“Every action has an equal and opposite reaction.”
I have a query about the word every in that sentence.
Suppose we have two objects A and B. A pushes B with a force of 5N and B will push A with a force of 5N. However, won’t the reaction that B has caused on A, serve as an action for A, causing A to again push B with its reaction and thus making a total of 10N? (And then, of course, B will also apply a force of 10N on A.)
Best Answer
The way we are all taught Newton's Laws (by reciting them like mantras as children) is unfortunate because the traditional wording is misleading in many ways.
A big problem (though not the only one) with the traditional wording of both Newton's second and third laws is that they incorrectly suggest cause and effect (and hence imply a chain of events, as you put it).
Newton's second law, for example, suggests that a force 'causes' an acceleration, implying it happens first. It doesn't. The force and the acceleration occur jointly and concurrently, despite the persistent misconception and stubborn illusion of a temporal sequence.
But let's not get distracted with the second law right now, because you are understandably perplexed by the third ...
Again, the wording of the third law suggests that an 'action' happens first and then it 'causes' a 'reaction'. If this were literally true, you'd have every right to cry infinite regress!
The truth is, the forces occur jointly and simultaneously, and are not the causes of each other. If you want a better way to think about it, you can hardly do better than the way Newton himself came up with the third law. He argued for it as follows:
Suppose you had a system of two objects interacting with each other, with no external forces acting on the system. Then you should be able to consider that system as a 'whole' if you want to, and from that perspective the system as a whole must not accelerate as it has no net force acting on it. But this can only be the case if the two objects making up the system have equal and opposite forces between them (i.e. all internal forces of the system must cancel out).
Do you see how this argument does not involve any 'causal sequence' or 'chain' of forces? It is just an observation about what must be the case in order for Newton's force-based scheme to work consistently.
Not convinced? Let me try an analogy. You and your friend each have a certain amount of money. You buy something from your friend. Your balance goes down and your friend's goes up. Was there a time-delayed causal sequence here? Nope. Your balance decreased concurrently (as you handed over the money) as your friend's balance increased. Looking at the system as a whole, we know that since no money flowed into or out of the system during the transaction, the net balance must be zero. Every payment entails a receipt and every receipt entails a payment, but, despite the illusion, there is no sequence (much less a perpetual one!).
Note: You could also translate this argument into the language of momentum conservation, but I have tried to answer the question in the same language in which you phrased it.
UPDATE: The 'infinite regress' problem highlighted here is not the only confusion that arises when we use the suggestive language of 'action' and 'reaction'. I've identified two other problems this language causes along with my proposed solution here.