Energy

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ENERGY

In classical physics, energy is defined as the amount of work a body or system is capable of doing against a force. In elementary particle physics, the domain of the smallest known objects, quantum mechanics and special relativity govern physical behavior. Here energy is a more fundamental concept than force, and energy is a measure of the ability of a particle or system to change the state of another particle or system of particles. Energy can also be determined relative to the instruments with which elementary particles are manipulated: energy imparted to a charged particle by an accelerator is equal to the work done on the particle by the electric fields of the accelerator.

Types of Energy

The two most important forms of energy in elementary particle physics are kinetic energy (energy of motion) and rest energy. Rest energy is the energy associated with the mass of an elementary particle. Potential energy is associated with external fields, generally electric and magnetic. If a particle is composite, that is, composed of more fundamental constituents, such as the proton, which is composed of quarks, then internal potential energy can also be considered, but this potential energy, in combination with the internal kinetic and rest energy of the constituents, may also be considered as the rest energy of the composite particle. The difference between the rest energy of the composite particle and the combined rest energies of the constituents is called the binding energy of the composite particle. Albert Einstein showed with his special theory of relativity that this internal energy appears in the mass.

Kinetic energy must be defined relativistically for elementary particle physics because, as noted below, the energies of interest are typically large compared to the rest energies of at least some of the particles being studied. Using special relativity, we find the following relations between total energy E, rest energy E₀, mass m, kinetic energy T, and momentum p , where c is the speed of light: The relativistic momentum of a particle is defined as p = ?mv , where v is the velocity and ? is the Lorentz factor, ? = 1/?1 - v²/c² For speeds much less than c, the kinetic energy from the above equations reduces to the classical value, ½mv ².

Conservation of Energy and Virtual Processes

Energy is conserved in physical processes, that is, the total energy is unchanged, although it may be transformed, as in the transformation of kinetic energy into rest energy of new particles as a result of a collision of particles.

Conservation of energy (along with other conservation rules) constrains the possible energy transfers and particle transformations in collisions. The conservation laws are closely related to symmetry principles, that is, symmetries associated with changes that preserve the laws of physics. These symmetries may then tell us what processes are possible. Conservation of energy is related to time translation symmetry, that is, to the fact that the laws of physics are the same at different times.

An example of the constraint introduced by conservation of energy can be seen in the process by which the antiproton was discovered. This discovery was made in 1955 via the reaction ? + ? ? ? + ? + ? + p?, by colliding a high-energy proton with a stationary proton, where ? refers to the proton, ? to the antiproton. Conservation of energy requires that the kinetic energy of the incoming proton be sufficient to supply the additional rest energies of the newly created ? and p? as well as the kinetic energies of all the outgoing particles. For this process, we can calculate that the minimum kinetic energy of the incoming proton must be 5.6 GeV, while the proton beam energy in the actual experiment was 6.2 GeV, leaving additional kinetic energy to be distributed among the reaction products.

The Heisenberg uncertainty principle of quantum mechanics permits momentary violations of the conservation of energy. For example, the B meson decays into lighter particles by transforming to a W particle that is nearly 20 times more massive than the B. The W then decays very rapidly into the lighter decay products. These processes that violate strict conservation of energy for very short times cannot be observed directly and are called virtual processes. Nonetheless, events that would not be expected to be observed at all at a particular energy sometimes occur and can be explained by virtual processes. The uncertainty principle places strong constraints on the duration and probability of virtual processes, so these do not violate conservation of energy in directly observed events.

Energy and the Creation of New Particles

Because of the relation between energy and mass discovered in special relativity, it is possible to "trade" kinetic energy for mass in high-energy collisions. Particles that are much more massive than the initial particles can be created if sufficient energy is supplied by an accelerator. Heavy particles have been discovered in this way. For example, two protons, each having an energy of 500 GeV, can be brought to collide head on with the possibility, in principle, that two new particles are produced at rest with rest energies about 500 GeV each, or 500 times as much as the initial protons.

Momentum conservation requires that any momentum carried by the center of mass of a system of particles before collision continue with the center of mass after collision. This momentum associates energy with center-of-mass motion that is not available to create new particles or to explore internal structure. In fact, the only energy available for the purpose of investigating elementary particles is the energy of one particle relative to another. Therefore, when it is possible to make beams of both kinds of particles collide, it is most effective to collide them in such a way that the center of mass of the system of particles is at rest. This approach, used in colliding beam accelerators, makes all of the accelerator energy available to rest energies of the collision products, with any excess energy going to kinetic energies while maintaining the center of mass at rest.

Typical Energies of Interest in Elementary Particle Physics

Elementary particle physics is sometimes called high-energy physics. Energies of interest in elementary particle physics are large compared to the rest energies of at least some of the particles being studied for two reasons: (1) new particles of higher mass are created in collisions of sufficiently high energy; (2) particles have wavelike properties, with wavelength given by the de Broglie relation, ? = h/? , where h is Planck's constant, and p is the magnitude of the momentum. This means that particles will have a very short de Broglie wavelength only if they have very large momentum (and hence high kinetic energy). The particle wavelength determines how small a region of space can be probed experimentally, so to study internal structure of very small particles like protons, we need to do scattering experiments at very high momentum.

Typical units of energy in elementary particle physics are multiples of electron volts (eV). An electron volt is the amount of energy acquired by an electron as it falls through a potential difference of 1 V. Since electrons have exceedingly small charge, the eV is a small unit of energy (1 eV = 1.6 × 10^-19 J). Rest energies of elementary particles range from zero for photons, to 0.511 MeV (10⁶ eV) for electrons, nearly 1 GeV (10⁹ eV) for protons and neutrons, to 175 GeV for t quarks, the heaviest quarks.

Energy and Machines: Accelerators and Detectors

Accelerators are designed to produce directed particle beams with energies up to about 1 TeV, as of 2001. Beams of charged particles are accelerated by electric fields and are kept in a prescribed path by magnetic fields, sometimes in combination with electric fields. There are nine major operating accelerator facilities used in elementary particle physics. These include the Stanford Linear Accelerator, which accelerates electrons up to 50 GeV, and large circular synchrotrons at Fermilab in Illinois; the European Laboratory for Particle Physics (CERN) in Geneva, Switzerland; the Deutsches Elekronen-Synchrotron Laboratory (DESY) in Hamburg, Germany; the Japanese High-energy Accelerator Research Organization (KEK) in Japan; the Institute for High-energy Physics (IHEP) in Beijing, China; the Cornell Electron-Positron Collider (CESR); the Budker Institute of Nuclear Physics (BINP) in Russia; and at the Brookhaven National Laboratory in New York. The Fermilab machine accelerates protons to 900 GeV, with center-of-mass energies possible up to 1,800 GeV. A planned new facility, the LHC scheduled for 2007, will increase the energy of proton-proton collisions possible at CERN to 14 TeV in the center-of-mass reference frame.

Elementary particle detectors depend on the particles of interest interacting with some detector material and exchanging energy that can be measured. Detectors are designed to use some very well understood physical process, such as the interaction of charged particles with matter. Then the presence, properties, and sometimes tracks of the particles can be inferred. The details of these interactions with detectors have been analyzed for the various kinds of detectors in use in elementary particle studies, such as bubble and spark chambers, proportional counters, silicon strip detectors, magnetic spectrometers, and particle calorimeters.