Schadenfreude

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Schadenfreude

Return to the Convent, by Eduardo Zamacois y Zabala, 1868. The painting depicts a group of monks laughing while a lone monk struggles with an ass.

Schadenfreude (/ˈʃɑːdənfrɔɪdə/; German: [ˈʃaːdn̩ˌfʁɔʏ̯də] (listen); lit. 'harm-joy') is the experience of pleasure, joy, or self-satisfaction that comes from learning of or witnessing the troubles, failures, or humiliation of another. It is a borrowed word from German, with no direct translation, that originated in the 18th century.

Schadenfreude has been detected in children as young as 24 months and may be an important social emotion establishing "inequity aversion".

Etymology

Schadenfreude is a term borrowed from German. It is a compound of Schaden ("damage/harm") and Freude ("joy"). The German word was first mentioned in English texts in 1852 and 1867, and first used in English running text in 1895. In German, it was first attested in the 1740s. The earliest seems to be Christoph Starke, Synopsis bibliothecae exegeticae in Vetus Testamentum. Leipzig 1750. Although common nouns normally are not capitalised in English, schadenfreude sometimes is capitalised following the German convention.

Psychological causes

Researchers have found that there are three driving forces behind schadenfreude – aggression, rivalry, and justice.

Self-esteem has a negative relationship with the frequency and intensity of schadenfreude experienced by an individual; individuals with lower self-esteem tend to experience schadenfreude more frequently and intensely.

It is hypothesized that this inverse relationship is mediated through the human psychological inclination to define and protect their self- and in-group- identity or self-conception. Specifically, for someone with high self-esteem, seeing another person fail may still bring them a small (but effectively negligible) surge of confidence because the observer's high self-esteem significantly lowers the threat they believe the visibly-failing human poses to their status or identity. Since this confident individual perceives that, regardless of circumstances, the successes and failures of the other person will have little impact on their own status or well-being, they have very little emotional investment in how the other person fares, be it positive or negative.

Conversely, for someone with low self-esteem, someone who is more successful poses a threat to their sense of self, and seeing this person fall can be a source of comfort because they perceive a relative improvement in their internal or in-group standing.

• Aggression-based schadenfreude primarily involves group identity. The joy of observing the suffering of others comes from the observer's feeling that the other's failure represents an improvement or validation of their own group's (in-group) status in relation to external (out-groups) groups (see In-group and out-group). This is, essentially, schadenfreude based on group versus group status.
• Rivalry-based schadenfreude is individualistic and related to interpersonal competition. It arises from a desire to stand out from and out-perform one's peers. This is schadenfreude based on another person's misfortune eliciting pleasure because the observer now feels better about their personal identity and self-worth, instead of their group identity.
• Justice-based schadenfreude comes from seeing that behavior seen as immoral or "bad" is punished. It is the pleasure associated with seeing a "bad" person being harmed or receiving retribution. Schadenfreude is experienced here because it makes people feel that fairness has been restored for a previously un-punished wrong, and is a type of moral emotion.

Synonyms

Schadenfreude has equivalents in many other languages (such as: in Dutch leedvermaak and Swedish skadeglädje), but no commonly-used precise English single-word equivalent. There are other ways to express the concept in English.

Epicaricacy is a seldom-used direct equivalent, borrowed from Greek epichairekakia (ἐπιχαιρεκακία, first attested in Aristotle) from ἐπί epi 'upon', χαρά chara 'joy', and κακόν kakon 'evil'.

Tall poppy syndrome is a cultural phenomenon where people of high status are resented, attacked, cut down, or criticized because they have been classified as better than their peers. This is similar to "begrudgery", the resentment or envy of the success of a peer. If someone were to feel joy by the victim's fall from grace, they would be experiencing schadenfreude.

Roman holiday is a metaphor from Byron's poem Childe Harold's Pilgrimage, where a gladiator in ancient Rome expects to be "butchered to make a Roman holiday" while the audience would take pleasure from watching his suffering. The term suggests debauchery and disorder in addition to sadistic enjoyment.

Morose delectation (Latin: delectatio morosa), meaning "the habit of dwelling with enjoyment on evil thoughts", was considered by the medieval church to be a sin. French writer Pierre Klossowski maintained that the appeal of sadism is morose delectation.

"Gloating" is an English word of similar meaning, where "gloat" means "to observe or think about something with triumphant and often malicious satisfaction, gratification, or delight" (e.g., to gloat over an enemy's misfortune). Gloating is different from schadenfreude in that it does not necessarily require malice (one may gloat to a friend without ill intent about having defeated him in a game), and that it describes an action rather than a state of mind (one typically gloats to the subject of the misfortune or to a third party). Also, unlike schadenfreude, where the focus is on another's misfortune, gloating often brings to mind inappropriately celebrating or bragging about one's own good fortune without any particular focus on the misfortune of others.

Related emotions or concepts

Permutations of the concept of pleasure at another's unhappiness are: pleasure at another's happiness, displeasure at another's happiness, and displeasure at another's unhappiness. Words for these concepts are sometimes cited as antonyms to schadenfreude, as each is the opposite in some way.

There is no common English term for pleasure at another's happiness (i.e.; vicarious joy), though terms like 'celebrate', 'cheer', 'congratulate', 'applaud', 'rejoice' or 'kudos' often describe a shared or reciprocal form of pleasure. The pseudo-German coinage freudenfreude is occasionally used in English. Writers on Buddhism speak of mudita and polyamorists speak of compersion. The Hebrew slang term firgun refers to happiness at another's accomplishment.

