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Thursday, July 3, 2025

Criminalization of homosexuality

"Love is not a crime" signs at Paris Pride 2019

Some or all sexual acts between men, and less frequently between women, have been classified as a criminal offense in various regions. Most of the time, such laws are unenforced with regard to consensual same-sex conduct, but they nevertheless contribute to police harassment, stigmatization, and violence against homosexual and bisexual people. Other effects include exacerbation of the HIV epidemic due to the criminalization of men who have sex with men, discouraging them from seeking preventative care or treatment for HIV infection.

The criminalization of homosexuality is often justified by the scientifically discredited idea that homosexuality can be acquired or by public revulsion towards homosexuality, in many cases founded on the condemnation of homosexuality by the Abrahamic religions (Judaism, Christianity, and Islam). Arguments against the criminalization of homosexuality began to be expressed during the Enlightenment. Initial objections included the practical difficulty of enforcement, excessive state intrusion into private life, and the belief that criminalization was not an effective way of reducing the incidence of homosexuality. Later objections included the argument that homosexuality should be considered a disease rather than a crime, that criminalization violates the human rights of homosexuals, and that homosexuality is not morally wrong.

In many countries, criminalization of homosexuality is based on legal codes inherited from the British Empire. The French colonial empire did not lead to criminalization of homosexuality, as this was abolished in France during the French Revolution in order to remove religious influence from the criminal law. In other countries, the criminalization of homosexuality is based on sharia law. In the Western world, a major wave of decriminalization started after World War II. It diffused globally and peaked in the 1990s. In recent years, many African countries have increased enforcement of anti-homosexual laws due to politicization and a mistaken belief that homosexuality is a Western import. As of 2024, homosexuality is criminalized de jure in 61 UN member states and de facto in two others; at least seven of these have a death penalty for homosexuality.

History

Ancient through early modern world

The burning of the knight Richard Puller von Hohenburg with his servant before the walls of Zürich, for sodomy, 1482

The Assyrian Laws contain a passage punishing homosexual relations, but it is disputed if this refers to consensual relations or only non-consensual ones. The first known Roman law to mention same-sex relations was the Lex Scantinia. Although the actual text of this law is lost, it likely prohibited free Roman citizens from taking the passive role in same-sex acts. The Christianization of the Roman Empire made social attitudes increasingly disapproving of homosexuality. In the sixth century, Byzantine emperor Justinian introduced other laws against same-sex sexuality, referring to such acts as "contrary to nature". The Syro-Roman law book, which was influential in the Middle Eastern legal tradition and especially in Lebanon, prescribed the death penalty for homosexuality. Some Ottoman criminal codes called for fines for sodomy (liwat), but others did not mention the offense. In 15th-century central Mexico, homosexual acts between men could be punished by disembowelment and smothering in hot ashes.

During the late Middle Ages, many jurisdictions in Europe began to add prohibitions of sodomy to secular law. They also toughened enforcement, with vice squads appearing in some European cities. In some cases, sodomy was punished by investigation and denunciation, in others by fines, and in some cases by the burning of the participants or the location where the act had taken place. The death penalty for sodomy was common in early modern Europe. It is unclear how strictly sodomy laws were enforced; one theory is that enforcement was related to moral panics in which homosexuals were a scapegoat. English monarch Henry VIII codified the prohibition of homosexuality in England into secular law with the Buggery Act 1533, an attempt to gain the high ground in the religious struggle of the English Reformation. This law, based on the religious prohibition in Leviticus, prescribed the death penalty for buggery (anal sex).

Impact of colonialism and imperialism

Participant carrying a poster against Section 377 during Bhubaneswar Pride Parade, India

Many present-day jurisdictions criminalize homosexuality based on colonial criminal codes they adopted under British rule. The Indian Penal Code and its Section 377 criminalizing homosexuality were applied to several British colonies in Asia, Africa, and Oceania. The Wright Penal Code was drafted for Jamaica and ultimately adopted in Honduras, Tobago, St. Lucia, and the Gold Coast. The Stephen Code was adopted in Canada (and in a modified form in New Zealand), expanding the criminalization of homosexuality to cover any same-sex activity. The Griffith Code was adopted in Australia and several other Commonwealth countries including Nauru, Nigeria, Kenya, Tanzania, Papua New Guinea, Zanzibar and Uganda, and in Israel. Once established, laws against homosexuality are often maintained by inertia and inclusion in postcolonial criminal codes. Some states adopted British-inspired laws criminalizing homosexuality on the basis of informal influence, while other former British colonies criminalize homosexuality under the influence of sharia law. Both China and Japan, which had not historically prosecuted homosexuality, criminalized it based on Western models in the nineteenth century.

During the French Revolution in 1791, the National Constituent Assembly abolished the law against homosexuality as part of its adoption of a new legal code without the influence of Christianity. Although the assembly never discussed homosexuality, it has been legal in France since then. Previously it could be punished by burning to death, although this was infrequently enforced. The abolition of criminality for sodomy was codified in the 1810 penal codeNapoleon's conquests and the adoption of civil law and penal codes on the French model led to abolition of criminality in many jurisdictions and replacement of death with imprisonment in others. Via military occupation or emulation of the French criminal code, the Scandinavian countries, Spain, the Netherlands, Portugal, Belgium, Japan, and their colonies and territories—including much of Latin America—decriminalized homosexuality. Former French colonies are less likely than British ones to criminalize homosexuality. The Ottoman Empire is often considered to have decriminalized homosexuality in 1858, when it adopted a French-inspired criminal code, but Elif Ceylan Özsoy argues that homosexuality had already been decriminalized. However, some Ottoman men were executed for sodomy including two boys in Damascus in 1807.

The unification of Germany reversed some of the gains of the Napoleonic conquests as the unified country adopted the Prussian penal code in 1871, re-criminalizing homosexuality in some areas. In Germany, the prohibition of homosexuality was not frequently enforced until 1933. In Nazi Germany from 1933 to 1945, an estimated 57,000 men were convicted of violating Paragraph 175. Never before or since have so many homosexuals been convicted in such a short period of time. Thousands of men were imprisoned and killed in Nazi concentration campsWest Germany convicted about the same number of men under the same law until 1969, when homosexuality was partially decriminalized.

In the Russian Empire, homosexuality was criminalized in 1835 and decriminalized in 1917 as a result of the Russian Revolution. The criminalization was reinstated in 1934, with a harsher penalty than before, for unknown reasons.

