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Name: Alan M. V.
Status: other
Age: 50s
Location: N/A
Country: N/A
Date: 8/22/2004

This is both a rather complicated and simple question but one that has always bothered and confused me.

It is always taught that the four forces - gravity, electro-magnetic,weak and strong nuclear forces are the result of the exchange of particles. Indeed, on one TV special concerning String Theory, I witnessed a so-called demonstration of this which showed two men in rowboats facing each other throwing a ball back and forth, the ball, representing the quantum particle that manifests the force. The subjects in their rowboats were shown being drawn to each other on the water as they continued to "play catch".

This brings about the question of the entire concept of attractive forces. If two protons in the nucleus are "stuck" together by the strong nuclear force by the exchange of a particle how does that in fact work?

The first proton would feel a repulsive "kick" as the gluon jumped to the other proton which should also feel a repulsive kick from the momentum of the gluon it absorbs and vice versa. It seems to me that ANY exchange of particles, waves or energy would ultimately turn out to be a REPULSIVE force and NOT an ATTRACTIVE force.

Please help me to understand this seemingly contradictory concept.

You are indeed correct! Gravity is mediated by the exchange of gravitons, EM forces by the exchange of photons, weak forces by intermediate bosons (W+, W-, and Z0) and strong forces by gluons, of which there are 8 kinds. Of course, these are just names, but I hope you enjoy knowing the vocabulary anyway.

As you correctly point out, one can simulate the force transmitted by force carriers being exchanged by tossing bowling balls back and forth. One weakness of this analogy, as you correctly point out, is that it always leads to a repulsive force. I presume you meant to say that "The subjects in their rowboats were shown being REPELLED by each other on the water as they continued to 'play catch'". However, exchange of particles can also lead to attractive forces. You cannot simulate that by throwing things to a friend because it is a basically quantum mechanical effect which cannot be simulated classically.

The quantum mechanics cannot easily be explained in an elementary way, but I will try to give you the flavor. Consider an electron which emits a photon which will interact with another electron. Afterwards, in the coordinate system in which the electron was at rest, you will see the photon speeding off with some kinetic energy and by conservation of momentum the electron is recoiling and so has some kinetic energy also. Notice that energy is not conserved! Initially the electron at rest has just its rest mass energy. Afterwards the energy is increased by the kinetic energies of both the electron and photon!

But energy must be conserved!!! The answer to this conundrum is provided by the Heisenberg Uncertainty Principle, one form of which can be written as dE * dt >= hbar, where dE is the uncertainty in the energy of a system, dt is the time available to measure that energy, and hbar is Planck's constant divided by two pi. Notice that if dt is VERY small, dE can be very large and so energy need not conserved by a large amount. So the mediating particle is virtual in that it cannot exist for long and in some sense its energy can be negative. So if you could exchange virtual bowling balls with your friend, you might produce an attractive force.

Notice that the mass of the mediating particle is related to the range of the force (how far apart the particles can be and still feel the force). For EM forces for which the mediating particle (the photon) has zero mass, it can have very little energy and so can exist a relatively long time. Since it has zero mass, it is always travelling at the speed of light. This explains why the electromagnetic force has an infinite range (though it falls off like the inverse square of the separation). Conversely the intermediate bosons have a large mass (close to 100 times the mass of the proton), so they must be given a relatively large amount of energy to exist at all, even in a virtual state. They there exist only for a very short time while mediating a force and so the force is very short range. Similarly the graviton mas zero mass so gravity has an infinite range and gluons have an intermediate mass and so the strong force has a short range, but much larger than the weak force.

I hope you find this helpful. Quantum mechanics is a mysterious business!

Best, Dick Plano, Professor of Physics emeritus, Rutgers University

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