Speed of light and Related Topics

Albert Einstein around 1905, the year his "Annus Mirabilis papers" were published. These included Zur Elektrodynamik bewegter Körper, the paper founding special relativity.

Special relativity

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1) The laws of physics are invariant (that is, identical) in all inertial frames of reference (that is, frames of reference with no acceleration).

Figure 2–1. The primed system is in motion relative to the unprimed system with constant velocity v only along the x-axis, from the perspective of an observer stationary in the unprimed system. By the principle of relativity, an observer stationary in the primed system will view a likewise construction except that the velocity they record will be −v. The changing of the speed of propagation of interaction from infinite in non-relativistic mechanics to a finite value will require a modification of the transformation equations mapping events in one frame to another.

Figure 4–1. The three events (A, B, C) are simultaneous in the reference frame of some observer O. In a reference frame moving at v = 0.3c, as measured by O, the events occur in the order C, B, A. In a reference frame moving at v = −0.5c with respect to O, the events occur in the order A, B, C. The white lines, the lines of simultaneity, move from the past to the future in the respective frames (green coordinate axes), highlighting events residing on them. They are the locus of all events occurring at the same time in the respective frame. The gray area is the light cone with respect to the origin of all considered frames.

Figure 5–1. Highly simplified diagram of Fizeau's 1851 experiment.

Figure 5–2. Illustration of stellar aberration

Figure 5–3. Transverse Doppler effect for two scenarios: (a) receiver moving in a circle around the source; (b) source moving in a circle around the receiver.

Figure 5–4. Comparison of the measured length contraction of a cube versus its visual appearance.

Figure 5-5. Galaxy M87 streams out a black-hole-powered jet of electrons and other sub-atomic particles traveling at nearly the speed of light.

Figure 10–1. Orthogonality and rotation of coordinate systems compared between left: Euclidean space through circular angle φ, right: in Minkowski spacetime through hyperbolic angle φ (red lines labelled c denote the worldlines of a light signal, a vector is orthogonal to itself if it lies on this line).

Figure 10–2. Three-dimensional dual-cone.

2) The speed of light in vacuum is the same for all observers, regardless of the motion of the light source or observer.

Electromagnetic radiation

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In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, propagating through space, carrying electromagnetic radiant energy.

Shows the relative wavelengths of the electromagnetic waves of three different colours of light (blue, green, and red) with a distance scale in micrometers along the x-axis.

In electromagnetic radiation (such as microwaves from an antenna, shown here) the term "radiation" applies only to the parts of the electromagnetic field that radiate into infinite space and decrease in intensity by an inverse-square law of power, so that the total radiation energy that crosses through an imaginary spherical surface is the same, no matter how far away from the antenna the spherical surface is drawn. Electromagnetic radiation thus includes the far field part of the electromagnetic field around a transmitter. A part of the "near-field" close to the transmitter, forms part of the changing electromagnetic field, but does not count as electromagnetic radiation.

Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D animation shows a plane linearly polarized wave propagating from left to right. The electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together.

Representation of the electric field vector of a wave of circularly polarized electromagnetic radiation.

Electromagnetic spectrum with visible light highlighted

Rough plot of Earth's atmospheric absorption and scattering (or opacity) of various wavelengths of electromagnetic radiation

In a vacuum, electromagnetic waves travel at the speed of light, commonly denoted c.

Einstein in 1921, by Ferdinand Schmutzer

Albert Einstein

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German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time.

Albert Einstein and Mileva Marić Einstein, 1912

Olympia Academy founders: Conrad Habicht, Maurice Solovine and Albert Einstein

The New York Times reported confirmation of "the Einstein theory" (specifically, the bending of light by gravitation) based on 29 May 1919 eclipse observations in Principe (Africa) and Sobral (Brazil), after the findings were presented on 6 November 1919 to a joint meeting in London of the Royal Society and the Royal Astronomical Society. (Full text)

Einstein with his second wife, Elsa, in 1921

Einstein's official portrait after receiving the 1921 Nobel Prize in Physics

Albert Einstein at a session of the International Committee on Intellectual Cooperation (League of Nations) of which he was a member from 1922 to 1932.

Albert Einstein (left) and Charlie Chaplin at the Hollywood premiere of City Lights, January 1931

Cartoon of Einstein after shedding his "pacifism" wings (Charles R. Macauley, c. 1933)

Albert Einstein's landing card (26 May 1933), when he landed in Dover (United Kingdom) from Ostend (Belgium) to visit Oxford.

