This post will put forward the view that Zeno’s paradoxes represent something fundamentally wrong with our understanding of the structure of space and time.
This forms a problem that runs through the whole of human mathematics.
That starts with the discovery of irrational numbers in ancient Greece and forms infinities at the base of Newton and Leibniz calculus.
It can also be seen at the heart of Cantor’s set theory and also as a paradox in his continuum hypothesis.
Quantum electrodynamics also suffers from the problem of infinities that has not properly been solved.
There is also the measurement problem of quantum physics that has no logical explanation.
All this can only be explained by a fundamental change in our concept of space and time.
Zeno’s paradox can be expressed in many ways but for the purpose of this post it is best to think of dropping an object and measuring the time it takes to reach the ground.
We can always half the length of time the object takes to reach the ground and by doing this we will form an infinite series therefore the object will never reach the ground.
Zeno rejected the idea of infinity and so he had a paradox and believed that moving and changing to be an illusion and that only what ‘was’ mattered!
But the theory I am now going explain does not reject infinity but explains it as a universal process that forms the arrow of time and geometry of spacetime. (This does not mean that Zeno was wrong)
In this theory the forward passage of time is formed by the forward motion or momentum of light (EMR) forming the geometry of spacetime.
The probabilistic nature of the wave particle duality of light forms the flow of time itself. This is explained by Schrodinger equation that represents the quantum wave particle function.
Therefore Heisenberg’s Uncertainty Principle is the same uncertainty that we have with any future event and represents potential future possibilities.
The answer to the problem of infinity is that it only has the potential probability to exist. Aristotle was the first to introduce the idea of something being potentially infinite.
In this theory we have a potential infinity of probabilities at every degree and angle of spacetime because one thing after another is always coming into existence as part of the time continuum.
Cantor believed that we have more than one kind of infinity. There are more numbers between 0 and 1 than there are integers, more than infinity.
Set theory lies at the heart of mathematics but Cantor’ set theory relies on there being something called the empty set a set of nothingness.
One of the axioms (principles) of set theory is that we have a choice of choosing one member of any non-empty subset of the set.
This has caused a problem proving the continuum hypothesis. Because there is no explanation of human interaction, how is the choice to be made?
In this theory we have a physical starting point to any infinite series. We can choose when and where to collapse the quantum wave particle function forming new particles in space and new moments in time.
This will form a new wave function of future potential that will expand out from zero in all directions along the x and y axis forming part of an infinite process.
Just has Cantor could mathematically build up a never-ending series of larger and larger infinities this theory can also do the same in the physical world. This fits in with Pythagoras’ most central belief that reality has a mathematical base.
Therefore the infinities in the mathematics of Quantum electrodynamics are not a problem; they represent the continuum of time itself that is infinite and there is no need for the process call renormalization.
Sir Isaac Newton
This continuous process of change can be seen has a universal process of symmetry forming and breaking that forms fractal self similarities
Fractals, chaos theory shows that it is possible to have infinity in a finite world (Koch curve) all we need is a way of dividing space up into infinitely small portions.
This theory explains a process of how spacetime can be continuously formed that can always be dived up into infinitely small portions (mathematical infinity).
This also explains Kurt Gödel, Incompleteness Theorem some problems in mathematics can’t be solved no matter how you approach the problem.
Therefore we have the Measurement Problem and can never know the position and momentum of a quantum particle at the same time. This is because in the world something is in existence or it has the potential to exist, but never both.
In this theory mathematical infinity, physical infinity and absolute infinity are all one and the same.
“If the door of perception were cleansed everything would appear to man as it is, infinite”.
William Blake 1757…