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Miles Mathis: The Probability Wave of QM is not reality
Formal disproof of the Copenhagen interpretation

Please note that this paper is a simplification by me of a paper or papers written and copyrighted by Miles Mathis on his site. I have replaced "I" and "my" with "MM" to show that he is talking. All links within the papers, not yet simplified, are linked directly to the Miles Mathis site and will appear in another tab. (It will be clear which of these are Miles Mathis originals because they will be still contain "I" and "my".) The original papers on his site are the ultimate and correct source. All contributions to his papers and ordering of his books should be made on his site.
(This paper incorporates parts of Miles Mathis' quant paper - Philosophies of Bishop Berkeley and Karl Popper not included).

Heisenberg               Bohr


Quantum Mechanics currently faces two major problems, one mathematical and the other theoretical.

The mathematical problem concerns the accretion during the 20th century of a large quantity of heuristics. The perfect example of this heuristics is renormalization. Even its inventor, Richard Feynman, called renormalization a "dippy" process (QED, ch. 4, 13). Feynman and many of the other big names in Quantum Mechanics made a lot of mathematical messes. These messes are going to have to be cleaned up at some point in the near future.

By far the worst problem in Quantum Mechanics is theoretical which began with the so-called Copenhagen interpretation of Bohr and Heisenberg. Using Heisenberg's math, Bohr turned Quantum mechanics into a mystical realm governed by probabilities and we have not recovered from even today in the 21th century. These theoretical messes that began in the early part of the 20th century, having been augmented and multiplied by many others in the years since have given us such massive theoretical failures as the "god particle" and string theory.

The basic mistake of Quantum Mechanics is a mistake of theory. To speak even more directly, it is a lack of precision in defining terms. In Miles Mathis' paper A Physical Point has No Dimensions it is shown that we must differentiate between a real point and a mathematical point. (This principle is used in the formal disproof of the Copenhagen interpretation which will be shown further on.)

Throughout history we have failed to make this distinction many times and it has cost us clarity in many fields. This imprecision has lain at the foundation of the calculus since the beginning and it has since infected all physical and mathematical fields. (See MM's paper: A Revaluation of Calculus)

Once you can understand the faulty assumptions concerning a point and its misuse in calculus, it will be clear that the basic problem of Quantum Mechanics is one of mistaking the math for the reality. Applied mathematics represents physical reality, but it is not that reality itself.

A mathematical point represents a physical point, but it is not that point itself. This is not simply a matter of metaphysics or semantics, since the difference between the mathematical point and the physical point is not just a matter of words or ideas. The difference between the two points can be stated in mathematically precise language. There is nothing "fuzzy" about it:
A physical point has no mathematical dimensions. A mathematical point has at least one mathematical dimension (and more commonly has two or more).
You can perform mathematical calculations upon a mathematical point, but you cannot perform mathematical calculations upon a physical point. That is why we create the mathematical point in the first place: so that we can do math.

The fundamental problem of Quantum Mechanics is a problem of the same sort. It is a mistaking of the math for the reality. The current theory of QM starts with the assumption that the probability wave is the reality. But the probability wave is the math. The math cannot be the reality. The math represents the reality. But it is not logically equivalent to the reality.

Heisenberg’s main fault therefore was not in his math but in the interpretation of that math. He made a simple definitional error, one of equating the math with the reality. Bohr accepted this error, it became the famous Copenhagen interpretation, and particle physics has followed it ever since. All of the biggest paradoxes in QM are caused by this error. Superposition and entanglement, for instance, are both caused by mistaking the math for the reality. Superposition was historically just an addition of wave amplitudes. In Quantum Mechanics, these waves are probability waves, and so superposition seems to imply, in some circumstances, a multiple existence. Schrodinger’s cat is both alive and dead until we open the box.

The entire problem is in assuming that the math is the reality. It is not. The math is the math, and the reality is the reality. The math in QM is statistical. The wave is a probability wave. Therefore the math can never transcend the probability. Probability math cannot fully represent reality. Even regular math cannot fully represent reality, in that the dimensions will always be incommensurate: mathematical fields cannot match physical fields due to the fact that you cannot mathematically represent (or graph) a zero-dimensional variable. But probability math represents reality even less fully, for obvious reasons. Probability math gives us only probabilities.

