Re: resolve to perpendicular components, because they are independent


Hero.van.Jindelt@xxxxxx wrote:
> Ken S. Tucker wrote:
> > It's reasonable to consider 5D, just look around your office and
> > see that your desk is denser than the air above it, so far so good.
> > OTOH, the density of the desk may be described by a 4D warp.
> > Some physicists perfer to impose a 5th D variable on an orthogonal
> > 4D, but then that becomes a nonorthogonal 4D, as in GR.

> Can You explain, how a fourth dimension can be orthogonal to the three
> of space, measured in cm³?

One of the best explanations I've seen is in the movie "Time Machine"
(Original with Rod Taylor). Orthogonality can't always be assumed.

> My results so far: Density ( Volume of particles /( Volume of space
> swept out by particles in movement) ) can be described in assigning a
> value of density [ cm³/ cm³] to every point of Your desk and the air
> above it. This makes a scalar field.

Yes I think with care you can think of it that way. In GR a socalled
"curvature scalar" is proportional to a density scalar.

This is rather like the density of air changing the amount it refracts
light, the refraction being the curvature.

> Regards
> Hero

Regards
Ken

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