Displeasure at another's happiness is involved in envy, and perhaps in jealousy. The coinage "freudenschade" similarly means sorrow at another's success.

Displeasure at another's good fortune is Gluckschmerz, a pseudo-German word coined in 1985 as a joke by the pseudonymous Wanda Tinasky; the correct German form would be Glücksschmerz. It has since been used in academic contexts.

Displeasure at another's unhappiness is sympathy, pity, or compassion.

Sadism gives pleasure through the infliction of pain, whereas schadenfreude is pleasure on observing misfortune and in particular, the fact that the other somehow deserved the misfortune.

Neologisms and variants

The word schadenfreude had been blended with other words to form neologisms as early as 1993, when Lincoln Caplan, in his book Skadden: Power, Money, and the Rise of a Legal Empire, used the word Skaddenfreude to describe the delight that competitors of Skadden Arps took in its troubles of the early 1990s. Others include spitzenfreude, coined by The Economist to refer to the fall of Eliot Spitzer, and Schadenford, coined by Toronto Life in regard to Canadian politician Rob Ford.

Literary usage and philosophical analysis

The Biblical Book of Proverbs mentions an emotion similar to schadenfreude: "Rejoice not when thine enemy falleth, and let not thine heart be glad when he stumbleth: Lest the LORD see it, and it displease him, and he turn away his wrath from him." (Proverbs 24:17–18, King James Version).

In East Asia, the emotion of feeling joy from seeing the hardship of others was described as early as late 4th century BCE. The phrase Xing zai le huo (Chinese: 幸災樂禍) first appeared separately as xing zai (幸災), meaning the feeling of joy from seeing the hardship of others, and le huo (樂禍), meaning the happiness derived from the unfortunate situation of others, in the ancient Chinese text Zuo zhuan (左傳). The phrase xing zai le huo (幸災樂禍) is still used among Chinese speakers.

In the Nicomachean Ethics, Aristotle used epikhairekakia (ἐπιχαιρεκακία in Greek) as part of a triad of terms, in which epikhairekakia stands as the opposite of phthonos (φθόνος), and nemesis (νέμεσις) occupies the mean. Nemesis is "a painful response to another's undeserved good fortune", while phthonos is a painful response to any good fortune of another, deserved or not. The epikhairekakos (ἐπιχαιρέκακος) person takes pleasure in another's ill fortune.

Lucretius characterises the emotion in an extended simile in De rerum natura: Suave, mari magno turbantibus aequora ventis, e terra magnum alterius spectare laborem, "It is pleasant to watch from the land the great struggle of someone else in a sea rendered great by turbulent winds." The abbreviated Latin tag suave mare magno recalled the passage to generations familiar with the Latin classics.

Caesarius of Heisterbach regards "delight in the adversity of a neighbour" as one of the "daughters of envy... which follows anger" in his Dialogue on Miracles.

During the seventeenth century, Robert Burton wrote:

Out of these two [the concupiscible and irascible powers] arise those mixed affections and passions of anger, which is a desire of revenge; hatred, which is inveterate anger; zeal, which is offended with him who hurts that he loves; and ἐπιχαιρεκακία, a compound affection of joy and hate, when we rejoice at other men's mischief, and are grieved at their prosperity; pride, self-love, emulation, envy, shame, [etc.], of which elsewhere.

— The Anatomy of Melancholy

The philosopher Arthur Schopenhauer mentioned schadenfreude as the most evil sin of human feeling, famously saying "To feel envy is human, to savor schadenfreude is diabolic."

The song "Schadenfreude" in the musical Avenue Q, is a comedic exploration of the general public's relationship with the emotion.

Rabbi Harold S. Kushner in his book When Bad Things Happen to Good People describes schadenfreude as a universal, even wholesome reaction that cannot be helped. "There is a German psychological term, Schadenfreude, which refers to the embarrassing reaction of relief we feel when something bad happens to someone else instead of to us." He gives examples and writes, "[People] don't wish their friends ill, but they can't help feeling an embarrassing spasm of gratitude that [the bad thing] happened to someone else and not to them."

Susan Sontag's book Regarding the Pain of Others, published in 2003, is a study of the issue of how the pain and misfortune of some people affects others, namely whether war photography and war paintings may be helpful as anti-war tools, or whether they only serve some sense of schadenfreude in some viewers.

Philosopher and sociologist Theodor Adorno defined schadenfreude as "... largely unanticipated delight in the suffering of another, which is cognized as trivial and/or appropriate."

Schadenfreude is steadily becoming a more popular word according to Google.

Scientific studies

A New York Times article in 2002 cited a number of scientific studies of schadenfreude, which it defined as "delighting in others' misfortune". Many such studies are based on social comparison theory, the idea that when people around us have bad luck, we look better to ourselves. Other researchers have found that people with low self-esteem are more likely to feel schadenfreude than are those who have high self-esteem.

A 2003 study examined intergroup schadenfreude within the context of sports, specifically an international football (soccer) competition. The study focused on the German and Dutch football teams and their fans. The results of this study indicated that the emotion of schadenfreude is very sensitive to circumstances that make it more or less legitimate to feel such malicious pleasure toward a sports rival.

