## Special relativity

In the special relativity paper (in 1905), Einstein noted that, given a specific definition of the word "force" (a definition which he later agreed was not advantageous), and if we choose to maintain (by convention) the equation mass x acceleration = force, then one arrives at

as the expression for the

transverse massThe transverse mass is a useful quantity to define for use in particle physics as it is invariant under Lorentz boost along the z direction. In natural units it is:Hadron collider physicists use another definition of transverse mass, in the case of a decay into two particles:-References: - See...

of a fast moving particle. This differs from the accepted expression today, because, as noted in the footnotes to Einstein's paper added in the 1913 reprint, "it is more to the point to define force in such a way that the laws of energy and momentum assume the simplest form", as was done, for example, by Max Planck in 1906, who gave the now familiar expression

for the transverse mass.

As Miller points out, this is equivalent to the transverse mass predictions of both Einstein and Lorentz. Einstein had commented already in the 1905 paper that "With a different definition of force and acceleration, we should naturally obtain other expressions for the masses. This shows that in comparing different theories... we must proceed very cautiously."

## Superconductivity

Einstein published (in 1922) a qualitative theory of superconductivity based on the vague idea of electrons shared in orbits. This paper predated modern quantum mechanics, and today is regarded as being incorrect. The current theory of low temperature superconductivity was only worked out in 1957, thirty years after the establishing of modern quantum mechanics. However, even today, superconductivity is not well understood, and alternative theories continue to be put forward, especially to account for high-temperature superconductors.

## Gravitational waves

After introducing the concept of gravitational waves in 1917, Einstein subsequently entertained doubts about whether they could be physically realized. In 1937 he published a paper saying that the focusing properties of geodesics in general relativity would lead to an instability which causes plane gravitational waves to collapse in on themselves. While this is true to a certain extent in some limits, because gravitational instabilities can lead to a concentration of energy density into black holes, for plane waves of the type Einstein and Rosen considered in their paper, the instabilities are under control. Einstein retracted this position a short time later.

## Black holes

Einstein denied several times that black holes could form. In 1939 he published a paper that argues that a star collapsing would spin faster and faster, spinning at the

speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

with infinite

energyIn physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

well before the point where it is about to collapse into a black hole. This paper received no citations, and the conclusions are well understood to be wrong. Einstein's argument itself is inconclusive, since he only shows that stable spinning objects have to spin faster and faster to stay stable before the point where they collapse. But it is well understood today (and was understood well by some even then) that collapse cannot happen through stationary states the way Einstein imagined. Nevertheless, the extent to which the models of black holes in classical general relativity correspond to physical reality remains unclear, and in particular the implications of the central singularity implicit in these models are still not understood. Efforts to conclusively prove the existence of event horizons have still not been successful.

Closely related to his rejection of black holes, Einstein believed that the exclusion of singularities might restrict the class of solutions of the field equations so as to force solutions compatible with quantum mechanics, but no such theory has ever been found.

## Quantum mechanics

In the early days of quantum mechanics, Einstein tried to show that the uncertainty principle was not valid. By 1927 he had become convinced that of its utility, but he always opposed it.

## EPR paradox

In the

EPR paperThe EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...

, Einstein argued that quantum mechanics cannot be a complete realistic and local representation of phenomena, given specific definitions of "realism", "locality", and "completeness". The modern consensus is that Einstein's concept of realism is too restrictive.

## Cosmological term

Einstein himself considered the introduction of the cosmological term in his 1917 paper founding cosmology as a "blunder". The theory of general relativity predicted an expanding or contracting universe, but Einstein wanted a universe which is an unchanging three dimensional sphere, like the surface of a three dimensional ball in four dimensions.

He wanted this for philosophical reasons, so as to incorporate

Mach's principleIn theoretical physics, particularly in discussions of gravitation theories, Mach's principle is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach....

in a reasonable way. He stabilized his solution by introducing a

cosmological constantIn physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...

, and when the universe was shown to be expanding, he retracted the constant as a blunder. This is not really much of a blunder – the cosmological constant is necessary within general relativity as it is currently understood, and it is widely believed to have a nonzero value today.

## Minkowski's work

Einstein did not immediately appreciate the value of Minkowski's four-dimensional formulation of special relativity, although within a few years he had adopted it within his theory of gravitation.

## Heisenberg's work

Finding it too formal, Einstein believed that Heisenberg's

matrix mechanicsMatrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925.Matrix mechanics was the first conceptually autonomous and logically consistent formulation of quantum mechanics. It extended the Bohr Model by describing how the quantum jumps...

was incorrect. He changed his mind when Schrödinger and others demonstrated that the formulation in terms of the

Schrödinger equationThe Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....

, based on wave-particle duality was equivalent to Heisenberg's matrices.

## Unified field theory

Einstein spent many years pursuing a

unified field theoryIn physics, a unified field theory, occasionally referred to as a uniform field theory, is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles to be written in terms of a single field. There is no accepted unified field theory, and thus...

, and published many papers on the subject, without success.