Jedi, If you're a TMer you'll understand transcendental consciousness can be achieved and experienced by anyone. And that one can experience TC along with the waking, dreaming and sleeping consciousness.
If you read the Shiva Sutras, the slokas are also talking about the same experiences that is taught by MMY. So, TC is the same as samadhi. This is the difference that TM teaches as compared to the other Indian gurus or even books that you've read. As far as spacial dimensions are concerned, it is my own theory that the various states of consciousness are really the extended higher dimensions from the basic space-time continuum. I've talked about this idea several times in this forum. This is why I believe the scientists at CERN are probably NOT going to discover any higher dimensions with their sophisticated giant machines in Switzerland.