The Distance between two points in a hypothetical universe.

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I have a hypothetical universe where the distance between two points is defined as: ds²=−(ϕ²t²)dt²+dx²+dy²+dz² 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).

Mathematics

Matlab and Mathematica

Project ID: 17735500

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@dinhfreedom

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$250 USD in 5 days

4.9

(72 reviews)

6.7

@olaideejiwole

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5.8

@rabbora

Dear sir. I am mathematics expert. I can help you. I have experience to solve many mathematics projects using mathematica.

$500 USD in 3 days

4.9

(38 reviews)

5.4

@Valuesolutions

Hello, i have read the details provided..please contact me to discuss more on the project deadline and some other few things

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4.7

(22 reviews)

4.7

@prefectworld

I am an expert, in mathematics I have effectively executed numerous solution errands than you can ever envision both on consultant and off consultant. It will be a joy working with you on this one, Sir

$250 USD in 2 days

4.7

(24 reviews)

4.8

@Raghavanps

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.

$555 USD in 20 days

5.0

(5 reviews)

4.3

@braincenter

I believe that my experience and skill in this background will prove to be of great help to you. Contact me to discuss more on the details

$250 USD in 4 days

4.2

(6 reviews)

4.1

@deepak1iit

I have graduated from the best university of India. I have 1 US patent and multiple IEEE papers. I have good knowledge about python,matlab. Hope , I will be able to help you.

$555 USD in 10 days