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Figure is a graph of t versus x. An arrow labeled e minus goes up and right and meets the base of another arrow labeled e minus going up and left. The junction is labeled z0 boson emitted from an electron. To the right of this is an arrow going up and left. The tip meets the base of another arrow going up and right. Both these are labeled v subscript e and the junction is labeled z0 boson absorbed by an electron neutrino. The two junctions on the graph are connected by a ray labeled z0. This points right and slightly up.
In this Feynman diagram, the exchange of a virtual Z 0 carries the weak nuclear force between an electron and a neutrino.

Electromagnetic force

According to QED, the electromagnetic force is transmitted between charged particles through the exchange of photons. The theory is based on three basic processes: An electron travels from one place to the next, emits or absorbs a photon, and travels from one place to another again. When two electrons interact, one electron emits the photon and the other receives it ( [link] ). Photons transfer energy and momentum from one electron to the other. The net result in this case is a repulsive force. The photons exchanged are virtual. A virtual particle    is a particle that exists for too short a time to be observable. Virtual photons may violate the law of conservation of energy. To see this, consider that if the photon transit time Δ t is extremely small, then Heisenberg’s uncertainty principle states that the uncertainly in the photon’s energy, Δ E , may be very large.

Figure shows four arrows labeled e minus. One goes up and right and meets the base of another arrow going up and left. To the right of this is an arrow going up and left. The tip meets the base of another arrow going up and right. The two junctions on the graph are connected by a wavy line labeled virtual photon. This points right and slightly up.
Feynman diagram of two electrons interacting through the exchange of a photon.

To estimate the range of the electromagnetic interaction, assume that the uncertainty on the energy is comparable to the energy of the photon itself, written

Δ E E .

The Heisenberg uncertainly principle states that

Δ E h Δ t .

Combining these equations, we have

Δ t h E .

The energy of a photon is given by E = h f , so

Δ t h h f 1 f = λ c .

The distance d that the photon can move in this time is therefore

d = c Δ t c ( λ c ) = λ .

The energy of the virtual photon can be arbitrarily small, so its wavelength can be arbitrarily large—in principle, even infinitely large. The electromagnetic force is therefore a long-range force.

Weak nuclear force

The weak nuclear force is responsible for radioactive decay. The range of the weak nuclear force is very short (only about 10 −18 m) and like the other forces in the Standard Model, the weak force can be described in terms of particle exchange. (There is no simple function like the Coulomb force to describe these interactions.) The particle exchanged is one of three bosons: W + , W , and Z 0 . The Standard Model predicts the existence of these spin-1 particles and also predicts their specific masses. In combination with previous experiments, the mass of the charged W bosons was predicted to be 81 GeV/ c 2 and that of the Z 0 was predicted to be 90 GeV/ c 2 . A CERN experiment discovered particles in the 1980s with precisely these masses—an impressive victory for the model.

The weak nuclear force is most frequently associated with scattering and decays of unstable particles to light particles. For example, neutrons decay to protons through the weak nuclear force. This reaction is written

n p + e + ν e ,

where n is the neutron, p is a proton, e is an electron, and ν e is a nearly massless electron neutrino. This process, called beta decay, is important in many physical processes. A Feynman diagram of beta decay is given in [link] (a). The neutron emits a W and becomes a proton, then the W produces an electron and an antineutrino. This process is similar to the scattering event

Practice Key Terms 5

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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