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Undecidability and Quantum Mechanics
Recently, great attention has been devoted to the problem of the undecidability of specific questions in quantum mechanics. In this context, it has been shown that the problem of the existence of a spectral gap, i.e., energy difference between the ground state and the first excited state, is algorithmically undecidable. Using this result herein proves that the existence of a quantum phase transition, as inferred from specific microscopic approaches, is an undecidable problem, too. Indeed, some methods, usually adopted to study quantum phase transitions, rely on the existence of a spectral gap. Since there exists no algorithm to determine whether an arbitrary quantum model is gapped or gapless, and there exist models for which the presence or absence of a spectral gap is independent of the axioms of mathematics, it infers that the existence of quantum phase transitions is an undecidable problem. 
  • 1.3K
  • 18 Oct 2022
Topic Review Peer Reviewed
Development of the Concept of Space up to Newton
The concept of space, ubiquitous among all humans from birth, has changed profoundly in the course of the history of Western civilization, the only one to be considered here. An important contribution to this change was the theoretical elaborations of the philosophers of nature and mathematicians, started in Ancient Greece. Here, the process is considered up to Newton, when the concept of space for physicists, who then replaced the traditional philosophers of nature, took on a connotation that remained substantially undisputed for two centuries—that of absolute space. 
  • 521
  • 18 Oct 2022
Topic Review
Conceptual Programs in Physics
Different subfields of physics have different programs for determining the state of a physical system.
  • 283
  • 18 Oct 2022
Topic Review
Europa Thermal Emission Imaging System
The Europa Thermal Emission Imaging System (E-THEMIS) instrument is designed to scan the surface of Europa and identify areas of geologically recent resurfacing through the detection of subtle thermal anomalies. This 'heat detector' will provide high spatial resolution, multi-spectral thermal imaging of Europa to help detect active sites such as outflows and plumes. E-THEMIS will be launched on board the planned Europa Clipper astrobiology mission to Jupiter's moon Europa in 2025. The E-THEMIS uses technology inherited from the THEMIS camera flown on board the 2001 Mars Odyssey orbiter, and the OSIRIS-REx OTES instruments.
  • 403
  • 18 Oct 2022
Topic Review
Lockheed Martin CFR
The Lockheed Martin Compact Fusion Reactor (CFR) is a proposed nuclear fusion reactor project at Lockheed Martin’s Skunk Works. Its high-beta configuration, which implies that the ratio of plasma pressure to magnetic pressure is greater than or equal to 1 (compared to tokamak designs' 0.05), allows a compact fusion reactor (CFR) design and expedited development. The CFR chief designer and technical team lead, Thomas McGuire studied fusion as a source of space propulsion in response to a NASA desire to improve travel times to Mars.
  • 425
  • 18 Oct 2022
Topic Review
Raksha Bandhan
Raksha Bandhan, also Rakshabandhan, or Rakhi, is a popular, traditionally Hindu, annual rite, or ceremony, which is central to a festival of the same name, celebrated in parts of South Asia, and among people influenced by South Asian culture around the world. On this day, sisters of all ages tie a talisman, or amulet, called the rakhi, around the wrists of their brothers, symbolically protecting them, receiving a gift in return, and traditionally investing the brothers with a share of the responsibility of their potential care. Raksha Bandhan is observed on the last day of the Hindu lunar calendar month of Shraavana, which typically falls in August. The expression "Raksha Bandhan," Sanskrit, literally, "the bond of protection, obligation, or care," is now principally applied to this ritual. Until the mid-20th-century, the expression was more commonly applied to a similar ritual, also held on the same day, with precedence in ancient Hindu texts, in which a domestic priest ties amulets, charms, or threads on the wrists of his patrons, or changes their sacred thread, and receives gifts of money; in some places, this is still the case. In contrast, the sister-brother festival, with origins in folk culture, had names which varied with location, with some rendered as Saluno, Silono, and Rakri. A ritual associated with Saluno included the sisters placing shoots of barley behind the ears of their brothers. Of special significance to married women, Raksha Bandhan is