A 2011 study by Cikara and colleagues using functional magnetic resonance imaging (fMRI) examined schadenfreude among Boston Red Sox and New York Yankees fans, and found that fans showed increased activation in brain areas correlated with self-reported pleasure (ventral striatum) when observing the rival team experience a negative outcome (e.g., a strikeout). By contrast, fans exhibited increased activation in the anterior cingulate and insula when viewing their own team experience a negative outcome.

A 2006 experiment about "justice served" suggests that men, but not women, enjoy seeing "bad people" suffer. The study was designed to measure empathy by watching which brain centers are stimulated when subjects observed via fMRI see someone experiencing physical pain. Researchers expected that the brain's empathy center of subjects would show more stimulation when those seen as "good" got an electric shock, than would occur if the shock was given to someone the subject had reason to consider "bad". This was indeed the case, but for male subjects, the brain's pleasure centers also lit up when someone got a shock that the male thought was "well-deserved".

Brain-scanning studies show that schadenfreude is correlated with envy in subjects. Strong feelings of envy activated physical pain nodes in the brain's dorsal anterior cingulate cortex; the brain's reward centers, such as the ventral striatum, were activated by news that other people who were envied had suffered misfortune. The magnitude of the brain's schadenfreude response could even be predicted from the strength of the previous envy response.

A study conducted in 2009 provides evidence for people's capacity to feel schadenfreude in response to negative events in politics. The study was designed to determine whether or not there was a possibility that events containing objective misfortunes might produce schadenfreude. It was reported in the study that the likelihood of experiencing feelings of schadenfreude depends upon whether an individual's own party or the opposing party is suffering harm. This study suggests that the domain of politics is prime territory for feelings of schadenfreude, especially for those who identify strongly with their political party.

In 2014, research in the form of an online survey analyzed the relationship between schadenfreude and 'Dark Triad' traits (i.e. narcissism, Machiavellianism, and psychopathy). The findings showed that those respondents who had higher levels of Dark Triad traits also had higher levels of schadenfreude, engaged in greater anti-social activities and had greater interests in sensationalism.

Mental health in education

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

Mental health in education is the impact that mental health (including emotional, psychological, and social well-being) has on educational performance. Mental health often viewed as an adult issue, but in fact, almost half of adolescents in the United States are affected by mental disorders, and about 20% of these are categorized as “severe.” Mental health issues can pose a huge problem for students in terms of academic and social success in school. Education systems around the world treat this topic differently, both directly through official policies and indirectly through cultural views on mental health and well-being. These curriculums are in place to effectively identify mental health disorders and treat it using therapy, medication, or other tools of alleviation.

Primary school children in classroom

Prevalence of mental health issues in adolescents

According to the National Institute of Mental Health, approximately 46% of American adolescents aged 13–18 will suffer from some form of mental disorder. About 21% will suffer from a disorder that is categorized as “severe,” meaning that the disorder impairs their daily functioning, but almost two-thirds of these adolescents will not receive formal mental health support. The most common types of disorders among adolescents as reported by the NIMH is anxiety disorders (including generalized anxiety disorder, phobias, post-traumatic stress disorder, obsessive-compulsive disorder, and others), with a lifetime prevalence of about 25% in youth aged 13–18 and 6% of those cases being categorized as severe. Next is mood disorders (major depressive disorder, dysthymic disorder, and/or bipolar disorder), with a lifetime prevalence of 14% and 4.7% for severe cases in adolescents. A similarly common disorder is Attention deficit hyperactivity disorder (ADHD), which is categorized as a childhood disorder but oftentimes carries through into adolescence and adulthood. The prevalence for ADHD in American adolescents is 9%, and 1.8% for severe cases.

An effect of this high prevalence is high suicide rates among adolescents. In 2021 study conducted by NIMH, mental health concerns were identified in a third (31.4%) of the suicide deaths examined, with the most common diagnoses being attention-deficit/hyperactivity disorder (ADHD) or depression. Suicide was the second leading cause of death among persons aged 10–29 years in the United States during 2011–2019. More teenagers and young adults die from suicide than cancer, heart disease, AIDS, birth defects, stroke, pneumonia, influenza, and chronic lung disease combined. There are an average of over 3,470 attempts by students [per year? -- DJS] in grades 9–12.

According to APA, the percentage of students going for college mental health counselling has been rising in recent years, which by report for anxiety as the most common factor, depression as the second, stress as the third, family issues as the fourth, and academic performance and relationship problems as the fifth and sixth most.

Common disorder's effects on academics and school life

Mental disorders can affect classroom learning, such as poor attendance, difficulties with academic performance, poor social integration, trouble adjusting to school, problems with behavior regulation, and attention and concentration issues, all of which is critical to the success of the student. High school students who screen positive for psychosocial dysfunction report three times as many absent and tardy days as students who do not identify dysfunction. This leads to much higher dropout rates and lower overall academic achievement. In the United States, only 40 percent of students with emotional, behavioral and mental health disorders graduate from high school, compared to the national average of 76 percent. Some of these disorders may also cause students to prioritize their academics over their own health which will in turn, will only cause their health to decline even more (Beresin et al. 2017).

Anxiety

Students with anxiety disorders are statistically less likely to attend college than those without, and those with social phobias are twice as likely to fail a grade or not finish high school as students who have never had the condition. Anxiety disorders are typically more difficult to recognize than disruptive behavior disorders such as ADHD because the symptoms are internalized. Anxiety may manifest as recurring fears and worries about routine parts of every day life, avoiding activities, school or social interactions and it can interfere with the ability to focus and learn.

