Einstein would have very likely agreed with me. He chose to end his final and definitive book on his Theory of Relativity with the words:
" One can give good reasons why reality cannot at all be
represented by a continuous field. ... This does not seem
to be in accordance with a continuum theory, and must
lead to an attempt to find a purely algebraic theory for
the description of reality. But nobody knows how to obtain
the basis of such a theory.”
Those are the words of a person who knows that his continuum theory (Relativity) is not correct. If you want to read Einstein's exact words for yourself click here.
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In 1976 my mathematical paper “Useful Thoughts on Infinity” proved that there were errors in the Math Community's concept of infinity and of infinitesimals and in Einstein’s " Theory of Relativity", the bulk of which is Einstein's theory of gravity. My paper was studied by mathematicians at Yale, MIT and Caltech for at least a year, and they found no errors in my paper, as you will see from the letters I can find at this time (in 2023), 47 years after 1976. My paper also received high praise from a respected journal.
About twenty-two years after I wrote “Useful Thoughts On Infinity” information obtained by NASA demonstrated that my paper was correct not just theoretically, but also for our universe (the real world). However, the Math Community has continued to teach the wrong concept of infinity and infinitesimals and the Theoretical Physics Community continues to teach Einstein's "Theory of Relativity" as the correct theory of gravity, despite the fact that my paper and NASA's research proved Einstein to be wrong.
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Why does science continue to use Einstein's "Theory of Relativity" ?
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Using Einstein's "Theory of Relativity" to study the universe allows astrophysicists, cosmologists and physicists, world-wide, to get hundreds of millions (possible billions) of dollars in salaries and research grants every year, because of the complexity of Einstein's field equations and because the results they produce are not verifiable as they are either dealing with matters too far from our solar system to be directly verified, or they are dealing with matters too small to be directly verified. In his book, at page 94, Einstein wrote that when dealing with something that is sufficiently large (such as the universe) you cannot know what you are observing.
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The below letter from Professor Gian-Carlo Rota of the Massachusetts Institute of Technology (MIT) indicates that he studied my paper and found no errors. As seen from his letter, I mailed my paper to him on September 9, 1976, he kept my paper for close to 5 weeks and then he personally replied to me on October 13, 1976. If MIT and the journal "Advances in Mathematics" was simply going to send me a form rejection letter that would have been done by one of Professor Rota’s assistants sometime in September of 1976.
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The next letter shows that I wrote to a professor at Yale University. (In the 1970's there was no Internet, information was from journals and people working in the field; the information I was able to obtain was a few years old, which back in the 70's was current enough when it came to getting a person's Who's Who credentials and address.) His wife responded from the Yale Department of Mathematics and directed me to a noted mathematician, Professor Luxemburg, at the California Institute of Technology (Caltech). The Yale math department had my paper for several months (and found no errors in my paper) before recommending that I contact Professor Luxemburg at Caltech; if Yale had found errors in my paper they would have simply told that to me and they would not have recommended that I contact Professor Luxemburg.
(The math on infinity created by Georg Cantor had been taught and studied since about the turn of the 20th century, if my paper "Useful Thoughts on Infinity" was correct, then Cantor’s teachings on infinity were wrong, which meant that Cantor’s work, which had been studied and taught for about 75 years, and which was included in the curriculums, text books and papers of every university in the world, was wrong, and that would be a huge embarrassment for the math world, including for the professors who were studying my paper; everything on infinity and on infinitesimals would have to be redone and re-taught according to my paper (the paper of an undergrad student at a public university in Canada).
Yale wasn’t telling me to write to Professor Luxemburg at Caltech to prank Professor Luxemburg, they were hoping that Professor Luxemburg could find an error in my work.
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By the end of July of 1977 I had sent a copy of my paper "Useful Thoughts on Infinity" to Professor Luxemburg at Caltech, he could not find any errors in my paper and advised me that he had passed it on to Professor Stroyan (who was also a math professor at Caltech). Professor Stroyan advised me that he was studying my paper and would respond to me as soon as he had finished studying it; months went by and on November 25, 1977 I again wrote to Professor Luxemburg, who responded to me on December 7, 1977, advising me that Professor Stroyan was still studying my paper and that he would respond to me as soon as he finished studying my paper.
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I heard nothing further from Caltech; they knew that my paper was correct and that the math on infinity which had been taught since about the beginning of the 20th century was wrong, but they weren't about to take the information to the world math community that an undergrad student at a public university in Canada had proven the last about 75 years of math on infinity to be wrong, and the books and courses now had to be re-written.
Between September of 1976 and (if Professor Luxemburg was correct in his
December 7, 1977 letter, where he wrote that Professor Stroyan was continuing to study my paper) some time into 1978 or beyond, my paper "Useful Thoughts on Infinity" was studied by some of the greatest math minds in the world, and they found no errors in my work.
In the mid to late 1970's "The Journal of Irreproducible Results" was a well respected journal in the scientific Ph.D. community in general, it published facetious articles, often of supposed results (which were erroneous) for the intellectual entertainment of the general scientific community. I thought that I could get my paper into that journal even though my paper was a serious paper, because it showed the current teachings on infinity to be wrong. They ultimately responded that my paper was excellent, but that most of their readers would not understand it and therefore they were not going to publish my paper. It is correct to say that to understand the math in my paper a person would have to have a sophisticated knowledge in a specialized area of math.