Portrait of Einstein taken in 1935 at Princeton

Einstein accepting US citizenship certificate from judge Phillip Forman

Albert Einstein (right) with writer, musician and Nobel laureate Rabindranath Tagore, 1930

Albert Einstein with his wife Elsa Einstein and Zionist leaders, including future President of Israel Chaim Weizmann, his wife Vera Weizmann, Menahem Ussishkin, and Ben-Zion Mossinson on arrival in New York City in 1921

Eddington's photograph of a solar eclipse

Einstein with Millikan and Georges Lemaître at the California Institute of Technology in January 1933.

Einstein at his office, University of Berlin, 1920

The photoelectric effect. Incoming photons on the left strike a metal plate (bottom), and eject electrons, depicted as flying off to the right.

Einstein during his visit to the United States

The 1927 Solvay Conference in Brussels, a gathering of the world's top physicists. Einstein is in the center.

Einstein (second from left) at a picnic in Oslo during the visit to Denmark and Norway in 1920. Heinrich Goldschmidt (left), Ole Colbjørnsen (seated in center) and Jørgen Vogt behind Ilse Einstein.

Observationally, the effects of these changes are most apparent at high speeds (where objects are moving at speeds close to the speed of light).

Luminiferous aether

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The postulated medium for the propagation of light.

The Michelson–Morley experiment compared the time for light to reflect from mirrors in two orthogonal directions.

In addition, Maxwell's equations required that all electromagnetic waves in vacuum propagate at a fixed speed, c.

Light

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Electromagnetic radiation within the portion of the electromagnetic spectrum that is perceived by the human eye.

The electromagnetic spectrum, with the visible portion highlighted

Beam of sun light inside the cavity of Rocca ill'Abissu at Fondachelli-Fantina, Sicily

$Due to refraction, the straw dipped in water appears bent and the ruler scale compressed when viewed from a shallow angle.$

Hong Kong illuminated by colourful artificial lighting.

$Thomas Young's sketch of a double-slit experiment showing diffraction. Young's experiments supported the theory that light consists of waves.$

Its speed in a vacuum, 299 792 458 metres a second (m/s), is one of the fundamental constants of nature.

Spacetime

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Mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold.

Figure 1–4. Hand-colored transparency presented by Minkowski in his 1908 Raum und Zeit lecture

Figure 2-2. Galilean diagram of two frames of reference in standard configuration

Figure 2–3. (a) Galilean diagram of two frames of reference in standard configuration, (b) spacetime diagram of two frames of reference, (c) spacetime diagram showing the path of a reflected light pulse

Figure 2–4. The light cone centered on an event divides the rest of spacetime into the future, the past, and "elsewhere"

Figure 2–5. Light cone in 2D space plus a time dimension

Figure 2–6. Animation illustrating relativity of simultaneity

Figure 2–7. (a) Families of invariant hyperbolae, (b) Hyperboloids of two sheets and one sheet

Figure 2–8. The invariant hyperbola comprises the points that can be reached from the origin in a fixed proper time by clocks traveling at different speeds

Figure 2–9. In this spacetime diagram, the 1 m length of the moving rod, as measured in the primed frame, is the foreshortened distance OC when projected onto the unprimed frame.

Figure 2-11. Spacetime explanation of the twin paradox

Figure 3–2. Relativistic composition of velocities

Figure 3-3. Spacetime diagrams illustrating time dilation and length contraction

Figure 3–5. Derivation of Lorentz Transformation

Figure 3–7. Transverse Doppler effect scenarios

Figure 3–8. Relativistic spacetime momentum vector

Figure 3–9. Energy and momentum of light in different inertial frames

Figure 3-10. Relativistic conservation of momentum

Figure 4–2. Plot of the three basic Hyperbolic functions: hyperbolic sine ([[:File:Hyperbolic Sine.svg|sinh]]), hyperbolic cosine ([[:File:Hyperbolic Cosine.svg|cosh]]) and hyperbolic tangent ([[:File:Hyperbolic Tangent.svg|tanh]]). Sinh is red, cosh is blue and tanh is green.

Figure 4-4. Dewan–Beran–Bell spaceship paradox

Figure 4–5. The curved lines represent the world lines of two observers A and B who accelerate in the same direction with the same constant magnitude acceleration. At A' and B', the observers stop accelerating. The dashed lines are lines of simultaneity for either observer before acceleration begins and after acceleration stops.

Figure 4–6. Accelerated relativistic observer with horizon. Another well-drawn illustration of the same topic may be viewed [[:File:ConstantAcceleration02.jpg|here]].

Figure 5–3. Einstein's argument suggesting gravitational redshift

Figure 5-5. Contravariant components of the stress–energy tensor

Figure 5–9. (A) Cavendish experiment, (B) Kreuzer experiment

Figure 5-11. Gravity Probe B confirmed the existence of gravitomagnetism

The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.

General relativity

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Geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics.

