The Distance between two points in a hypothetical universe.

I have a hypothetical universe where the distance between two points is defined as:


Where t is time, x, y & z are space and ϕ is a constant has units of km / s². The space in this universe grows quadratically with time (and, as I understand it, probably isn’t Minkowski spacetime). A particle travelling at the speed of causality, c, will follow this contour from point O to point P (see attached image).

Given the time between point O and point Q, is it possible to find the distance from point P to point Q (e.g. does a function exist such that f(Δt)=dL)? If so, what is that formula?

Note that I've had some preliminary work done in Mathematica to describe this space (see attached also).

Taidot: Matematiikka, Matlab ja Mathematica

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( 6 arvostelua ) Bolton, United States

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You have Minkovski space with redefined time. You can return in usual Minkovski space by defining time t1=Integral(phi t dt). If you want to know more about distances in 4-dimensional pace along geodesic line you can l Lisää

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This should be solvable - appears like a problem to determine the distance as you call it. There are a few more details that I will ask you later.

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