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洛倫茲提出洛倫茲變換是基于以太存在的前提的，然而以太被證實是不存在的，根據光速不變原理，相對于任何慣性參考系，光速都具有相同的數值。愛因斯坦據此提出了狹義相對論。在狹義相對論中，空間和時間并不相互獨立，而是一個統一的四維時空整體，不同慣性參考系之間的變換關系式與洛倫茲變換在數學表達式上是一致的，即： 
其中x、y、z、t分別是慣性坐標系S下的坐標和時間，x'、y'、z'、t'分別是慣性坐標系S'下的坐標和時間。v是S'坐標系相對于S坐標系的運動速度，方向沿X軸。 由狹義相對性原理，只需在上述洛倫茲變換中把v變成－v，x'、y'、z'、t'分別與x、y、z、t互換，就得到洛倫茲變換的反變換式： 
洛倫茲變換是高速運動的宏觀物體在不同慣性參考系之間進行坐標和時間變換的基本規律。當相對速度v遠小于光速c時，洛倫茲變換退化為經典力學中的伽利略變換： x'=x－ut y'=y z'=z t'=t 所以，狹義相對論與經典力學并不矛盾，狹義相對論將經典力學擴展到了宏觀物體在一切運動速度下的普遍情況，經典力學只是相對論在低速時（v遠小于c）的近似情況。一般在處理運動速度不太高的物體時（如天體力學中計算行星的運行軌道），不需考慮到相對論效應，因為用相對論進行處理時計算往往變得非常繁瑣，而結果與經典情況相差不大。當處理高速運動的物體時，比如高能加速器中的電子，則必須要考慮相對論效應對結果帶來的修正。
Lorenz proposed that Lorenz transformation is based on the premise of the existence of the ether, however, the ether is confirmed to be non-existent, according to the speed of light constant principle, with respect to any inertial reference frame, the speed of light has the same value. Einstein put forward the theory of special relativity. In the theory of relativity, space and time are not independent, but a four-dimensional space-time unity, transform relation and Lorenz transform between different inertial reference system is consistent in mathematical expression, i.e.:
The X, y, Z and T are the coordinates and time of the inertial coordinate system S, X', Y', z'and t' are the coordinates and time of the inertial coordinate system S'respectively. V is the S'coordinate system relative to the S coordinates of the movement speed, the direction along the X axis.
By the special relativity principle, only need to change the V into V, X', Y',, t',, z', y, Z, and X,, t, and, respectively, to obtain the inverse transform of the Lorenz transform: Lorenz transformation is the basic law of the coordinate and time transformati-on between the macroscopic objects of the high speed motion in different inertial reference systems. When the relative velocity V is much less than the speed of light C, the Lorenz transform is reduced to the classical mechanics: X'=xut y'=y z'=z t'=t Therefore, special relativity and the classical mechanics are not contradictory, special relativity will be extended to the general situation of classical mechanics in all velocity under the macroscopic object, classical mechanics theory of relativity only at low speed (V far less than C) approximation of. The general speed is not too high in the processing of motion objects (such as the calculation of planetary orbits in celestial mechanics), without considering the relativistic effect, because the calculation is dealt with by relativity often become very complex, and the situation is similar with the classic. When dealing with high speed moving objects, such as electrons in high energy accelerators, it is necessary to consider the effect of relativistic effects on the correction of the results.
基本公理狹義相對性原理：一切物理定律（力學定律、電磁學定律以及其他相互作用的動力學定律）在所有慣性系中均有效；或者說，一切物理定律的方程式在洛倫茲變換下保持數學形式不變。 光速不變原理：單向光速是個常數且與光源的運動無關。換言之，在所有慣性系中，真空中的光速不變。
推導過程洛倫茲變換可以由狹義相對性原理和光速不變原理推導出來。下面根據這兩個基本原理，推導坐標的變換式。 設想有兩個慣性坐標系S系、S'系，S'系的原點O'相對S系的原點O以速率v沿X軸正方向運動。任意一事件在S系、S'系中的時空坐標分別為（x，y，z，t）、（x'，y'，z'，t'）。t、t'分別是S系和S'系時刻。兩慣性坐標系重合時，分別開始計時. 若x= 0，則x'+vt' =0。這是變換須滿足的一個必要條件，故猜測任意一事件的坐標從S'系到S系的變換為 x=γ（x'+vt'） (1) 式中引入了常數γ，命名為洛倫茲因子。 引入相對性原理，即不同慣性系的物理方程的形式應相同。故上述事件坐標從S系到S'系的變換為 x'=γ（x－vt） (2) y與y'、z與z'的變換可以直接得出，即 y'=y (3) z'=z (4) 把（2）代入（1），解t'得 t'=γt +(1－γ2) x/γv (5) 在上面推導的基礎上，引入光速不變原理，以尋求γ的取值。 由重合的原點O（O'）發出一束沿X軸正方向的光，設光束的波前坐標為（X，Y，Z，T)、(X'，Y'，Z'，T')。根據光速不變原理，有 X=cT (6) X'=cT' (7) 相對論的光速不變原理得出：坐標值X等于光速c乘時刻T，坐標值X'等于光速c乘時刻T'。（1）（2）相乘得 xx'=γ2(xx'－x'vt+xvt'－v2tt') (8) 以波前這一事件作為對象，則（8）寫成 XX'=γ2(XX'－X'VT+XVT'－V2TT') (9) （6）（7）代入（9），化簡得洛倫茲因子 γ= (1－（v/c）2)－1/2 (10) （10）代入（5），化簡得 t'=γ(t－vx/c2) (11) 把（2）、（3）、（4）、（11）放在一起，即S系到S'系的洛倫茲變換 x'=γ(x－vt)， y'=y， z'=z， t'=γ(t－vx/c2) (12) 根據相對性原理，由（12）得S'系到S系的洛倫茲變換 x=γ(x'+vt')， y=y'， z=z'， t=γ(t'+vx'/c2) (13) 洛倫茲變換結合動量定理和質量守恒定律，可以得出狹義相對論的所有結論。 愛因斯坦在1905年提出的狹義相對論（一種新的平直時空理論），出發點是兩條基本假設：狹義相對性原理和光速不變原理。理論的核心方程式是洛倫茲變換。狹義相對論預言了牛頓經典物理學所沒有的一些新效應（相對論效應），如時間膨脹、長度收縮、橫向多普勒效應、質速關系、質能關系等，它們已經獲得大量實驗的直接證明。狹義相對論已經成為現代物理理論的基礎之一：一切微觀物理理論（如基本粒子理論）和宏觀引力理論（如廣義相對論）都滿足狹義相對論的要求。這些相對論性的動力學理論已經被許多高精度實驗所證實 。
