- #1
Hyperreality
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The four velocity component u^\mu with coordinate of x^\mu(\lambda) is given by
u^\mu = \frac{dx^\mu}{d\lambda}
where \lambda is the proper time. So, the component of acceleration a^\mu is
a^\mu = \frac{du^\mu}{d\lambda}
Using the chain rule we have
a^\mu = \frac{\partial u^\mu}{\partial x^\alpha} \frac{dx^\alpha}{d\lambda} = u^\alpha \partial_{\alpha}u^\mu
Everything was straight forward except the last part, I don't understand what the notation of \partial_{\alpha} meant.
u^\mu = \frac{dx^\mu}{d\lambda}
where \lambda is the proper time. So, the component of acceleration a^\mu is
a^\mu = \frac{du^\mu}{d\lambda}
Using the chain rule we have
a^\mu = \frac{\partial u^\mu}{\partial x^\alpha} \frac{dx^\alpha}{d\lambda} = u^\alpha \partial_{\alpha}u^\mu
Everything was straight forward except the last part, I don't understand what the notation of \partial_{\alpha} meant.
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