antization as an Eigenvalue Problem“. In this article, he published his now-famous Schrödinger’s equation, where he describes how the quantum state of a quantum system changes with time. This paper has been universally celebrated as one of the most important achievements of the twentieth century and created a revolution in most areas of quantum mechanics, as well as all physics and chemistry.
Interestingly enough, in time, Einstein would become displeased with the theory of quantum mechanics that he helped create, feeling that it was inspiring a sense of chaos and randomness in the sciences. In response, he made his famous quote: “God is not playing at dice”, and returned to the study of quantum phenomena.
This led him to propose the Einstein–Podolsky–Rosen paradox (EPR paradox) named for Einstien and his associates – Boris Podolisky and Nathan Rosen. In their 1935 article titled, “Can quantum-mechanical description of physical reality be considered complete?”, they claimed to demonstrate that quantum entanglement violated the local realist view of causality – with Einstein referring to it as “spooky action at a distance”.
In so doing, they asserted that the wave function of quantum mechanics did not provide a complete description of physical reality, an important paradox that would have important implications for the interpretation of quantum mechanics. While the EPR paradox would be proven incorrect after Einstein’s death, it helped contribute to a field that he helped create, but would later attempt to disprove until the end of his days.
Cosmological Constant and Black Holes:
In 1917, Einstein applied the General Theory of Relativity to model the structure of the universe as a whole. Though he preferred the idea of a universe that was eternal and unchanging, this was not consistent with his theories about relativity, which predicted that the universe was either in a state of expansion or contraction.
To address this, Einstein introduced a new concept to the theory, known as the Cosmological Constant (represented by a Lambda). The purpose of this was to rectify the effects of gravity and allow the whole system to remain an eternal, static sphere. However, in 1929, Edwin Hubble confirmed that the universe is expanding. After visiting the Mount Wilson Observatory with Hubble, Einstein formally discarded the cosmological constant.
However, the concept was revisited in late 2013, when a previously undiscovered manuscript by Einstein (titled “About the Cosmological Problem“) was discovered. In this manuscript, Einstein proposed a revision of the model, in which the constant was responsible for the creation of new matter as the universe expanded – thus ensuring that the average density of the universe never changed.
This is consistent with the now-obsolete Steady State model of cosmology (proposed later in 1949) and with today’s modern understanding of dark energy. In essence, what Einstein described in many of his biographies as his “biggest blunder” would eventually come to be reassessed and considered as part of a larger mystery of the universe – the existence of invisible mass and energy that maintains the cosmological balance.
In 1915, a few months after Einstein had published his Theory of General Relativity, German physicist and astronomer Karl Schwarzschild found a solution to the Einstein field equations that described the gravitational field of a point and spherical mass. This solution, now called the Schwarzschild radius, describes a point where the mass of a sphere is so compressed that the escape velocity from the surface would equal the speed of light.
In time, other physicists came to the same conclusions independently. In 1924, English astrophysicist Arthur Eddington commented on how Einstein’s theory allows us to rule out overly large densities for visible stars, claiming that they would “produce so much curvature of the space-time metric that space would close up around the star, leaving us outside (i.e., nowhere).”
In 1931, Indian-American astrophysicist Subrahmanyan Chandrasekhar calculated, using Special