How many dimensions are there?

Factual Questions
1

Hey all.

This has bugged me for a little while, and because I’m not a complete maths/physics genius, I can’t get a simple straight answer out of anyone.

  1. How many dimensions are there? I always thought 3 - X, Y, Z. I could even understand if someone said Time was the 4th Dimesion. But there are people who say 11, 12 or 13! I cant even begin to imagine what these are.

  2. What is the deal with Tesseracts / Hypercubes / Klein bottles?

  3. How do we know there are dimensions that we cannot see?

  4. Why do people bother? Is there any practical use to these equations? Or is it just another step on the road to complete knowledge.

Can anyone put this in Lay-man language for me? I’m really interested to know what the 6th Dimension is!

2

BTW - ive just seen the SD article about it back from 1999 - but it only gives me part of the answer.

3

Currently, according to M-Theory, there are 9 spatial dimensions and one (or two) time dimension(s). Three of the spatial dimentions are extended and visible to use as we go about our lives, while the remaining 6 are “folded up” on the scale of the planck length and cannot be seen. If there is a second time dimension, as some theorists believe, it is similarly “folded up” in a small scale and cannot be directly observed. These additional dimensions appear to be required in superstring and M-Theory and follow naturally from the mathematics of these theories. It has to do with allowable modes of vibrations of the strings which make up all matter and energy. with the addition of the extra dimensions, exactly the right modes of vibration emerge to account for all the matter particles we know, as well as the force-carrying particles, and the yet-to-be-observed graviton.

4

Here’s one theory:

Four dimensions…length, width, depth, time…describe a field which, when distorted by mass, produces gravity. This is the General theory of Relativity.

Adding a fifth dimension produces electromagnetism.

Seven dimensions give rise to the Weak Nuclear Force, and 11 dimensions produce the Strong Nuclear Force.

NOTE; this is just an extension of Relativity.

A similar multi-force theory based on Quantum Mechanics has up to 26 dimensions.

5

Here’s a pretty readable explanation of M-Theory.

6

Hypercubes are just four dimensional cubes. If a regular cube has three dimensions and six faces that are squares, then a hypercube has four dimensions and eight faces which are cubes. You don’t have to be able to visualize it, but the math for it works just fine. This common image of a hypercube is a three-dimensional projection of a four-dimensional cube. It is analogous to a two dimensional projection of a three-dimensional cube.

A Klein bottle is just a three dimensional moebius strip. It is interesting because it is a three dimensional shape that only has one side.

7

Cool, so far this is all very confusing.

I’m not gonna ask you to go into why Electromagnetism deserves its own dimenstion - surely its just an enery - because we will be here all day.

But I swear I was taught once that Strong nuclear forces were simply the exchange of Gluons between particles.

So far, we have discussed Relativity, Membrane theory, string theory, Quantum Mechanics… and there is no simple answer.

Do we really have to be high on Acid to understand these dimensions?

8

We can conceptualize a world of 3 spatial dimensions, moving steadily forward through one dimension of time, but it is difficult to grasp a 5th dimension. We would be unaware of it, just as the flatlander living in his 2-dimensional world would be unaware of a third dimension. Any spatial dimension, if existing, cannot extend further than the width of an atom. If it did, air molecules in a sealed room would leak away into the extra dimension.

Any further dimension would have to be rolled up into an ultratiny loop much smaller than an atom. A subatomic particle, even when at rest in normal space, can loosely be thought of as traveling ceaselessly around a tiny loop of the 5th dimension like a hamster on a wheel. This is an explanation of the electromagnetic force, the source of which is an electric charge, as the source of the gravitational force is mass. The electric charge, in this theory, is just the motion of a particle in the 5th dimension.

But there are four forces. In addition to electromagnetism and gravity, there are the strong and weak forces, apparent only within the nucleus of an atom.

The best shot at a unified description of the forces is a string theory, and it uses not 5 dimensions, but a total of 10: 9 of space and one of time. In string theory, 4 large dimensions are needed to explain the observed properties of gravity, and a further compact 6 dimensions to explain the electromagnetic, strong, and weak forces. Each point in normal space, rather than being a single loop of extradimensional space, is a loop of 6-dimensional space. As the “hamster-on-a-wheel” motion of a particle in the 5th dimension explains electric charge, in string theory, similar orbital dances in multidimensional space explain the particle properties that give rise to the strong and weak nuclear forces. These extra dimensions are each the size of the “Planck length.”

The enormously high energy at which gravity becomes as strong as the other forces is known as the “Planck energy.” High energy is synonymous with short distances. The distance associated with the Planck energy is the Planck length. Ultrastrong gravity is found at the Planck energy, which corresponds to the Planck length. Recently, some scientists have theorized that the extra dimensions may be larger.