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Lelan Thara

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A brief background:

My lifelong interest in science fiction led me to start reading about relativity and quantum physics around 20 years ago. However, I am stricly a layman with no mathematical formalism. What knowledge I have of these topics comes mostly from reading authors like Paul Davies, Michio Kaku. John Gribbin, Steven Hawking and other popularizers of physics.

When I read such books, I am always acutely aware that the language of physicists is math, and that I am getting my information from "translators". So when I run into concepts that I have trouble accepting, I always wonder whether the problem is the concept - or the translation.

So my question has to do with the "higher spatial dimensions" of string theory.

I am aware that a "dimension" to a mathematician is not necessarily the same thing as a "dimension" to a classical physicist, or anyone using dimensions in the real world. A mathematician's dimensions can be abstractions, but a physical dimension is a usable means of measurement.

If you'll forgive a simple example - a mathematician can draw two crosses - two sets of axes - on a sheet of paper. He can label one set of axes, "x,y", and one set of axes "a, b", and say that he has "four spatial dimensions" - right?

But obviously the surface of his sheet of paper still remains two dimensional. Two measurements at right angles to each other are "necessary and sufficient" to locate any point on the paper.

My question is - are the "higher spatial dimensions" of string theory mathematical abstractions only? Do physicists actually believe that these extra dimensions are describing some unseen place, some space, that can't be measured and located within the standard three dimensions of length. width, and depth?

What exactly is a "higher spatial dimension" to a theoretical physicist?

I have clues that the literal existence of these higher spatial dimensions is intended to be taken seriously. I've heard them described as "compactified", and the analogy of the interior of a garden hose, which looks one dimensional from a distance but reveals other dimensions close up. I can only accept this as a mathematical abstraction. It's the same as saying "small measurements are in a different dimension than big measurements." A mathematician could say, "I define anything bigger than a meter as dimension X and smaller than a meter as dimension Y" - but to suggest that creates a new physical space, or a higher dimension as laymen think of such things, makes no sense to me.

I've heard that the extra spatial dimensions are curled up into manifolds. A dimension in the real world is a means of measurement, not a place, not a thing. How can a means of measurement be curled up? If I curl up a tape measure, I can still locate any point on that tape measure with straight yardsticks in the standard three dimensions of length, width, and depth.

The whole idea of "higher spatial dimensions" and "hyperspace" just sounds so Flatland to me. It seems the exact same as Flatlanders talking about "higher area dimensions" or "hyperplanes".

Sorry for revealing my bias. Can anyone explain whether these higher spatial dimensions are meant to be taken literally - what they are - how they describe any space that can't be measured in 3 dimensions?

(Just to let you know, I'm aware of time as a dimension and am leaving it out of my comments as a convenience.)

If anyone can help me understand this better, in layman's language, I would be extremely grateful. Thanks in advance!