Post-World War II decriminalization trend

Proportion of the world population living in a country where homosexual acts are not criminalized, 1760–2020
Number of jurisdictions criminalizing homosexuality, 1990–2024

In the decades after World War II, anti-homosexuality laws saw increased enforcement in Western Europe and the United States. During the 1950s and 1960s, there was a tendency to legalize homosexuality with a higher age of consent than for heterosexual relationships; this model was recommended by various international organizations to prevent young men from becoming homosexual. Convergence occurred both through the partial decriminalization of homosexuality, as in the United Kingdom (1967), Canada (1969), and West Germany (1969), or through the partial criminalization of homosexuality, such as in Belgium, where the first law against same-sex activity came into effect in 1965.

There was a wave of decriminalization in the late twentieth century; ninety percent of changes to these laws between 1945 and 2005 involved liberalization or abolition. Eighty percent of repeals between 1972 and 2002 were done by a legislature, and the remainder by the laws being ruled unconstitutional by a court. Decriminalization began in Europe and the Americas and spread globally in the 1980s. The pace of decriminalization reached a peak in the 1990s. Following the dissolution of the Soviet Union, many former Soviet republics decriminalized homosexuality, but others in Central Asia retained these laws. China decriminalized homosexuality in 1997. Following a protracted legal battle, the Supreme Court of India ruled that the criminalization of homosexuality violated the Constitution of India in the 2018 Navtej Singh Johar v. Union of India judgement.

One explanation for these legal changes is increased regard for human rights and autonomy of the individual and the effects of the 1960s sexual revolution. The trend in increased attention to individual rights in laws around sexuality has been observed around the world, but progresses more slowly in some regions, such as the Middle East. Studies have found that modernization, as measured by the Human Development Index or GDP per capita, and globalization (KOF Index of Globalization) was negatively correlated with the criminalization of homosexuality.

Resistance to decriminalization

Africa is the only continent where decriminalization of homosexuality has not been widespread since the mid-twentieth century. In Africa, one of the primary narratives cited in favor of the criminalization of homosexuality is "defending ordre public, morality, culture, religion, and children from the assumed imperial gay agenda" associated with the Global North. Such claims ignore the fact that many indigenous African cultures tolerated homosexuality, and historically the criminalization of homosexuality derives from British colonialism. In the Middle East, homosexuality has been seen as a tool of Western domination for the same reason.

The application of international pressure to decriminalize homosexuality has had mixed results in Africa. While it led to liberalization in some countries, it also prompted public opinion to be skeptical of these demands and encouraging countries to pass even more restrictive laws in resistance to what is seen as neocolonial pressure. Politicians may also target homosexuality to distract from other issues. Following decolonization, several former British colonies expanded laws that had only targeted men in order to include same-sex behavior by women. Others, especially Muslim-majority countries in Africa, passed new laws to criminalize homosexual behavior. In many African countries, anti-homosexuality laws were little-enforced for decades only to see increasing enforcement, politicization, and calls for harsher penalties beginning in the mid-1990s. The rise of Evangelical Christianity and especially Pentecostalism has increased the politicization of homosexuality as these churches have been engaged in anti-homosexual mobilizations as a form of nation building. While such calls often come from domestic religious institutions, the influence of US conservative Christian groups, who have provided networking, training and funding support, has been instrumental in advancing anti-homosexual discourse in Africa.

Current status

As of 2020, 21 percent of the world population lives in countries where homosexuality is criminalized. In its 2023 Database, the International Lesbian, Gay, Bisexual, Trans and Intersex Association (ILGA) found that homosexuality is criminalized in 62 of 193 UN member states, while two UN member states, Iraq and Egypt, criminalize it de facto but not in legislation. In at least seven UN member states—Brunei, Iran, Mauritania, Nigeria (only northern Nigeria), Saudi Arabia, Uganda, and Yemenit is punishable by death. Two-thirds of countries that criminalize sexual activity between men also criminalize it between women. In 2007, five countries conducted executions as a penalty for homosexual acts. In 2020, the ILGA named Iran and Saudi Arabia as the only countries in which executions for same-sex activity have reportedly taken place. In other countries, such as Yemen, Somalia, Iraq, and Libya, extrajudicial executions are carried out by militias such as Al-Shabaab, the Islamic State, or Al-Qaeda. In 2021, Téa Braun of the Human Dignity Trust estimated that more than 71 million LGBT people live in countries where homosexuality is criminalized.

  Criminalized
  Decriminalized 1791–1850
  Decriminalized 1850–1945
  Decriminalized 1946–1989
  Decriminalized 1990–present
  Unknown date of legalization
  Never criminalized

Scope of laws

Laws against homosexuality make some or all sex acts between people of the same sex a crime. While some laws are specific about which acts are illegal, others use vague terminology such as "crimes against nature", "unnatural offenses", "indecency", or "immoral acts". Some laws exclusively criminalize anal sex while others include oral sex or manual sex. Some sodomy laws explicitly target same-sex couples, while others apply to sexual acts that might be performed by heterosexual couples but are usually enforced against same-sex couples only. It is more common for men who have sex with men to be criminalized than women who have sex with women, and there are no countries that only criminalize female same-sex activity. This has been due to a belief that eroticism between women is not really sex and that it will not tempt women away from heterosexuality. Unlike other laws, which criminalized specific sexual acts, the British Labouchère Amendment in 1885 and the 1935 revision of Germany's Paragraph 175 simply criminalized any sexual act between two men. Both laws made it much easier to convict men for homosexuality, leading to an increase in convictions.

Penalties vary widely, from fines or short terms of imprisonment to the death penalty. Some laws target both partners in the sex act equally, while in other cases the punishment is unequal. While homosexuality is criminalized country-wide in many cases, in other countries, specific jurisdictions pass their own criminal laws against homosexuality, such as in Aceh province. Most laws criminalizing homosexuality are codified in statutory law, but in some countries such as Saudi Arabia they are based on the direct application of Islamic criminal jurisprudence.

