Einstein’s E = mc2 Derivable from Heisenberg’s Uncertainty Relations

dc.contributor.authorBaşkal, Sibel
dc.contributor.authorKim, Young S.
dc.contributor.authorNoz, Marilyn E.
dc.date.accessioned2023-11-14T15:04:30Z
dc.date.available2023-11-14T15:04:30Z
dc.date.issued2019-11-09
dc.description.abstractHeisenberg’s uncertainty relation can be written in terms of the step-up and step-down operators in the harmonic oscillator representation. It is noted that the single-variable Heisenberg commutation relation contains the symmetry of the 𝑆𝑝(2) group which is isomorphic to the Lorentz group applicable to one time-like dimension and two space-like dimensions, known as the 𝑂(2,1) group. This group has three independent generators. The one-dimensional step-up and step-down operators can be combined into one two-by-two Hermitian matrix which contains three independent operators. If we use a two-variable Heisenberg commutation relation, the two pairs of independent step-up, step-down operators can be combined into a four-by-four block-diagonal Hermitian matrix with six independent parameters. It is then possible to add one off-diagonal two-by-two matrix and its Hermitian conjugate to complete the four-by-four Hermitian matrix. This off-diagonal matrix has four independent generators. There are thus ten independent generators. It is then shown that these ten generators can be linearly combined to the ten generators for Dirac’s two oscillator system leading to the group isomorphic to the de Sitter group 𝑂(3,2) , which can then be contracted to the inhomogeneous Lorentz group with four translation generators corresponding to the four-momentum in the Lorentz-covariant world. This Lorentz-covariant four-momentum is known as Einstein’s 𝐸=𝑚𝑐2.
dc.description.urihttps://doi.org/10.3390/quantum1020021
dc.identifierhttps://doi.org/10.13016/dspace/ovqp-exz7
dc.identifier.citationBaşkal, S.; Kim, Y.S.; Noz, M.E. Einstein’s E = mc2 Derivable from Heisenberg’s Uncertainty Relations. Quantum Rep. 2019, 1, 236-251.
dc.identifier.urihttp://hdl.handle.net/1903/31380
dc.language.isoen_US
dc.publisherMDPI
dc.relation.isAvailableAtCollege of Computer, Mathematical & Natural Sciencesen_us
dc.relation.isAvailableAtPhysicsen_us
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_us
dc.relation.isAvailableAtUniversity of Maryland (College Park, MD)en_us
dc.subjectE = mc2 from Heisenberg’s uncertainty relations
dc.subjectone symmetry for quantum mechanics and special relativity
dc.titleEinstein’s E = mc2 Derivable from Heisenberg’s Uncertainty Relations
dc.typeArticle
local.equitableAccessSubmissionNo

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