Abstract: Research in superstring theory rests upon the theoretical physics tradition that seeks mathematical simplicity and beauty in the fundamental laws of nature. In this article I show how string theorists have interpreted and adapted to their own needs the consensually declared beauty of some exemplary theories of twentieth century physics: electromagnetism, quantum mechanics, particle physics, and general relativity. I also explore the specific circumstances under which superstring theory began to be considered a beautiful theory. The problems raised by these reinterpretations are then discussed.
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SELECTED READINGS FOR ESSAY 3 (I)
SELECTED READINGS FOR ESSAY 3 (I)
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Introduction
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Many physicists are aware of the fact that at the very beginning of modern science, Galileo Galilei, the founding father of the discipline, was convinced that God had written the great book of nature in geometrical and mathematical characters. They are acquainted with what Galileo wrote in 1623 in Il Saggiatore: “This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is humanly impossible to comprehend a single word of it, and without which one wanders in vain through a dark labyrinth.”[source] Four hundred years after Galileo, contemporary physicists embrace his philosophical stance. Eugene Wigner, considered to be one of the first theoretical physicists to consistently make recourse to symmetry arguments, was a key figure in this regard. He once asserted that ‘‘the statement that the laws of nature are written in the language of mathematics was properly made three hundred years ago [in a note he also notices that this original idea ‘‘is attributed to Galileo’’]; it is now more true than ever before.’’[source] Wigner wrote this in an article that has become ever since a reference to all those interested in the role of mathematical thinking in theoretical physics. Wigner’s creed on this point is similar to Einstein’s; as in that famous quote where Einstein declares that “the most incomprehensible thing about the world is that it is comprehensible.” Of course, “comprehensible” here means mathematically comprehensible.
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Nowadays, references to Galileo and the book of nature are very common. At the 1980 Nobel Conference, Chen Ning Yang, one of the most influential theoretical particle physicists of the last century, said to his attentive audience: “It was Galileo who taught the world of science the lesson that you must make a selection, and if you judiciously select the things that you observe, you will find that the purified, idealized experiments of nature result in physical laws which can be described in precise mathematical terms. That is the truly great lesson of Galileo, and that, of course also introduced the beginning of the quantitative science of physics. Galileo’s was a profound and beautiful idea.”[source]
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According to this belief, widely held among theoretical physicists, the natural world coexists with, and reflects, a hidden changeless reality where mathematical symbols, and their relations, live. What we experience by means of our senses is then the chaotic projection of an ordered transcendent world. This is a brief outline of the Platonist view of the correspondence between the physical world and mathematics. To this ontological stand, modern physicists have added a methodological one. The latter can be summarized as follows: since mathematics is an exact and logical system, the laws of nature can be ‘‘grasped by pure thought.’’ Or, in other words, the fundamental laws of nature can, in principle, be discovered by mathematical reasoning, and without any resort to experiments or observations. Maybe this is not precisely what Galileo thought, but, as we shall see, it is the posture taken by many contemporary physicists, especially string theorists. This prevalent historical interpretation of physics research, highly valued during the twentieth century, has marked in a profound manner the way these theoreticians envisage their work.
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For some, including several prominent theoretical physicists, mathematical skills do not suffice to read the book of nature; a fine aesthetic sense is also required. Fifty years ago the prominent art historian Erwin Panofsky, following in the footsteps of the philosopher and historian of science Alexandre Koyré, declared:
*******You can read this blog for free! Please, do not copy its content.*******
Many physicists are aware of the fact that at the very beginning of modern science, Galileo Galilei, the founding father of the discipline, was convinced that God had written the great book of nature in geometrical and mathematical characters. They are acquainted with what Galileo wrote in 1623 in Il Saggiatore: “This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is humanly impossible to comprehend a single word of it, and without which one wanders in vain through a dark labyrinth.”[source] Four hundred years after Galileo, contemporary physicists embrace his philosophical stance. Eugene Wigner, considered to be one of the first theoretical physicists to consistently make recourse to symmetry arguments, was a key figure in this regard. He once asserted that ‘‘the statement that the laws of nature are written in the language of mathematics was properly made three hundred years ago [in a note he also notices that this original idea ‘‘is attributed to Galileo’’]; it is now more true than ever before.’’[source] Wigner wrote this in an article that has become ever since a reference to all those interested in the role of mathematical thinking in theoretical physics. Wigner’s creed on this point is similar to Einstein’s; as in that famous quote where Einstein declares that “the most incomprehensible thing about the world is that it is comprehensible.” Of course, “comprehensible” here means mathematically comprehensible.
*******You can read this blog for free! Please, do not copy its content.*******
Nowadays, references to Galileo and the book of nature are very common. At the 1980 Nobel Conference, Chen Ning Yang, one of the most influential theoretical particle physicists of the last century, said to his attentive audience: “It was Galileo who taught the world of science the lesson that you must make a selection, and if you judiciously select the things that you observe, you will find that the purified, idealized experiments of nature result in physical laws which can be described in precise mathematical terms. That is the truly great lesson of Galileo, and that, of course also introduced the beginning of the quantitative science of physics. Galileo’s was a profound and beautiful idea.”[source]
*******You can read this blog for free! Please, do not copy its content.*******
According to this belief, widely held among theoretical physicists, the natural world coexists with, and reflects, a hidden changeless reality where mathematical symbols, and their relations, live. What we experience by means of our senses is then the chaotic projection of an ordered transcendent world. This is a brief outline of the Platonist view of the correspondence between the physical world and mathematics. To this ontological stand, modern physicists have added a methodological one. The latter can be summarized as follows: since mathematics is an exact and logical system, the laws of nature can be ‘‘grasped by pure thought.’’ Or, in other words, the fundamental laws of nature can, in principle, be discovered by mathematical reasoning, and without any resort to experiments or observations. Maybe this is not precisely what Galileo thought, but, as we shall see, it is the posture taken by many contemporary physicists, especially string theorists. This prevalent historical interpretation of physics research, highly valued during the twentieth century, has marked in a profound manner the way these theoreticians envisage their work.