Even in countries where there are no specific laws against homosexuality, homosexuals may be disproportionately criminalized under other laws, such as those targeting indecency, debauchery, prostitution, pornography, homelessness, or HIV exposure. In some countries such as (historically) China and (currently) Egypt, such laws serve as de facto criminalization of homosexuality. One analysis of the United States found that, instead of being directly arrested under sodomy laws, "most arrests of homosexuals came from solicitation, disorderly conduct, and loitering laws, which were based on the assumption that homosexuals (unlike heterosexuals), by definition, were people who engaged in illicit activity". In 2014, Nigeria passed the Same Sex Marriage (Prohibition) Act 2013, criminalizing people who have a same-sex marriage ceremony with five years' imprisonment. Although homosexuality was already illegal, the law led to increasing persecution of Nigerian homosexuals.

Enforcement

Laws criminalizing homosexuality are inherently difficult to enforce, because they concern acts done by consenting individuals in private. Enforcement varies from active persecution to non-enforcement; more often than not, laws are nearly unenforced for private, consensual sex. In some countries, there are no prosecutions for decades or there is a formal moratorium.

In Nazi Germany, the site of the most severe persecution of homosexual men & women in history, only about 10% of the homosexual male & female population was ever convicted and imprisoned. In Iran, the 2013 penal code forbids authorities from proactively investigating same-sex acts unless kidnapping or assault are suspected. In some countries such as India (prior to 2018, when the sodomy law was declared unconstitutional) and Guyana, the laws are not commonly enforced but are used to harass LGBT people. Indian police have used the threat of prosecution to extort money or sexual favors. Arrests, even without conviction, can often lead to publicity causing the accused to lose their job. Those prosecuted under such laws tend to be disproportionately from working-class backgrounds, unmarried, and between twenty and forty years old.

States including Nazi Germany and Egypt commonly use torture to extract confessions from men suspected of being homosexual. In Egypt, possession of condoms or sexual lubricant or stereotypically feminine characteristics are cited as circumstantial evidence that the suspect has committed sodomy. Online dating apps have also been used to identify and target men for prosecution.

Physical examinations purporting to detect evidence of homosexual practices have been employed since at least 1857, when the French physician Auguste Ambroise Tardieu published a book claiming to identify several signs that a person had participated in receptive anal intercourse. As of 2018, at least nine states, including Tanzania, Egypt, and Tunisia, use medically discredited anal examinations in an effort to detect same-sex acts between men or transgender women. There is no evidence that such tests are effective at detecting whether the victim has taken part in homosexual activity. This practice is considered to constitute acts of torture under the United Nations Convention Against Torture.

Effects

The criminalization of homosexuality is often seen as defining all gays and lesbians as criminals or outlaws. Even when not enforced, such laws express a symbolic threat of state violence and reinforce stigma and discrimination. Homosexuals may fear prosecution and are put at risk of blackmail, arbitrary arrest and imprisonment, police beatings, and involuntary medical interventions. The criminalization of homosexuality in some cases pushes LGBT culture and socialization to the margins of society, exposing LGBT people to crimes such as assault, robbery, rape, or murder from other citizens. They may be afraid to report these crimes or may be ignored by the authorities. Such issues lead to severe psychological harm. The laws also justify discrimination against homosexuals—being cited to deny child custody, registration of associations, and other civil rights—and prevent LGBT people from exercising their rights to freedom of expression and freedom of association.

Reactions of homosexuals to the laws range from internalizing stigma to losing respect for the laws and civic community in general. Historian Robert Beachy argues that a confluence of factors including the criminalization of homosexuality meant that a sense of homosexual identity was first developed in Germany around 1900, ultimately catalyzing the first homosexual movementLGBT movements often developed after the repeal of criminal laws, but in some cases they contributed to repeal efforts. LGBT activism against criminalization can take multiple forms, including directly advocating the repeal of the laws, strategic litigation in the judicial system in order to reduce enforceability, seeking external allies from outside the country, and capacity building within the community. A 1986 study found that the decriminalization of homosexuality in South Australia did not lead to an increase in undesirable effects (such as child abuse, public solicitation, or disease transmission) as claimed in parliamentary debates.

The criminalization of homosexuality has been identified as an exacerbating feature of the HIV epidemic in Africa and Central Asia, because it dissuades many people at risk of HIV infection from disclosing their sexual behavior to healthcare providers or seeking preventative care, testing, or treatment. Criminalization both reinforces societal disapproval of homosexuality, which is another factor in decreasing the effectiveness of anti-HIV efforts and is independently associated with less access to HIV services.

Support and opposition

Religions

The Abrahamic religions all have traditionally held negative attitudes towards homosexuality. The Hebrew Bible prescribes the death penalty for "lying with another man as with a woman" (Leviticus 20:13) but does not directly address lesbianism. It is disputed if the biblical prohibition was originally intended to prohibit temple prostitution or particular sexual acts between multiple men, particularly those that are seen as compromising a man's masculinity. The total prohibition of homosexual behavior is considered to have evolved relatively late in the Jewish tradition. Some Christians cite various Bible passages in order to justify the criminalization of homosexuality. Although the Holy See officially opposes the criminalization of homosexuality, in 2014 Roman Catholic bishops from Malawi, Kenya, Sudan, Tanzania, Eritrea, Zambia, Uganda, and Ethiopia united to demand criminal punishment of homosexuals, calling homosexuality unnatural and un-African.

According to sharia law, liwat (anal intercourse) and sihaq or musahiqa (tribadism) are considered sins or criminal offenses. The Sunni Hanafi school, unlike other Islamic schools and branches, rejects analogy as a principle of jurisprudence. Since there is no explicit call for the punishment of homosexuals in the accepted statements of Muhammed, Hanafi jurists classified homosexuality as a sin rather than a crime according to religious law and a tazir offense, meaning the punishment is left to the discretion of secular rulers. According to the Maliki, Shafi'i, Hanbali (Sunni), and Ja'afari (Shia) schools, any penetrative sex outside of marriage or between a man and his female slave is zina, a more serious crime. Zina is punishable by lashes or death by stoning; whether the death penalty is allowed depends on the school, whether the man has been married, and whether he is the active or passive partner. However, the death penalty can only be applied upon a confession repeated four times by the accused or testimony by four witnesses. All Sunni schools, but not the Shia Ja'afari, consider non-anal sex between men to be a tazir offense. In recent times, some progressive Muslims have argued for a new interpretation of liwat (which is never defined in the Quran) to mean something other than consensual homosexual acts.

