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I am not into String or M theory.

Recently I am again reminded that M-theory "requires extra dimensions" beyond the usual string theories, beyond the usual space-time dimensions.

To me, dimensions mean orthogonality - the complete non-overlapping coverage of the field by the components of the field.

Let's look at the statics/dynamics of our awareness
  1. 3 orthogonal directions of space.
  2. 3 orthogonal directions of rotation.
  3. 3 orthogonal directions of compression/rarefaction
Let's throw the monkey at the wrench, without needing to understand 3-D time.
  1. 3 orthogonal directions of time.

That makes a total 12 physical mutually orthogonal dimensions easily visualizable by anyone familiar with statics, dynamics (and statistics).

They are mutually orthogonal because, for example
  • you could spin all you want, and never traverse any distance
  • some states of matter can endure variation in some amount of compressive or rarefactive forces without changing shape, spinning or moving.

Let's visualize time as the passing of events, so that in a repetitive time loop of repetitively sampling the same field of events, you would have at least 2 time dimensions. Where when referencing to a particular point in time, you would have to specify which instance of loop.

Somehow, we will be able to wiggle out 12 mutually orthogonal dimensions that are quite within our human mental grasps.

Questions

  1. Aren't these 12 dimensions sufficient or good 'nuf already? When would you need to manufacture new dimensions that are beyond the grasp of our human minds?

  2. If M theory would not consider some of these humanly possible dimensions, then how does the theory treat the existence of these dimensions?

  3. Are our humanly imaginable dimensions not compatible with M theory. Or perhaps, these dimensions are indeed considered but perceive with transformed perspectives?

Pls don't get mad at me for trying to understand M theory from the perspectives of statics, dynamics and statistics.

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Cynthia Avishegnath
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I will not go into explaining what dimensions actually are, but as can be found out for example by reading the respective Wikipedia article, the number of dimensions of a space(-time) coincides with the minimal number of coordinates needed to specify a point. The directions you refer to do not coincide with dimensions as they are generally understood. To answer your questions:

  1. M-Theory is formulated in eleven dimensions, not twelve. But no matter what the number actually is, it is not manufactured or put in arbitrarily. It rather comes out as a prediction of the theory, it follows from mathematical/physical consistency conditions. Whether something is "beyond the grasp of our human minds" does not matter to science, as we have seen in the context of quantum mechanics or relativity.
  2. As I mentioned above, the existence of the extra dimensions follows from the consistency of the theory: it is required for example to preserve Lorentz invariance for the full theory, i.e. it follows from the fact that we take special relativity seriously. An explanation for why we do not "see" or notice these dimensions is that they might be "curled up" and extremely small, so that their consequences could only be directly measured at small distance scales.
  3. The four space-time dimensions we see are definitely compatible with string/M-theory, they are simply the ones that are not curled up, the ones that remain large.
Frederic Brünner
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