Sometimes a mass will change to energy. Common examples of elements that make these changes we call radioactivity are radium and uranium. An atom of uranium can lose an "alpha particle" (the atomic nucleus of helium) and become a new element with a lighter nucleus. Then that atom will emit two electrons, but it will not be stable yet. It will emit a series of alpha particles and electrons until it finally becomes the element Pb or what we call lead. By throwing out all these particles that have mass it has made its own mass smaller. It has also produced energy.
In most radioactivity, the entire mass of something does not get changed to energy. In an atomic bomb, uranium is transformed into krypton and barium. There is a slight difference in the mass of the resulting krypton and barium, and the mass of the original uranium, but the energy that is released by the change is huge. One way to express this idea is to write Einstein's equation as:
E = (m – m) c
The c in the equation stands for the speed of light squared. To square something means to multiply it by itself, so if you were to square the speed of light, it would be 299,792,458 meters per second, times 299,792,458 meters per second, which is approximately
(3•10) =
(9•10 meters)/seconds=
90,000,000,000,000,000 meters/seconds
So the energy produced by one kilogram would be:
E = 1 kg • 90,000,000,000,000,000 meters/seconds
E = 90,000,000,000,000,000 kg meters/seconds
or
E = 90,000,000,000,000,000 joules
or
E = 90,000 terajoule
About 60 terajoules were released by the atomic bomb that exploded over Hiroshima. So about two-thirds of a gram of the radioactive mass in that atomic bomb must have been lost (changed into energy), when the uranium changed into krypton and barium.
The idea of a Bose-Einstein condensate came out of a collaboration between S. N. Bose and Prof. Einstein. Einstein himself did not invent it but, instead, refined the idea and helped it become popular.
The concept of zero-point energy was developed in Germany by Albert Einstein and Otto Stern in 1913.
In classical physics, momentum is explained by the equation:
where
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:
where
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 m = 0, then:
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 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:
which is just
Therefore, the quantity "m" 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:
In this case, we can say that E = mc is also true for moving particles.
The General Theory of Relativity was published in 1915, ten years after the special theory of relativity was created. Einstein's general theory of relativity uses the idea of spacetime. Spacetime is the fact that we have a four-dimensional universe, having three spatial (space) dimensions and one temporal (time) dimension. Any physical event happens at some place inside these three space dimensions, and at some moment in time. According to the general theory of relativity, any mass causes spacetime to curve, and any other mass follows these curves. Bigger mass causes more curving. This was a new way to explain gravitation (gravity).
General relativity explains gravitational lensing, which is light bending when it comes near a massive object. This explanation was proven correct during a solar eclipse, when the sun's bending of starlight from distant stars could be measured because of the darkness of the eclipse.
General relativity also set the stage for cosmology (theories of the structure of our universe at large distances and over long times). Einstein thought that the universe may curve a little bit in both space and time, so that the universe always had existed and always will exist, and so that if an object moved through the universe without bumping into anything, it would return to its starting place, from the other direction, after a very long time. He even changed his equations to include a "cosmological constant," in order to allow a mathematical model of an unchanging universe. The general theory of relativity also allows the universe to spread out (grow larger and less dense) forever, and most scientists think that astronomy has proved that this is what happens. When Einstein realized that good models of the universe were possible even without the cosmological constant, he called his use of the cosmological constant his "biggest blunder," and that constant is often left out of the theory. However, many scientists now believe that the cosmological constant is needed to fit in all that we now know about the universe.
A popular theory of cosmology is called the Big Bang. According to the Big Bang theory, the universe was formed 15 billion years ago, in what is called a "gravitational singularity". This singularity was small, dense, and very hot. According to this theory, all of the matter that we know today came out of this point.
Einstein himself did not have the idea of a "black hole", but later scientists used this name for an object in the universe that bends spacetime so much that not even light can escape it. They think that these ultra-dense objects are formed when giant stars, at least three times the size of our sun, die. This event can follow what is called a supernova. The formation of black holes may be a major source of gravitational waves, so the search for proof of gravitational waves has become an important scientific pursuit.
Many scientists only care about their work, but Einstein also spoke and wrote often about politics and world peace. He liked the ideas of socialism and of having only one government for the whole world. He also worked for Zionism, the effort to try to create the new country of Israel.
Prompted by his colleague L. E. J. Brouwer, Einstein read the philosopher Eric Gutkind's book "Choose Life", a discussion of the relationship between Jewish revelation and the modern world. On January 3, 1954, Einstein sent the following reply to Gutkind: "The word God is for me nothing more than the expression and product of human weaknesses, the Bible a collection of honourable, but still primitive legends which are nevertheless pretty childish. ... For me the Jewish religion like all other religions is an incarnation of the most childish superstitions." In 2018 his letter to Gutkind was sold for $2.9 million.