An Etymological Dictionary of Astronomy and Astrophysics
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A → thought experiment conceived by Einstein (1879-1955) at the age of sixteen in the Swiss town of Aarau where he attended the Argovian cantonal school. If an → observer moved at the → speed of light, pursuing a → beam of light, would he → observe such a beam of light as a spatially oscillatory → electromagnetic field at rest? The answer came some ten years later from Einstein himself by his theory of → special relativity. Accordingly, the speed of light is constant for all observers and no observer can move at the light velocity.

Aarau, the Swiss town, the capital of the northern Swiss canton of Aargau; → paradox.

A hydrodynamical paradox arising from the neglect of → viscosity in the → steady flow of a fluid around a submerged solid body. According to this paradox, the submerged body would offer no resistance to the flow of an → inviscid fluid and the pressure on the surface of the body would be symmetrically distributed about the body. This paradox may be traced to the neglect of the viscous forces, which are indirectly responsible for fluid resistance by modifying the velocity field close to a solid body (Meteorology Glossary, American Meteorological Society).

→ d'Alembert's principle; → paradox.

→ EPR paradox.

A. Einstein, B. Podolsky, N. Rosen: "Can quantum-mechanical description of physical reality be considered complete?" Phys. Rev. 41, 777 (15 May 1935); → paradox.

A thought experiment developed in 1935 by A. Einstein (1879-1955), Boris Podolsky (1896-1966), and Nathan Rosen (1909-1995) to demonstrate that there is a fundamental inconsistency in → quantum mechanics. They imagined two physical systems that are allowed to interact initially so that they will subsequently be defined by a single quantum mechanical state. For example, a neutral → pion at rest which decays into a pair of → photons. The pair of photons is described by a single two-particle → wave function. Once separated, the two photons are still described by the same wave function, and a measurement of one → observable of the first system will determine the measurement of the corresponding observable of the second system. For example, if photon 1 is found to have → spin up along the x-axis, then photon 2 must have spin down along the x-axis, since the final total → angular momentum of the two-photon system must be the same as the angular momentum of the initial state. This means that we know the spin of photon 2 even without measuring it. Likewise, the measurement of another observable of the first system will determine the measurement of the corresponding observable of the second system, even though the systems are no longer physically linked in the traditional sense of local coupling (→ quantum entanglement). So, EPR argued that quantum mechanics was not a complete theory, but it could be corrected by postulating the existence of → hidden variables that furthermore would be "local". According to EPR, the specification of these local hidden parameters would predetermine the result of measuring any observable of the physical system. However, in 1964 John S. Bell developed a theorem, → Bell's inequality, to test for the existence of these hidden variables. He showed that if the inequality was satisfied, then no local hidden variable theory can reproduce the predictions of quantum mechanics. → Aspect experiment.

A. Einstein, B. Podolsky, N. Rosen: "Can quantum-mechanical description of physical reality be considered complete?" Phys. Rev. 41, 777 (15 May 1935); → paradox.

The contradiction between a colder Sun (about 30% less luminous) some 4 billion years ago, as predicted by models, and the warm ancient Terrestrial and Martian climates derived from geological evidence.

→ faint; → early; → sun; → paradox.

The apparent contradiction between the high probability of the existence of extraterrestrial civilizations and the lack of evidence of contact with such civilizations.

→ fermi; → paradox.

A paradox raised in 1976 by S. Hawking (1942-2018) whose analysis of the thermodynamic properties of → black holes led him to the prediction that black holes are not in fact black, but radiate due to quantum effects. This implied that, due to the → Hawking radiation, a black hole would eventually evaporate away, leaving nothing. This deduction presented a problem for → quantum mechanics, which maintains that information can never be lost. This topic is a matter of intense debate. Many solutions have been proposed, but all of them have serious drawbacks. In order to analyze better these solutions one needs a quantum gravity theory, which does not exist at the moment. In brief, either the idea of → quantum unitarity must be given up, or a mechanism should be found by which information is not lost after it falls into a black hole.

→ information; → paradox.

The puzzle of why the night sky is not as uniformly bright as the surface of the Sun if, as used to be assumed, the Universe is infinitely large and filled uniformly with stars. It can be traced as far back as Johannes Kepler (1571-1630), was discussed by Edmond Halley (1656-1742) and Philippe Loys de Chéseaux (1718-1751), but was not popularized as a paradox until Heinrich Olbers took up the issue in the nineteenth century. This paradox has been resolved by the → Big Bang theory. In a Universe with a beginning, we can receive light only from that part of the Universe close enough so that light has had time to travel from there to here since the Big Bang. The night sky is dark because the galaxies are only about ten billion years old and have emitted only a limited amount of light, not because that light has been weakened by the expansion of the Universe (P. S. Wesson et al., 1987, ApJ 317, 601).

