- #1

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I am puzzled by a question about the concept of action. I have:

[tex]S=\int_{\tau_{1}}^{\tau_{2}}-mc^2d\tau = -mc^2\int_{a}^{b}ds[/tex]

with

[tex]ds = \sqrt{c^2dt^2-dx^2-dy^2-dz^2}[/tex]

The textbook says: "By the principle of least action

[tex]\delta S =0[/tex]

and so

[tex]\delta\int_{a}^{b}ds=0[/tex]

The integral takes its maximum value along a straight world-line and so this implies reassuringly that free particles move along straight lines."

I don't understand the last sentence. What is a straight world-line? Is it a path along the time axis? and how do we show the result mathematically?

Thank you for any help!