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Does anyone know if physicists, mathematicians, or any other scientists have assigned an $X$, $Y$, $Z$ value for the known 3 dimensions we understand as 'space'?

If we were to attempt to build a 3D representation in a computer (of just our Galaxy for example), we would need to assign these axes for a coordinate system, so what I am asking is essentially if this $X$, $Y$, $Z$ has been used to map out space, and if so, is there an assigned 0 value for each axis?

I am not a physicist, nor a mathematician, so I know my understanding is limited, however I don't think it is too hard to imagine how we might simply map something out in a 3D application.

ProfRob
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Kalamalka Kid
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3 Answers3

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For problems in our own Galaxy then we use a set of Cartesian 3D Galactic coordinates. This coordinate system is centred on the Sun and is measured such that positive $X$ is towards the Galactic centre, positive $Y$ is orthogonal to this, in the plane of the Galaxy and in the direction of Galactic rotation. The $Z$ coordinate is perpendicular to these and points out of the Galactic plane in the direction of the north Galactic pole.

This actually makes it a left-handed orthogonal coordinate system. Further details can be found here.

ProfRob
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For convenience, space scientists assign "north" to the direction pointing "up" out of the plane in which the planets orbit the sun.

But the way our universe is fundamentally constituted admits no special or privileged directions or locations anywhere in space i.e., there is no "north" or "south" to the universe as a whole, and no unique "center" at which to place the origin of an (x, y, z) coordinate system either- since the universe has no geometric center anywhere.

We can still assign directions in space which can be used by astronomers to identify the locations of points of interest, but those convention directions are entirely arbitrary.

niels nielsen
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No, even if the universe were only a three-dimensional spatial space, it would be represented by a Euclidean Space, which, mathematically, is an Affine Space. That is a set of points in $\mathbb{R}^3$ together with a 3D vector space of displacements between those points. There is no origin of space.

Of course, our universe is actually a 4-dimensional spacetime. This must be represented as a 4D manifold. A manifold is a generalization of the affine space: a set of points, which in any small neighborhood can look like $\mathbb{R}^4$, together with a vector space at any point (the tangent space). Again there is no origin, or indeed any preferred set of coordinates (axes).

Ben H
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