Formulated in 1826 by Heinrich Wilhelm Olbers (1758-1840), German physician and amateur astronomer, who discovered the asteroids Pallas and Vesta as well as five comets; → paradox.

A statement, proposition, or situation that seems self-contradictory or absurd but in reality is or may be true. → Fermi paradox; → faint early Sun paradox; → twins paradox; → paradox of youth.

From L. paradoxum "contrary to expectation," from Gk. paradoxon, from neuter of adj. paradoxos "contrary to common opinion, unbelievable," from → para- "contrary to" + dox(a) "opinion, belief" + -os adj. suffix. The main component dox, from dokein "to appear, seem, think," is cognate with Av. daēs- "to show;" Skt. diś- "to show, point out," diśati "he shows;" L. dicere "to utter;" PIE base *deik- "to show, pronounce solemnly."

Pârâdaxš (on the model of Gk. paradoxos), from pârâ-, → para-, + daxš, from Av. daxš- "to reveal, instruct, point out," fradaxštar- "teacher," *daxšārə "revelations;" Mod.Pers. daxš "task, effort;" cf. Skt. daks- "to be able," dáksa- "able, expert."

The observed presence of young stars in the immediate vicinity of the → supermassive black hole (SMBH), → Sgr A*, residing in the center of our Galaxy. The stellar population within 1 pc of the SMBH contains a variety of young and → massive stars orbiting the SMBH. Some of them are only about 20 Myr old and get as close as a few light-days to the SMBH, while from 0.1 to 0.4 pc even younger stars are found with ages of 3-7 Myr. The presence of these stars so near to the SMBH is a paradox. Their → in situ formation should be almost impossible, since the environment is too hostile for these stars to form. Indeed the strong → tidal influence of the SMBH should hamper their formation. On the other hand, the scenario considering their → migration from other places does not seem to be adequate. The time required for the migration from > 1 pc by dynamical friction would exceed their inferred ages unless the migration rate were somehow accelerated. This apparent contradiction was termed "paradox of youth" by Ghez et al. (2003, ApJ 586, L127). See also Genzel et al. (2010, Rev.Mod.Phys. 82, 3121, also at astro-ph/1006.0064).

Youth, the condition of being → young; → paradox.

A thought experiment in special relativity, according to which if one of a pair of twins (A) remains on Earth, and the other (B) travels at a speed near the speed of light, B will be younger than A upon returning to Earth. In fact there is no paradox, because the two perspectives, A and B's, are actually not completely symmetric. There is no fixed time difference between the events, and different observers experience different intervals of time between the same two events. In fact, B returns younger than A because only B travels in a non-inertial (accelerating) reference frame. From A's point of view, B experiences time dilation, but from B's point of view the distance traveled is shortened because of length contraction. If B leaves in the year 2000 and returns in 2020, for A 20 years have elapsed. For B it depends on his travel speed. If has has moved as fast as 86% of the speed of light for him 10 years have passed. If his speed has been 99.5% of the speed of light the travel duration for him has been 2 years. This effect has been verified experimentally by measurements with atomic clocks.

Twin M.E.; O.E. twinn; cf. O.N. tvinnr, O.Dan. tvinling, Du. tweeling, Ger. zwillung; → paradox.

Pârâdaxš, → paradox; hamzâdhâ, plural of hamzâd "twin," literally "born together," from ham- "together" → syn- + zâd "born," from zâdan "to bring forth, give birth" (Mid.Pers. zâtan; Av. zan- "to bear, give birth to a child, be born," infinitive zazāite, zāta- "born;" cf. Skt. janati "begets, bears," janitár "progenitor, father;" Gk. genetor "progenitor;" L. gignere "to beget," nasci "to be born," as above, PIE base *gen- "to give birth, beget").

A → rotating star cannot simultaneously achieve → hydrostatic equilibrium and → rigid body rotation. The paradox can be solved if → baroclinic flows (essentially a → differential rotation and a → meridional circulation) are included. For a broader view of the subject see: M. Rieutord, 2006, in Stellar Fluid Dynamics and Numerical Simulations: From the Sun to Neutron Stars, ed. M. Rieutord & B. Dubrulle, EAS Publ., 21, 275, arXiv:astro-ph/0608431.

→ von Zeipel theorem; → paradox.

Same as → paradox of youth.