Why string theory requires extra dimensions

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String theory requires extra dimensions for mathematical consistency. The number of dimensions depends on the specific theory, but all string theories require more than the four dimensions we’re aware of. For example, M-theory predicts 11 dimensions, while Bosonic string theory requires 26. 

String theory is a candidate for a theory of everything, which is a single mathematical framework that describes the entire known universe.  String theory models subatomic particles as one-dimensional “stringlike” entities, rather than zero-dimensional point particles.  The way strings vibrate determines what type of particle it is. However, physicists have discovered that strings need more space than our three dimensions to express all their vibrational patterns. 

String theory requires ten dimensions for quantum mechanical reasons. Some symmetries that the theory needs to make sense are spoiled in the classical->quantum transition in anything other than 10D. 

Despite precise experiments, no deviations that could indicate the presence of extra dimensions have ever been found. However, if the size of the compact space is of order the string scale (10-33 cm), we wouldn’t be able to detect the presence of these extra dimensions directly.

If the universe does not have enough dimensions to give strings the freedom they need to explain all of physics, then we must add most dimensions to the universe. Modern versions of string theory state that we have either ten or eleven spatial dimensions (the difference come from different formulations of the theory

According to Quora, the reason string theory requires 26 dimensions is because the dynamics of the theory shouldn’t depend on the numbers used to track a string’s location in spacetime

According to physics.stackexchange.com, if the particles are massless, they have fewer internal states than massive particles. For them to be massless and preserve Lorentz symmetry, M2=0, so d=26. 

According to mathoverflow.net, bosonic string theory is the least sophisticated candidate, and it says that the world is 26 dimensional. However, it’s not realistic due to the presence of tachion

According to Space.com, current versions of string theory require 10 dimensions. Superstring theory posits that the universe exists in 10 dimensions, with nine dimensions of space and one dimension of time. 

String theory predicts the number of dimensions of spacetime, which is unique among other theories of physics. For the mathematics of string theory to be consistent, the number of dimensions of spacetime must be 10. 

String theory also requires the existence of 10 space-time dimensions for the strings to wiggle around in. Every vibration mode corresponding to a matter particle must come with another mode signifying a force particle.

A space is considered infinite-dimensional if it doesn’t have a finite covering dimension. 

String theory is a theoretical framework that attempts to explain how and why the universe is the way it is. It postulates that the universe’s fundamental building blocks are not point particles, but rather small loops or strings that move around and interact with each other in space and time. 

String theorists believe that our world has more than three dimensions. Superstring theory requires spacetime to have 10 dimensions, with three dimensions of regular space, one dimension of time, and six dimensions of hyperspace.

According to string theory, the universe is one of an infinite number of parallel universes. String theorists believe that there are nearly infinite possible arrangements of the curled-up dimensions. 

String theory predicts a multiverse with 10^500 different universes. Each compactification produces a different spacetime, meaning that each universe has its own laws of physics

String theory is a part of quantum physics. It’s a theoretical framework that combines the two main pillars of quantum physics: quantum mechanics and the concept of general relativity

String theory is an attempt to provide a more fundamental and unified description of the universe, including gravity, within a quantum framework. Quantum mechanics makes its predictions in the form of probabilities. 

Here are some differences between string theory and quantum theory: 

  • Quantum field theory Quantum field theory has been successful in describing the behavior of elementary particles and their interactions. String theories are an attempt to unify Quantum Field Theory with General Relativity. 
  • Loop quantum gravity Loop quantum gravity is a conservative “quantization” of general relativity. It doesn’t work in higher dimensions, while string theory requires that space-time have 10 dimensions. 
  • Predictions Quantum theory predictions are improved by probing the system after the measurement and evolving a model backward in time. String theory predicts that the production of quark-like and gluon-like particles would lead to near-spherical distributions of many hadron-like objects.

(Full article source google)

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