Yes indeed, not an easy question to answer without refering to energy conservation. Remember that energy conservation exists in two foirms potential and kinetic energy. All energy appears to be related to certain fields of force, e.g. the eletromagnetic field such that potential energy is stored or exists without being actualised by say a charge being placed in a given position in an electric field, the charge now posseses the potential to move, once it moves it makes use of this potential energy and expresses it through kinetic energy or energy of motion. Naturally it is the electric field which has made the charge move but in principle you can still talk of energy as a concept by itself because it has been found that all fields of force possess it and possess the ability to convert potential into kinetic and back again.

Even in the billiard ball example energy is transfered, this time through the Coulomb force holding atoms together in the two balls. This force allows the balls to hold themselves together and act as solid balls rather than some kind of mushy thing. This idea also holds for the concept of momentum of course which is also conserved. After the construction of general relativity and concepts from differential geometry and symmetry principles it was noticed that certain vector fields e.g d/dt, a differential can be used to say something about conservation priciples. In fact we see immediately that this gives rise to energy conservation dE/dt = 0, change in energy is constant over time.

However, many such so-called laws such as energy and momentum conservation are laws because they ahve been found to be obeyed and their absolute justification is not to understand but much more easily to be just accepted.

Consider for example why the speed of light is what it is, why is it constant and why is it not larger or smaller? At the moment there are no answers for this question. Much more physics yet to come I'd say.

Yes indeed, not an easy question to answer without refering to energy conservation. Remember that energy conservation exists in two foirms potential and kinetic energy. All energy appears to be related to certain fields of force, e.g. the eletromagnetic field such that potential energy is stored or exists without being actualised by say a charge being placed in a given position in an electric field, the charge now posseses the potential to move, once it moves it makes use of this potential energy and expresses it through kinetic energy or energy of motion. Naturally it is the electric field which has made the charge move but in principle you can still talk of energy as a concept by itself because it has been found that all fields of force possess it and possess the ability to convert potential into kinetic and back again.

Even in the billiard ball example energy is transfered, this time through the Coulomb force holding atoms together in the two balls. This force allows the balls to hold themselves together and act as solid balls rather than some kind of mushy thing. This idea also holds for the concept of momentum of course which is also conserved. After the construction of general relativity and concepts from differential geometry and symmetry principles it was noticed that certain vector fields e.g d/dt, a differential can be used to say something about conservation priciples. In fact we see immediately that this gives rise to energy conservation dE/dt = 0, change in energy is constant over time.

However, many such so-called laws such as energy and momentum conservation are laws because they ahve been found to be obeyed and their absolute justification is not to understand but much more easily to be just accepted.

Consider for example why the speed of light is what it is, why is it constant and why is it not larger or smaller? At the moment there are no answers for this question. Much more physics yet to come I'd say.

Hi Derek,

I'm prepared to have a go here based on Noether's theorem arguments (and some of these arguments seem to be stated in Frank's response also). I'm also going to assume we have one of the fancy frictionless pool tables. I'm also going to assume that the two billiard balls are the same mass, but that really doesn't change anything from the centre of mass point of view.

For a single billiard ball, momentum will be conserved as long as space is translationally invariant. Hence the ball continues on as it pleases until it reaches a discontinuity in space. In this case the other billiard ball, and for sake of argument we will assume that all of the present discussion is in the laboratory frame, and the second ball was initially at rest with respect to this frame.

OK, the first billard ball hits the second and because space is not translationally invariant, something has got to happen. There are Coulombic forces that work to repel the two balls and so the particles cannot co-exist (note that of course we do not need Pauli principal at the classical levels were are interested with here).

Now globally, the system is translationally invariant - the properties of space are the same everywhere, hence the momentum must be conserved. Of course we can take a microscopic view and observe each individual interaction between each particle (and in reality, each Coulombic force field), but because the space is globally invariant, so too must the momentum, which must therefore continue without being concerned about this interaction, hence being transferred from one ball to the other.

Conservation of energy also follows from the fact that the total system is also invariant under translations in time, although by the same reasoning above, it is not invariant for individual subsystems.

Noether aside, one of my good friends, Jared Cole, is fond of telling me that Conservation of Energy is really a bit of a dodge, because every time we do experiments we notice that energy is not conserved, and so we make up a new form of energy so that it IS conserved. Roll a ball up a hill, you start with kinetic energy, and end up with no kinetic energy: so we mus have gravitational potential energy. Explosion? No kinetic energy before hand: kinetic energy afterwards - so there must have been chemical potential energy that we used up. Things got hotter in your fusion reactor as the mass decreased? Mass-energy! If your energy budget doesn't work out, then you've missed some sort of energy and if no-one has seen it before you get to name it. This argument is only slightly facetious, and is a good way (in my opinion) to provoke deep thought into what energy really is and why its conservation is so central to physics.

Very intriguing and thought-provoking question.

Note however, that we are talking here about very specific situation, when the velocity of the attacking ball points exactly to the center of mass of the other, resting ball. After any other collision both balls wil be moving, albeit in different directions. The kinetic energy of this system will now be redistributed between its parts, rather than transferred from one ball to another. But let's return to the original situation. I think that the momentum, not kinetic energy, should be considered as a primary variable in this case. The impenetrability of balls is the reason why the effect occurs. Energy seems a secondary quatity, no matter that it is strictly related to momentum, as E=p^2/2m. Interestingly, we have the energy in first power and the momentum in a second power in this formula ("my" balls are not rotating) - another surprise. Things are going to be even more complicated: now the "transferred spirit" is no longer a scalar variable, it is a vector!