rooted in the practice of territorial or village exogamy, in which a bride marries out of her natal village or town, and her parents, by custom, do not visit her in her married home. In rural north India, where village exogamy is strongly prevalent, large numbers of married Hindu women travel back to their parents' homes every year for the ceremony. Their brothers, who typically live with the parents or nearby, sometimes travel to their sisters' married home to escort them back. Many younger married women arrive a few weeks earlier at their natal homes and stay until the ceremony. The brothers serve as lifelong intermediaries between their sisters' married and parental homes, as well as potential stewards of their security. In urban India, where families are increasingly nuclear, the festival has become more symbolic, but continues to be highly popular. The rituals associated with this festival have spread beyond their traditional regions and have been transformed through technology and migration, the movies, social interaction, and promotion by politicized Hinduism, as well as by the nation state. Among women and men who are not blood relatives, there is also a transformed tradition of voluntary kin relations, achieved through the tying of rakhi amulets, which have cut across caste and class lines, and Hindu and Muslim divisions. In some communities or contexts, other figures, such as a matriarch, or a person in authority, can be included in the ceremony in ritual acknowledgement of their benefaction.
  • 1.7K
  • 18 Oct 2022
Topic Review
Baltimore–Washington Superconducting Maglev Project
The Baltimore–Washington Superconducting Maglev Project (SCMAGLEV) is a proposed project connecting the United States cities of Baltimore, Maryland, and Washington, D.C., with a 40 mi (64 km) maglev train system between their respective central business districts. It is the first segment of the planned Washington-New York Northeast Maglev project. The maglev proposal is not related to the Baltimore–Washington hyperloop proposed by the Boring Company.
  • 584
  • 18 Oct 2022
Topic Review
Yield (Engineering)
In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation. The yield strength or yield stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically. The yield strength is often used to determine the maximum allowable load in a mechanical component, since it represents the upper limit to forces that can be applied without producing permanent deformation. In some materials, such as aluminium, there is a gradual onset of non-linear behavior, making the precise yield point difficult to determine. In such a case, the offset yield point (or proof stress) is taken as the stress at which 0.2% plastic deformation occurs. Yielding is a gradual failure mode which is normally not catastrophic, unlike ultimate failure. In solid mechanics, the yield point can be specified in terms of the three-dimensional principal stresses ([math]\displaystyle{ \sigma_1, \sigma_2 , \sigma_3 }[/math]) with a yield surface or a yield criterion. A variety of yield criteria have been developed for different materials.
  • 3.1K
  • 17 Oct 2022
Topic Review
Guru Purnima
Guru Purnima (Poornima) is an eastern spiritual tradition dedicated to spiritual and academic teachers, who are evolved or enlightened humans, ready to share their wisdom, with very little or no monetary expectation, based on Karma Yoga. It is celebrated as a festival in Nepal by the Nepalese Hindus and Buddhists. This festival is traditionally observed by Hindus, Buddhists and Jains to revere their chosen spiritual teachers / leaders and express their gratitude. The festival is celebrated on the full moon day (Purnima) in the Hindu month of Ashadha (June–July) as it is known in the Hindu calendar of India and Nepal. This day marks the first peak of the lunar cycle after the peak of the solar cycle.
  • 299
  • 17 Oct 2022
Topic Review
Dirac Equation in the Algebra of Physical Space
The Dirac equation, as the relativistic equation that describes spin 1/2 particles in quantum mechanics, can be written in terms of the Algebra of physical space (APS), which is a case of a Clifford algebra or geometric algebra that is based on the use of paravectors. The Dirac equation in APS, including the electromagnetic interaction, reads Another form of the Dirac equation in terms of the Space time algebra was given earlier by David Hestenes. In general, the Dirac equation in the formalism of geometric algebra has the advantage of providing a direct geometric interpretation.
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  • 17 Oct 2022
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