View source for Einstein's unsuccessful investigations

{{More citations needed|date=November 2023}}

[[Albert Einstein]] conducted several unsuccessful investigations. These pertain to [[quantum mechanics]], [[superconductivity]], and his details on his own [[theory of relativity]].

== Special relativity ==

=== Transverse mass ===
{{Further|History of special relativity}}
In one of his three [[Annus mirabilis papers]] of 1905, on [[special relativity]], Albert 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) [[Newton's laws of motion|Newton's second law of motion]] {{Math|''F'' {{=}} ''ma''}} ([[mass]] times [[acceleration]] equals force), then one arrives at <math>\scriptstyle m/(1 - v^2/c^2)</math> as the expression for the [[transverse mass]] 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 <math>\scriptstyle m/\sqrt{1 - v^2/c^2}</math> for the transverse mass. 

As historian [[Arthur I. Miller]] points out, this is equivalent to the transverse mass predictions of both Einstein and [[Hendrik 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."<ref>{{Citation |author=Miller, Arthur I. |title=Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911) |url=https://archive.org/details/alberteinsteinss0000mill/page/325 |pages=[https://archive.org/details/alberteinsteinss0000mill/page/325 325–331] |year=1981 |location=Reading |publisher=Addison–Wesley |isbn=978-0-201-04679-3}}</ref>

=== Minkowski's work ===
{{See also|Minkowski space}}

Einstein did not immediately appreciate the value of [[Hermann Minkowski]]'s four-dimensional formulation of special relativity, although within a few years he had adopted it within his theory of gravitation.{{Citation needed|date=June 2010}}

== General relativity and cosmology ==
{{Further|History of general relativity}}

=== Black holes ===
{{Further|History of black holes}}
Einstein denied several times that [[black holes]] could form.{{Citation needed|date=June 2010}} In 1939 he published a paper that argues that a [[star]] collapsing would spin faster and faster, spinning at the [[speed of light]] with infinite [[energy]] well before the point where it is about to collapse into a [[Schwarzschild metric|Schwarzchild singularity]], or black hole.
{{quotation | The essential result of this investigation is a clear understanding as to why the "Schwarzschild singularities" do not exist in physical reality. Although the theory given here treats only clusters whose particles move along circular paths it does not seem to be subject to reasonable doubt that more general cases will have analogous results. The "Schwarzschild  cannot be concentrated arbitrarily. And this is due to the fact that otherwise the constituting particles would reach the velocity of light.<ref>{{cite journal |last1=Einstein |first1=Albert |title=On a Stationary System With Spherical Symmetry Consisting of Many Gravitating Masses |journal=Annals of Mathematics |date=October 1939 |volume=40 |issue=4 |pages=922–936 |doi=10.2307/1968902 |jstor=1968902 }}</ref>}}
Einstein's argument itself only shows that stable spinning objects have to spin faster and faster to stay stable before the point where they [[Gravitational collapse|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.

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.{{Citation needed|date=June 2010}}

=== Cosmological constant ===
Einstein himself considered the introduction of the [[cosmological constant]] in his 1917 paper founding [[cosmology]] as a "blunder".<ref name="Wright">{{cite web |last=Wright |first=Karen |date=30 September 2004 |title=The Master's Mistakes |url=http://discovermagazine.com/2004/sep/the-masters-mistakes/article_view?b_start:int=1&-C= |access-date=15 October 2009 |publisher=Discover Magazine}}</ref> The theory of [[general relativity]] predicted an expanding or contracting universe, but Einstein wanted a [[static 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 principle]] in a reasonable way. He stabilised his solution by introducing a cosmological constant, 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.

==Quantum mechanics==
{{Further|History of quantum mechanics}}

=== Heisenberg's work ===
Finding it too formal, Einstein believed that [[Werner Heisenberg]]'s [[matrix mechanics]] was incorrect. He changed his mind when [[Erwin Schrödinger]] and others demonstrated that the formulation in terms of the [[Schrödinger equation]], based on [[wave–particle duality]] was equivalent to Heisenberg's matrices.{{Citation needed|date=June 2010}}

Einstein also tried to show that Heisenberg's [[uncertainty principle]] was not valid. By 1927 he had become convinced of its utility, but he always opposed it.{{Citation needed|date=June 2010}}

=== EPR paradox ===
In the [[EPR paradox|EPR paper]], Einstein, [[Boris Podolsky]] and [[Nathan Rosen]] argued that quantum mechanics cannot be a complete [[Local hidden-variable theory|realistic and local representation of phenomena]], given specific definitions of "realism", "[[Principle of locality|locality]]", and "completeness". The modern consensus is that Einstein's concept of realism is too restrictive.{{Citation needed|date=June 2010}}

==Superconductivity==
{{Further|History of superconductivity}}
Einstein published (in 1922) a qualitative theory of [[superconductivity]] based on the vague idea of [[Electron|electrons]] shared in [[Atomic orbital|orbits]]. This paper predated modern [[quantum mechanics]], and today is regarded as being incorrect. The current theory of low temperature superconductivity, [[BCS theory]] (by [[John Bardeen]], [[Leon Cooper]] and [[John Robert Schrieffer]]) 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 superconductivity|high-temperature superconductors]].{{Citation needed|date=November 2015}}

==Unified field theory==
Einstein spent many years pursuing the [[unified field theory]] of physics, and published many papers on the subject spanning from 1918 up until his passing in April of 1955. Einstein was never able to prove the unified field theory. Theoretical physicists have not yet formulated a widely accepted, consistent theory that combines general relativity and quantum mechanics to form a [[theory of everything]]. Trying to combine the [[graviton]] with the [[Strong interaction|strong]] and [[Electroweak interaction|electroweak interactions]] leads to fundamental difficulties and the resulting theory is not [[renormalizable]]. The incompatibility of the two theories remains a key [[List of unsolved problems in physics|unsolved problems in physics]].

==References==
{{reflist}}

{{Einstein}}

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