Why Are the Terms Squared in the Lorentz Transformation?

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Discussion Overview

The discussion revolves around the mathematical formulation of the Lorentz transformation in special relativity, specifically focusing on the reasoning behind the squaring of terms in the equations presented in a paper. The scope includes conceptual clarification and mathematical reasoning related to the geometry of spacetime.

Discussion Character

  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant questions the assumption regarding the squared terms in the Lorentz transformation, seeking clarification on their necessity.
  • Another participant references the Pythagorean theorem, explaining that the relationship between the sides of a right triangle involves squaring the lengths, which can be extended to three-dimensional space.
  • A further contribution reiterates the extension of the Pythagorean theorem, emphasizing that the square of the hypotenuse is equal to the sum of the squares of the other sides, suggesting a geometric interpretation of the squared terms.

Areas of Agreement / Disagreement

Participants appear to agree on the geometric interpretation of the squaring of terms as an extension of the Pythagorean theorem, though the initial question remains open without a definitive resolution.

Contextual Notes

The discussion does not address potential limitations or assumptions underlying the application of the Pythagorean theorem to the context of spacetime in special relativity.

Dark_knight90
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Hello
This is a part of a simple paper about special relativity

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

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

thank you
 
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Do you remember the Pythagorean rule? In two-dimensional space, \Delta x and \Delta y are the lengths of two sides of a right triangle, and \Delta r is the length of the hypotenuse:

(\Delta r)^2 = (\Delta x)^2 + (\Delta y)^2

What you have is the three-dimensional version.
 
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.
 
Got it .. Thank you :)
 

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