So I get the first 4 (height, width, depth and time) but I’ve heard lots of scientists mention that there’s up to 12 or 14 or so dimensions on top of that?
In: Mathematics
What I haven’t seen mentioned here is the matter of *metric*.
What’s a metric?
Well first off, there are already no limitations to the number of dimensions. Literally, you just need an additional number for each dimensions. If you have a physical theories that require 20 numbers, voila, that’s 20 dimensions. Most physical theories have a lot of numbers.
However, something usually missing is having a *meaningful* metric. If someone tell you that you need to walk east 3km and north 4km and ask you the length between the start and the end you can deduce that means the total displacement is 5km. But if someone ask you to raise the heater by 3degree and add 4litre of water to the tank and then ask you the total length between the starting and ending state, you raise your eyebrow and ask “what does that mean”. This illustrate the different: in the first case you have a meaningful metric, the second case you don’t.
Generally, different dimensions don’t interfere with each other, like the example above. Except for space, because for some reasons, as far we know, physical laws don’t change when you rotate. The ability for vectors from several dimensions to have the concepts of “length” and “angle” give you the metric. And this ability exist because we have rotation.
For a long time, time don’t interfere with space, or so it was believed. When relativity come, it was discovered that time and space are intrinsically linked: you can “rotate” time into (part of) space by moving very fast. Because of this, the entire spacetime got a metric, which is why both space and time must be considered together.
The next dimensions are very similar. People simply consider putting in a metric into additional physical characteristic (for example, electromagnetic potential), and consider model where you can “rotate” between different physical quantities. What matter is whether it is useful and meaningful, and this is a matter of experimental fact and opinion. The mathematics work out the same no matter what.
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