So, what's a dimension?

It's as far as we know now, something that carries a field of values that associate with every point of it. But one may ask, every point of what?

Well, every point of “what there is”. You see, a dimension isn't “somewhere”, because it's only inside a dimension that “somewhere” means anything.

So any “thing” by being a value defined in a dimension, excludes the dimensions from being a “thing”! So you won't find a dimension anywhere, don't search for it. A dimension is “inside what” you exist.

What does exist are contained, inside a dimension, so a dimension is a container, therefore it doesn't “exist”.

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So now to answer the question:

1. “it is possible that there is a dimension”: Yes
2. Then I have to add: “is it possible that there is a dimension that we are not aware of”: Yes
3. “…a dimension that people can go to and live”: No, you don't go to a dimension, you exist in it. You never can enter or leave it. Dimensions define you, always have and always will be.

For 2., think about magnetic fields for example: we don't see the one of even a strong magnet, yet some sharks hunt by measuring the tiny magnetic field created by the nerves of hidden fishes or any animal.

For 3., you don't go to a dimension. You don't go to x, y or z, you don't go to t (for “time”), etc. But you move left and right, up and down. And your reach a certain future time by waiting.