Galilean Transformation

• The primed frame moves with velocity v in the x direction with respect to the fixed reference frame.
  撇去的参考系相对于固定参考系以速度v沿x方向运动。
• The reference frames coincide at t=t'=0.
  参考系在 t=t'=0 时重合。
• The point x' is moving with the primed frame.
  点 x' 在素框架中运动。
• The Galilean transformation gives the coordinates of the point as measured from the fixed frame in terms of its location in the moving reference frame.
  伽利略变换给出了该点在固定参考系中的坐标，这是以运动参考系中该点的位置来表示的。

Lorentz Transformation

The primed frame moves with velocity v in the x direction with respect to the fixed reference frame. The reference frames coincide at t=t'=0. The point x' is moving with the primed frame. 带撇号的参考系相对于固定参考系以速度 v 沿 x 方向运动。两个参考系在 t = t' = 0 时重合。点 x' 随带撇号的参考系一起运动。

The reverse transformation is: 逆变换为：

Much of the literature of relativity uses the symbols β and γ as defined here to simplify the writing of relativistic relationships. 相对论的许多文献使用这里的β和γ符号来简化相对论关系的书写。 Evaluation of symbols 符号的评估

Speed of Light

Experimental measurements of the speed of light have been refined in progressively more accurate experiments since the seventeenth century. Recent experiments give a speed of

but the uncertainties in this value are chiefly those of comparisons to previous standards for the length of the meter. Therefore the above speed of light has been adopted as a standard value and the length of the meter is redefined to be consistent with this value.

The speed of light in a medium is related to the electric and magnetic properties of the medium, and the speed of light in vacuum can be expressed as

In vacuum, all electromagnetic waves travel at c, the speed of light.

Relativity Factor

Much of the literature of relativity uses the symbols β and γ as defined here to simplify the writing of relativistic relationships. 相对论的许多文献使用这里的β和γ符号来简化相对论关系的书写。

For relatively low velocities where the relativity factor gamma is close to one, the binomial expansion can be used to evaluate the small relativistic corrections.

c as Speed Limit

The speed of light c is said to be the speed limit of the universe because nothing can be accelerated to the speed of light with respect to you. A common way of describing this situation is to say that as an object approaches the speed of light, its mass increases and more force must be exerted to produce a given acceleration. There are difficulties with the "changing mass" perspective, and it is generally preferrable to say that the relativistic momentum and relativistic energy approach infinity at the speed of light. Since the net applied force is equal to the rate of change of momentum and the work done is equal to the change in energy, it would take an infinite time and an infinite amount of work to accelerate an object to the speed of light. (Sorry, Captain Kirk. We can't give you warp speed!)

A common resistance to the speed limit is to suggest that you just accelerate two different objects to more than half of the speed of light and point them toward each other, giving a relative speed greater than c. But that doesn't work! Time and space are interwoven in such a way that no one observer ever sees another object moving toward them at greater than c. The Einstein velocity addition deals with the transformation of velocities, always yielding a relative velocity less than c. It doesn't agree with your common sense, but it appears to be the way the universe works.