This used to be common sense. Mathematicians understood that probabilities were probabilities. Probabilities were imprecise, due to the very definition of the word. But scientists in the 20th century could not live with this imprecision. They were so proud of their new theory that they could not bear to admit that it was not a full expression of reality. They could not live with the “gap” in knowledge. So they simply closed the gap, by main force. They just defined probability as reality. They said, in effect, “This is what we know. Our math is all we know and it is all we can know. Therefore, it is reality for us. Therefore it is reality.”

Until the 20th century, the first assumption of science was that the physical world existed. Quantum Mechanics has overturned that assumption. What exists for the modern physicist is the mathematics. By closing the gap between probability and reality, Heisenberg made the math the reality. But math is an abstraction and therefore an idea. In this way, modern physicists are idealists. They have accepted the argument of Bishop Berkeley without realizing it. (See "the full discussion on Bishop Berkeley philosophy on MM's site.)

The greatest difference between Heisenberg and Bishop Berkeley is that Heisenberg’s argument directly concerns math. Math is the idea that seeds the idealism. But this makes Heisenberg’s idealism quite easy to disprove. To disprove Heisenberg’s idealism, all I have to do is define the gap between his math and reality using his math. I have already done this. I have shown that the gap between a mathematical point and a physical point is not just a prejudice. This gap can be defined in precise mathematical terms. A physical point has zero dimensions. A mathematical point has one or more dimensions. These two definitions are not metaphysical prejudices. They are mathematical statements with real content. To say it another way: the "field" of reality is always at least one dimension removed from any mathematics. It must be by all the rules of logic and by the definition of "math" of "field" and of "number". This means that the gap between math and reality cannot be closed.

It does not matter what existential status you give to "math" or to "reality". It does not matter whether you believe that one, both, or neither exists, by any meaning of the word exist. The only thing that is important is that math and reality are not and cannot logically be equivalent. You cannot close the gap. You cannot say that math is reality. If you do so, you are making a logical and mathematical error. You are being inconsistent, since you are saying that mathematics is your primary operational tool or term, and then you are jettisoning a logical finding of that mathematics to suit yourself.

In this way mathematical idealism is the prejudice. Heisenberg makes mathematics primary in his definition of reality, and then he proceeds to close the gap between mathematics and reality to suit his own desire. But his own mathematics defines that gap. To close the gap, he must ignore his own mathematics. In doing so, he has killed his own god, slaughtered his own logic. You cannot accept mathematics to get you from point A to point B, and then ignore that same mathematics to get you from point B to point C. That is what Heisenberg has done, and that is what Quantum Mechanics has done.

You will say that QM mathematics is not traditional mathematics, and that therefore my argument fails. But QM mathematics is derived from traditional mathematics. QM has not supplanted calculus and linear and vector algebra and so on. The foundations of math have not changed. My definition of the gap, as a necessary separation of dimensionality, must affect QM just as much as it affects all other math and science. Besides, it is quite easy to show mathematically that probability math creates a wider gap than calculus and linear algebra and so on, not a smaller gap. That is all that it is necessary for me to show. I don’t even have to show it, I just have to remind the reader that it is already accepted by everyone, including those in QM, QED, QCD and string theory. No one in the history of the world has ever argued that probability math is more precise than addition or subtraction. But the only way to counter my argument would be to suggest that probability math somehow closes the gap simply by being probability math. The definition of "probability", by itself, dictates against this.

Formal disproof of the Copenhagen interpretation

(No math or symbols are used and not stenography but rather direct and broad communication in simple sentences. The bold parts are the formal parts of the proof; the italicized parts may be taken by purists as commentary or elucidation for non-purists.)

  • Definition 1: A physical point, line, curve, or figure exists in the physical world. This world we call reality.
  • Definition 2: A mathematical point, line, curve, or figure represents the physical world. It is therefore an abstraction of the physical world.
  • Definition 3: A physical point has zero dimensions and may not be graphed, diagrammed, or mathematically represented in any way, including the assigning of a number to it. A mathematician cannot possibly assign a number or variable to a physical point.
  • Definition 4: Mathematics must be performed on a mathematical point, which point must have at least one dimension. A point diagrammed on one axis (a line) has one dimension. A point diagrammed on two axes (a Cartesian graph) has two dimensions, and so on. Assigning a number or potential number (variable) or symbol to a point automatically assigns it at least one dimension.

  • Deduction 1: deduced from def. 3: A point drawn on a piece of paper or on a computer screen or diagrammed upon the memory is a mathematical point, not a physical point. This is because we draw or diagram the point in order to assign it a number or variable or other symbol. If we do not assign it a number or variable or at least one dimension, then it is useless to us mathematically or as an abstraction. In that case it remains a dot on a piece of paper, which is, of course, a physical thing. Once we use it mathematically, however, its physical status is overwritten and is no longer important. Its use determines its status.
  • Deduction 2: deduced from defs. 3 & 4: All mathematics and all logical symbolism is at least one dimension away from the physical world it represents.

