# I need to understand the Lorentz transformation [closed]

Two observers A and B, in different initial system describe the same physical event with their particular, different space time coordinates . Let the coordinate of the event be $x^\mu$ for observer A and ${x^\prime}^\mu$ for observer B .Both coordinates are connected by means of the Lorentz transformation. $${x^\prime}^\mu = \sum_{\mu=0}^{3}a^{\nu}_{\mu}x^\mu\equiv a^{\nu}_{\mu}x^\mu\ = (\hat{a}\overset{\Rightarrow}{x})$$ Where $\hat{a}$ denotes the abbreviated version of the transformation matrix and $\overset{\Rightarrow}{x}$ is a 4 dimensional world vector .

I need to understand the Lorentz transformation equation that how it transformed .

EDITED : How both coordinates are connected in that transformation .

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So, which part are you trying to understand? Describe it more explicit in your questions. –  hwlau Jan 1 '13 at 8:03
Forhad_jnu, hwlau is right, it's not at all clear what you want to know. Once you edit the question to make it clear what you're asking, I'll be happy to reopen this. Here's a hint: it can sometimes help you formulate a clearer question if you try to phrase your question as a question. –  David Z Jan 1 '13 at 8:20
The equation already specified explicitly how to relate the x' and x using the summation. What is the problem then? –  hwlau Jan 1 '13 at 8:28
Why did we use 4 dimensional world vector ? –  Unlimited Dreamer Jan 1 '13 at 8:35
@Forhad_jnu: we usually choose our axes so the $x$ axis lines up with the direction of motion. In that case the $y$ and $z$ coordinates are unchanged by the Lorentz transformation and the problem becomes two dimensional $(t, x)$ to $(t', x')$. However in the general case the axes are not aligned with the direction of motion and all four components of the position will change. –  John Rennie Jan 1 '13 at 9:18