Lorentz transformation

  • #1
Dark_knight90
14
0
Hello
This is a part of a simple paper about special relativity

[PLAIN]http://img15.imageshack.us/img15/8789/91001769.jpg [Broken]

I don't understand the assumption in the red box .. why are they all squared ?

thank you
 
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Answers and Replies

  • #2
jtbell
Mentor
15,894
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Do you remember the Pythagorean rule? In two-dimensional space, [itex]\Delta x[/itex] and [itex]\Delta y[/itex] are the lengths of two sides of a right triangle, and [itex]\Delta r[/itex] is the length of the hypotenuse:

[tex](\Delta r)^2 = (\Delta x)^2 + (\Delta y)^2[/tex]

What you have is the three-dimensional version.
 
  • #3
ghwellsjr
Science Advisor
Gold Member
5,122
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That's basically an extension of the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two sides. You can then repeat the process, adding in the square of the length of the third side giving you the square of the total length.
 
  • #4
Dark_knight90
14
0
Got it .. Thank you :)
 

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