Massless particles
In relativity, all energy moving along with a body adds up to the total energy, which is exactly proportional to the relativistic mass. Even a single photon In physics, a photon is an elementary particle, the quantum of the electromagnetic field and the basic "unit" of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force. The effects of this force are easily observable at both the microscopic and macroscopic level, because the, graviton In physics, the graviton is a hypothetical elementary particle that mediates the force of gravity in the framework of quantum field theory. If it exists, the graviton must be massless and must have a spin of 2 (because gravity is a second-rank tensor field[clarification needed]). To prove the existence of the graviton, physicists must be able to, or neutrino Neutrinos are elementary particles that often travel close to the speed of light, lack an electric charge, are able to pass through ordinary matter almost undisturbed and are thus extremely difficult to detect. Neutrinos have a minuscule, but nonzero mass. They are usually denoted by the Greek letter ν (nu) traveling in empty space has a relativistic mass, which is its energy divided by c2. But the rest mass of a photon is slightly subtler to define in terms of physical measurements, because a photon is always moving at the speed of light—it is never at rest.
If you run away from a photon, having it chase you, by moving fast enough in the same direction, when the photon catches up to you the photon would be seen as having less energy, and even less the faster you were traveling when it caught you. As you approach the speed of light, the photon looks redder and redder, by doppler shift The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842, is the change in frequency of a wave for an observer moving relative to the source of the waves. It is commonly heard when a vehicle sounding a siren approaches, passes and recedes from an observer. The received frequency is increased (compared to the (although for a photon the Doppler shift is relativistic), and the energy of a very long-wavelength photon approaches zero. This is why a photon is massless; this means that the rest mass of a photon is zero. A massless particle in relativity is the limit of a particle with very small mass, but which is moving so close to the speed of light, so that it has a non-negligible total energy.
Two photons moving in different directions can't both be made to have arbitrarily small total energy by changing frames, by chasing them. The reason is that in a two-photon system, the energy of one photon is decreased by chasing it, but the energy of the other will increase. Two photons not moving in the same direction still have an inertial frame In physics, an inertial frame of reference is a reference frame, tied to the state of motion of an observer, with the property that each physical law portrays itself in the same form in every inertial frame. The contrasting case is the set of non-inertial frames, in which the laws of physics change from frame to frame, and the usual forces where the combined energy is smallest, but not zero. This is called the center of mass The center of mass of a system of particles is a specific point where, for many purposes, the system behaves as if its mass were concentrated there. The center of mass is a function only of the positions and masses of the particles that compose the system. In the case of a rigid body, the position of its center of mass is fixed in relation to the frame or the center of momentum frame; these terms are almost synonyms (the center of mass frame is the special case of a center of momentum frame where the center of mass is put at the origin). If you move at the same direction and speed as the center of mass of the two photons, the total momentum of the photons is zero. Their combined energy E in this frame gives them, as a system, a mass equal to the energy divided by c2. This mass is called the invariant mass The invariant mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference. When the system as a whole is at rest, the invariant mass is equal to the total energy of the system divided by c2, which is equal to the mass of the of the pair of photons together.
If the photons formed by the collision of a particle and an antiparticle, the invariant mass is the same as the total energy of the particle and antiparticle (their rest energy plus the kinetic energy), in the center of mass frame where they are moving in equal and opposite directions. If the photons are formed by the disintegration of a single particle with a well-defined rest mass, like the neutral pion In particle physics, a pion is any of three subatomic particles: π0, π+ and π−. Pions are the lightest mesons and play an important role in explaining low-energy properties of the strong nuclear force, the invariant mass of the photons is equal to rest mass of the pion. In this case, the center of mass frame for the pion is just the frame where the pion is at rest, and the center of mass doesn't change. After the two photons are formed, their center of mass is still moving the same way the pion did, and their total energy in this frame adds up to the mass energy of the pion. So the invariant mass of the photons is equal to the pion's rest energy. So by calculating the invariant mass The invariant mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference. When the system as a whole is at rest, the invariant mass is equal to the total energy of the system divided by c2, which is equal to the mass of the of pairs of photons in a particle detector, pairs can be identified which were probably produced by pion disintegration.
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