Additionally, anxiety disorders can prevent students from seeking or forming social connections, which negatively affects students' sense of belonging and in turn impacts their school experience and academic performance. Students may suffer from social anxiety, preventing them from going out and creating new relationships with new people or any social reaction one might come across.

There is a specific character in which people with anxiety often experience. People with anxiety experience frequent worries and fears about everyday situations. Anxiety can also be identified as a sudden feeling of intense fear or terror that can reach a peak within minutes. These anxiety symptoms usually develops during childhood or teen years and may continue into adulthood. Some examples of symptoms include: feeling nervous, restless or tense, having a sense of impeding danger, panic, or doom, having an increased heart rate, breathing rapidly, sweating, trembling, feeling weak or tired, trouble concentrating or thinking about anything other than the present worry, having trouble sleeping, experiencing gastrointestinal problems, having difficulty controlling worry, or having the urge to avoid things that trigger anxiety. Also, there are several different types of anxiety disorders which are agoraphobia, anxiety disorder due to a medical condition, generalized anxiety disorder, panic disorder, selective mutisim, separation anxiety disorder, social anxiety disorder, specific phobias, substance-induced anxiety disorder, etc.

Depression

Depression can cause students to have problems in class, from completing their work, to even attending class at all. In 2020, approximately 13% of youth aged 12 to 17 years old have had one major depressive episode (MDE) in the past year, with an overwhelming 70% left untreated. According to the National Center for Mental Health Checkups at Columbia University, "High depression scores have been associated with low academic achievement, high scholastic anxiety, increased school suspensions, and decreased ability or desire to complete homework, concentrate, and attend classes." Depression symptoms can make it challenging for students to keep up with course loads, or even find the energy to make it through the full school day.

Depression can be defined as medical illness that negatively affects how you feel, think, and act. The good side is that depression is treatable. Depression is when you get feelings of sadness or loss of interest in activities you once enjoyed. This can later lead onto having varieties of emotional and physical problems. Also, this can decrease the ability to function inside and outside. Some examples of depression symptoms are feeling sad, loss of interest, changes in appetite, trouble sleeping, loss of energy, increase in purposeless physical activity, feeling worthless, difficulty in thinking, concentrating, or making decisions, and thoughts of death or suicide. These symptoms must usually last two weeks and also represent a change in functioning in order for a diagnosis of depression.

Attention deficit hyperactivity disorder

Attention disorders are the principal predictors of diminished academic achievement. Students with ADHD tend to have trouble mastering behaviors and practices demanded of them by the public education system in the United States, such as the ability to quietly sit still or to apply themselves to one focused task for extended durations. ADHD can mean that students have problems concentration, filtering out distracting external stimuli, and seeing large tasks through to completion. These students can also struggle with time management and organization.

ADHD stands for attention-deficit/hyperactivity disorder. This is considered as one of the most common mental disorders for children, however it affects many adults as well. Some examples of symptoms are not paying attention to details and making careless mistakes, having problems of staying focused on activities, not being able to be seen as listening, having problems in organizing, avoiding tasks, and forgetting daily tasks.

Other common struggles for adolescents

Alcoholism

More than 90 percent of all alcoholic drinks consumed by young people are consumed through binge drinking, which can lead to Alcoholism. Alcoholism can affect ones’ mental health by being dependent on it, putting drinking before their own classwork. People who consume alcohol before the age of fourteen are more likely to drink more often without thinking about the consequences later on. Students who drink alcohol can also experience consequences such as higher risk of suicide, memory problems, and misuse of other drugs. A 2017 survey found that 30% of high school students have drunk alcohol and 14% of high schoolers have binge drank.

Suicide

According to the California Dept. of Public Health there were 2,210 suicides in 2019 in the US age range of 15-19 and a total of 6,500 suicides from ages 5–25. Some research estimates that among 15-24 year-olds, there are approximately 100-200 suicide attempts for every suicide. Adolescent suicidality may be a product of network positions characterized by either relative isolation or structural imbalance and a growing body of research links social isolation to suicide. Most suicides reported in Ohio from 1963 to 1965 revealed that they tended to be social outcasts (played no sports, had no hobbies, and were not part of any clubs). They also suggested that half of these students were failing or near-failing at the time of their deaths. These periods of failure and frustration lower the individual's self-concept to a point where they have little sense of self-worth. In fact, students who perceive their academic performance as "failing" are three times more likely to attempt suicide than those who perceive their performance to be acceptable. However, academic failure in school is not the only cause of suicide in schools. Bullying, social isolation, and issues at home are all reasons why students commit suicide.

Reaching Out For Help

The American Psychological Association reports that from 2008 to 2018, a survey showed that 5.8% of American people were not receiving the care they needed for their mental health.  According to the survey's results, 12.7% of young people between the ages of 18 and 25 said that their mental health issues weren't addressed. The majority of respondents to the survey stated that cost considerations were one of the primary reasons why their needs weren't met. Students in education often find themselves in difficult situations that require assistance. For those who require assistance, it is essential to acknowledge mental health services. According to the poll, 26% of respondents believed they could manage their mental needs without receiving treatment.  Many students shy away from the main problem because they think their problems aren't serious enough to warrant assistance. By consuming their thoughts and emotions, students discover that they are increasing their stress and anxiety. In order to encourage students to seek treatment when necessary, educational materials should mention the mental health services that are accessible. 

