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How can we expand the matrix if there is no pre-existing vector space to expand the Matrix into?My answer <[]> = light intensity

If I shine a flashlight, and the beam is passing through nothing, can I observe and thereby measure its intensity?If I am "missing the boat," please forgive my ignorance. I strive to learn. It is my drug of choice.

Yes, I agree. However, in order to detect the intensity would there need to be something beyond the expanding array.

Let the vector space be 0 , an empty matrix[]How can we expand the matrix if there is no pre-existing vector space to expand the Matrix into?

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Euclidean universe

In a universe with zero curvature, the local geometry is flat. The most obvious global structure is that of Euclidean space, which is infinite in extent. ... The ultimate fate of the universe is the same as that of an open universe. A flat universe can have zero total energy.

Curvature is a result of velocity

QuoteCurvature is a result of velocityPerhaps you are implying acceleration? Consider an airplane flying. In general, the acceleration forwards or backwards has to do with changes in velocity, and that acceleration sideways has to do with curvature.However, if the object is traveling at a constant v, then the dv/dt=0. So, wouldn't anything traveling at the speed of light have no dv/dt, and therefore no curvature?

Thank you, it does clear things up for me.My point with light was simply to say that, in the absence of a significantly massive object, light cannot curve. I suppose that in the presence of a significantly massive object, any curvature is due to gravitational forces affecting the local spacetime. Would those forces be perpendicular to the vector of travel, as in your rope - ball example?

I see the Photon to be a perturbation in fields. A field ''particle''.

QuoteI see the Photon to be a perturbation in fields. A field ''particle''. Interesting.

I'm going to need to ponder that one for a bit, but on the surface, I agree that it seems plausible.