Basic axiom The principle of special relativity: all the laws of Physics (mechanics, electromagnetism dynamics law and other laws of interaction) are effective in all inertial systems; or, all the laws of physics equations remain unchanged in mathematical form Lorenz transform. Principle of constant speed of light: one way speed of light is constant and has nothing to do with the motion of the light source. In other words, the speed of light in a vacuum is constant in all inertial systems. Derivation process Lorenz transform can be derived from the special relativity principle and the speed of light invariant principle. According to the following two basic principles, the derivation of the transformation of coordinates. The assumption is that there are two inertial coordinate system S series, S'series, S' series of the origin O'relative to the origin of the O system S at the rate of V along the X axis of the positive direction of motion. The spatial and temporal coordinates of any event in S system and S'system are (x, y, Z, t), (X', Y', z',, t'). T', t are S series and S' system time. Two the inertial coordinate system coincides with the start time. If x= 0, then =0 x'+vt'. This is a necessary condition for the transformation to be satisfied, so that the coordinates of any one event can be guessed from the S'system to the S system. X= gamma (x'+vt') (1) In the formula, the constant gamma is introduced, named Lorenz factor. The relativity principle is introduced, that is, the form of the physical equation of different inertial systems should be the same. Therefore, the coordinate transformation from S system to S'system is the X'= gamma (Xvt) (2) Y and Y', Z and z' transform can be directly drawn, that is Y'=y (3) Z'=z (4) The (2) into (1), t'solution T'= gamma T + (1 - 2) x/ gamma V (5) On the basis of the above derivation, the principle of the speed of light is introduced to search for the value of gamma. The (X'), which is coincident with the origin O (O'), emits a beam of light along the X axis, and the wave front coordinates (X, Y, Z, T), (, Y',, Z',, T') are located. According to the principle of constant speed of light, there are X=cT (6) X'=cT'(7) The theory of relativity of the speed of light: the coordinate value X is equal to the speed of light C time T, the coordinate value X'is equal to the speed of light C time T'. (1) (2) by multiplying Xx'= gamma 2 (Xx'x'vt+xvt'v2tt') (8) To wave front this event as an object, then (8) XX'= gamma 2 (XX'X'VT+XVT'V2TT') (9) (6) (7) (9), by simplifying the Lorenz factor Gamma = (1 - (v/c) 2) 1/2 (10) (10) by (5), to simplify T'= gamma (Tvx/c2) (11) The (2), (3), (4), (11) put together, that is, S system to the S'Lorenz transform X'= gamma (Xvt), Y'=y, Z'=z, T'= gamma (Tvx/c2) (12) According to the relativity principle, by (12) the S'system to the S system of the Lorenz transform X= gamma (x'+vt'), Y=y', Z=z', T= gamma (t'+vx'/c2) (13) By combining the momentum theorem and the law of mass conservation, the Lorenz transform can obtain all the conclusions of the special relativity. Einstein's special theory of relativity in 1905 (a new flat space-time theory), the starting point is the two basic assumptions: the special relativity principle and the principle of the speed of light. The core of the theory is the Lorenz transform. Some new effects predicted Newton classical physics have special relativity (relativity), such as time dilation and length contraction, the transverse Doppler effect, the mass velocity relation, mass energy relation, they have a direct proof of a lot of experiments. Special relativity has become one of the basic theories of modern physics. All the micro physical theory (such as the basic particle theory) and the theory of gravity (such as general relativity) meet the requirements of special relativity. These relativistic dynamical theories have been proved by many high precision experiments.
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