Covid-19 and mental health

Early Covid-19 Predictions

Outbreaks of disease forecast a rise in mental health policies. Increased levels of unemployment and emotional distress during the global COVID-19 pandemic led to and evidenced such as rise in 2020. There were cases of increased isolation and depression rates of the elderly, xenophobia against people of Asian descent, and resulting mental health effects of large-scale quarantine and business closures. Not only is an achievement gap projected for students that undergo the COVID-19 pandemic, but significant repercussions are expected for the mental health and well-being of students in low-income families, since more than half of students utilize reduced-priced or free mental health resources provided by schools. JAMA Pediatrics expects that the global health crisis will worsen pre-existing mental health disorders in students and the number of childhood mental health disorders will increase with the higher prevalence of social isolation and familial income decline due to economic recession.

The Kaiser Family Foundation reported that 56% of Americans have endured at least one negative mental health effect due to stress related to the outbreak. This can surface as increased alcohol and drug use, frequent headaches, trouble sleeping and eating, or short tempers. Additionally, in May 2020, Well Being Trust reported that the pandemic could lead to 75,000 additional "deaths of despair" from overusing drugs and alcohol or suicide from unemployment, social isolation, and general anxiety regarding the virus. Thus, although as of 2020 there are no federal requirements in place, a rise in mental health awareness and approval of policies is expected post-COVID-19.

Current Covid-19 Effects

"The COVID-19 pandemic led to a worldwide lockdown and school closures, which have placed a substantial mental health burden on children and college students. Through a systematic search of the literature on PubMed and Collabovid of studies published January 2020–July 2021, findings of five studies on children and 16 studies on college students found that both groups reported feeling more anxious, depressed, fatigued, and distressed than prior to the pandemic. As a result of COVID-19, children, adolescent, and college students are experiencing long duration of quarantine, physical isolation from their friends, teachers, and extended family members, and are forced to adapt to a virtual way of learning. A two-year study during the pandemic on Greek University students revealed severe prevalence of stress, anxiety, and depression especially during the second year of the pandemic. Due to this unexpected and forced transition, children and college students may not have adequate academic resources, social contact and support, or a learning-home environment, which may lead to a heightened sense of loneliness, distress, anger, and boredom—causing an increase in negative psychological outcomes. Mental health issues may also arise from the disease itself, such as grief from loss of lives, opportunities, and employment."

Policies in public schools

United States

Concerning U.S. state policies as of 2020, three states have approved mandatory mental health curriculums. In July 2018, New York and Virginia passed legislation that made mental health instruction mandatory in public education. New York has made it mandatory for students from Kindergarten to 12th grade to undergo mental health instruction. After experiencing traumatizing suicidal behavior with his own son, Virginia Senator Creigh Deeds thought it necessary to teach warning signs to 9th and 10th graders so they can look out for the safety of their peers and themselves. The board of education is in charge of deliberating details of the curriculum but the senator is hopeful that teachers will also receive training on warning signs. Even though investment in mental health has never been higher, the state legislature has yet to approve extra funding to implement the curriculum. In July 2019, Florida's board of education made 5 hours of mental health education mandatory for grades 6 through 12, making it the third state to approve such instruction.

Nationally, there has been some effort to increase education on mental health in the public school system. In 2020, the U.S. Department of Education awarded School-Based Mental Health Services grants to 6 state education agencies (SEAs) to increase the number of qualified (i.e., licensed, certified, well-trained, or credentialed) mental health service providers that provide school-based mental health services to students in local educational agencies (LEAs) with demonstrated need. There has been a growing popularity with school-based mental health services in United States public school systems, in which schools have their students covered for mental health care. People, on both the local and federal level, across the states are taking steps to redesign a system that is more favorable for students. This includes focusing on providing mental health services to them.  This concept has the potential to allow students to have access to services that can help them understand and work through any stressors they may face within their schooling, as well as a better chance of intervention for those students who need it.

Based on a study conducted in 2018 by Harvard Medical School, it was found that around 20% of college students in the United States had made attempts at suicide. Furthermore, a more recent report by Healthy Minds in 2021 revealed that 5% of students had reported having planned to commit suicide in the preceding year.

Canada

In Canada, the Mental Health Strategy highlights the importance of mental health promotion, stigma reduction, and early recognition of mental health problems in schools to be a priority (Mental Health Commission, 2012).

Ontario conducts a survey every year to keep track of how effective policies are for public schools. Administered by People for Education, the 2022-23 annual report provided insight into the lack of mental health support for students and how inaccessible specialists are for not only students, but educators as well. These surveys are useful data in making decisions on how money can be spent on public schools and what policies should or should not be enforced. 

Implementing comprehensive school health and post-secondary mental health initiatives that promote mental health and prevention for those at risk was recommended by the Mental Health Commission of Canada.

Bhutan

In Bhutan, efforts toward developing education began in 1961 thanks to Ugyen Wangchuck and the introduction of the First Development Plan, which provided free primary education. By 1998, 400 schools were established. Students' tuition, books, supplies, equipment, and food were all free for boarding schools in the 1980s, and some schools also provided their students with clothing. The assistance of the United Nations Food and Agriculture Organizations' World Food Programme allowed free midday meals in some primary schools. This governmental assistance is important to note in the country's Gross National Happiness (GNH), which is at the forefront of developmental policies and is the responsibility of the government. Article 9 of the Constitution of Bhutan states that "the state shall strive to promote those conditions that will enable the pursuit of Gross National Happiness."

