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Dimensions as I understand are possible directions so:

I don't understand how anything other than space can have dimensions.

If any quantity has a dimension what does that practically mean? Rather what makes it have a dimension?

Like in time, mass, charge, how can we have dimensions when we are doing dimensional analysis?

I tried to look up for answer to this but seems I am completely going wrong in some concept.

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    $\begingroup$ Is it possible that you are confusing dimension (as in spatial dimension, i.e. a direction you can walk in) and the dimension of a physical quantity, i.e. current, temperature, luminous intensity? $\endgroup$ – Clever Sep 12 '16 at 7:02
  • $\begingroup$ @Clever yes.. Are they not the same? $\endgroup$ – user282856 Sep 12 '16 at 7:03
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    $\begingroup$ No, they aren't the same. It is an unfortunate use of terminology. $\endgroup$ – John Rennie Sep 12 '16 at 7:03
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You are confusing two distinct concepts of "dimension":

  • dimension = spacetime directions;
  • dimension = nature of a quantity.

Note that for spacetime dimensions one identifies opposite direction: left and right form together only one dimension)

Since you understand correctly the first let me explain the second. The concept of dimension of a physical quantity determines its nature in the sense that you cannot compose (add/subtract/compare) objects of different types. For example there is no meaning in adding meters and kilograms, in the same way that apples and cats are different objects and you cannot say that 3 apples and 5 cats give you 8 apples/cats (OK you could say 8 things but then this is not precise for being useful in anything). As you can see this is different from spacetime dimensions, only words are identical.

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  • $\begingroup$ Are vectors used to represent dimensions or tensors? $\endgroup$ – user282856 Sep 27 '16 at 19:49
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    $\begingroup$ I am not sure to precisely to understand your question. Scalar, vector and tensor objects are all physical quantities that have a unit (and thus a dimension): the difference is (roughly) the number of different components and the way they relate to each other under symmetry transformations. $\endgroup$ – Harold Sep 30 '16 at 20:00

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