The principle of relativity and the de Broglie relation

Güémez, J.; Fiolhais, M.; Fernández, L.A.

doi:10.1119/1.4941569

Cited by 11 publications

(4 citation statements)

References 16 publications

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“…where resolution increases with decreasing wavelength, λ . Electron wavelength increases with increasing accelerating voltage, as described by the relativistic de Broglie relation [798][799][800] ,…”

Section: Microscopesmentioning

confidence: 99%

Review: Deep Learning in Electron Microscopy

Ede

2020

Preprint

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Deep learning is transforming most areas of science and technology, including electron microscopy. This review paper offers a practical perspective aimed at developers with limited familiarity. For context, we review popular applications of deep learning in electron microscopy. Following, we discuss hardware and software needed to get started with deep learning and interface with electron microscopes. We then review neural network components, popular architectures, and their optimization. Finally, we discuss future directions of deep learning in electron microscopy.

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Section: Microscopesmentioning

confidence: 99%

Review: Deep Learning in Electron Microscopy

Ede

2020

Preprint

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“…In the asynchronous formulation of relativity [35], a contra-variant four-vector in frame S, with A μ ≡ (A, A 4 ) = (A 1 , A 2 , A 3 , A 4 ), is transformed into the corresponding four-vector in frame S ¯, ) , by applying the Lorentz transformation,…”

Section: Introductionmentioning

confidence: 99%

Relativistic thermodynamics on conveyor belt

Güémez

Mier

2023

Phys. Scr.

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Two thermodynamic processes are analysed by using a relativistic four-vector fundamental equation formalism: the launching of a projectile by forces produced by chemical reactions inside a cannon (equivalent to a person launching a ball) placed on a moving platform, a mechanical energy production process, and the Joule-Kelvin process implemented on a conveyor belt. Each process is first studied in frame S, in which the device -- the cannon or the porous plug --, is at rest, obtaining its four-vector fundamental equation ${\rm d} E^\mu = \delta W^\mu + \delta Q^\mu$. Using the Lorentz transformation, the corresponding four-vector equation in frame ${\bar {\rm S}}$ -- in which the processes are carried out on a moving platform or a conveyor belt -- ${\rm d} {\bar E}^\mu = \delta {\bar W}^\mu + \delta {\bar Q}^\mu$, is obtained, obeying Einstein's principle of relativity. For the relativistic description to be coherent, one has to assign linear momentum to the non-mechanical energies and consider their variations in the corresponding Newton's second law equation and the relativistic non-simultaneity and conveyor belt effects. In relativistic thermodynamics, Newton's second law and the first law of thermodynamics are not independent equations. It is shown that entropy variations and fuel consumption are frame independent magnitudes.

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“…The four-tensor for the Lorentz transformation V ( )  n m (a 4 × 4-matrix with Greek letter superscript and subscript)-from frame S to frame S ¯, moving with velocity V = (V, 0, 0) in the standard configuration with respect to S -, is [20] :…”

Section: Introductionmentioning

confidence: 99%

On the relativistic conveyor belt

Güémez¹,

González-Lavín²

2022

Phys. Scr.

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A relativistic four-vector fundamental equation formalism is used to analyse processes that are carried out on a conveyor belt, in reference frames S (with the conveyor belt at rest, ground) and ${\bar {\rm S}}$ (moving conveyor belt frame); these processes involve thermal effects. Examples solved are: a block thrown with initial speed on an inclined plane conveyor belt, and a ring launched with initial linear velocity on a moving belt. For each process, a four-vector fundamental equation is obtained, first in frame S, and then it is transformed by the Lorentz transformation to the process' four-vector fundamental equation in ${\bar {\rm S}}$. It is shown that Newton's second law and the first law of thermodynamics are no-independent equations. In this description, Newton's second law in frame ${\bar {\rm S}}$, in which forces are non simultaneously applied, includes terms related to linear momentum for heat (relativistic Doppler effect). The first law of thermodynamics in ${\bar {\rm S}}$ includes the motor's performed work to keep the belt moving at a constant speed (conveyor belt effect). Classical descriptions of processes are obtained by taking the relativistic equations' low-speed limit, keeping the conveyor belt effect.

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The principle of relativity and the de Broglie relation

Cited by 11 publications

References 16 publications

Review: Deep Learning in Electron Microscopy

Review: Deep Learning in Electron Microscopy

Relativistic thermodynamics on conveyor belt

On the relativistic conveyor belt

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