Recent content by Gordon Jump

OK - I think I have an answer. Tell me what you think. I have two metrics that I can define: dx^2+dy^2 and dx^2 + sin^2( x) dy^2. These are intrinsically different in some way in that I don't think there is a coordinate transformation that can take one to the other.

https://iopscience.iop.org/article/10.1088/0264-9381/9/6/011/meta

You are agreeing with me. We choose the Lorentzian metric because it is physically interesting, but we could equally well choose the Euclidean metric - it just wouldn't be as interesting. My actual question is "What is the significance of a change of signature in general relativity"

Yes, and after I measure the coordinates of an object, I am free to enter those numbers into any metric function I choose.

Thank you, but I don't think this is the correct answer. I measure coordinates, and their infinitesimal changes. I am free to plug those coordinates into any scalar function I choose.

I'm a bit confused about the idea of "Change of Signature in Classical Relativity". As I see it, a metric is just a scalar function that I make up. For example, in the x,y plane I can define the functions x^2+y^2 and x^2-y^2 simultaneously. What, then, is the significance of "changing" the...