If every action has an equal opposite reaction, why isn't the world at a stand-still?
Sir Isaac Newton is one of the top physicists of all times, and a key figure in the scientific revolution. In 1687 he published his book "Mathematical Principles of Natural Philosophy", where he laid the foundation of classical mechanics.
In his book, he formulated the famous three laws of motion (known, naturally, as "Newton's laws of motion"):
First law: When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force. Second law: The vector sum of the external forces F on an object is equal to the mass m of that object multiplied by the acceleration vector a of the object: F = ma. Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.
Newton used these laws to explain and investigate the motion of many physical objects and systems. For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion.
So, here is the source of confusion. According to Newton's third law of motion, when a body exerts a force on a second body, the second body exerts force equal in magnitude, but opposite in direction on the first body. So, indeed, "every action has an opposite reaction": but one has to be careful in identifying the bodies onto which the force associated with these action applies. Since the forces apply to different bodies, the fact that every action has a reaction does not mean that the world needs to be at stand still.
To demonstrate this, let's take a simple example. Suppose you throw a ball in the air at an angle to the horizontal. Once the ball leaves your hand, it is subject to the force of gravity, which pulls it down to the ground (more precisely: towards the centre of the earth). As a result of this force, the ball will make a parabolic trajectory: first rises, until it reaches some maximum height, and then reverse its direction and falls down at increasing speed.
However, at the same time as the ball falls towards the ground, being pulled by gravity, the ball itself also exerts gravitational force on the earth!. This force, according to Newton's third law, is equal in magnitude, and opposite in direction to the gravitational force that the earth exerts on the ball. Thus, the earth is being pulled towards the ball!. We could say that "the entire earth falls towards the ball", in exactly the same way as the ball falls towards the earth. Of course, the difference is that the earth is much much much bigger than the ball. Thus, while the outcome of the gravitational force that the earth exerts on the ball can easily be seen (the ball falls), the outcome of the gravitational force that the ball exerts on the earth are so tiny, that they can very hardly be noticed (or measured). Nonetheless, they do exist. So the world really isn't really at a stand still.