String theory is one of the deepest mysteries that has not been fully understood, which is why it is defined only in 10 or 26 dimensions. If string theory is 3-dimensional, it cannot unify known laws of physics in any reasonable way. Therefore, it is high-dimensional geometry that is the core feature of string theory.
If we calculate how strings decompose and reorganize in N-dimensional space, we often find some meaningless terms unexpected occurrences, which damages those wonderful properties of string theory. Fortunately, these annoying terms are multiples of (N-10). Therefore, in order to eliminate these exceptions, we have no other way except to get N equal to 10. In fact, string theory is the only known quantum theory that specifically requires that the spatial and temporal dimension is fixed to a number.
Unfortunately, string theorists are currently having a hard time explaining why 10 dimensions are selected. The answer lies entirely in mathematics, within the range of a so-called modular function: whenever we use the KSV circle diagram generated by the interactive string, we encounter these strange modular functions, and the number 10 appears in the strangest place. These modular functions are as mysterious as an Oriental who studies them. If we had a thorough understanding of the work of this Indian talent, we might be able to understand why we live in our current universe.
The mystery of modular functions
Ramanujan ( Ramanujan ) is the strangest person in the history of mathematics and may also be the most strange person in the history of science. When he was 33 years old, he was unfortunately taken away by tuberculosis ; before that, he was regarded as a sudden supernova , illuminating the most hidden and meaningful corner of mathematics. Ramanujan works completely isolated from the mainstream of his field and can actually re-derive something equivalent to 100 years of Western mathematics alone. The tragedy of his life is that most of his work is wasting itself in rediscovering known mathematics. The fuzzy equations scattered in his notebook are these modular functions. These functions are the strangest things found in the history of mathematics. They reappear in far-reaching and inconsistent branches of mathematics. A function that appears repeatedly in modular function theory is now named Ramanujan function in memory of Ramanujan. This weird function contains an item with a power of up to 24.
In Ramanujan's work, the number 24 appears repeatedly. This is an example of what mathematicians call magic number . Magic numbers keep appearing when no one knows the reason, and appearing in places we didn't expect. Surprisingly, the Ramanujan function also appears in string theory. The number 24 that appears in the Ramanujan function is actually the source of magical offset in string theory. In string theory, each of the 24 modes in the Ramanujan function corresponds to some physical vibration of the string. Whenever the string performs its complex motion by decomposing and reorganizing in space-time, a large number of highly complex mathematical identity must be satisfied. These identities happen to be mathematical identities discovered by Ramanujan.
Because physicists add 2 dimensions when calculating the total number of vibrations that appear in the theory of relativity, this means that space-time must have 24+2=26 space-time dimensions.
When the Ramanujan function is generalized, the number 24 is replaced by the number 8. Therefore, the critical number of in superstring theory is 8+2, that is, 10. This is the origin of the 10th dimension. The string vibrates in 10 dimensions because in order to maintain self-consistent, it requires these generalized Ramanuqin functions. That is, physicists don't understand at all why 10 and 26 dimensions are chosen as the dimensions of the string. It is as if there is some kind of numerology to be proven in these functions that no one understands. It is these magic numbers that appear in the elliptical mode function that determines that the -dimensional of space-time is 10.
In short, the origin of the 10-dimensional theory is as mysterious as Ramanujan himself. When the listener asked why nature might exist in 10 dimensions, physicists were forced to answer, "We don't know." We vaguely know why certain dimensions of space-time are selected (otherwise the string cannot vibrate in self-consistent quantum form), but we don't know why these special numbers are selected. Maybe the answer will be until it is discovered in Ramanujan's lost notebook.
creates another century of mathematics
Ramanujan was born in Erod, India in 1887. Although his family is Brahmin (the highest caste in India), the whole family is still poor and rely on Ramanujan's father to make a living as a staff member in the office of a clothing dealer.
html From 0 to 10 years old, Ramanujan obviously doesn't like other children. Like Riemann , he is famous throughout the village for his amazing computing power. As a child, he has re-derived the Euler identity between the trigonometric function and the exponent.There is a turning point in every young scientist's life, and for Einstein , it is an obsession with observing the compass needle. For Riemann, it is a book by Lejeune on Number Theory . For Ramanujan, it was a vague and forgotten math book he stumbled upon by George Carr. This book is famous for the following fact: It records the only time that Ramanujan discovered modern Western mathematics as people know. According to his sister, "It was this book that inspired his genius. He was determined to build the formula given in the book. He had no other reference books, and as long as he was interested, every solution was part of the research.
Because of his talent, he was able to get a scholarship to go to middle school. But because he was tired of the boredom of classroom teaching and his concentration on the equations that kept lingering in his mind, he did not enter the senior class and his scholarship was cancelled. After being frustrated, he ran away from home. Finally he returned home, but was only sick and failed the exam again.