Schematic representation of the gravitational redshift of a light wave escaping from the surface of a massive body

Deflection of light (sent out from the location shown in blue) near a compact body (shown in gray)

Ring of test particles deformed by a passing (linearized, amplified for better visibility) gravitational wave

Newtonian (red) vs. Einsteinian orbit (blue) of a lone planet orbiting a star. The influence of other planets is ignored.

Orbital decay for PSR 1913+16: time shift (in s), tracked over 30 years (2006).

Orbital decay for PSR J0737−3039: time shift (in s), tracked over 16 years (2021).

Einstein cross: four images of the same astronomical object, produced by a gravitational lens

Artist's impression of the space-borne gravitational wave detector LISA

Simulation based on the equations of general relativity: a star collapsing to form a black hole while emitting gravitational waves

This blue horseshoe is a distant galaxy that has been magnified and warped into a nearly complete ring by the strong gravitational pull of the massive foreground luminous red galaxy.

Penrose–Carter diagram of an infinite Minkowski universe

The ergosphere of a rotating black hole, which plays a key role when it comes to extracting energy from such a black hole

Projection of a Calabi–Yau manifold, one of the ways of compactifying the extra dimensions posited by string theory

Simple spin network of the type used in loop quantum gravity

Observation of gravitational waves from binary black hole merger GW150914

(The defining symmetry of special relativity is the Poincaré group, which includes translations, rotations, boosts and reflections.) The differences between the two become significant when dealing with speeds approaching the speed of light, and with high-energy phenomena.

Photon

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Elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force.

Photoelectric effect: the emission of electrons from a metal plate caused by light quanta – photons.

The cone shows possible values of wave 4-vector of a photon. The "time" axis gives the angular frequency (rad⋅s−1) and the "space" axis represents the angular wavenumber (rad⋅m−1). Green and indigo represent left and right polarization

Thomas Young's double-slit experiment in 1801 showed that light can act as a wave, helping to invalidate early particle theories of light.

In 1900, Maxwell's theoretical model of light as oscillating electric and magnetic fields seemed complete. However, several observations could not be explained by any wave model of electromagnetic radiation, leading to the idea that light-energy was packaged into quanta described by . Later experiments showed that these light-quanta also carry momentum and, thus, can be considered particles: The photon concept was born, leading to a deeper understanding of the electric and magnetic fields themselves.

Up to 1923, most physicists were reluctant to accept that light itself was quantized. Instead, they tried to explain photon behaviour by quantizing only matter, as in the Bohr model of the hydrogen atom (shown here). Even though these semiclassical models were only a first approximation, they were accurate for simple systems and they led to quantum mechanics.

Photons in a Mach–Zehnder interferometer exhibit wave-like interference and particle-like detection at single-photon detectors.

Stimulated emission (in which photons "clone" themselves) was predicted by Einstein in his kinetic analysis, and led to the development of the laser. Einstein's derivation inspired further developments in the quantum treatment of light, which led to the statistical interpretation of quantum mechanics.

Different electromagnetic modes (such as those depicted here) can be treated as independent simple harmonic oscillators. A photon corresponds to a unit of energy E = hν in its electromagnetic mode.

Photons are massless, so they always move at the speed of light in vacuum, 299,792,458 m/s (or about 299792458 m/s).

Gravitational wave

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Primordial gravitational waves are hypothesized to arise from cosmic inflation, a faster-than-light expansion just after the Big Bang (2014).

The effect of a plus-polarized gravitational wave on a ring of particles

The effect of a cross-polarized gravitational wave on a ring of particles

The gravitational wave spectrum with sources and detectors. Credit: NASA Goddard Space Flight Center

Two stars of dissimilar mass are in circular orbits. Each revolves about their common center of mass (denoted by the small red cross) in a circle with the larger mass having the smaller orbit.

Two stars of similar mass in circular orbits about their center of mass

Two stars of similar mass in highly elliptical orbits about their center of mass

Artist's impression of merging neutron stars, a source of gravitational waves

Two-dimensional representation of gravitational waves generated by two neutron stars orbiting each other.

Now disproved evidence allegedly showing gravitational waves in the infant universe was found by the BICEP2 radio telescope. The microscopic examination of the focal plane of the BICEP2 detector is shown here. In January 2015, however, the BICEP2 findings were confirmed to be the result of cosmic dust.

A schematic diagram of a laser interferometer

LIGO measurement of the gravitational waves at the Hanford (left) and Livingston (right) detectors, compared to the theoretical predicted values.

Gravitational waves are disturbances or ripples in the curvature of spacetime, generated by accelerated masses, that propagate as waves outward from their source at the speed of light.

Gauss's law for magnetism: magnetic field lines never begin nor end but form loops or extend to infinity as shown here with the magnetic field due to a ring of current.

Maxwell's equations