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Do Extra Dimensions Exist?


Silly Druid

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(Sorry for posting this 2 days later than usual.)

In some physical theories there are not only the 4 dimensions we know (3 space and 1 time), but also some small extra ones. But they hasn't been observed yet, so do they really exist? Well, there is a very convincing argument (for me at least) that they do. It's called "CPT symmetry".

Symmetry is a very important concept in physics, it means that some differences between two systems don't really affect the way they work. For example the "translation symmetry" means that the place where something is located is not important for its physical evolution (if all other conditions are the same).

So what do these 3 letters mean? C is "charge symmetry", which means replacing all matter with anti-matter and vice versa. P is "parity", and means making a mirror image of the universe, and "T" is reversing the direction of time. The interesting thing is that individually all these symmetries are broken (not very strongly, but there are some subtle physical effects that don't obey them), but the combination of all three of them, as far as we know, holds. It also means that combinations of two of them are also broken, and are equivalent to the third one, for example CP = T.

Without the extra dimensions, all this doesn't make much sense. The P symmetry is about space, T is about time, and C is about... some numbers we attribute to the particles to describe how they interact with each other. But, the extra dimensions that appear is some theories (starting with the Kaluza-Klein theory, and including some newer ones, like the string theory) are used to explain the charges as movement of the particles in these extra dimensions (which, due to their small size, is quantified, that's why the charges have discrete values).

Making a mirror image (P symmetry) can be viewed as reversing all 3 spatial dimensions, T symmetry is reversing the time dimension, and if there are extra dimensions, then C symmetry is also reversing them. So, in other words, the CPT symmetry can be interpreted as "if you reverse all the dimensions, it's like you reversed none." So it all starts making sense, by grouping 3 similar symmetries into one. Coincidence? I think not.

  • Brohoof 1

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In matrix transformations, you add one extra dimension in order to transform from the current dimension, down to the lower one. An example is transforming a point from 2D space to 1D space, so you will add a dimension to [X, Y], so it becomes [X, Y, Z] (2D now became 3D, but what we are calculating is a 1D coordinate).

For a world coordinate [X, Y, Z], in order to transform it to a screen coordinate [X, Y], we must add one more dimension to allow translation as part of the matrix transformation. So we end up with a coordinate [X, Y, Z, W].

So all of a sudden, we have 4 dimensions, and the W one is called Homogeneous W. Welcome to the world of homogeneous coordinates. And if that is the 4th dimension, what is time then? The fifth?

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