Adherence to Islam is a major predictor of maintaining laws criminalizing homosexuality and the death penalty for it. The majority of studies have found no association for Christianity. State interference in religious matters, for example religious courts having jurisdiction beyond family law or bans on interfaith marriage, is strongly correlated with maintaining the criminalization of homosexuality. In Africa, anti-homosexual campaigns promoted by conservative Christians, sometimes with support from U.S. conservative evangelical Christian groups, have seen increased law enforcement efforts and the introduction of harsher penalties against homosexual activity.

Under Buddhist religious law, there is no punishment for homosexuality among laypeople. Although harsh penalties are prescribed for penetrative sexual activity by male monks, novitiates suffer less punishment than for heterosexual activity.

Arguments for

A prominent reason cited for criminalizing homosexuality is the claim, made without evidence, that it could be spread, and that laws against it would prevent homosexuals from recruiting children. This rationale was later proved wrong by scientific research showing that sexual orientation was fixed by a young age. Both Philo of Alexandria and Heinrich Himmler believed that if allowed to spread unchecked, homosexuality would lead to depopulation; therefore, they advocated harsh punishments. The belief that the West is conspiring to depopulate Africa using homosexuality is also a common argument for retaining the criminalization of homosexuality in Africa.

Supporters of paternalism argues that the state can interfere in citizens' private lives to secure a vision of the common good. A common argument is that criminalization of homosexuality is necessary to maintain public morality, traditional values, and cultural or social norms. Anxieties around public morality gained prominence in nineteenth-century Western Europe and North America. Before the medicalization of homosexuality in the nineteenth and twentieth centuries, it was commonly seen as a vice, similar to drunkenness, that occurred as a result of moral degradation rather than being an innate predisposition. Soviet officials argued that homosexuality was a social danger that contravened socialist morality, and that criminalization was an essential tool to lower its prevalence. Some countries have cited the perception that the criminalization of homosexuality would prevent the transmission of sexually transmitted infections, in particular HIV/AIDS, as a reason to keep their laws.

Another reason cited in favor of criminalizing homosexuality is public opinion. The rarity of prosecutions is also cited as a reason not to repeal the laws.

Arguments against

Criticism of the criminalization of homosexuality began to be expressed by Enlightenment thinkers such as legal philosopher Cesare Beccaria in his 1764 treatise On Crimes and Punishments. Early opponents argued that the laws were impractical to enforce, ineffective at deterring homosexuality, and overly intrusive into private life. For example, Napoleon believed that "The scandal of legal proceedings would only tend to multiply" homosexual acts. In 1898, socialist politician August Bebel highlighted the disproportionate enforcement of Paragraph 175 against working-class German men as a reason for repeal. One argument leading to the decriminalization of homosexuality in countries such as Canada, Czechoslovakia, East Germany, and Bulgaria was that homosexuality was a pathological disease and therefore inappropriate as an object of criminal sanctions.

Another argument cited for the decriminalization of homosexuality is that morality is distinct from law, which should concern itself only with the public good. Based on the work of John Stuart Mill, the harm principle posits that conduct should only be considered criminal if it harms people other than those performing the action. According to this principle, homosexuality should not be criminalized. The 1957 Wolfenden Report, which proposed the decriminalization of homosexuality in the United Kingdom, sparked a famous debate between Lord Devlin, H. L. A. Hart, and others about whether the law was a suitable instrument for the enforcement of morality when the interests of non-consenting parties are not affected. Many of these justifications are consistent with a strong moral condemnation of homosexuality and are disputes over how best to handle the perceived social problem of homosexuality, rather than being based on the inalienable rights of LGBT people.

Another line of reasoning argues that homosexuality is not morally wrong. Utilitarian philosopher Jeremy Bentham wrote the first systematic defense of sexual freedom, arguing that homosexuality and other forms of consensual sex were morally acceptable as they were pleasurable to their participants and forbidding these acts destroyed a great deal of human happiness. In the 1860s and 1870s, German Karl Heinrich Ulrichs was the most prominent critic of the criminalization of homosexuality. His demand for equality before the law and in religion on the basis of an innate, biologically based sexual drive—beginning with the decriminalization of homosexuality and ending with same-sex marriage—are similar to those sought by LGBT rights organizations in the twenty-first century. As a result of social changes, in the twenty-first century, the majority of people in many Western countries view homosexuality as morally acceptable or not a moral issue.

Human rights

The criminalization of homosexuality is a violation of international human rights law. The European Court of Human Rights found that laws criminalizing homosexuality violated the right to private life guaranteed by Article 8 of the European Convention on Human Rights in Dudgeon v. United Kingdom (1981), Norris v. Ireland (1988), and Modinos v. Cyprus (1993). In the 1994 case Toonen v. Australia, the Human Rights Committee ruled that the criminalization of homosexuality in Tasmania violated the right to privacy and non-discrimination guaranteed in the International Covenant on Civil and Political Rights, even though the applicant was never arrested or charged with violating the law. While Tasmania argued that the law was necessary to protect traditional morals and prevent the transmission of HIV, the Human Rights Committee found that arguments about morals are not insulated from international human rights norms.

In 2014, the African Union's Commission on Human and People's Rights issued a landmark resolution calling for the decriminalization of homosexuality. In 2020, the Inter-American Commission on Human Rights found in Gareth Henry and Simone Carline Edwards v. Jamaica that Jamaica's laws criminalizing same-sex activities violated the applicants' right to privacy, right to humane treatment, freedom of movement, and principle of legality guaranteed by the American Convention on Human Rights. The commission recommended that Jamaica repeal the laws against same-sex activity in order to guarantee the non-repetition of similar human rights abuses in the future. Persecution on the grounds of sexual orientation is a reason to seek asylum in some countries, including Canada, the European Union, and the United Kingdom, although depending on the case the mere existence of criminal sanctions may not be sufficient for an applicant to be granted asylum.

Public opinion

According to a 2017 worldwide survey by ILGA, the criminalization of homosexuality is correlated with more negative opinions on LGBT people and LGBT rights. Overall, 28.5 percent of those surveyed supported the criminalization of homosexuality, while 49 percent disagreed. In states that criminalize homosexuality, 42 percent agree, and 36 percent disagree, compared with non-criminalizing states where 22 percent agree, and 55 percent disagree. Knowing someone who is gay, lesbian, or bisexual is correlated with less support for criminalization. The number of Americans who agree that homosexuality should be a criminal offense has dropped from 56 percent in 1986 to 18 percent in 2021. Public opinion surveys show that while 78 percent of Africans disapprove of homosexuality, only 45 percent support it being criminalized.

