C: Technical Proofs for Special Relativity

The principle postulate of general relativity appears to be that curved space or curved spacetime is gravitational, in that mass curves the spacetime around it, and that this curved spacetime acts on mass in a manner we call gravity. Here, I use the theory of special relativity to show that curved spacetime can be non-gravitational, by showing that curve-linear space or curved spacetime can be observed without exerting a gravitational force on mass to induce motion- as well as showing gravity can be observed without spacetime curvature. This is done using the principles of special relativity in accordance with Einstein to satisfy the reader, using a gravitational equivalence model. Curved spacetime may appear to affect the apparent relative position and dimensions of a mass, as well as the relative time experienced by a mass, but it does not exert gravitational force (gravity) on mass. Thus, this paper explains why there appears to be more gravity in the universe than mass to account for it, because gravity is not the resultant of the curvature of spacetime on mass, thus the â€œdark matterâ€ and â€œdark energyâ€ we are looking for to explain this excess gravity doesnâ€™t exist.

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The irreversible part of special relativity.ver4

10.31219/osf.io/e7yf6 ◽

2020 ◽

Author(s):

Vitaly Kuyukov

Keyword(s):

Special Relativity

The irreversible part of special relativity

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An analogy between electromagnetic and internal waves

Доклады Академии наук ◽

10.31857/s0869-56524854428-433 ◽

2019 ◽

Vol 485 (4) ◽

pp. 428-433

Author(s):

V. G. Baydulov ◽

P. A. Lesovskiy

Keyword(s):

Angular Momentum ◽

Conservation Laws ◽

Internal Wave ◽

Special Relativity ◽

Internal Waves ◽

Maxwell Equations ◽

Wave Equations ◽

Lagrange Function ◽

Lorentz Transformations ◽

Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

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Quantum Entanglement & Special Relativity Connected with Everything from Neutrons, Dark Matter & Ocean Tides to Matrix Maths, Dark Energy & Higher Dimensions

SSRN Electronic Journal ◽

10.2139/ssrn.3419669 ◽

2019 ◽

Author(s):

Rodney Bartlett

Keyword(s):

Dark Matter ◽

Dark Energy ◽

Special Relativity ◽

Quantum Entanglement ◽

Higher Dimensions ◽

Ocean Tides

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Hunting for the Luminiferous Ether

10.1093/oso/9780198797258.003.0009 ◽

2018 ◽

Author(s):

Roberto Lalli

Keyword(s):

Twentieth Century ◽

Special Relativity ◽

Early Twentieth Century ◽

Null Result ◽

Morley Experiment

This chapter re-examines the view widely held by physicists that the luminiferous ether became an outdated concept in the early twentieth century and that Albert Einstein’s special relativity killed it. A second common narrative is that the null result of the 1887 Michelson–Morley ether-drift experiment led to Einstein’s theory and the demise of the ether. On the basis of these two simplified narratives, it has become part of the physicists’ ‘imagined past’ that the Michelson–Morley experiment provided the key evidence decreeing the end of the ether. Using scientometrics, this chapter argues that the first part of this idealised narrative is misleading and that the two parts of this narrative are deeply intertwined, as both had historical roots in the reception of Einstein’s relativity theories. In this perspective, the well-known episode of Dayton C. Miller’s repetition of the Michelson–Morley experiment in the 1920s appears in a new light.

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The Equivalence Principle

10.1093/oso/9780199658633.003.0013 ◽

2018 ◽

Author(s):

David M. Wittman

Keyword(s):

General Relativity ◽

Special Relativity ◽

Equivalence Principle ◽

Time Dilation ◽

Gravitational Redshift ◽

Coordinate Systems ◽

Spacetime Metric

The equivalence principle is an important thinking tool to bootstrap our thinking from the inertial coordinate systems of special relativity to the more complex coordinate systems that must be used in the presence of gravity (general relativity). The equivalence principle posits that at a given event gravity accelerates everything equally, so gravity is equivalent to an accelerating coordinate system.This conjecture is well supported by precise experiments, so we explore the consequences in depth: gravity curves the trajectory of light as it does other projectiles; the effects of gravity disappear in a freely falling laboratory; and gravitymakes time runmore slowly in the basement than in the attic—a gravitational form of time dilation. We show how this is observable via gravitational redshift. Subsequent chapters will build on this to show how the spacetime metric varies with location.

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Spacetime Geometry

10.1093/oso/9780199658633.003.0011 ◽

2018 ◽

Author(s):

David M. Wittman

Keyword(s):

Coordinate System ◽

Special Relativity ◽

Displacement Vector ◽

Proper Time ◽

Plane Geometry ◽

Spatial Displacement ◽

Spacetime Geometry ◽

Space And Time ◽

Displacement Vectors

This chapter shows that the counterintuitive aspects of special relativity are due to the geometry of spacetime. We begin by showing, in the familiar context of plane geometry, how a metric equation separates frame‐dependent quantities from invariant ones. The components of a displacement vector depend on the coordinate system you choose, but its magnitude (the distance between two points, which is more physically meaningful) is invariant. Similarly, space and time components of a spacetime displacement are frame‐dependent, but the magnitude (proper time) is invariant and more physically meaningful. In plane geometry displacements in both x and y contribute positively to the distance, but in spacetime geometry the spatial displacement contributes negatively to the proper time. This is the source of counterintuitive aspects of special relativity. We develop spacetime intuition by practicing with a graphic stretching‐triangle representation of spacetime displacement vectors.

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Special Relativity: Putting it All Together

10.1093/oso/9780199658633.003.0008 ◽

2018 ◽

Author(s):

David M. Wittman

Keyword(s):

Special Relativity ◽

Moving Object ◽

Velocity Addition

We have introduced the ideas of special relativity in quick succession because none of those ideas can really be understood in isolation. This chapter works through examples in some detail so you can practice applying the ideas and solidifying your understanding.We start with an overview of how to use spacetime diagrams to solve problems in special relativity, then we walk through examples ofmeasuring the length of a moving object; the train‐in‐tunnel paradox; velocity addition; and how clock readings are arranged so that each observer measures the other’s clocks as ticking slowly.

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