Gross national happiness

GNH in Bhutan is based on four principles: sustainable and equitable economic development, conservation of the environment, preservation and promotion of culture, and good governance. Their constitution prescribes that the state will provide free access to public health services through a three-tiered health system which provides preventative, promotive, and curative services. Because of this policy, Bhutan was able to eliminate iodine deficiency disorder in 2003, leprosy in 1997, and achieved childhood immunization for all children in 1991. It became the first country to ban tobacco in 2004, and cases of malaria decreased from 12,591 cases in 1999 to 972 cases in 2009. The elimination of these diseases and the strong push for GNH allows for all people (including adolescents who are provided with many necessary items and free education) to live happier lives than they otherwise may have had.

United Kingdom

The Department for Education in United Kingdom is working on developing an organizational approach to support mental health and character education. An October 2017 joint report from the Departments for Education and Health outlines this approach with regard to staff training, raising awareness of mental health challenges that children face, and involvement of parents and families in students' mental health.

Singapore

REACH is a program in Singapore that looks to provide interventions for students struggling with mental illness. A quote from the REACH website reads, "The majority of children and adolescents do not suffer from mental illness. However, when a student has been identified, the school counselor, with consultation from the school’s case management team, will look into managing the care of the student. When necessary, guidance specialists and educational psychologists from the Ministry of Education will render additional support.

In 2010, the Voluntary Welfare Organizations (VWOs), in collaboration with the National Council of Social Service (NCSS), have also been invited to join this network to provide community and clinical support to at-risk children. Students and children with severe emotional and behavioral problems may need more help. The REACH team collaborates with school counselors/VWOs to provide suitable school-based interventions to help these students. Such school/VWO based interventions often provide the requisite, timely help that these students and children need. Further specialized assessment or treatment may be necessary for more severe cases. The student or child may be referred to the Child Guidance Clinic after assessment by the REACH team for further psychiatric evaluation and intervention. These interventions may include medications, psychotherapy, group or family work and further assessments."

Mexico

Traditionally, mental health was not considered a part of public health in Mexico because of other health priorities, lack of knowledge about the true magnitude of mental health problems, and a complex approach involving the intervention of other sectors in addition to the public health sector. Among the key documents anticipating the policy change was a report presented by the Mexican Health Foundation in 1995, which opened a very constructive debate. It introduced basic tenets for health improvement, elements for an analysis of the health situation related to the burden of disease approach, and a strategic proposal with concurrent recommendations for reforming the system. Mexico has an extensive legal frame of reference dealing with health and mental health. The objectives are to promote a healthy psychosocial development of different population groups, and reduce the effects of behavioral and psychiatric disorders. This should be achieved through graded and complementary interventions, according to the level of care, and with the coordinated participation of the public, social, and private sectors in municipal, state, and national settings. The strategic lines consider training and qualification of human resources, growth, rehabilitation, and regionalization of mental health service networks, formulation of guidelines and evaluation. All age groups as well as specific sub-populations (indigenous groups, women, street children, populations in disaster areas), and other state and regional priorities are considered.

Japan and China

In Japan and China, the approach to mental health is focused on the collective of students, much like the national aims of these Asian countries. Much like in the US, there is much research done in the realm of student mental health, but not many national policies in place to prevent and aid mental health problems students face. Japanese students face considerable academic pressure as imposed by society and school systems. In 2006, Japanese police gathered notes left from students who had committed suicide that year and noted overarching school pressures as the primary source of their problems. Additionally, the dynamic of collective thinking—the centripetal force of Japan's society, wherein individual identity is sacrificed for the functioning benefit of a greater collective—results in the stigmatization of uniqueness. As child psychiatrist Dr. Ken Takaoka explained to CNN, schools prioritize this collectivism, and “children who do not get along in a group will suffer.”

South Korea

South Korea has traditionally placed much value on education. As a nation that has a degree of enthusiasm like no other for education has created an environment where children are pressured to study more than ever. When mental health issues affect students there are very few resources available to help students cope. The nation's general view of mental health problems, such as anxiety, depression or thoughts of suicide, is that they are believed to be a sign of personal weakness that could bring shame upon a family if a member would be discovered to have such an illness. This is true if the problem arises in a social, educational or family setting. Rather than perceiving mental health issues as a medical condition and concern requiring treatment especially in students, a majority of Korea's population has perceived them as a cultural stigma. A study conducted by Yuri Yang, a professor at the University of Florida and a member of the Department of Aging and Mental Health, found when surveying over 600 Korean citizens from the age of 20-60+ years in 2008, most of the older people, many of whom are parents, shared similar and negative views on mental health issues such as depression. The older adults generally were also found to have a negative view of mental health services, including those offered through the educational system, as they are deeply influenced by the cultural stigma around the topic. This negative view of mental health services in education has provided implications for students who are struggling emotionally, as many do not know what, if any, help might be available in the facilities of education. However, this does not mean no mental health services exist in the world or in the educational setting. The World Health Organization (WHO) in 2006 collected data  regarding Korea's mental health system. The goal of collecting this information was to attempt to improve the mental health system and to provide a baseline for monitoring the change. Despite Korea having a low budget for mental health services compared to other developed countries, it has taken steps to create long term mental health plans to advance its national health system such as raising more awareness for mental health, creating communities for students, and removing the cultural stigma around mental health.