With the help of his friends, Ramanujan managed to become a low-level clerk at the Port Trust of Madras, earning only a paltry £20 a year. But like Einstein at the Swiss Patent Office, it allowed Ramanujan to pursue his dreams in his spare time. Ramanujan then sent some of the results of his "dream" to three well-known British mathematicians, Hope to get in touch with other mathematical minds. After receiving this letter from the unofficially educated unnamed Indian clerk, two mathematicians threw it away immediately. The third was the outstanding Cambridge University mathematician Hardy . Due to his lofty prestige in Britain, Hardy was used to receiving mail from weirdos. In the thick scribbled handwriting, he noticed many of the mathematical theorems that had been discovered. He thought it was a clear stolen work and threw it away. But something was wrong, and something disturbed him, he couldn't help but pay attention to the monster letter.
At dinner on January 16, 1913, Hardy and his colleague Littlewood discussed the monster letter and decided to read its content again. The beginning of the letter was very naive,
Please forgive me for introducing myself to you, I am a clerk in the Account Office of the Port Trust Company of Madras, and my annual salary is only 20 GBP.
But the letter from this poor Madras clerk contained many theorems that Western mathematicians knew nothing about. Together, it contained 120 theorems. Hardy was stunned. He remembered that proofing several of them "completely convinced me." He recalled that
I had never seen even a little similar before. Just a glance at them was enough to show that they could only come from the hands of top mathematicians.
Littlewood and Hardy reached the same assertion: This is obviously a masterpiece of genius, who was committed to re-deriveing the century-old mathematics of Europe. He was crossing insurmountable obstacles, A poor, lonely Indian uses its intelligence to fight the wisdom accumulated by Europeans.
Hardy asked Ramanujan to go to him, and after a while, he arranged for him to stay in Cambridge in 1914. Ramanujan was able to communicate regularly with his peers (European mathematical community) for the first time. So he began his vigorous work: a short and tense three years of cooperation with Hardy at Trinity College of Cambridge .
Later, Hardy tried to evaluate the mathematical skills Ramanujan possessed. He gave Hilbert, one of the greatest mathematicians in the 19th century, to Ramanujan, he gave 100. Hardy gave himself 25.According to Hardy's recollection,
I remember that he lived in Putnei once when he was sick. I went to see him and was riding a taxi carriage with the number 1729. I noticed that this number seemed to be a pretty boring number, and I just hope it was not a bad omen. Ramanuqin immediately realized that 1729 is a very interesting number, which is the smallest number that can be represented in two different ways as the sum of two numbers.
It is the sum of 1×1×1 and 12×12×12, and it is also the sum of 9×9×9 and 10×10×10. He can immediately use formulas to list complex theorems that require modern computers to prove.
After working with Hardy for three years, Ramanujan couldn't afford to get sick. He managed to return to his hometown in 1919 and died of illness a year later.
Ramanujan's legacy
Ramanujan's legacy is his mathematical study. His research consists of 4,000 formulas written in three large volumes of notebooks. Those formulas have incredible powers without any comments; those confusing theorems have no proof. However, in 1976, new discoveries were made. A 130-page lost paper containing the results of his last year of his life was discovered by chance in a box at , Trinity College, . Now this is called Ramanujan's "lost notebook". Mathematician Asky said when adding a bet on the "lost notebook":
The work of his death in the year he faced death was equivalent to the life of a great mathematician. The work he accomplished was incredible. If it were a novel, no one would believe it.
Looking at the calculation of Ramanujan's equation, it is like we have been influenced by Beethoven for many years and suddenly heard another kind of music, a kind of harmonious rhythmic blending, mysterious and wonderful oriental music that we have never heard in Western music.
As physicists know, "events" will not happen for no reason. When physicists complete a lengthy, difficult calculation, and suddenly thousands of annoying items miraculously sum to zero, they know that this will not happen without a deep inner cause. Now, physicists know that these "events" indicate that symmetry is at work. As far as strings are concerned, this symmetry is called conformal symmetry, that is, the symmetry of the world face of stretching or deforming the string.
This is exactly where Ramanujan's work works. In order to protect the original conformal symmetry from being destroyed by quantum theory, a large number of mathematical identities must be miraculously satisfied. These identities happen to be the identities of the Ramanujan modular function.
The laws of nature are simplified when expressed in high dimensions. However, given quantum theory, the correct statement should now be that the laws of nature are simplified when expressed in a self-consistent manner in a high dimension. It is crucial to add the word to self-consistent . This restriction forces us to use Ramanujan's modulus function, which fixes the spatial and temporal dimensions to 10. This gives us a decisive clue to explain the origin of the universe.
Einstein often asks himself whether God has a choice to create the universe. According to superstring theorists, once we ask quantum theory to be unified with general relativity , God has no choice. They declare that the self-consistent alone will force God to create this universe as he created.
Although the mathematical complexity introduced by superstring theory has reached a dizzying level and shocked mathematicians, critics of the theory still tapped it at its most vulnerable point. They point out that any theory must be testable. Since the theory of electron volt Planck energy defined at 10^28 is untestable, superstring theory is not a real theory.
As mentioned above, the key problem lies in theory rather than experiments. If we are extremely smart, we can completely solve this theory and find the true non-perturbation solution. However, this cannot be a reason why we do not seek to use experimental means to verify the theory. To test the theory, we must wait for the signal from the tenth dimension.
