I was reading about work. My thoughts are that work is the quantity somewhat related to the total momentum transfer over a distance. This is a way to predict an objects path over another distance. Evidently this work does not depend on time. Now what the heck does work mean in spacetime? Please make it seem as intuitive and as logical, thanks.
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2$\begingroup$ You are wrong. If you read the definitions, you would have "total energy transfer over a distance", not momentum. Now, it is a complete mystery why it has to be the case that the time rate of change of momentum is equal to the position rate of change of potential energy, but you need to at least get this correct before you can start asking more. $\endgroup$– naturallyInconsistentCommented Aug 13 at 7:46
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3$\begingroup$ I am very confused as to what is actually being asked... $\endgroup$– Kenny LauCommented Aug 13 at 12:39
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$\begingroup$ "My thoughts are that work is the quantity somewhat related to the total momentum transfer over a distance. " Did you read the article you linked to? $\endgroup$– WillOCommented Aug 13 at 18:51
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In spacetime space is unified with time into the spacetime four-vector, which is written $(c t, x,y,z)$. There are other four-vectors which unify concepts in spacetime that were thought to be separate in earlier physics. For example, the four-momentum unites energy and momentum. Energy is to momentum as time is to space: $(E/c,p_x,p_y,p_z)$.
Power is the rate of work, which is the change in energy, so power is the rate of change of energy. Similarly, force is the rate of change of momentum. So since energy and momentum are unified, we would naturally expect the rate of change of energy (power) and the rate of change of momentum (force) to be unified. This is the four-force: $\gamma \ ( P/c, f_x, f_y, f_z)$ where the $\gamma$ arises from how the derivative is taken in spacetime.
So, to directly answer the question, in spacetime the rate of work is the time component of the force in spacetime.
