Quote by arivero
Well, because such is not the case in let me italize the Kaluza Klein approach to string and superstring theories. It could be the case in other approaches, I can not tell. Of course you can rely on relativity and quantum principles to convert between mass, length, energy, frequency and wavelength. .

Now that I know that you accept extra spatial dimensions in Kaluza Klein models, but don't necessarily believe these models are descriptive of reality, I understand what you're telling me better.
Quote by arivero
...the thing they need is a very special cancelation condition in an algebra, and they could have some other tricks to get that condition without a background space.

I am totally blowing smoke now, and I admit it  but a "very special cancellation condition" sounds like something that could be modeled with destructive interference of waves, and that dimensions describing wavelengths and frequencies might actually be more useful than extra spatial dimensions.
There is a fundamental question I should have asked much earlier  how do you guys define a "space"?
I am aware that there are Minkowski spaces, Riemann spaces, Hilbert spaces, and I'm sure there must be others. I can't adequately describe all these spaces, but I know that they allow for more dimensions, or are ndimensional.
But I have been using "space" as analogous to "volume".
Can someone tell me how a theoretical physicist defines "space"? I'm afraid I have to ask you to translate into layman's terms, or I won't get your answer.
Thanks again.