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You can get a copy of my paper “Useful Thoughts On Infinity” from the Library of Congress or you can download a pdf copy of it using this link.
You can get a pdf copy of the initial rough draft of my paper “Infinity In A Finite World”, using this link; it explains some of my main points on infinity without using any math.
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People, including physicists, get hung up on the length and complexity of Einstein's field equations and try to understand the "Theory of Relativity" by solving those parts of the equations which are solvable and which they can solve. However, the math is not the physics, the physics is the physics; the math is the translation of the physics into equations, if the physics is wrong then the equations will give you wrong results, because the equations are simply telling you the numbers that the physics told the equations to tell you. Look at it this way, if I dictate instructions on how to make a cola drink, and my instructions are wrong, when you follow my instructions you will not end up with a cola drink; if my instructions are really screwed up you might end up with a poisonous drink. The equations are the instructions that the physics dictated.
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Mathematicians deal in a world of perfection, where 1 + 1 = 2 and where 1,000,000 + 1,000,000 = 2,000,000. In the real world 1 + 1 rarely equals 2. One dollar plus one dollar does equal two dollars, however, for people, only identical twins come close to equaling two of the exact 100% same person. In the real world there are not even 10 trees that are 100% identical. In the real world most things have differences, sometimes the differences are so trivial as to make them irrelevant for the thing's purpose, but they are still different, and sometimes the differences do matter. In the real universe you will not have two or ten or a thousand of the exact 100% same thing; but in mathematics, when you write 1,000,000 + 1,000,000 = 2,000,000 you are saying that you have two million of the 100% exact same thing.
When you take three tennis balls out of a new container, you don't have 3 exactly 100% the same tennis balls. When measured to four or more significant figures they will be different, when weighed to four or more significant figures they will be different; but that's not the worst of it, as soon as you start playing tennis, even if those 3 tennis balls are used in equal rotation, they will become increasingly different from each other; now consider the real universe after billions of years, it is extremely heterogeneous. The math that Einstein used required the universe to be the equivalent of homogenous, which is the opposite of the reality of the universe.
When theoretical physicists try to connect the intrinsic perfection of mathematics to the real world, they can sometimes succeed, as long as they deal with the real world and not with a simplified imaginary world in which a large amount of the real world has been removed. For example, click here to see what Einstein called a mathematical proof for the real world.
Mathematics is phenomenal at predicting things when it is based on reality and a valid and completely accurate theory, however, it is useless at predicting things when it is based on an invalid theory or not on reality, and mathematics will make errors in predicting things when it is based on a theory that has errors or too many unrealistic simplifications in it, the greater the errors or unrealistic simplifications in the theory, the more the math based on that theory will give erroneous results.
A mathematical equation is only as good as the theory it is based on; a computer program tells the computer what steps to take to produce the end result, a mathematical equation tells you what to add, subtract, divide, etc (what steps to take) to get the answer.
For example, Distance = Speed x Time.
If you traveled at 54 kilometers per hour and you traveled for 1.25 hours you will have gone:
Distance = 54 kilometers/hour x 1.25 hours = 67.5 kilometers.
But suppose that Newton had written the wrong equation, suppose he had written that:
Distance = Speed x time x 14;
that would tell you that if you traveled at 54 kilometers per hour and you traveled for 1.25 hours you will have gone:
Distance = 54 kilometers/hour x 1.25 hours x 14 = 945 kilometers, which is obviously wrong.
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The math is NOT the physics, the math is a statement of what the physics says in the form of an equation. Equations are the language of mathematics. 3 + 7 = 10 is an equation. An equation is what it says it is, it is an equality. The 3 + 7 on the left is equal to the 10 on the right, it is an equality, which math calls an equation. Math is a language, it is not a tool that repairs errors. Einstein’s Relativity was written in German, when that German was translated into English, the translation did not fix any errors in Einstein’s theory; similarly, when Einstein's theory was put into mathematical equations that translation did not fix any errors in his theory. If what the physics says is wrong (ie. if the theory behind the math is wrong) then the math based on that theory will produce wrong results. The math can be done correctly, but if it is based on wrong physics (for example, if the physics said that Distance = Speed x time x 14) then the math will give you wrong results.
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Back in my physics and math university days, to know what Einstein wrote I went through his most recent book "The Meaning of Relativity", it was a compilation of all of his previous works on Relativity revised with his latest thoughts and the thoughts of others with which Einstein agreed. If you want to read the portions of Einstein's Book that are quoted in this paper, to verify that the quotes are accurate, you can download the relevant excerpts from Einstein's book on Relativity using this link; I will refer to it as Einstein's Book.
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Whenever numbers are put into one side of an equation answers pop out of the other side. What those answers mean is not explained by the equation. The theory (which is the physics) on which the equation was based, is supposed to explain what the numbers which popped out of the other side of the equation mean. If the theory is wrong then what it tells you the numbers mean will be wrong. In my distance equation example, which you can see by clicking here, one theory said that the numbers meant that after half an hour the object’s mass increased, another theory said that after a half hour the object was now passing through a denser medium, another theory said that after a half hour the object was at a location where there was now a force pulling it back toward the half hour location; without verified data you have no way to know which of those theories is correct, of if they are all wrong. The equation can’t tell you which explanation (ie. which physics) is correct, or if they are all wrong; only verified data (ie. data which needs no interpretation, and needs no assumptions, and is not explainable by more than one theory, can tell you if the theory (ie. the physics) is correct.
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