*******You can read this blog for free! Please, do not copy its content.*******
For some, including several prominent theoretical physicists, mathematical skills do not suffice to read the book of nature; a fine aesthetic sense is also required. Fifty years ago the prominent art historian Erwin Panofsky, following in the footsteps of the philosopher and historian of science Alexandre Koyré, declared:
Galileo’s aesthetic judgement [italics added] – whether of music, painting or poetry – thus appear to be dictated by a consistent principle or, if you will, by an insurmountable prejudice: a classicistic prejudice in favor of simplicity, order, and separation des genres [italics in the original], and against complexity, imbalance, and all kinds of conflation.[source]
Thus, modern science, some have argued, has always required a “sense of beauty” from the scientist; more or less in the same way as the fine arts does.
Many theoretical physicists today sustain that the main goal of research carried out within the domain should be the discovery of these imperishable beautiful mathematical truths. As particle physicist Steven Weinberg, Nobel laureate and enthusiastic supporter of the theory of superstrings, puts it: ‘‘There is a ‘hard’ part of modern physical theories (‘hard’ meaning not difficult, but durable, like bones in paleontology or potsherds in archeology) that usually consists of the equations themselves, together with some understandings about what the symbols mean operationally and about the sort of phenomena to which they apply.’’[source] And he states firmly that: ‘‘What drives us onward in the work of science is precisely the sense that there are truths out there to be discovered, truths that once discovered will form a permanent part of human knowledge.’’[source] Additionally, as we pointed out, these ‘‘truths out there to be discovered’’ are thought to be as beautiful as artworks: “But the great equations of modern physics are permanent part of scientific knowledge, which may outlast even the beautiful cathedrals of earlier ages.”[source] (This is the sentence with which Weinberg chose to close an edited volume on the relationship between aesthetics and science. Authors include historians of science and professional scientists. Among these, several are theoretical physicists: two of them were honored with a Nobel Prize, Weinberg and Frank Wilczek, and the other is a well-known public figure, Roger Penrose.) In addition to the above aesthetico-ontological position, in the same text Weinberg also sustains the epistemological thesis putting forward that a fine aesthetic sense can lead us to the most fundamental laws of nature. Theoretical physicists from other fields share this belief. Stephen Hawking, a gravitational physicist and a public supporter of superstring theory, claims that ‘‘to a large extent, we shall have to rely on mathematical beauty and consistency to find the ultimate theory of everything.’’[source]
Before concluding this introduction, it must be said that this metaphysical discourse about the book of nature and its supposed beauty is not exclusively oriented to senior and young physicists (as for example in Yang’s talk and Weinberg’s book). By diverse means, such as magazines and science books, it is also addressed to the more general public. For instance, in one of the first popular books dealing with string theory, science writer Paul Davies wrote:
Perhaps the greatest scientific discovery of all times is that nature is written in mathematical code. We do not know the reason for this, but it is the single most important fact that enables us to understand, control, and predict the outcome of physical processes. Once we have cracked the code for some particular physical system, we can read nature like a book.[source]
Other popular books, such as those written by Penrose and Hawking, are abound with comments of the same sort. In The Large, the Small and the Human Mind, Penrose states: “The more we understand about the physical world, and the deeper we probe into the laws of nature, the more it seems as though the physical world almost evaporates and we are left only with mathematics.”[source] At the beginning of the second chapter he also mentions the “famous lecture” Eugene Wigner delivered in 1960 and which above we have referred to.
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In this paper, I try to seize the meanings of the terms ‘‘simplicity,’’ ‘‘elegance,’’ and ‘‘beauty,’’ in modern theoretical physics and especially in superstring theory. Firstly, I revise the different interpretations that the above terms received in four fundamental theories of twentieth-century physics: electromagnetism, quantum mechanics, particle physics, and general relativity. At the same time, I examine how superstring theorists have interpreted them. Finally, I conclude with a section on the relationship between string theory, its beauty, and the experimental tradition in physics. My intention is to provide a context for understanding declarations made by string theorists such as the following by Andrew Strominger: ‘‘There is disappointment that despite all our efforts, experimental verification or disproof still seems far away. On the other hand, the depth and beauty of the subject, and the way it has reached out, influenced and connected other areas of physics and mathematics, is beyond the wildest imaginations of 20 years ago.’’[source] Comments of these kinds are repeated time and time again. For instance, Dennis Overbye, science writer and deputy science editor of The New York Times, a couple of years ago declared that: “As of now, however, there is scant evidence other than the beauty of their equations that the string theorists are right.”[source] But, what do they mean by beauty? Can we consider superstrings to be a beautiful theory? And, what are the implications of this? I’ll try to answer.
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SELECTED READINGS FOR ESSAY 3 (I)
SELECTED READINGS FOR ESSAY 3 (I)
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