Alleviation and fostering adjustment

Prevention

The pressures of school, extracurricular activities, work and relationships with friends and family can be a lot for an individual to manage and at times can be overwhelming. In order to prevent these overwhelming feelings from turning into a mental health problem, taking measures to prevent these emotions from escalating is essential. School-based programs that help students with emotional-regulation, stress management, conflict resolution, and active coping and cognitive restructuring are a few suggested ways that give students resources that can promote their mental health (Mental Health Commission, 2012).

According to the research Students who receive social-emotional and mental health will have a higher chance of more academic achievements. Since most children spend a large portion of the day at school, about 6 hours, schools are the ideal place for students to receive the services they need. When mental health is not addressed, this can cause issues with causing distractions to fellow students and teachers.

According to a 2019 article regarding school social workers, the field of social workers in schools is continuing to grow. In 1996, there were only about 9,000 social workers in schools. This had increased to be between 20,000 and 22,000 social workers. According to the United States Department of Labor, Bureau of Labor Statistics, it is estimated the field will continue to grow from 2016 to 2026 due to the increase of mental health services that are being demanded in schools.

Belonging

Belonging in the school environment may be the most important and relevant factors affecting students' performance in an academic setting. School-related stress and an increase in academic expectations may increase school-related stress and in turn negatively affect their academic performance. The absence of social acceptance has been shown to lead lowered interest and engagement because students have difficulty sustaining engagement in environments where they do not feel valued and welcome. The feeling of belonging creates a buffer between students and depressive symptoms and lessens the feelings of anxiety in school. Other components of not belonging can also affect students' feeling of belonging, which include not being represented racially, ethnically minority, or lack of first-generation representation in schools.

An issue that is faced in our society today is bullying which can happen at school or even in class. Bullying can cause issues for students such as chemical dependency, physical harm, and a decrease in performance academically. According to the NASP, a large percentage, about 70%-80%, of people have experienced bullying in their school years in which the student could have been the bully, victim, or even the bystander. In order for staff at schools to understand how to notice this as an issue and what to do to resolve it, NASP advocates for guiding principals in how to resolve these issues as well as providing information on available programs.

Redshift

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Redshift

Absorption lines in the visible spectrum of a supercluster of distant galaxies (right), as compared to absorption lines in the visible spectrum of the Sun (left). Arrows indicate redshift. Wavelength increases up towards the red and beyond (frequency decreases).

In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in frequency and energy, is known as a negative redshift, or blueshift. The terms derive from the colours red and blue which form the extremes of the visible light spectrum. The three main causes of electromagnetic redshift in astronomy and cosmology are, first, radiation traveling between objects that are moving apart ("relativistic" redshift, an example of the relativistic Doppler effect); second, the gravitational redshift due to radiation traveling towards an object in a weaker gravitational potential; and third, the cosmological redshift due to radiation traveling through expanding space. All sufficiently distant light sources show redshift for a velocity proportionate to their distance from Earth, a fact known as Hubble's law.

Relativistic, gravitational, and cosmological redshifts can be understood under the umbrella of frame transformation laws. Gravitational waves, which also travel at the speed of light, are subject to the same redshift phenomena. The value of a redshift is often denoted by the letter z, corresponding to the fractional change in wavelength (positive for redshifts, negative for blueshifts), and by the wavelength ratio 1 + z (which is greater than 1 for redshifts and less than 1 for blueshifts).

Examples of strong redshifting are a gamma ray perceived as an X-ray, or initially visible light perceived as radio waves. Subtler redshifts are seen in the spectroscopic observations of astronomical objects, and are used in terrestrial technologies such as Doppler radar and radar guns.

Other physical processes exist that can lead to a shift in the frequency of electromagnetic radiation, including scattering and optical effects; however, the resulting changes are distinguishable from (astronomical) redshift and are not generally referred to as such (see section on physical optics and radiative transfer).

History

The history of the subject began with the development in the 19th century of classical wave mechanics and the exploration of phenomena associated with the Doppler effect. The effect is named after Christian Doppler, who offered the first known physical explanation for the phenomenon in 1842. The hypothesis was tested and confirmed for sound waves by the Dutch scientist Christophorus Buys Ballot in 1845. Doppler correctly predicted that the phenomenon should apply to all waves, and in particular suggested that the varying colors of stars could be attributed to their motion with respect to the Earth. Before this was verified, however, it was found that stellar colors were primarily due to a star's temperature, not motion. Only later was Doppler vindicated by verified redshift observations.

The first Doppler redshift was described by French physicist Hippolyte Fizeau in 1848, who pointed to the shift in spectral lines seen in stars as being due to the Doppler effect. The effect is sometimes called the "Doppler–Fizeau effect". In 1868, British astronomer William Huggins was the first to determine the velocity of a star moving away from the Earth by this method. In 1871, optical redshift was confirmed when the phenomenon was observed in Fraunhofer lines using solar rotation, about 0.1 Å in the red. In 1887, Vogel and Scheiner discovered the annual Doppler effect, the yearly change in the Doppler shift of stars located near the ecliptic due to the orbital velocity of the Earth. In 1901, Aristarkh Belopolsky verified optical redshift in the laboratory using a system of rotating mirrors.

Arthur Eddington used the term red shift as early as 1923. The word does not appear unhyphenated until about 1934 by Willem de Sitter.