Introduction to quantum mechanics

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Introduction_to_quantum_mechanics

Quantum mechanics
is the study of matter and matter's interactions with energy on the scale of atomic and subatomic particles. By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the Moon. Classical physics is still used in much of modern science and technology. However, towards the end of the 19th century, scientists discovered phenomena in both the large (macro) and the small (micro) worlds that classical physics could not explain. The desire to resolve inconsistencies between observed phenomena and classical theory led to a revolution in physics, a shift in the original scientific paradigm: the development of quantum mechanics.

Many aspects of quantum mechanics yield unexpected results, defying expectations and deemed counterintuitive. These aspects can seem paradoxical as they map behaviors quite differently from those seen at larger scales. In the words of quantum physicist Richard Feynman, quantum mechanics deals with "nature as She is—absurd". Features of quantum mechanics often defy simple explanations in everyday language. One example of this is the uncertainty principle: precise measurements of position cannot be combined with precise measurements of velocity. Another example is entanglement: a measurement made on one particle (such as an electron that is measured to have spin 'up') will correlate with a measurement on a second particle (an electron will be found to have spin 'down') if the two particles have a shared history. This will apply even if it is impossible for the result of the first measurement to have been transmitted to the second particle before the second measurement takes place.

Quantum mechanics helps people understand chemistry, because it explains how atoms interact with each other and form molecules. Many remarkable phenomena can be explained using quantum mechanics, like superfluidity. For example, if liquid helium cooled to a temperature near absolute zero is placed in a container, it spontaneously flows up and over the rim of its container; this is an effect which cannot be explained by classical physics.

History

James C. Maxwell's unification of the equations governing electricity, magnetism, and light in the late 19th century led to experiments on the interaction of light and matter. Some of these experiments had aspects which could not be explained until quantum mechanics emerged in the early part of the 20th century.

Evidence of quanta from the photoelectric effect

The seeds of the quantum revolution appear in the discovery by J.J. Thomson in 1897 that cathode rays were not continuous but "corpuscles" (electrons). Electrons had been named just six years earlier as part of the emerging theory of atoms. In 1900, Max Planck, unconvinced by the atomic theory, discovered that he needed discrete entities like atoms or electrons to explain black-body radiation.

Black-body radiation intensity vs color and temperature. The rainbow bar represents visible light; 5000 K objects are "white hot" by mixing differing colors of visible light. To the right is the invisible infrared. Classical theory (black curve for 5000 K) fails to predict the colors; the other curves are correctly predicted by quantum theories.

Very hot – red hot or white hot – objects look similar when heated to the same temperature. This look results from a common curve of light intensity at different frequencies (colors), which is called black-body radiation. White hot objects have intensity across many colors in the visible range. The lowest frequencies above visible colors are infrared light, which also give off heat. Continuous wave theories of light and matter cannot explain the black-body radiation curve. Planck spread the heat energy among individual "oscillators" of an undefined character but with discrete energy capacity; this model explained black-body radiation.

At the time, electrons, atoms, and discrete oscillators were all exotic ideas to explain exotic phenomena. But in 1905 Albert Einstein proposed that light was also corpuscular, consisting of "energy quanta", in contradiction to the established science of light as a continuous wave, stretching back a hundred years to Thomas Young's work on diffraction.

Einstein's revolutionary proposal started by reanalyzing Planck's black-body theory, arriving at the same conclusions by using the new "energy quanta". Einstein then showed how energy quanta connected to Thomson's electron. In 1902, Philipp Lenard directed light from an arc lamp onto freshly cleaned metal plates housed in an evacuated glass tube. He measured the electric current coming off the metal plate, at higher and lower intensities of light and for different metals. Lenard showed that amount of current – the number of electrons – depended on the intensity of the light, but that the velocity of these electrons did not depend on intensity. This is the photoelectric effect. The continuous wave theories of the time predicted that more light intensity would accelerate the same amount of current to higher velocity, contrary to this experiment. Einstein's energy quanta explained the volume increase: one electron is ejected for each quantum: more quanta mean more electrons.

Einstein then predicted that the electron velocity would increase in direct proportion to the light frequency above a fixed value that depended upon the metal. Here the idea is that energy in energy-quanta depends upon the light frequency; the energy transferred to the electron comes in proportion to the light frequency. The type of metal gives a barrier, the fixed value, that the electrons must climb over to exit their atoms, to be emitted from the metal surface and be measured.

Ten years elapsed before Millikan's definitive experiment verified Einstein's prediction. During that time many scientists rejected the revolutionary idea of quanta. But Planck's and Einstein's concept was in the air and soon began to affect other physics and quantum theories.

Quantization of bound electrons in atoms

Experiments with light and matter in the late 1800s uncovered a reproducible but puzzling regularity. When light was shown through purified gases, certain frequencies (colors) did not pass. These dark absorption 'lines' followed a distinctive pattern: the gaps between the lines decreased steadily. By 1889, the Rydberg formula predicted the lines for hydrogen gas using only a constant number and the integers to index the lines. The origin of this regularity was unknown. Solving this mystery would eventually become the first major step toward quantum mechanics.

Throughout the 19th century evidence grew for the atomic nature of matter. With Thomson's discovery of the electron in 1897, scientists began the search for a model of the interior of the atom. Thomson proposed negative electrons swimming in a pool of positive charge. Between 1908 and 1911, Rutherford showed that the positive part was only 1/3000th of the diameter of the atom.

Models of "planetary" electrons orbiting a nuclear "Sun" were proposed, but cannot explain why the electron does not simply fall into the positive charge. In 1913 Niels Bohr and Ernest Rutherford connected the new atom models to the mystery of the Rydberg formula: the orbital radius of the electrons were constrained and the resulting energy differences matched the energy differences in the absorption lines. This meant that absorption and emission of light from atoms was energy quantized: only specific energies that matched the difference in orbital energy would be emitted or absorbed.

Trading one mystery – the regular pattern of the Rydberg formula – for another mystery – constraints on electron orbits – might not seem like a big advance, but the new atom model summarized many other experimental findings. The quantization of the photoelectric effect and now the quantization of the electron orbits set the stage for the final revolution.

