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Full-Text Articles in Physics
Why Was Nicholson's Theory So Successful: An Explanation Of A Mysterious Episode In 20 Century Atomic Physics, Olga Kosheleva, Vladik Kreinovich
Why Was Nicholson's Theory So Successful: An Explanation Of A Mysterious Episode In 20 Century Atomic Physics, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In the early 1910s, John Nicholson suggested that all atoms are formed by four basic elementary particles. This theory had a spectacular match with observations: it explained, with an unbelievable accuracy of 0.1, the atomic weights of all 92 elements known at that time. Specifically, it was shown that every atomic weight can be represented, with this accuracy, as an integer combination of four basic atomic weights. However, in a few years, this theory turned out to be completely wrong: atoms consist of protons, neutrons, and electrons, not of Nicholson's particles. This mysterious episode seems to contradict the usual development …
Need For Shift-Invariant Fractional Differentiation Explains The Appearance Of Complex Numbers In Physics, Olga Kosheleva, Vladik Kreinovich
Need For Shift-Invariant Fractional Differentiation Explains The Appearance Of Complex Numbers In Physics, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Complex numbers are ubiquitous in physics, they lead to a natural description of different physical processes and to efficient algorithms for solving the corresponding problems. But why this seemingly counterintuitive mathematical construction is so natural here? In this paper, we provide a possible explanation of this phenomenon: namely, we show that complex numbers appear if take into account that some physical system are described by derivatives of fractional order and that a physically meaningful analysis of such derivatives naturally leads to complex numbers.
Why Physical Processes Are Smooth Or Almost Smooth: A Possible Physical Explanation Based On Intuitive Ideas Behind Energy Conservation, Olga Kosheleva, Vladik Kreinovich
Why Physical Processes Are Smooth Or Almost Smooth: A Possible Physical Explanation Based On Intuitive Ideas Behind Energy Conservation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
While there are some non-smooth (and even discontinuous) processes in nature, most processes are smooth or almost smooth. This smoothness help estimate physical quantities, but a natural question is: why are physical processes smooth or almost smooth? Are there any fundamental reasons for this ubiquitous smoothness? In this paper, we provide a possible physical explanation for emirical smoothness: namely, we show that smoothness naturally follows from intuitive ideas behind energy conservation.
A Possible (Qualitative) Explanation Of The Hierarchy Problem In Theoretical Physics, Olga Kosheleva, Vladik Kreinovich
A Possible (Qualitative) Explanation Of The Hierarchy Problem In Theoretical Physics, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the important open problem in theoretical physics is the hierarchy problem: how to explain that some physical constant are many orders of magnitude larger than others. In this paper, we provide a possible qualitative explanation for this phenomenon.
Why Strings, Why Quark Confinement: A Simple Qualitative Explanation, Olga Kosheleva, Vladik Kreinovich
Why Strings, Why Quark Confinement: A Simple Qualitative Explanation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In this pedagogical article, we recall the infinities problem of modern physics, and we show that the natural way to overcome this problem naturally leads to strings and to quark confinement.
Can We Preserve Physically Meaningful "Macro" Analyticity Without Requiring Physically Meaningless "Micro" Analyticity?, Olga Kosheleva, Vladik Kreinovich
Can We Preserve Physically Meaningful "Macro" Analyticity Without Requiring Physically Meaningless "Micro" Analyticity?, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Physicists working on quantum field theory actively used "macro" analyticity -- e.g., that an integral of an analytical function over a large closed loop is 0 -- but they agree that "micro" analyticity -- the possibility to expand into Taylor series -- is not physically meaningful on the micro level. Many physicists prefer physical theories with physically meaningful mathematical foundations. So, a natural question is: can we preserve physically meaningful "macro" analyticity without requiring physically meaningless "micro" analyticity? In the 1970s, an attempt to do it was made by using constructive mathematics, in which only objects generated by algorithms are …
Need For Simplicity And Everything Is A Matter Of Degree: How Zadeh's Philosophy Is Related To Kolmogorov Complexity, Quantum Physics, And Deep Learning, Vladik Kreinovich, Olga Kosheleva, Andres Ortiz-Muñoz
Need For Simplicity And Everything Is A Matter Of Degree: How Zadeh's Philosophy Is Related To Kolmogorov Complexity, Quantum Physics, And Deep Learning, Vladik Kreinovich, Olga Kosheleva, Andres Ortiz-Muñoz
Departmental Technical Reports (CS)
Many people remember Lofti Zadeh's mantra -- that everything is a matter of degree. This was one of the main principles behind fuzzy logic. What is somewhat less remembered is that Zadeh also used another important principle -- that there is a need for simplicity. In this paper, we show that together, these two principles can generate the main ideas behind such various subjects as Kolmogorov complexity, quantum physics, and deep learning. We also show that these principles can help provide a better understanding of an important notion of space-time causality.