The term “dimension” always conjures up ideas of parallel universes, time travel, and all manner of topics fit for late-nite AM radio, but “dimension” here simply means another degree of freedom that is “orthogonal” and independent of the previously known one(s). They allow quantum systems to store energy of motion or configuration in new places in order to satisfy conservation and symmetry laws.
Thanks for clearing that up.
The Big Bang Theory
Leonard: At least I didn’t have to invent 26 dimensions just to make the math come out.
Sheldon: I didn’t invent them, they are there!
Leonard: In what universe?
Sheldon: In all of them, that’s the point.
Piaget did studies with children to determine at what age they went from two dimensional perception to three dimensional perception. It is a gradual shift where you have both perceptions after the shift takes place.
The same thing is true when you go three dimensional to fourth dimensional. You still can perceive the old way, but a new reality begins to form.
As well as journals of physics, in peer-reviewed articles written by quite serious theoretical physicists.
“dimension” here simply means another degree of freedom that is “orthogonal” and independent of the previously known one(s).
You are using a definition couched strictly in narrow mathematical terms (much too narrow even for math, really). But the mathematical representation stands for quite real physical dimensions just as real as the lower three, if not visible to us (neither is the third dimension visible to the mythical flatlanders).