Throughout the first and the modern era of quantum mechanics the concept that classical mechanics must be valid macroscopically constrained possible quantum models. This concept was formalized by Bohr in 1923 as the correspondence principle. It requires quantum theory to converge to classical limits. A related concept is Ehrenfest's theorem, which shows that the average values obtained from quantum mechanics (e.g. position and momentum) obey classical laws.

Quantization of spin

Stern–Gerlach experiment: Silver atoms travelling through an inhomogeneous magnetic field, and being deflected up or down depending on their spin; (1) furnace, (2) beam of silver atoms, (3) inhomogeneous magnetic field, (4) classically expected result, (5) observed result

In 1922 Otto Stern and Walther Gerlach demonstrated that the magnetic properties of silver atoms defy classical explanation, the work contributing to Stern’s 1943 Nobel Prize in Physics. They fired a beam of silver atoms through a magnetic field. According to classical physics, the atoms should have emerged in a spray, with a continuous range of directions. Instead, the beam separated into two, and only two, diverging streams of atoms. Unlike the other quantum effects known at the time, this striking result involves the state of a single atom. In 1927, T.E. Phipps and J.B. Taylor obtained a similar, but less pronounced effect using hydrogen atoms in their ground state, thereby eliminating any doubts that may have been caused by the use of silver atoms.

In 1924, Wolfgang Pauli called it "two-valuedness not describable classically" and associated it with electrons in the outermost shell. The experiments lead to formulation of its theory described to arise from spin of the electron in 1925, by Samuel Goudsmit and George Uhlenbeck, under the advice of Paul Ehrenfest.

Quantization of matter

In 1924 Louis de Broglie proposed that electrons in an atom are constrained not in "orbits" but as standing waves. In detail his solution did not work, but his hypothesis – that the electron "corpuscle" moves in the atom as a wave – spurred Erwin Schrödinger to develop a wave equation for electrons; when applied to hydrogen the Rydberg formula was accurately reproduced.

Example original electron diffraction photograph from the laboratory of G. P. Thomson, recorded 1925–1927

Max Born's 1924 paper "Zur Quantenmechanik" was the first use of the words "quantum mechanics" in print. His later work included developing quantum collision models; in a footnote to a 1926 paper he proposed the Born rule connecting theoretical models to experiment.

In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow-moving electrons at a crystalline nickel target which showed a diffraction pattern indicating wave nature of electron whose theory was fully explained by Hans Bethe. A similar experiment by George Paget Thomson and Alexander Reid, firing electrons at thin celluloid foils and later metal films, observing rings, independently discovered matter wave nature of electrons.

Further developments

In 1928 Paul Dirac published his relativistic wave equation simultaneously incorporating relativity, predicting anti-matter, and providing a complete theory for the Stern–Gerlach result. These successes launched a new fundamental understanding of our world at small scale: quantum mechanics.

Planck and Einstein started the revolution with quanta that broke down the continuous models of matter and light. Twenty years later "corpuscles" like electrons came to be modeled as continuous waves. This result came to be called wave-particle duality, one iconic idea along with the uncertainty principle that sets quantum mechanics apart from older models of physics.

Quantum radiation, quantum fields

In 1923 Compton demonstrated that the Planck-Einstein energy quanta from light also had momentum; three years later the "energy quanta" got a new name "photon" Despite its role in almost all stages of the quantum revolution, no explicit model for light quanta existed until 1927 when Paul Dirac began work on a quantum theory of radiation that became quantum electrodynamics. Over the following decades this work evolved into quantum field theory, the basis for modern quantum optics and particle physics.

Wave–particle duality

The concept of wave–particle duality says that neither the classical concept of "particle" nor of "wave" can fully describe the behavior of quantum-scale objects, either photons or matter. Wave–particle duality is an example of the principle of complementarity in quantum physics. An elegant example of wave-particle duality is the double-slit experiment.

The diffraction pattern produced when light is shone through one slit (top) and the interference pattern produced by two slits (bottom). Both patterns show oscillations due to the wave nature of light. The double slit pattern is more dramatic.

In the double-slit experiment, as originally performed by Thomas Young in 1803, and then Augustin Fresnel a decade later, a beam of light is directed through two narrow, closely spaced slits, producing an interference pattern of light and dark bands on a screen. The same behavior can be demonstrated in water waves: the double-slit experiment was seen as a demonstration of the wave nature of light.

Variations of the double-slit experiment have been performed using electrons, atoms, and even large molecules, and the same type of interference pattern is seen. Thus it has been demonstrated that all matter possesses wave characteristics.

If the source intensity is turned down, the same interference pattern will slowly build up, one "count" or particle (e.g. photon or electron) at a time. The quantum system acts as a wave when passing through the double slits, but as a particle when it is detected. This is a typical feature of quantum complementarity: a quantum system acts as a wave in an experiment to measure its wave-like properties, and like a particle in an experiment to measure its particle-like properties. The point on the detector screen where any individual particle shows up is the result of a random process. However, the distribution pattern of many individual particles mimics the diffraction pattern produced by waves.

Uncertainty principle

Werner Heisenberg at the age of 26. Heisenberg won the Nobel Prize in Physics in 1932 for the work he did in the late 1920s.

Suppose it is desired to measure the position and speed of an object—for example, a car going through a radar speed trap. It can be assumed that the car has a definite position and speed at a particular moment in time. How accurately these values can be measured depends on the quality of the measuring equipment. If the precision of the measuring equipment is improved, it provides a result closer to the true value. It might be assumed that the speed of the car and its position could be operationally defined and measured simultaneously, as precisely as might be desired.

In 1927, Heisenberg proved that this last assumption is not correct. Quantum mechanics shows that certain pairs of physical properties, for example, position and speed, cannot be simultaneously measured, nor defined in operational terms, to arbitrary precision: the more precisely one property is measured, or defined in operational terms, the less precisely can the other be thus treated. This statement is known as the uncertainty principle. The uncertainty principle is not only a statement about the accuracy of our measuring equipment but, more deeply, is about the conceptual nature of the measured quantities—the assumption that the car had simultaneously defined position and speed does not work in quantum mechanics. On a scale of cars and people, these uncertainties are negligible, but when dealing with atoms and electrons they become critical.

