Classical mechanics of special relativity in a Riemannian space‐time

1991 ◽  
Vol 32 (7) ◽  
pp. 1788-1795 ◽  
Author(s):  
Daniel Zerzion ◽  
L. P. Horwitz ◽  
R. I. Arshansky
Keyword(s):  
Special Relativity ◽  
Riemannian Space ◽  
Classical Mechanics ◽  
Space Time

scholarly journals Complex Covariance

10.14311/1809 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Frieder Kleefeld
Keyword(s):  
Quantum Theory ◽  
Phase Space ◽  
Special Relativity ◽  
Degrees Of Freedom ◽  
Classical Mechanics ◽  
Space Time ◽  
Complex Phase ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Complex Valued

According to some generalized correspondence principle the classical limit of a non-Hermitian quantum theory describing quantum degrees of freedom is expected to be the well known classical mechanics of classical degrees of freedom in the complex phase space, i.e., some phase space spanned by complex-valued space and momentum coordinates. As special relativity was developed by Einstein merely for real-valued space-time and four-momentum, we will try to understand how special relativity and covariance can be extended to complex-valued space-time and four-momentum. Our considerations will lead us not only to some unconventional derivation of Lorentz transformations for complex-valued velocities, but also to the non-Hermitian Klein-Gordon and Dirac equations, which are to lay the foundations of a non-Hermitian quantum theory.

Psychological Space-time Reinforcement Sensitivity Hypothesis & Mental Disorders: From Special to General Relativity Interpretation

2021 ◽  
Vol 19 (4) ◽  
pp. 01-14
Author(s):  
Meriama Hansali Mebarki
Keyword(s):  
General Relativity ◽  
Mental Disorders ◽  
Special Relativity ◽  
Conscious Experience ◽  
Space Time ◽  
The Self ◽  
Psychological Space ◽  
The Past ◽  
Reinforcement Sensitivity ◽  
Spatio Temporal

The reinforcement sensitivity theory lacks basic sources of any human experience :time, place, and learning contexts that have shaped the reinforcement; therefore I have assumed a missing link in Gray's framework based on special relativity relying on the «what, where, and when of happenning»? as major resources of human conscious experience, which under punishment or reward exceed the sensitivity to pleasant or unpleasant stimuli transcending therefore the Weber law, that's why I called it: Psychological Space-Time Reinforcement Sensitivity “PSTRS” axis. The lasts explains BAS and BIS systems sensitivity to reinforcement across the cognitive space-time continuum of episodic memory, and not only across the two great dimensions of fear/anxiety and defensive distance of the McNaughton & Corr model of 2004. So, based on the disruption of the high-sensitivity information processing system in the brain, the four-dimensional conscious experience is distorted by its underlying sources and context. Thus, one of the timedominating records prevents the individual from overcoming the present., such in depression, obsessive compulsive disorder and post-traumatic stress disorder (psychological sensitivity to the past). These temporal records clearly lose their sequence and associative nature in dissociative symptoms due to the disruption of the most important milestone on which Einstein's physics was based. Consequently, psychological space-time reinforcement sensitivity supposes that psychological disorders can be interpreted according to the laws of special relativity (acceleration / deceleration), but this seems more complicated when it comes to mental disorders where the self is disturbed on its spatio-temporal axis as observed in schizophrenia. Schizophrenia looks like a three-componements disorder characterized by a disruption of the experience of time, place and self, which could be asummed up as a “self space-time disturbance". Notably schizophrenic patients appear losing the ability to gather in a dynamic way these componements, as if the world seemed missig the gestalt characteristic or fragmented. The past felt like an inevitable destiny inhibits the direction towards the future; sometimes disorient the self to the point of feeling lost, as if the psychological time slows down to the point of feeling separated from the « now » the physical time. So are we dealing with an Euclidian space? The article attempts to provide a non-traditional interpretation of mental disorders by including general relativity in psychological studies, based on the neurobiological bases involved in the spatio-temporal processing of the conscious experience in the quantum brain.

Related to Relativity

2019 ◽  
pp. 265-284
Author(s):  
Steven J. Osterlind
Keyword(s):  
Twentieth Century ◽  
General Relativity ◽  
Special Relativity ◽  
Golden Age ◽  
Albert Einstein ◽  
Space Time ◽  
Theory Of Relativity ◽  
Scientific Exploration ◽  
Richard Burton ◽  
Time Continuum

This chapter provides the context for the early twentieth-century events contributing to quantification. It was the golden age of scientific exploration, with explorers like David Livingstone, Sir Richard Burton, and Sir Ernest Shackleton, and intellectual pursuits, such as Hilbert’s set of unsolved problems in mathematics. However, most of the chapter is devoted to discussing the last major influencer of quantification: Albert Einstein. His life and accomplishments, including his theory of relativity, make up the final milestone on our road to quantification. The chapter describes his time in Bern, especially in 1905, when he published several famous papers, most particularly his law of special relativity, and later, in 1915, when he expanded it to his theory of general relativity. The chapter also provides a layperson’s description of the space–time continuum. Women of major scientific accomplishments are mentioned, including Madame Currie and the mathematician Maryam Mirzakhani.

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