How the Discontinuity of Motion Resolves Old Problems

The Paradoxes and Contradictions
of Continuous Motion

We are naturally inclined to believe that we have become very sophisticated in matters scientific; yet it is an object of record that ever since Zeno of Elea, all the philosophers of the world, from Aristotle to Einstein and including the seers of divine mentality who presumed to found religions, have remained incapable of solving the paradoxes which Zeno proposed 400 years before Christ.

Incapable, that is, except by proposing new paradoxes which were by nature more insoluble than the first for being more remote from any possibility of perception.

Never has perception produced any paradoxes.

When we see a thing, and especially if we can show this thing to everybody else, then the thing is there; it is real. It is only when we start imagining qualities about this thing that paradoxes appear.

When Zeno saw that his Achilles could, in practice, not only reach but outdistance the tortoise, he had access to a fact of reality; but when he started imagining qualities that did not properly belong to this fact of reality, then he found that there were contradictions between this real fact and the products of his imagination. These contradictions are termed paradoxes, and they come from the mind only, not from objective fact.

All paradoxes of motion are solved if we can prove experimentally that motion is quantized or discrete, just like the energy that produces it.

The experiments in these web pages demonstrate that, contrarily to continuity, the discreteness of motion is both logical and mathematical, for it is perfectly accessible to our sensory perception. In this case, our mathematics are real or objective, and not merely abstract or imaginative.

We now present some of the outstanding problems and paradoxes of motion.

The Paradoxes of Zeno

Achilles and the Tortoise:

Solution:
This is logically correct as long as the distance between the two remains longer than one "ultimate cosmic step" of Achilles. Since this last step, like all others, is ten times as long as that of the tortoise, this is where Achilles will overtake and start to outdistance the tortoise.

The purely logical nature of Zeno's concept of continuous motion must then give way to the practical discontinuity that is a matter of everyday experience, and that is now perceptively demonstrated in these web pages.

The Arrow:

Solution:
The discontinuity of motion allows us to realize that at each cosmic stop any moving body is in a perfect local state relatively to all other bodies in the cosmos, and to realize also that this perfect universal relation is instantaneously altered at each cosmic step. This is both the practicality and the intelligibility of a displacement from where a body is, to where it is going. It is Zeno's logic, and not our everyday practical experience, that is faulty.

The Dichotomy:

Solution:
In practice, a point is is reached by jumping instantaneously from one point to another (see Quantum Leap).

The points are not in space really, but they constitute the extreme limits of the body itself, and are carried by it through the nothingness of space.

It is therefore only because Zeno's logic was imaginative rather than perceptive, that for him motion was logically impossible. Had he known of the discontinuous nature of motion, his paradoxes would never have occurred to him.

The Stadium:

Solution:
The answer, of course, is that time has nothing to do with the actual displacement, since the steps are instantaneous. Time is only the measure of the stops, or of the durations of perfect immobility between the steps. As these stops were all simultaneous, there is no question at all of "half the time" being involved in the shifting of the columns. Both shiftings took their full time.

Zeno's Paradoxes - Conclusion

If motion were continuous we must agree with Zeno, against all experience, that motion is impossible. To claim that the continuity of motion is explained by the presumed continuity of our abstract mathematics is not an empirical answer and therefore is no answer at all, for it is using the imaginary to prove the imaginary. Since we do perceive motion, we either must reject the value of sense experience, or else reject the logical assumption that is contradicted by sense experience. This logical assumption is that of the continuity of motion.

Aristotle's Wheel Paradox

Problem:
The big wheel rolls from A to B. Each time a point on the rim of the large wheel touches line AB, a point on the rim of the small wheel touches line CD. All points on the small wheel are thus put into one-to-one correspondence with all points on the large wheel. This would indicate that the circumferences of the two wheels are equal in length, which evidently is not the case.

Solution:
Our difficulty here is that we presume that the small wheel and the big wheel can be put into point-to-point correspondence in motion, just as it can in immobility. In reality, the points on the big wheel make longer quantum leaps than the points on the small wheel. They are not therefore in real correspondence.

A good way to understand this, is to realize that no matter whether a moving body spins, wobbles, or produces any form of displacement whatever, it is always the centre of gravity that determines both positions in relation to the centre of gravity. In motion, there is no such thing as a correspondence of points, for all points make their own necessary leaps to retain their relative position.

We always have to remember that time is the only constant, while leaps are all variable.

The Lorentz-Fitzgerald Contraction and The Michelson-Morely Experiment

Problem:
The Lorentz-Fitgerald Contraction theorized that any object moving at a high velocity should contract in the direction it travels until it reaches the velocity of light, at which point it will disappear completely. The amount of contraction can never be properly measured because any measuring device would contract with the object being measured.

Being convinced of the reality of the space-time continuum, which means the continuity of space and time and therefore of motion itself, Albert Einstein accepted the Lorentz contraction as the reason for the perceivable effect of the Michelson-Morely experiment. It eventually became the basis for his Theory of Relativity.