Heisenberg gave, as an illustration, the measurement of the position and momentum of an electron using a photon of light. In measuring the electron's position, the higher the frequency of the photon, the more accurate is the measurement of the position of the impact of the photon with the electron, but the greater is the disturbance of the electron. This is because from the impact with the photon, the electron absorbs a random amount of energy, rendering the measurement obtained of its momentum increasingly uncertain, for one is necessarily measuring its post-impact disturbed momentum from the collision products and not its original momentum (momentum which should be simultaneously measured with position). With a photon of lower frequency, the disturbance (and hence uncertainty) in the momentum is less, but so is the accuracy of the measurement of the position of the impact.

At the heart of the uncertainty principle is a fact that for any mathematical analysis in the position and velocity domains, achieving a sharper (more precise) curve in the position domain can only be done at the expense of a more gradual (less precise) curve in the speed domain, and vice versa. More sharpness in the position domain requires contributions from more frequencies in the speed domain to create the narrower curve, and vice versa. It is a fundamental tradeoff inherent in any such related or complementary measurements, but is only really noticeable at the smallest (Planck) scale, near the size of elementary particles.

The uncertainty principle shows mathematically that the product of the uncertainty in the position and momentum of a particle (momentum is velocity multiplied by mass) could never be less than a certain value, and that this value is related to the Planck constant.

Wave function collapse

Wave function collapse means that a measurement has forced or converted a quantum (probabilistic or potential) state into a definite measured value. This phenomenon is only seen in quantum mechanics rather than classical mechanics.

For example, before a photon actually "shows up" on a detection screen it can be described only with a set of probabilities for where it might show up. When it does appear, for instance in the CCD of an electronic camera, the time and space where it interacted with the device are known within very tight limits. However, the photon has disappeared in the process of being captured (measured), and its quantum wave function has disappeared with it. In its place, some macroscopic physical change in the detection screen has appeared, e.g., an exposed spot in a sheet of photographic film, or a change in electric potential in some cell of a CCD.

Eigenstates and eigenvalues

Because of the uncertainty principle, statements about both the position and momentum of particles can assign only a probability that the position or momentum has some numerical value. Therefore, it is necessary to formulate clearly the difference between the state of something indeterminate, such as an electron in a probability cloud, and the state of something having a definite value. When an object can definitely be "pinned-down" in some respect, it is said to possess an eigenstate.

In the Stern–Gerlach experiment discussed above, the quantum model predicts two possible values of spin for the atom compared to the magnetic axis. These two eigenstates are named arbitrarily 'up' and 'down'. The quantum model predicts these states will be measured with equal probability, but no intermediate values will be seen. This is what the Stern–Gerlach experiment shows.

The eigenstates of spin about the vertical axis are not simultaneously eigenstates of spin about the horizontal axis, so this atom has an equal probability of being found to have either value of spin about the horizontal axis. As described in the section above, measuring the spin about the horizontal axis can allow an atom that was spun up to spin down: measuring its spin about the horizontal axis collapses its wave function into one of the eigenstates of this measurement, which means it is no longer in an eigenstate of spin about the vertical axis, so can take either value.

The Pauli exclusion principle

Wolfgang Pauli

In 1924, Wolfgang Pauli proposed a new quantum degree of freedom (or quantum number), with two possible values, to resolve inconsistencies between observed molecular spectra and the predictions of quantum mechanics. In particular, the spectrum of atomic hydrogen had a doublet, or pair of lines differing by a small amount, where only one line was expected. Pauli formulated his exclusion principle, stating, "There cannot exist an atom in such a quantum state that two electrons within [it] have the same set of quantum numbers."

A year later, Uhlenbeck and Goudsmit identified Pauli's new degree of freedom with the property called spin whose effects were observed in the Stern–Gerlach experiment.

Dirac wave equation

Paul Dirac (1902–1984)

In 1928, Paul Dirac extended the Pauli equation, which described spinning electrons, to account for special relativity. The result was a theory that dealt properly with events, such as the speed at which an electron orbits the nucleus, occurring at a substantial fraction of the speed of light. By using the simplest electromagnetic interaction, Dirac was able to predict the value of the magnetic moment associated with the electron's spin and found the experimentally observed value, which was too large to be that of a spinning charged sphere governed by classical physics. He was able to solve for the spectral lines of the hydrogen atom and to reproduce from physical first principles Sommerfeld's successful formula for the fine structure of the hydrogen spectrum.

Dirac's equations sometimes yielded a negative value for energy, for which he proposed a novel solution: he posited the existence of an antielectron and a dynamical vacuum. This led to the many-particle quantum field theory.

Quantum entanglement

In quantum physics, a group of particles can interact or be created together in such a way that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. This is known as quantum entanglement.

An early landmark in the study of entanglement was the Einstein–Podolsky–Rosen (EPR) paradox, a thought experiment proposed by Albert Einstein, Boris Podolsky and Nathan Rosen which argues that the description of physical reality provided by quantum mechanics is incomplete. In a 1935 paper titled "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?", they argued for the existence of "elements of reality" that were not part of quantum theory, and speculated that it should be possible to construct a theory containing these hidden variables.

The thought experiment involves a pair of particles prepared in what would later become known as an entangled state. Einstein, Podolsky, and Rosen pointed out that, in this state, if the position of the first particle were measured, the result of measuring the position of the second particle could be predicted. If instead the momentum of the first particle was measured, then the result of measuring the momentum of the second particle could be predicted. They argued that no action taken on the first particle could instantaneously affect the other, since this would involve information being transmitted faster than light, which is forbidden by the theory of relativity. They invoked a principle, later known as the "EPR criterion of reality", positing that: "If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity." From this, they inferred that the second particle must have a definite value of both position and of momentum prior to either quantity being measured. But quantum mechanics considers these two observables incompatible and thus does not associate simultaneous values for both to any system. Einstein, Podolsky, and Rosen therefore concluded that quantum theory does not provide a complete description of reality. In the same year, Erwin Schrödinger used the word "entanglement" and declared: "I would not call that one but rather the characteristic trait of quantum mechanics."

The Irish physicist John Stewart Bell carried the analysis of quantum entanglement much further. He deduced that if measurements are performed independently on the two separated particles of an entangled pair, then the assumption that the outcomes depend upon hidden variables within each half implies a mathematical constraint on how the outcomes on the two measurements are correlated. This constraint would later be named the Bell inequality. Bell then showed that quantum physics predicts correlations that violate this inequality. Consequently, the only way that hidden variables could explain the predictions of quantum physics is if they are "nonlocal", which is to say that somehow the two particles are able to interact instantaneously no matter how widely they ever become separated. Performing experiments like those that Bell suggested, physicists have found that nature obeys quantum mechanics and violates Bell inequalities. In other words, the results of these experiments are incompatible with any local hidden variable theory.

