In the (momentarily) comoving inertial coordinate system, we have u=(c,0,0,0), not (γc,0,0,0), and this is only at one specific moment. The four-acceleration is the rate of change of the four-velocity as a function of proper time, and the four-velocity is just the normalized tangent vector to the world line. The four-acceleration is telling us how that tangent vector's direction in spacetime is changing with proper time, so you can't compute it from knowledge of that direction at only one point on the world line.black_hole said:If say I transform into a rest frame, the only component of the four velocity that is nonzero is the time component which is γc but γ=dt/dτ so uβ∂β = d/dτ which makes the whole thing work! (yay)
You do, actually. Recall that the chain rule is about taking the derivative of the composition of two functions. Can you figure out what the two functions are in this case?black_hole said:yeah you really don't have to use chain rule
Fredrik said:You do, actually. Recall that the chain rule is about taking the derivative of the composition of two functions. Can you figure out what the two functions are in this case?
Yes, I noticed. My reply to it was deleted as well. I just said that in the homework forum, we try to give hints, not complete solutions. It can be hard to do this when the calculation is this short.andrien said:I replied to this thread by using chain rule which gives answer in one line.someone deleted it,and send me an infraction for it.
The Contracting over Indices Chain Rule is a mathematical rule used in tensor calculus to simplify and manipulate equations involving tensors. It is also known as the Einstein summation convention.
The rule states that when there are two indices in an equation that are repeated, they are automatically summed over in the final result. This allows for a more concise representation of tensor equations and reduces the number of terms that need to be written out.
The Contracting over Indices Chain Rule is important because it simplifies and streamlines calculations involving tensors, which are widely used in physics, engineering, and other scientific fields. It also allows for more elegant and concise representations of equations, making them easier to understand and work with.
Yes, there are some exceptions to the rule, such as when the indices are not repeated in the same order or when there are multiple terms in an equation with different index orders. In these cases, the rule cannot be applied and the full equation must be written out.
If you are working with tensor equations, you can use the Contracting over Indices Chain Rule to simplify and manipulate them. This can make your calculations more efficient and your equations easier to understand. It is important to understand the rules and any exceptions to ensure accurate and consistent results.