The Lorentz contraction can only be explained through abstract mathematics. It is, in fact, an infinite sequence equation and admittedly beyond our sense experience. Like the paradoxes of Zeno, it is a purely logical assumption.

This assumption of contraction leads to the following postulates:

1. The velocity of light is constant throughout the cosmos;
   
2. The velocity of light is the highest attainable velocity;
   
3. Interstellar space travel is forever impossible.
   

And yet there is little real empirical evidence to support either the contraction or the theory of relativity. It is easy to understand why the contraction would remain unpercievable here on earth, since all measuring rods would themselves contract; but is this not an a priori admission that we cannot prove what we are saying?

And what about the sun?

We know that the milky way nebula travels away from the cosmic center at 45,000 miles per second. This is roughly 25% of the velocity of light which would mean a quite perceivable contraction in the direction of the nebulas's travel. Twice a year also we would be privileged to observe the sun's contraction in line with its rotation around the nebula; the sun would be contracted in at least two ways at once, and since it is rotating, its surface would be caved in continually in both ways at once.

And what about the planets and their moons, and our moon? Do they not all travel at the speed of the nebula? How do we explain that there is not a trace of contraction in any one of them, and no indication of cave-in or squeezing in the crust of our own earth?

In addition to all this, velocities higher than the speed of light have already been perceived by astronomers, notably in the Crab Nebula, and in some subatomic particles. The higher-than-light velocity of some of these particles has even been described as non-relativistic. But why should some cosmic events follow relativistic laws and others not? And if the Lorentz-Fitzgerald Contraction is factual, how is it we can see these events at all? Objects moving faster than the speed of light are supposed to disappear.

Solution:
If the scienctific establishment defines relativistic motion as a continuous motion that cannot exceed the velocity of light, and then admits at the same time that there is such a thing as non-relativisitic motion, it is evident that scientists are confused on the nature of motion.

The answer of course is that there is no such thing as a contraction. The Lorentz-Fitzgerald Contraction was formulated in order to explain the Michelson- Morely experiment in terms of motion continuity; that is, before we knew motion was discontinuous.

If an object perceivably exceeds the velocity of light it means that it did not disappear, and it means also that the contraction equation is purely imaginary and has no basis in physical reality. Finally, it means that Einstein's Theory of Relativity is also purely imaginary, since it is based on the contraction principle.

The real reason for the effect of the Michelson-Morely experiment was much simpler and much more perceivable than the explanation offered by the Lorentz-Fitzgerald Contraction.

This effect was obtained because light travels during the stops of the earth, and not during the steps or instantaneous displacements, for there is no time in which to travel in instantaneity. The effect was then produced because, relatively to light, the earth is always standing still.

The ether that Michelson and Morely were trying to discover really does exist, but not in the way it had been imagined. This ether is not an inert gaseous substance, but the very energy photons that permeate all cosmic space. Far from being inert, they are the source of all power and the cause of all displacements. They do not slip past the earth, but a huge concentration of them form the magnetic field of the earth and of all magnetic bodies. They also form the gravitational field of all cosmic bodies. No such body can slip by its own magnetic or gravitational field.

The Contradiction of Our Logical Mathematics by Our Sensory Perception

To be objective a number must represent a real object. No one has ever perceived an infinity of objects anywhere, and especially not in a finite unit of space. Never have we detected an infinity of matter or of energy particles, or an infinity of waves, in a definite length of space. What is it then that gives us reason to presume that the reality of Nature must necessarily subscibe to the dictates of our imagination? Even our imagination does not really transcend the finite; it only starts an enumeration procedure that it then presumes, against all practical experience, that it can pursue ad infinitum. It confuses the infinite with the indefinite!

Our imagination is a physcial action that requires energy, and this energy exists in quanta and is therefore finite.

The Sensory Contradiction of the Space-Time Continuum

1. Both infinities are enclosed within finite limitations. The finite then transcends the infinite!
   

2. There are perceivable variations of velocities, so that in the lower velocities the instants must be longer than in the higher velocities, or else each instant does not correspond to each point. How then are we to define long instants, and account for an infinity of such instants in a finite duration? Where is intelligibility in this?

The Contradiction of the Continuity of Motion by Planck's Quantum Theory of Energy

Boisvert's Paradox of Life and Death

Problem:

When do we die? In the past, the present, or the future?

Not in the past, as we are still living in the present.

Not in the present, as we are still living in the present. No one can be both dead and living at the same time.

Not in the future, as the future has yet to come.

Solution:
The present has a 1/64,000 of a second duration. After each such period, we make an instantaneous leap into the next period. There can be no motion and therefore no change during any of these periods.

To die is to fail to make this instantaneous atomic leap into the next such period. We therefore die precisely between the present and the future.

If quantum mechanics had been understood in the past, no paradoxes of motion would ever have surfaced.