page_title: Albert Einstein
section_title: Momentum, mass, and energy
hierarchical_section_title: Albert Einstein / Momentum, mass, and energy
caption_attribution_description: English: Albert Einstein
context_page_description: Albert Einstein was a German-born scientist. He worked on theoretical physics. He developed the theory of relativity. He received the Nobel Prize in Physics in 1921 for theoretical physics. His famous equation is.
  At the beginning of his career, Einstein did not think that Newtonian mechanics was enough to reconcile the laws of classical mechanics and the laws of the electromagnetic field. Between 1902–1909 he developed the theory of special relativity to correct that. Einstein also thought that Isaac Newton's idea of gravity was not completely correct. So, he extended his ideas on special relativity to include gravity. In 1916 he published a paper on general relativity with his theory of gravitation.
  In 1933, Einstein was visiting the United States. In Germany, Adolf Hitler and the Nazis came to power. Einstein, being of Jewish ethnicity, did not return to Germany due to Hitler’s anti-Semitic policies. He lived in the United States and became an American citizen in 1940. On the beginning of World War II, he sent a letter to President Franklin D.
context_section_description: In classical physics, momentum is explained by the equation:
  p = mv
  where
  p represents momentum
  m represents mass
  v represents velocity (speed)
  When Einstein generalized classical physics to include the increase of mass due to the velocity of the moving matter, he arrived at an equation that predicted energy to be made of two components. One component involves "rest mass" and the other component involves momentum, but momentum is not defined in the classical way. The equation typically has values greater than zero for both components:
  E² = (m₀c²)² + (pc)²
  where
  E represents the energy of a particle
  m₀ represents the mass of the particle when it is not moving
  p represents the momentum of the particle when it is moving
  c represents the speed of light.
  There are two special cases of this equation.
  A photon has no rest mass, but it has momentum. (Light reflecting from a mirror pushes the mirror with a force that can be measured.) In the case of a photon, because its m₀ = 0, then:
  E² = 0 + (pc)²
  E = pc
  p = E/c
  The energy of a photon can be computed from its frequency ν or wavelength λ. These are related to each other by Planck's relation, E = hν = hc/λ, where h is the Planck constant (6.626×10⁻³⁴ joule-seconds). Knowing either frequency or wavelength, you can compute the photon's momentum.
  In the case of motionless particles with mass, since p = 0, then:
  E₀² = (m₀c²)² + 0
  which is just
  E₀ = m₀c²
  Therefore, the quantity "m₀" used in Einstein's equation is sometimes called the "rest mass." (The "0" reminds us that we are talking about the energy and mass when the speed is 0.) This famous "mass-energy relation" formula (usually written without the "0"s) suggests that mass has a large amount of energy, so maybe we could convert some mass to a more useful form of energy. The nuclear power industry is based on that idea.
  Einstein said that it was not a good idea to use the classical formula relating momentum to velocity, p = mv, but that if someone wanted to do that, he would have to use a particle mass m that changes with speed:
  mᵥ² = m₀² / (1 – v²/c²)
  In this case, we can say that E = mc² is also true for moving particles.
caption: Einstein in his later years, c. 1950s
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