3. Solutions and
extending the model to the Strong and Weak
Forces
In the last section we saw how we could explain the
electromagnetic force using the exchange of virtual photons. We
also came up with a few problems:
1. How can you do an attractive force using this sort of picture?
The Feynman diagram provides a very pretty picture of electron-electron repulsion but we should not get too carried away and think that this is an accurate picture of how it happens: the tracks are not the actual paths of the particles. There is another form of Heisenberg's Uncertainty Principle for position and momentum so we cannot know the path in this much detail. Feynman diagrams are a pictorial shorthand for doing probability calculations for particle interactions.
A classical picture of the exchange model that describes
attraction and repulsion is as follows: the two particles are
imagined to be like people sitting on frictionless trays in the
middle of an iced-over lake. If one person throws a heavy ball to
the other then the thrower will recoil on throwing it and the
catcher will recoil on catching it. For an attractive force we use
boomerangs! The thrower faces away from the other person and
throws the boomerang, recoiling towards the catcher. The boomerang
flies behind the catcher; thus the catcher recoils towards the
thrower!
2. This is a very jerky picture - forces like this are smooth.
3. The electromagnetic force (Coulomb's law) is infinite - how can we borrow energy if the photon has to travel an infinite distance?
The single photon that we have considered can be thought of as being the sum of an infinite number of photons that are exchanged during the interaction from when the two particles are an infinite distance apart through the point of closest approach and out to an infinite distance apart again.
Long-range photons are not a problem; there is no lower limit
to the frequency of a photon and therefore no lower limit to its
energy. As the energy violation gets less the time it can go
undetected for gets longer and therefore the further it can travel
between the charged particles. A photon of zero energy can be
borrowed for ever and can travel an infinite distance!
4. Very clever but does it work for the other forces?
The electromagnetic force has an infinite range and therefore needs a zero mass exchange particle. The Strong and Weak Nuclear forces however are very short-range and can be explained by giving them massive exchange particles.
If we create a massive exchange particle it will require energy of at least mc2 where m is the rest mass of the particle and therefore this state cannot last for longer than
If we let this particle travel at nearly the speed of light then the furthest distance it can travel is the speed of light, c multiplied by Dt. We call this distance the range of the force.
We know the range of the strong nuclear force between protons and neutrons in the atomic nucleus: it is about 10-15m
Rearranging the equation and substituting in values gives an exchange particle mass of
In 1935 using arguments along these lines Yukawa predicted this particle and in 1947 the pion was discovered with a mass similar to the above value! Yukawa and Powell, the experimenter who found it, shared the Nobel Prize.
The Weak Force has a much shorter range, about 10-18m. The mass of the weak force exchange particles should therefore be
The electroweak theory predicted the W+, W- and Z0 particles to carry the weak force and were discovered in 1983 at CERN with masses very similar to the prediction. Nobel Prizes all round!
These exchange particles are the way forces are described in the best theory of matter and radiation that we have at the moment. The exchange particles are called Bosons.
There are two other bosons in these theories - gravitons for the Gravitational force and gluons for the Strong Nuclear force. Gravity is infinite in range so gravitons have to have zero mass like the photon. They have not been detected yet although there are experiments looking for them.
The model does not work for gluons. Although gluons have been
discovered, the strong force between quarks acts in a very
different way to all the other forces: it gets stronger as
distance increases! We have got a long way with our simple
approach and gained some useful insights into the Standard Model
but full treatment of the strong force is going to have to wait.
Four out of five isn't bad though!