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This equation holds for a body or system, such as one or more particles, with total energy E, invariant mass m 0, and momentum of magnitude p; the constant c is the speed of light. It assumes the special relativity case of flat spacetime [1] [2] [3] and that the particles are free.
The speed of light is the upper limit for the speeds of objects with positive rest mass, and individual photons cannot travel faster than the speed of light. [40] This is experimentally established in many tests of relativistic energy and momentum .
The expression for the four-momentum depends on how the coordinates are expressed. Time may be given in its normal units or multiplied by the speed of light so that all the components of the four-vector have dimensions of length. If the latter scaling is used, an interval of proper time, τ, defined by [54]
In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p. This derives from the following relativistic relation, with m = 0 : [ 27 ]
The dimension of momentum is T −1 L M. The dimension of energy is T −2 L 2 M. Dividing a unit of energy (such as eV) by a fundamental constant (such as the speed of light) that has the dimension of velocity (T −1 L) facilitates the required conversion for using a unit of energy to quantify momentum.
Its initial value is 1 (when v = 0); and as velocity approaches the speed of light (v → c) γ increases without bound (γ → ∞). α (Lorentz factor inverse) as a function of velocity—a circular arc. In the table below, the left-hand column shows speeds as different fractions of the speed of light (i.e. in units of c). The middle column ...
c is the speed of light in vacuum h is the Planck constant The photon energy at 1 Hz is equal to 6.626 070 15 × 10 −34 J , which is equal to 4.135 667 697 × 10 −15 eV .
For quantum mechanical waves, the wavenumber multiplied by the reduced Planck constant is the canonical momentum. Wavenumber can be used to specify quantities other than spatial frequency. For example, in optical spectroscopy, it is often used as a unit of temporal frequency assuming a certain speed of light.