Quantum field theory

The idea of quantum field theory began in the late 1920s with British physicist Paul Dirac, when he attempted to quantize the energy of the electromagnetic field; just as in quantum mechanics the energy of an electron in the hydrogen atom was quantized. Quantization is a procedure for constructing a quantum theory starting from a classical theory.

Merriam-Webster defines a field in physics as "a region or space in which a given effect (such as magnetism) exists". Other effects that manifest themselves as fields are gravitation and static electricity. In 2008, physicist Richard Hammond wrote:

Sometimes we distinguish between quantum mechanics (QM) and quantum field theory (QFT). QM refers to a system in which the number of particles is fixed, and the fields (such as the electromechanical field) are continuous classical entities. QFT ... goes a step further and allows for the creation and annihilation of particles ...

He added, however, that quantum mechanics is often used to refer to "the entire notion of quantum view".

In 1931, Dirac proposed the existence of particles that later became known as antimatter. Dirac shared the Nobel Prize in Physics for 1933 with Schrödinger "for the discovery of new productive forms of atomic theory".

Quantum electrodynamics

Quantum electrodynamics (QED) is the name of the quantum theory of the electromagnetic force. Understanding QED begins with understanding electromagnetism. Electromagnetism can be called "electrodynamics" because it is a dynamic interaction between electrical and magnetic forces. Electromagnetism begins with the electric charge.

Electric charges are the sources of and create, electric fields. An electric field is a field that exerts a force on any particles that carry electric charges, at any point in space. This includes the electron, proton, and even quarks, among others. As a force is exerted, electric charges move, a current flows, and a magnetic field is produced. The changing magnetic field, in turn, causes electric current (often moving electrons). The physical description of interacting charged particles, electrical currents, electrical fields, and magnetic fields is called electromagnetism.

In 1928 Paul Dirac produced a relativistic quantum theory of electromagnetism. This was the progenitor to modern quantum electrodynamics, in that it had essential ingredients of the modern theory. However, the problem of unsolvable infinities developed in this relativistic quantum theory. Years later, renormalization largely solved this problem. Initially viewed as a provisional, suspect procedure by some of its originators, renormalization eventually was embraced as an important and self-consistent tool in QED and other fields of physics. Also, in the late 1940s Feynman diagrams provided a way to make predictions with QED by finding a probability amplitude for each possible way that an interaction could occur. The diagrams showed in particular that the electromagnetic force is the exchange of photons between interacting particles.

The Lamb shift is an example of a quantum electrodynamics prediction that has been experimentally verified. It is an effect whereby the quantum nature of the electromagnetic field makes the energy levels in an atom or ion deviate slightly from what they would otherwise be. As a result, spectral lines may shift or split.

Similarly, within a freely propagating electromagnetic wave, the current can also be just an abstract displacement current, instead of involving charge carriers. In QED, its full description makes essential use of short-lived virtual particles. There, QED again validates an earlier, rather mysterious concept.

Standard Model

The Standard Model of particle physics is the quantum field theory that describes three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifies all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, proof of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy.

Although the Standard Model is believed to be theoretically self-consistent and has demonstrated success in providing experimental predictions, it leaves some physical phenomena unexplained and so falls short of being a complete theory of fundamental interactions. For example, it does not fully explain baryon asymmetry, incorporate the full theory of gravitation as described by general relativity, or account for the universe's accelerating expansion as possibly described by dark energy. The model does not contain any viable dark matter particle that possesses all of the required properties deduced from observational cosmology. It also does not incorporate neutrino oscillations and their non-zero masses. Accordingly, it is used as a basis for building more exotic models that incorporate hypothetical particles, extra dimensions, and elaborate symmetries (such as supersymmetry) to explain experimental results at variance with the Standard Model, such as the existence of dark matter and neutrino oscillations.

Interpretations

The physical measurements, equations, and predictions pertinent to quantum mechanics are all consistent and hold a very high level of confirmation. However, the question of what these abstract models say about the underlying nature of the real world has received competing answers. These interpretations are widely varying and sometimes somewhat abstract. For instance, the Copenhagen interpretation states that before a measurement, statements about a particle's properties are completely meaningless, while the many-worlds interpretation describes the existence of a multiverse made up of every possible universe.

Light behaves in some aspects like particles and in other aspects like waves. Matter—the "stuff" of the universe consisting of particles such as electrons and atoms—exhibits wavelike behavior too. Some light sources, such as neon lights, give off only certain specific frequencies of light, a small set of distinct pure colors determined by neon's atomic structure. Quantum mechanics shows that light, along with all other forms of electromagnetic radiation, comes in discrete units, called photons, and predicts its spectral energies (corresponding to pure colors), and the intensities of its light beams. A single photon is a quantum, or smallest observable particle, of the electromagnetic field. A partial photon is never experimentally observed. More broadly, quantum mechanics shows that many properties of objects, such as position, speed, and angular momentum, that appeared continuous in the zoomed-out view of classical mechanics, turn out to be (in the very tiny, zoomed-in scale of quantum mechanics) quantized. Such properties of elementary particles are required to take on one of a set of small, discrete allowable values, and since the gap between these values is also small, the discontinuities are only apparent at very tiny (atomic) scales.

Applications

Everyday applications

The relationship between the frequency of electromagnetic radiation and the energy of each photon is why ultraviolet light can cause sunburn, but visible or infrared light cannot. A photon of ultraviolet light delivers a high amount of energy—enough to contribute to cellular damage such as occurs in a sunburn. A photon of infrared light delivers less energy—only enough to warm one's skin. So, an infrared lamp can warm a large surface, perhaps large enough to keep people comfortable in a cold room, but it cannot give anyone a sunburn.

Technological applications

Applications of quantum mechanics include the laser, the transistor, the electron microscope, and magnetic resonance imaging. A special class of quantum mechanical applications is related to macroscopic quantum phenomena such as superfluid helium and superconductors. The study of semiconductors led to the invention of the diode and the transistor, which are indispensable for modern electronics.

In even a simple light switch, quantum tunneling is absolutely vital, as otherwise the electrons in the electric current could not penetrate the potential barrier made up of a layer of oxide. Flash memory chips found in USB drives also use quantum tunneling, to erase their memory cells.

Point (geometry)

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