Sunday, 15 January 2012

The God of Cantor, Pythagoras and Plato

Cantor, Pythagoras and Plato believed numbers were externally existing realities in the mind of God.

This blog puts forward the idea that the abstract mathematics of Cantor’s continuum hypothesis and his work on infinities represents the continuum of time as a physical process.

Time is infinite if we have a number line representing the time line we will have an infinity of numbers (quanta) along that time line. But at each number or moment we will have a far greater infinity of irrational numbers representing the possibilities of what could happened.

In this theory “Quantum Atom Theory” each new light photon oscillation represents a new moment in time as a process of continuous energy exchange.

Each new light photon oscillation represents zero representing a new moment in time (the moment of now) with the positive numbers marching off towards an infinite future, their negative numbers recede towards a limitless past (the positive and negative of EMW).

This process forms the continuous flow of electromagnetic fields the electric fields will always be at right-angles to the magnetic fields forming the local spacetime geometry in three dimensional space.

This gives us a physical reason why the imaginary numbers extend out on a number line at right-angles to the real number line. The imaginary numbers of quantum mechanics represent part of a physical process with the complex number representing the potential position of a potential future event.

This is only possible because in Einstein’s theories of relativity we have an infinite number of reference frames each one having a rate that time flows relative to the energy or mass of that reference frame.

In this theory energy and mass (you and me) slows the rate that time flow forming their own potential future probability within their own created reference frame.

Link to the video “A quantum field theory that explains the arrow of time

Each object or observer will have their own arrow of time or time line within their own reference frame as part of a process of continuous energy exchange, continuous change.

This theory gives us an objective understanding of quantum mechanics that Einstein always believed was possible. Quantum physics represents the physical process that we see and feel as the flow of time.

It also gives us an objective understanding to Cantor’s continuum hypothesis and his work on infinities.

Cantor found a hierarchy and structure to infinity as we approach greater and greater numbers we depart from infinity. Mathematical infinity has this property because the greater the number the fewer (relatively) are the squares contained in them. But the squares in infinity cannot be less than the totality of all the numbers.

This can make sense if we think of infinity as a physical process that forms the eternity of time. Each new moment in time is formed by a new photon oscillation forming a sphere of probability or wave function that we can calculate as a square of probability from its radius.

The axiom of choice that we have in Cantor’s set theory is the choice of where and when to collapse the wave function into a new moment of time!
Therefore we have free-will within our own reference frame and because this process is universal and we have an infinite number of reference frames we have an infinity of possibilities!


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