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What are the '10 dimensions' that physicists are always talking about?
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There have been many proposals since the 1920s to increase the number of dimensions to spacetime beyond the standard four that relativity uses.
In all cases, these extra dimensions are vastly smaller than an atom and are not accessable to humans...fortunately!

Current string theory proposes 6 additional dimensions while M-theory allows for a seventh.
These additional dimensions are sometimes called 'internal degrees of freedom' and are related to the
number of fundamental symmetries present in the physical world at the quantum scale.
The equations that physicists work with require these additional dimensions so that new
symmetries can be defined that allow physicists to understand physical relationships
between the various particle families.

They think these are actual, real dimensions
to the physical world, only that they are now 'compact' and have finite sizes unlike
our 4 dimensions of space and time which seem almost to be infinite in size. The figure above shows what these compact additional dimensions look like, mathematically.
Each
point in 4 dimensional space-time has another 6 dimensions attached to it which
'particles and forces' can use as extra degrees of freedom to define themselves
and how they will interact with each other. These spaces are called Calabi-Yau manifolds and it is their 6-dimensional geometry that determines the exact properties of fundamental particles.

Do not confuse them with 'hyperspace'
because the particles do not actually 'move' along these other dimensions.
They are not 'spatial' dimensions, but are as unlike space and time as time is unlike space!

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page at the ***Astronomy Cafe Blog*.**
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