Author:  Jacob Ghitis   < >

Abstract:  Physicists have misinterpreted the Euclidean concept of “point” when attempting to apply it to the universe.  Feynman's String Theory was an attempt to alleviate the inherent resulting problem.  Presented herein is a summary of the current situation along with a proposed particle theory where the concept of an unreachable "virtual center" in gravitational bodies is postulated rather than that of  "point." 

Keywords:  particle theory, gravity, mathematical concepts, Euclides, Zeno’s Paradox.

I believe to be in the position of explaining the reasons for the creation of the string theory, giving the gist of it, and of showing how wrong it is.   Most surprisingly, all this is derived from the "problem" of the physical law of inverse squares, with its cleverly deceiving arithmetical "infinite attraction."  I will show the wrong way this problem was approached, and how the right interpretation opens a whole new world of understanding.

The problem facing physicists attempting to figure out the shape of nuclear particles stemmed from their initial interpretation of the concept "point." The error actually was born when Euclides defined the line as a succession of points. This is true, if the mind thinks of a line being drawn by a person.  But “line” actually should be conceptualized as a Platonic Idea, not as the Aristotelian almost infinite number of possible drawn lines.

Think of a line 4 cm long, and signal its middle, at 2 cm. Would you mark that distance with a pencil or would you consider that there is no "point" there, but an intuitive boundary? Could you slice the line in exactly two pieces with the sharpest possible knife?  And the center of a perfect sphere: is it possible to mark it, or is it just a conceptual image? Thus, when physicists started to talk of particles not as objects but as "points," they committed the first error.

Then came the law of inverse squares:  the degree of electric attraction between two oppositely charged elements, and also of gravitationally attracted bodies, varies inversely with the square of their distance. If the distance decreases by half, from 8 to 4, the attraction is increased not by two, but by four.  Keep decreasing by halves and the attraction keeps increasing by 4, yet never reaching a finite number.  Meaning that there will never be a complete approach.  This is an example of  “Zeno's paradoxes.”    Yet the infinite does not exist in physics, but rather only in numbers, because numbers do not exist in reality.  Numbers like letters and words are merely symbolic representations of an idea or concept. 

Therefore in physics, in contrast with mathematics, the possibility of keeping the halving of distance forever is inexistent:  there is a physical limit to that halving.  And that limit has an entirely logical explanation.  Zeno's trick was to apply a law valid for mutual attraction, to a situation where Achilles had to overrun the turtle.  Had he been attracted to its center of gravity, then he would have been stuck to its carapace...

Actually, the physicists said that the two mutually attracting bodies would reach a distance of zero, which now made the situation really bad, because whatever formula uses zero as a divisor will ultimately result in an horizontally elongated 8, which is the symbol for "infinite." One could well argue intuitively that when two objects touch, they have arrived at their maximum possible attraction, which could now be considered as "infinite." 

But that's not the way mathematics works. Galileo said that mathematics is the language of physics.  I differ from him by not being a formally trained astronomer, physicist, or mathematician, yet as a philosopher I have repeatedly stated that mathematics is not a science but a discipline, and that it is the "core" or "heart" of physics. Therefore, mathematical equations must be taken at their word. In that sense, two bodies cannot diminish their distance to zero!

Of course, when you think of an apple "falling," you know that it actually is being "attracted." Yet it is still far away from the center of the earth, which is the center where the mass' attractions converge. Suppose you manage to let the apple continue its voyage to that center. Would it reach it? Of course not, because the distance cannot be 0.  (Matter's “heat” [“thermos” or “energy”] cannot be 0 either.)  This means that the center of the earth and the center of all “gravity objects” (celestial bodies) is empty, and so should be all nuclear particles when they become independent objects.  Such empty space is dependent on the mass of the gravitational body and its inner constitution. The earth's core is mainly made of molten iron and nickel. One could posit that as the iron is nearer to the “center of gravity,” it swirls faster, until reaching a limit where it constitutes the boundary with the "central emptiness."  The logic behind all this is that the center of gravity of the apple or any other matter cannot arrive at the center of gravity of the earth or any other body.  In a like fashion, the center of gravity of Achilles would never reach the turtle's center of gravity, if that had been Zeno's "paradox" idea…which it was not.*

Physicists were lead astray by the idea of points: "Particles are points," they said, "and the infiniteness inherent to the law of inverse squares is a pain in the neck," they added.  Then came Feynman who said, "They are not points, but elongated structures, yes that's right, they are strings! Even better if they are looped strings, because then there is a neutralization of forces in the loop's center."  I find this interesting because that latter image coincides with my idea of a central emptiness.…

It so happens that strings are actually a series of points, and if Feynman had not died prematurely, he would probably be his theory's most ardent opponent. But the momentum of the theory has carried it forward, in an exercise in futility. 

Particles are not points, and do not have to be strings:  they are very small objects with a hole in their center, a center that is determined by its swirling components!


*Editor’s Note:

For a further explanation of Zeno’s Paradox, the reader can go to:


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