10 dimensions
But string theory was just getting started and quickly disintegrated.
Claude Lovelace of Rutgers University found that there was a subtle mathematical flaw in the original Veneziano model that could not be eliminated unless there were 26 dimensions of space-time.
Similarly, the superstring models of Neviu, Schwartz, and Ramund are only possible if they have 10 dimensions. The discovery shocked physicists. In the entire history of science, I have never heard of such a thing before. In any other field, we will not find a single theory that needs to choose the dimension that suits itself. For example, the theories of Newton and Einstein can hold in any dimension. For example, the famous inverse square law of gravity can be summed up in four-dimensional space as an inverse-cube law. String theory, however, can only exist in certain dimensions.
From a practical application point of view, this is a catastrophic blow. Everyone believes that our world exists in three spatial dimensions (length, width, and height) and one dimension of time.
If you accept a universe with 10 dimensions, it means that the theory is simply science fiction. String theorists thus became the laughing stock of people. (John Schwartz remembers a time when Richard Feynman jokingly said to him in the elevator, John, how many dimensions are you living in today?) But no matter how hard string physicists try to save the model, it quickly dies. Only some die-hards continue to work on this theory. It was a period of solitude.
In those dismal years, there were two diehards who insisted on this theory, one was John Schwarz of the Galifni Institute of Technology, and the other was Joel Scherk of the École Normale Supérieure in Paris.0 Until then, it was thought that string models were only used to describe strong nuclear interactions. But there's a problem: The model predicts a particle that doesn't appear in a strong interaction, a weird particle with a mass of zero and two quantum units of spin. All attempts to get rid of this annoying particle have failed. Every time this spin_2 particle is eliminated, the model collapses and loses its magical properties. Somehow, this unpopular spin-2 particle seems to be hiding the secret of the whole model.
So Sdierk and Sdiwarz ventured to guess that this flaw might actually bring good luck. If they explain this tangled spin-2 particle as a graviton (gravitational particle produced from Einstein's theory), then the theory is actually in the middle of Einstein's theory of gravity! (In other words, Einstein's general theory of relativity only emerged as the lowest-level vibration or note of a superstring.) Ironically, in other quantum theories, physicists try to avoid talking about gravity, whereas string theory uses gravity. (In fact, this is one of the attractive properties of string theory, that is, it must contain gravity, otherwise the theory will not make sense.) With such a bold leap, scientists realized that the original string model had been misused in the wrong place. It is not just a theory of strong nuclear interactions, but rather a theory of everything. As Witten emphasized, the /' string theory is extremely appealing because it forces gravity into us. All known string theories that make sense include gravity. While the quantum field theory as we know it simply cannot tolerate gravity, it is indispensable in string theory. ”
However, Scherk and Schwarz's most influential ideas were ignored by all. If string theory were to be used to describe both gravitational and subatomic worlds, it would mean that those strings could only be io_33 centimeters long (i.e., Planck's length); in other words, they were a billion times smaller than protons. For most physicists, this is difficult to accept.
But by the mid-1980s, other attempts to establish a unified field theory had been disrupted. Theories that naively want to add gravity to the Standard Model are bogged down in supernumerary (I'll get to that shortly). Every time someone wants to artificially combine gravity with other quantum forces, mathematical contradictions arise and the theory is shot. (Einstein believed that perhaps God had no other choice in creating this universe.) This may be because only one theory can avoid all these mathematical contradictions. ）
There are two kinds of mathematical contradictions in this category. The first is the problem ofinfinities. Normally, quantum fluctuations are very weak. Quantum effects are only a small correction to Newton's laws of motion. That's why, in most cases, we can ignore them in the macroscopic world, because they are too faint to be perceived. However, when gravity is converted into a quantum theory, these quantum fluctuations actually become infinitely large, which is unreasonable. The second mathematical contradiction has to do with the "exception condition," which means that when we add quantum fluctuations to a theory, some small aberrations occur in that theory. These anomalies destroy the original symmetry of the theory, causing it to lose its original force.
For example, we can imagine a rocket designer who had to design a smooth, streamlined ship.
Used to cross the atmosphere. The rocket must be very symmetrical in order to reduce air friction and drag (in this case, cylindrical symmetry, that is, when we rotate the rocket on its axis, it is always in the same shape; This symmetry is called 0(2)). But there are two potential problems. First of all, due to the very high speed of the rocket, vibrations occur in the wings. For subsonic aircraft, this vibration is quite small. However, when flying at a speed far beyond the speed of sound, this fluctuation will become stronger and stronger, eventually tearing the wings off. Similar divergences constantly plague any kind of quantum gravity theory n2]. In general, they are small enough to be ignored, but in the theory of quantum gravity they occur on the spot.
The second problem with the spacecraft is that tiny cracks may appear on the hull. These flaws all cause the ship to lose its original 0(2) symmetry. Although these imperfections are very minor, they can spread until they eventually disintegrate the ship. By the same token, such "cracks" can also break the symmetry of gravity theory.
There are two ways to solve these problems. The first method is to find some headaches and foot-wrenching solutions, such as using glue to patch up cracks, and reinforcing the wings with stick support, hoping that the rocket will not explode in the atmosphere. Historically, most physicists who have tried to combine quantum theory with gravity have used this approach. They want to confuse these two issues. The second approach is to reinvent the wheel, adopting new shapes and novel materials that can withstand the enormous pressures of spaceflight.
Physicists have spent decades trying to piece together a theory of quantum gravity, only to find it devastated and full of countless strange and exceptional conditions. Slowly, they realized that the solution might be to abandon this way of treating headaches and feet and adopting a completely new theory.