded that the quantum-ness is only a naughty child of the supreme Daddy of Axiomatic physics.