Monday, 1 June 2020

newtonian mechanics - What exactly makes a force conservative?


I get that forces can be classified as either conservative or non-conservative, depending on whether the work done in a round trip is zero or non-zero.


What property of the force makes it to be, conservative or non-conservative, so that the work done in a round trip is zero/non-zero?


Note: I'm not asking the conditions for a force to be conservative. I'm asking what exactly makes it conservative.



Answer



All fundamental forces are conservatives and I would say that this is a postulate. Fundamental physics is constructed in such way that there is a quantity called energy which can be assigned to every possible state. If any fundamental process seems to violate conservation of energy we nowadays believe that there are some states, processes or even interactions that we are missing to take into account. Once we are able to take into account every state and interaction, the system and its interactions are conservative.


On the other hand, at macroscopic level, most of times we are not able to describe the system in terms of fundamental forces. We need to replace the zillions of coupled equations describing the dynamics of the system by a single equation or force, which we shall call effective, and which can describe the macroscopic results we observe. However, in this process we may miss many of the states and processes occurring such that we are no longer able to keep track of the mechanical energy balance. Energy balance would fail unless we consider other forms of energy, such as heat, which is also an effective quantity. A classic example is friction. We are not able to describe two macroscopic surfaces interacting in terms of every microscopic particle participating in the process. So we forget about it and assume there is an effective force called friction. Mechanical energy balance fails and we need to assume that the effective missing energy is present in the form of heat. That is why friction is non conservative. Another example is that of an time varying potential. It is only non conservative because we are effectively replacing a large, with many particles and closed system by one small, with few particles under external interaction. There is something that we are not able to keep track whose effect is the same as of a time varying potential.


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