  • Result 1: from ded. 2: A mathematical field cannot be dimensionally equivalent to the physical field it represents. This means that mathematics cannot fully express reality. It also means that mathematics cannot be defined as reality.

    Conclusion: Quantum Mechanics is applied mathematics. As such, it must be dimensionally inequivalent to the physical situation it represents. The fields that QM creates are not physical fields. Therefore QM cannot claim that its mathematical field is reality. This falsifies the Copenhagen interpretation.

Quantum Mechanics is only a statistical representation of reality. Reality cannot be fully symbolized; its ultimate qualities must be deduced. That is to say, we must use reason to interpret our symbols as best as we can, avoiding contradiction.

Critics will say that what was assumed is what was intended to be proved, since Definition 1 is logically equivalent to the conclusion. This has a twofold answer: 1) in every deduction, the conclusion is contained in the definitions. That is what deduction means. 2) the Conclusion and Definition are similar, but they are not strictly equal. The Conclusion is that the physical world exists and that mathematics does not define it. Definition 1 is only that the physical world exists—a definition that contemporary physicists would agree with, even those physicists who believe that the math of QM does define the existence of the physical world.

The crucial difference lies in Definition 4, since contemporary mathematicians and physicists will not have noticed the truth of this until now. They will have accepted Definition 3 as the definition of point underlying all their math. The necessary separation between 3 and 4 will then force them to admit that the final conclusion is correct.


Quantum Mechanics has been astonishingly successful in many ways. It has given us a good first look into the mechanics of the very small. But it is time to get past the self-congratulations and the backslapping and to realize that both mathematically and theoretically the explanation is very, very partial.

Physicists never tire of pointing out how accurate QM has been, but this accuracy is due in large part to the amount of fudging that has been allowed. If you are allowed to correct your math after every experiment—without ever being required to explain exactly how the mathematical corrections tie into the theory—then of course your math is going to be very accurate. Heuristics is always more accurate, since it is math that is chosen for the specific purpose. Heuristics is rigged math, and rigged math would be expected to be quite useful.

QM, as it stands now, is top-heavy, loaded with weighty accretions that the initial walls cannot bear. That is why we get roof collapses like the "spooky" forces. We reach impasse after logical impasse not because nature is illogical, as Bohr or Feynman would have it, but because our floor plan was illogical to begin with. The theory is causing the problems, not nature. Light is not unexplainable; it is only unexplainable by current theory. Likewise gravity and the rest.

In the whole history of science we have never blamed nature when our theories fell short of her. Now for some reason we do. We actually give more regard to our math than we do to nature. We no longer believe in nature or the physical world. We believe in our math. We have defined our math as the physical world. Math is now reality.

If our math does not make sense, then this means reality does not make sense. It is a convenient theory, since it means we will never again be wrong. Whatever theoretical or mathematical muddle we find ourselves in, we will imagine it is a necessity. A paradox is no longer a sign of a flaw in reasoning; a paradox is a sign that we are one to one, lip to rosy lip, with nature—nature who is herself a paradox. We stopped doing basic physics a century ago, and we should deeply regret it.

We have suffered theoretical shipwreck, and no amount of pointing to our feats of engineering can hide that any longer. Our two proudest achievements—Quantum Mechanics and Relativity—have brought us to a dead end. We cannot continue to toy with 11-dimensional maths, parallel universes, baby black holes, and the like, no matter how much money we make selling this drivel to the cheap sheets.

We first need to learn something about the mechanics of light propagation, about the mechanics of gravity, the mechanics of circular motion, the mechanics of electromagnetism, and so on. Rather than trying to link gravity to the other primary forces, we must reevaluate not only the theory of gravity, but also QM itself.

We have daily estimates on the size and age of the universe, and how many nanoseconds after creation the first electron congealed, but we can no more explain the mechanics of gravity than could Archimedes. We give cute names to sub-sub-subparticles and propose to measure their wobbles to the trillion-trillionth part of an eyelash, but we cannot explain the orbit of the moon.

We know nothing about dark matter: we do not know what it might consist of, how it was created, or if it exists at all beyond certain small possible categories, yet we are making grand estimates of how much there is in the universe. When we This is what happens when math describes reality instead of physics and imagination invents "god-particles" to create mass.

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