- #1

Arman777

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In a formal manner the 4-velocity defined as ##\vec{u} = \frac{d\vec{x}}{cd\tau}##. Now this is also equal to the unit tangent vector of the worldline. My confusion is actually more geometrical. ##d\vec{x}## is the infitesimal distance between two points in the worldline and ##cd\tau## is the infitesimal distance along the worldline. How can their ratio can give us the four-velocity ?

Note that in this definiton four-velocity its unitless.

Edit: For instance ##cd\tau = |d\vec{x}|_g = \sqrt{-g(d\vec{x}, d\vec{x})}## if ##d\vec{x}## is future directed.

This means that we are actually calculating $$\vec{u} = \frac{d\vec{x}}{|d\vec{x}|}$$ which seems strange. I guess 4-velocity in SR is just defined as the tangent vector to the worldline rather then the usual definition of the velocity in our world which is decribed as meter per second.

Note that in this definiton four-velocity its unitless.

Edit: For instance ##cd\tau = |d\vec{x}|_g = \sqrt{-g(d\vec{x}, d\vec{x})}## if ##d\vec{x}## is future directed.

This means that we are actually calculating $$\vec{u} = \frac{d\vec{x}}{|d\vec{x}|}$$ which seems strange. I guess 4-velocity in SR is just defined as the tangent vector to the worldline rather then the usual definition of the velocity in our world which is decribed as meter per second.

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