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The Klein paradox is an unexpected consequence of relativity on the interaction of quantum particles with electrostatic potentials. The quantum mechanical problem of free particles striking an electrostatic step potential has two solutions when relativity is ignored.
A two-dimensional representation of the Klein bottle immersed in three-dimensional space. In mathematics, the Klein bottle (/ ˈ k l aɪ n /) is an example of a non-orientable surface; that is, informally, a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down.
Klein paradox: When the potential of a potential barrier becomes similar to the mass of the impinging particle, it becomes transparent. Mott problem , also known as the Mott paradox: [ 5 ] Spherically symmetric wave functions, when observed, produce linear particle tracks.
Klein is also credited for inventing the idea, part of Kaluza–Klein theory, that extra dimensions may be physically real but curled up and very small, an idea essential to string theory. In 1938, he proposed a boson-exchange model for charge-charging weak interactions (radioactive decay), a few years after a similar proposal by Hideki Yukawa.
In physics, Kaluza–Klein theory (KK theory) is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the common 4D of space and time and considered an important precursor to string theory. In their setup, the vacuum has the usual 3 dimensions of space and one dimension of time ...
These problems included negative probabilities, hole theory, the Klein paradox, non-covariant expectation values, and so forth. [14] [15] [16] Most of these problems were never solved; they were avoided when quantum field theory (QFT) was adopted as the standard paradigm. The QFT perspective, particularly its formulation by Schwinger, is a ...
John Wheeler's original discussion of the possibility of a delayed choice quantum appeared in an essay entitled "Law Without Law," which was published in a book he and Wojciech Hubert Zurek edited called Quantum Theory and Measurement, pp 182–213. He introduced his remarks by reprising the argument between Albert Einstein, who wanted a ...
Kaluza–Klein theory; Quantum gravity; Solutions. Schwarzschild ... In physics, the twin paradox is a thought experiment in special relativity involving twins, ...