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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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    $\begingroup$ This is a very difficult topic, i can bet that most string theorists do not have a physical idea of these extra dimensions. These dimensions arise in a sense when the gravitational tensor is taken as a parameter (thus the number of dimensions is increased) and no they are not necessarily orthogonal, these extra dimensions can be correlated with each other and curved in various shapes out of view (for lack of better word) $\endgroup$ – Nikos M. Sep 30 '14 at 21:21
  • $\begingroup$ Related: physics.stackexchange.com/q/10527/2451 and physics.stackexchange.com/q/31882/2451 $\endgroup$ – Qmechanic Sep 30 '14 at 21:25
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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.
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  • $\begingroup$ In statistics, we don't care if a dimension relates to distance. Every point is information. As long the parameters in the population of data points are reduced to an minimal set of orthogonal components, those are our dimensions. We need to be blind to their mode of physical manifestation. So that if a point rotates with parametric rotational speed, acceleration and distance, etc, they are just as valid a dimension as any other. $\endgroup$ – Cynthia Avishegnath Sep 30 '14 at 21:40
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    $\begingroup$ @BlessedGeek: I suggest that you look up and try to understand the meaning of dimension in the context of physics, this will definitely help you find an answer to your question. $\endgroup$ – Frederic Brünner Sep 30 '14 at 21:49
  • $\begingroup$ In the simplicity of statistics, it is absolute that orthogonality and symmetry are the two sides of the same coin. That is essential because for example we need to find out, how the membership of a population with two mutually independent component of a field affect each other, DEVOID of any correlation between those two components. Otherwise, there would be no point in finding correlation. So that if symmetry does not require a basis of orthogonality, it would be like allowing some select people to vote for the President twice. Which is not fair. $\endgroup$ – Cynthia Avishegnath Sep 30 '14 at 21:55
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    $\begingroup$ Another simple explanation for why we do not see these dimensions is that they don't exist and string/M-theory models are all starting out with the wrong assumptions about physics altogether. Lacking any other evidence I would keep that possibility firmly in mind. $\endgroup$ – CuriousOne Sep 30 '14 at 22:56
  • $\begingroup$ @CuriousOne: While it is possible that this is true, I don't see how this contributes anything to an answer to this question, which is not about the "correctness" of string theory, but about its basic principles. $\endgroup$ – Frederic Brünner Oct 1 '14 at 9:20

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