# Can a straight line be produced in nature? [closed]

I understand that space is curved, but if one accounted for this curvature and warped the vector accordingly, could a straight line be produced?

When and how was it first proved that this can or cannot be done?

• A ray of light is a straight line, almost by definition. – Alexandre Eremenko Jul 19 '17 at 20:52
• @AlexandreEremenko but is the beam of light not curved by gravity? – DukeZhou Jul 19 '17 at 20:54
• Only at large distances. Strictly speaking no mathematical abstraction can be EXACTLY produced in nature. A point, for example, what is a point? Mathematical notions only approximately describe what we see in the real world. A line segment corresponds to a ray of light (not very long one). – Alexandre Eremenko Jul 19 '17 at 20:57
• If the geometry of the spacetime is not euclidean (in the sense of non-euclidean geometry), then a straight line is not "straight" in the euclidean sense. But what is the def of "straight line" ? See Euclid: "Definition 4. A straight line is a line which lies evenly with the points on itself." – Mauro ALLEGRANZA Jul 20 '17 at 8:46
• I made the question less trivial by asking for the history of this topic. – Tom Au Jul 21 '17 at 1:15

$${\ddot x}^{a} + \Gamma_{bc}{}^{a}{\dot x}^{b}{\dot x}^{c} = 0$$
where the path is given by $x^{a}$, the dots are derivatives along the path, and the $\Gamma_{ab}{}^{c}$ can be calculated from the geometry under consideration (all of them are zero for flat space in Cartesian coordinates, for example).