Finity Begets Finite Particles and Finite Motion

On ResearchGate[1], my esteemed colleague, Mohammad Ayaz Ahmad posed this question:

“Are particles discrete or not?

In order to understand the nature of motion it is first necessary to confront yet another fallacious concept in physics called continuity (infinite divisibility). It is a concept that scientists, especially mathematicians, hopelessly cling to in spite of its being blatantly illogical. This belief has led to the introduction of the theory of general relativity, which postulates a geometric solution to the phenomenon of gravity and introduced such harmful concepts as the existence of a space-time continuum (note 1) and the curvature of said space-time. Truth is, continuity is wrong simply because it leads to an infinite regress. Nature is discrete and, as a result, particles move in discrete steps, i.e., their positions change from one discrete value to another. Discreteness means that there exist only discrete positional properties and that things like lines, circles, curves, surfaces, angles, etc... are all abstract concepts. The old debate between Euclidean and non-Euclidean geometries about whether or not parallel lines meet becomes immediately pointless (not to mention stupid) since both wrongly assume the existence of lines and other continuous structures.”

Readers of "The Ten Assumptions of Science[2]" and "The Scientific Worldview[3]" know about the philosophical choices required to distinguish between determinism (science) and indeterminism (religion). They know that the debate between those two worldviews is interminable. That is because fundamental assumptions always have opposites, and in the end neither is completely provable. To do science properly, however, we must choose the correct fundamental assumptions before proceeding.

Ahmad’s age-old question about whether particles are discrete or not is interesting in that it serves as a nice illustration of how assumptive choice affects conclusions. The choice here is between infinity and finity. It is obvious that no one can ever prove which is correct. No one can go to the edge of the universe to get a yes or no on infinity; no one will ever find the smallest particle. One may have difficulty in imagining how the universe could have an end to it. Would there be dragons there? If matter exists in one place, would it not exist in every place? One may have difficulty imagining a partless particle. Is matter a solid crème-pie filling of some sort? At the Progressive Science Institute, we use the Eighth Assumption of Science, infinity (The universe is infinite, both in the microcosmic and macrocosmic directions) to confront the Big Bang Theory and to resolve the multitude of paradoxes and contradictions in today’s physics and cosmology.

Like Ahmad, most scientists assume finity. That is why the Big Bang Theory and Finite Particle Theory are so popular. Of course, any hint of the infinite must be “illogical” for those who consciously or subconsciously assume finity despite the endless variety we see all around us. Finity, however, poses many contradictions, some of which were pointed out by Ahmad. In the effort to save that assumption, scientists have proposed extra-Euclidean dimensions and geometrical and other mathematical solutions for understanding natural phenomena. Sorry Ahmad, but Einstein’s space-time concept was ultimately used, not to propose an infinite regress, but to do just the opposite: stuff the entire universe into a finite pre-Copernican bundle.

To do that, Einstein had to objectify motion. This was his most important philosophical error.[4] Although critical of relativity, Ahmad does the same thing: “Nature is discrete and, as a result, particles move in discrete steps, i.e., their positions change from one discrete value to another.” This would be a surprise to Newton and to anyone who has studied inertia, in which an object travels through space in a continuous fashion per the First Law of Motion. No energy inputs are required. For motion to occur in discrete steps, an object would require discrete collisions per the Second Law of Motion. Energy exchange would be required for each deceleration/acceleration step. Discrete material objects have xyz dimensions and location with respect to other objects. Motion does not have dimensions; like time, it is not “part” of the universe. It is what those parts do. The adjectives “discrete” or “continuous” do not apply to motion.

I have to agree with Ahmad that the continuity assumed in various abstractions is purely idealistic. Those are study aids, not real objects. How then do the adjectives “discrete” or “continuous” apply to real objects? In combination with infinity we use the Tenth Assumption of Science, Interconnection (All things are interconnected, that is, between any two objects exist other objects that transmit matter and motion). Thus, we know that the smooth, continuous surface of an object really is composed of discrete particles. Ahmad and I would not agree on the question of what is between those discrete particles. It is either something or nothing. One who assumes infinity would choose something; one who assumes finity would choose nothing.

The concept of nothing, however, is an idealization, just like the concept of solid matter. Empty space and solid matter are ideals, neither of which exists in nature. Everything that exists has the characteristics of both. Even as interconnection approaches infinity, there must be “empty space” for those intervening objects to transmit motion. Subdivision always produces what we call matter and empty space, ad infinitum.

Ahmad would say that it is “illogical” to assume infinity. True, for the cosmogonist that switch would amount to a revolution in thought, but it is no more difficult than believing the universe exploded out of nothing. As we showed in our latest book[5], the logical replacement for the Big Bang Theory is Infinite Universe Theory, the culmination of what Copernicus only started.

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[1] ResearchGate.net is an international community of scientists who share bibliographies and downloadable copies of peer-reviewed publications as well as manuscripts of work in progress. Both positive and negative results are encouraged. One lively feature allows investigators to ask public questions of each other in their fields of expertise.

[2] Borchardt, Glenn, 2004, The ten assumptions of science: Toward a new scientific worldview ( http://www.scientificphilosophy.com/assumptions.html

 ): Lincoln, NE, iUniverse, 125 p.

[3] Borchardt, Glenn, 2007, The scientific worldview: Beyond Newton and Einstein ( http://www.scientificphilosophy.com/The%20Scientific%20Worldview.html

 ): Lincoln, NE, iUniverse, 411 p.

[4] Borchardt, Glenn, 2011, Einstein's most important philosophical error, in Proceedings of the Natural Philosophy Alliance, 18th Conference of the NPA, 6-9 July, 2011 ( http://www.worldsci.org/pdf/abstracts/abstracts_5991.pdf

 ), College Park, MD, Natural Philosophy Alliance, Mt. Airy, MD, p. 64-68.

[5] Puetz, Stephen J., and Borchardt, Glenn, 2011, Universal cycle theory: Neomechanics of the hierarchically infinite universe: Denver, Outskirts Press ( www.universalcycletheory.com ), 626 p.