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Suppose every phenomena in this universe (of course most are reducible to some particular general ideal ones - basically I'm talking about those!) could be described as disturbances/waves/ripples/tensions in an $\mathbb{R}^n$ field. Is this possible? Can we find $n$?

Basically, I came up with this when I studied that General theory of relativity explains gravitation as a disturbance/tension in a 4-dimensional field of space-time. Basically, I'm asking whether the entire universe can be described as such.

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Try reading up on string theory.Here is a series of lectures with "string theory for pedestrians".

A particular quantum vibration mode of the closed string describes a graviton, the quantum of the gravitational field. A particular quantum vibration of an open string describes a photon, the quantum of the electromagnetic field.

In string theory all particles – matter particles and force carriers – arise as quantum fluctuations of the relativistic string.

One might well say that everything in the universe is described as the vibrations of some string, the entire universe. So yes, people have been working on this.

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