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Below are few ultrarelativistic approximations when .The rapidity is denoted : Motion with constant proper acceleration: d ≈ e aτ /(2a), where d is the distance traveled, a = dφ/dτ is proper acceleration (with aτ ≫ 1), τ is proper time, and travel starts at rest and without changing direction of acceleration (see proper acceleration for more details).
The acceleration of a falling body in the absence of resistances to motion is dependent only on the gravitational field strength g (also called acceleration due to gravity). By Newton's Second Law the force F g {\displaystyle \mathbf {F_{g}} } acting on a body is given by: F g = m g . {\displaystyle \mathbf {F_{g}} =m\mathbf {g} .}
The dominant energy condition stipulates that, in addition to the weak energy condition holding true, for every future-pointing causal vector field (either timelike or null) , the vector field must be a future-pointing causal vector. That is, mass–energy can never be observed to be flowing faster than light.
Another quantum effect that predicts the occurrence of faster-than-light speeds is called the Hartman effect: under certain conditions the time needed for a virtual particle to tunnel through a barrier is constant, regardless of the thickness of the barrier. [51] [52] This could result in a virtual particle crossing a large gap faster than ...
The Lorentz self-force derived for non-relativistic velocity approximation , is given in SI units by: = ˙ = ˙ = ˙ or in Gaussian units by = ˙. where is the force, ˙ is the derivative of acceleration, or the third derivative of displacement, also called jerk, μ 0 is the magnetic constant, ε 0 is the electric constant, c is the speed of light in free space, and q is the electric charge of ...
In order to find out the transformation of three-acceleration, one has to differentiate the spatial coordinates and ′ of the Lorentz transformation with respect to and ′, from which the transformation of three-velocity (also called velocity-addition formula) between and ′ follows, and eventually by another differentiation with respect to and ′ the transformation of three-acceleration ...
In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum. It is the extension of mass–energy equivalence for bodies or systems with non-zero momentum.
In special relativity, an object that has nonzero rest mass cannot travel at the speed of light. As the object approaches the speed of light, the object's energy and momentum increase without bound. In the first years after 1905, following Lorentz and Einstein, the terms longitudinal and transverse mass were still in use.