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Line 17: + − In classical [[physics]], the set of all ''events'' is 4-dimensional, since in order to specify an event, one needs to know both the position of the event in [[space]] (3 parameters), and the time the event took place (an additional 1 parameter). This predicates the idea (believed by most physicists since the time of [[Albert Einstein]]) that space and [[time]] form a single [[continuum]], and that time is a fourth dimension. However, time in not measured in units of distance such as meters so this system remains incompatible with [[Isaac Newton|Newtonian]] physics. [[Quantum]] physicists propose a different theory, namely that there are more than three dimensions in space itself, perhaps as many as eleven. But dimension four and above are all curled up so tightly that they extend no further than the diameter of a [[subatomic particle]], so humans are unable to notice them with the naked eye.+
dimension in physics = degrees of freedom
==Definition in physics==
==Definition in physics==
In classical [[physics]], '''dimension''' sometimes is takes to mean '''freedom degrees''' or the number of independent variables. For example, the study of the displacement of a [[pendulus]] is one-dimesional (because there is only one variable, the (oriented) angle that the pendulus forms with the vertical line), however, the [[three body problem]] in [[celestial mechanics]] is nine-dimensional (because there are three position vectors, each one in three dimensions). Sometimes (like in [[hamiltonian mechanics]]) the ''velocity'' is also considered to be a variable; so the pendulus would be two-dimensional, and the three-body problem would have eighteen dimensions.
Even before [[Relativity]], the set of all ''events'' is 4-dimensional, since in order to specify an event, one needs to know both the position of the event in [[space]] (3 parameters), and the time the event took place (an additional 1 parameter). This predicates the idea (believed by most physicists since the time of [[Albert Einstein]]) that space and [[time]] form a single [[continuum]], and that time is a fourth dimension. However, time in not measured in units of distance such as meters so this system remains incompatible with [[Isaac Newton|Newtonian]] physics. [[Quantum]] physicists propose a different theory, namely that there are more than three dimensions in space itself, perhaps as many as eleven. But dimension four and above are all curled up so tightly that they extend no further than the diameter of a [[subatomic particle]], so humans are unable to notice them with the naked eye.
For example, some models in [[high-energy physics]] postulate that [[spacetime]] has more than 4-dimensions. For example, in the Kaluza-Klein model, a point is specified by a point in 4D-spacetime, plus a point on a [[circle]] attached to that point in 4D-spacetime. Though this model is currently out of favor, it illustrates the basic flavor of additional spatial dimensions in the other models; for example, in [[string theory]].
For example, some models in [[high-energy physics]] postulate that [[spacetime]] has more than 4-dimensions. For example, in the Kaluza-Klein model, a point is specified by a point in 4D-spacetime, plus a point on a [[circle]] attached to that point in 4D-spacetime. Though this model is currently out of favor, it illustrates the basic flavor of additional spatial dimensions in the other models; for example, in [[string theory]].
[[Category:Mathematics]][[Category:Physics]]
[[Category:Mathematics]][[Category:Physics]]