High School Is the speed of light a degree of freedom?

[Killtech]

The fact that light travels on null curves is not dependent on the distance measure we use.

there is only one 2d-manifold in R3 such that the metric on it is exactly the L2 norm of R3 (apart from displacement) - a metric by which R3 is flat. so your metric defines the geometry of your manifold, its curvature and its geodesics.

and to quote wikipedia on manifolds:
"In 1828, Carl Friedrich Gauss proved his Theorema Egregium (remarkable theorem in Latin), establishing an important property of surfaces. Informally, the theorem says that the curvature of a surface can be determined entirely by measuring distances along paths on the surface."

so changing the metric is not just a change of coordinates. it is a change of geometry, curvature and so forth.

 

[PeterDonis]

changing the metric is not just a change of coordinates. it is a change of geometry, curvature and so forth.

The term "metric" means "the geometry of the manifold" (spacetime in this case), so your statement is a tautology: changing the geometry is changing the geometry.

The term "distance measure" as you have been using it means our choice of units, which can be changed without changing the geometry. Gauss was not saying that French people measuring in kilometers would get a different geometry for the surface of the Earth than British people measuring in miles.

 

[PeterDonis]

when EM force is changed such that c is increased by a factor and the effect of charge is reduced by square root alpha remains unable to detect that change?

I have no idea what you are talking about. There is a large body of literature describing various experiments attempting to detect changes in the fine structure constant. Look it up.

 

[PeterDonis]

Thread closed for moderation.