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## Summary:

- Why do we need to divide dX/dT, where dT is time according to particle.

## Main Question or Discussion Point

So I understand that time is now part of the four vector, and so dividing delta X by delta t (time according to me), would produce just c as the first dimension of the vector, which gives us no intuition as to how fast time is moving for the observer, so is not useful.

I understand why we divide by dT for the first dimension, but I don't understand why this is useful for the other spacial dimensions. What does dX1/dT, dX2/dT... Really mean intuitively? It means the distance between 2 events in my frame divided by time in the frame of the particle. But what does this enable us to do that couldn't be done by dividing dX1/dt?

So my class is defining the four vector for an event as this

X = (ct, x, y, z) (first is time * c, last 3 are spacial components)

dX/dt = (c, dx/dt, dy/dt, dz/dt)

V = dX/dT = dX/dt * dt/dT = (c/sqrt(1-v^2/c^2), v/sqrt(1 - v^2/c^2))

I understand why we divide by dT for the first dimension, but I don't understand why this is useful for the other spacial dimensions. What does dX1/dT, dX2/dT... Really mean intuitively? It means the distance between 2 events in my frame divided by time in the frame of the particle. But what does this enable us to do that couldn't be done by dividing dX1/dt?

So my class is defining the four vector for an event as this

X = (ct, x, y, z) (first is time * c, last 3 are spacial components)

dX/dt = (c, dx/dt, dy/dt, dz/dt)

V = dX/dT = dX/dt * dt/dT = (c/sqrt(1-v^2/c^2), v/sqrt(1 - v^2/c^2))

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