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Since dimensions usually refer to space and we naturally acknowledge three of them, we also perceive time and we separate space from time ("space AND time"), why is it, that time has ended up in the same shelf as spatial dimensions. Is time really a dimension "by nature"? Or is it a concesus, shifting our natural understanding what dimensions are, for practical reasons, similarly to defining particles?

EDIT: by Is time really a dimension "by nature"? I asked if there are good intrinsic reasons, given by to label time as a dimension, as opposed to us labeling it as such, to make it more tangible, explainable.

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    $\begingroup$ "Is time really a dimension "by nature"? Or is it a concesus, shifting our natural understanding what dimensions are, for practical reasons, similarly to defining particles?" It's the latter. In order to accommodate the special theory of relativity, we need to expand our definition of what a dimension is. However, time is nothing like space, and that distinction is still made when talk about a temporal dimension and a spatial dimension (even in relativity). This answer summarizes the point very succinctly I think. $\endgroup$ – Maximal Ideal May 6 '19 at 18:46
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    $\begingroup$ @User123 What do you mean by "true dimension?" If you make an attempt to actually define what you mean, you will end up presupposing your own conclusion. This is sort of the issue with the question to begin with. What is meant by "by nature?" If you say a dimension has to be something you can measure with a ruler, you will end up presupposing that all dimensions have to be spatial dimensions. If you say a dimension is any point of data (as mathematicians do), then you will get the opposite conclusion. Physicists use the latter definition of dimension. $\endgroup$ – Maximal Ideal May 6 '19 at 18:57
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    $\begingroup$ We all always travel at the speed of light (even when we stand because at that time we travel through time with a speed of light). $\endgroup$ – User123 May 7 '19 at 16:56
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    $\begingroup$ Gotta name it something. and it fits into a lot of equations exactly as a dimension would. $\endgroup$ – Wayfaring Stranger May 9 '19 at 14:48
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    $\begingroup$ This question depends on "our natural understanding what dimensions are" and I'm far from sure if there really is such an understanding shared at all widely. $\endgroup$ – Steve Linton May 9 '19 at 15:45
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(The speed of light) times (time) has the properties of a linear dimension. Just like length, width, or height, it can be used to measure how far you can go. The Lorentz contraction is consistent with applying the Pythagorean theorem to it and the other dimensions.

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The equations of general relativity especially the fundamental equation relating the shape of space to its contents:

$$\mathbf {G} ={\frac {8\pi G}{c^{4}}}\mathbf {T}$$

Can be expressed and manipulated in a very nice and simple way, that allows us to perform useful calculations by talking in terms of a four-dimensional "space-time" with certain properties. So basically we treat time as a dimension because it makes the equations nicer and the calculations easier.

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Dimensions has been abstract concept in math for long but we usually associate dimensions as a mean to locate object or measure its property like movement. You need to specify spatial plus time to convey any moving object location. Here, all X,y,z and t are independent and convey some point along that axis. But time has special property in sense that only movement in one direction is allowed. Don't need anything fancy till now but time is dimension in simple sense. However it becomes coupled with space since later we observed that time move differently for different observers. Basically different time passage at different X,y,z. So in a sense it is coupled by nature with space. However time still retains special status by moving in one direction so it is still different from space. I guess it would boil down to how strictly you define your dimension to be alike or not..but they are dependent on each other for practical purposes.

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