How come there is no conservation of force?

[russ_watters]

The forces vary but their sum does not.


Applying Newton's 3rd law at every instant should give sum(Force vectors) = 0 at every time. Isn't this a stronger statement than normal conservation?

I don't know if it is a "stronger" statement, but it is a different statement.

 

[Phrak]

Phrak, what if the system contains momentum-carrying fields? What happens to \sum_{i} \textbf{p}_i when momentum is transferred from a field to a particle?

Phrak, you haven't addressed my question yet: what happens when there are momentum carrying fields involved?

If \sum_i\textbf{p}_i represents the sum of the momenta of all particles in a closed system, it needn't be constant, since fields can transfer momentum to particles. Momentum for the system will still be conserved, but only when you include the momentum in the fields (which will be an integral of a momentum density). However, when fields are present (even if you include their sources in your system), the sum of the forces on all the particles in a system need not by zero, even if momentum is conserved .

Consider a field propagating at finite speed (like light) towards a stationary particle. Prior to the interaction of the field and the particle, there are no forces acting on either and the only momentum is stored in the field. After the two interact, some momentum may be transferred to the particle, and hence some force was exerted on it. Momentum is conserved in this interaction, but force is not since there is no equal and opposite force exerted on the field (which is presumed massless).

I'd like to know the premises you are using. I am assuming Newton's three laws. From the OPs second post, this is the context in which the question was being asked. It should go without saying that all the other peripheral premises such as homogeneity of space should be assumed, right?

 

[Studiot]

Let us review what we mean by conservation, in the light of conservation of energy which we are all agreed on, and see how the concept can or cannot be applied to force.

Energy is a positive definite scalar quantity that can be simply aggregated. An energy change may be given a positive or negaive sign, but that is merely an accounting. The energy is always positive. It is definite because equality to zero implies no energy at all.

Energy conservation implies the statement "energy can be neither created nor destroyed". The total energy before, during and after a process never changes. Energy is merely transformed from one form to another or moved from one location to another.

So one thing I cannot do with this type of conservation is to deploy a law that allows the total energy to vary ie to be turned on or off.

Now consider the implication of applying this to a vector quantity.

Let us consider an athlete exercising in a gym on a running platform.
The forward velocity of the runner exactly matches the backwards velocity of the platform so the net velocity of the runner is zero. If it does not the runner moves forwards or backwards.

What is conserved in this situation?
It is certainly not velocity. It is location.
Can I justify the statement the total velocity does not change, whether the runner moves forwards, backwards or is stationary? Obviously not.
Nor can I justify the statement that zero net velocity means the absence of velocity - ask the runner how fast he is running.
And what of the total velocity in the universe if he runs or goes down the pub instead and does not run?

I think situation with force is more akin to the situation with velocity than with energy.

That is why I originally simply said that the concept was not applicable to force.