Energy in Special Relativity

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I'm reading Taylor and Wheeler's, Exploring Black Holes.

I was doing okay until I reached their derivation of energy in Special Relativity.

They arrived at this equation:

[tex] \frac{t}{\tau} = \frac{E}{m} [/tex]

Tau is proper time, t is the frame time, E is energy and m is mass.

The authors used the Principle of Extremal Aging to derive the equation. How did they arrive at E/m as a constant of motion?
 
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robphy
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H-bar None said:
They arrived at this equation:

[tex] \frac{t}{\tau} = \frac{E}{m} [/tex]

Tau is proper time, t is the frame time, E is energy and m is mass.
t is the time-component of the position 4-vector with magnitude [tex]\tau [/tex].
[tex]t=\gamma \tau [/tex]

E is the time-component of the momentum 4-vector with magnitude [tex]m [/tex].
[tex]E=\gamma m [/tex]
 
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:confused:

I sort of understand the 4-vector part. How does that relate to "E/m"?
I'm going to do some more reading check back with you later on in life.

Could go into a litte more detail, maybe I'm missing something.
Thanks for the response.
 
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robphy
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Since [tex]t=\gamma \tau [/tex], we have [tex]\frac{t}{\tau}=\gamma[/tex].
Since [tex]E=\gamma m [/tex], we have [tex]\frac{E}{m}=\gamma[/tex].

Thus, [tex]\frac{t}{\tau}=\gamma=\frac{E}{m}[/tex].
 

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