Beginning with observations in 1912, Vesto Slipher discovered that most spiral galaxies, then mostly thought to be spiral nebulae, had considerable redshifts. Slipher first reports on his measurement in the inaugural volume of the Lowell Observatory Bulletin. Three years later, he wrote a review in the journal Popular Astronomy. In it he states that "the early discovery that the great Andromeda spiral had the quite exceptional velocity of –300 km(/s) showed the means then available, capable of investigating not only the spectra of the spirals but their velocities as well." Slipher reported the velocities for 15 spiral nebulae spread across the entire celestial sphere, all but three having observable "positive" (that is recessional) velocities. Subsequently, Edwin Hubble discovered an approximate relationship between the redshifts of such "nebulae" and the distances to them with the formulation of his eponymous Hubble's law. These observations corroborated Alexander Friedmann's 1922 work, in which he derived the Friedmann–Lemaître equations. In the present day they are considered strong evidence for an expanding universe and the Big Bang theory.

Measurement, characterization, and interpretation

High-redshift galaxy candidates in the Hubble Ultra Deep Field 2012

The spectrum of light that comes from a source (see idealized spectrum illustration top-right) can be measured. To determine the redshift, one searches for features in the spectrum such as absorption lines, emission lines, or other variations in light intensity. If found, these features can be compared with known features in the spectrum of various chemical compounds found in experiments where that compound is located on Earth. A very common atomic element in space is hydrogen. The spectrum of originally featureless light shone through hydrogen will show a signature spectrum specific to hydrogen that has features at regular intervals. If restricted to absorption lines it would look similar to the illustration (top right). If the same pattern of intervals is seen in an observed spectrum from a distant source but occurring at shifted wavelengths, it can be identified as hydrogen too. If the same spectral line is identified in both spectra—but at different wavelengths—then the redshift can be calculated using the table below.

Determining the redshift of an object in this way requires a frequency or wavelength range. In order to calculate the redshift, one has to know the wavelength of the emitted light in the rest frame of the source: in other words, the wavelength that would be measured by an observer located adjacent to and comoving with the source. Since in astronomical applications this measurement cannot be done directly, because that would require traveling to the distant star of interest, the method using spectral lines described here is used instead. Redshifts cannot be calculated by looking at unidentified features whose rest-frame frequency is unknown, or with a spectrum that is featureless or white noise (random fluctuations in a spectrum).

Redshift (and blueshift) may be characterized by the relative difference between the observed and emitted wavelengths (or frequency) of an object. In astronomy, it is customary to refer to this change using a dimensionless quantity called z. If λ represents wavelength and f represents frequency (note, λf = c where c is the speed of light), then z is defined by the equations:

Calculation of redshift, ${\displaystyle z}$

Based on wavelength	Based on frequency
${\displaystyle z=\frac{{\lambda }_{\mathrm{o}\mathrm{b}\mathrm{s}\mathrm{v}}-{\lambda }_{\mathrm{e}\mathrm{m}\mathrm{i}\mathrm{t}}}{{\lambda }_{\mathrm{e}\mathrm{m}\mathrm{i}\mathrm{t}}}}$	${\displaystyle z=\frac{f_{\mathrm{e}\mathrm{m}\mathrm{i}\mathrm{t}}-f_{\mathrm{o}\mathrm{b}\mathrm{s}\mathrm{v}}}{f_{\mathrm{o}\mathrm{b}\mathrm{s}\mathrm{v}}}}$
${\displaystyle 1+z=\frac{{\lambda }_{\mathrm{o}\mathrm{b}\mathrm{s}\mathrm{v}}}{{\lambda }_{\mathrm{e}\mathrm{m}\mathrm{i}\mathrm{t}}}}$	${\displaystyle 1+z=\frac{f_{\mathrm{e}\mathrm{m}\mathrm{i}\mathrm{t}}}{f_{\mathrm{o}\mathrm{b}\mathrm{s}\mathrm{v}}}}$

After z is measured, the distinction between redshift and blueshift is simply a matter of whether z is positive or negative. For example, Doppler effect blueshifts (z < 0) are associated with objects approaching (moving closer to) the observer with the light shifting to greater energies. Conversely, Doppler effect redshifts (z > 0) are associated with objects receding (moving away) from the observer with the light shifting to lower energies. Likewise, gravitational blueshifts are associated with light emitted from a source residing within a weaker gravitational field as observed from within a stronger gravitational field, while gravitational redshifting implies the opposite conditions.

Redshift formulae

In general relativity one can derive several important special-case formulae for redshift in certain special spacetime geometries, as summarized in the following table. In all cases the magnitude of the shift (the value of z) is independent of the wavelength.

Redshift summary

Redshift type	Geometry	Formula
Relativistic Doppler	Minkowski space (flat spacetime)	For motion completely in the radial or line-of-sight direction: ${\displaystyle 1+z=\gamma \left(1+\frac{v_{\parallel }}{c}\right)=\sqrt{\frac{1+\frac{v_{\parallel }}{c}}{1-\frac{v_{\parallel }}{c}}}}$ ${\displaystyle z\approx \frac{v_{\parallel }}{c}}$  for small ${\displaystyle v_{\parallel }}$ For motion completely in the transverse direction: ${\displaystyle 1+z=\frac{1}{\sqrt{1-\frac{v_{\perp }^2}{c^2}}}}$ ${\displaystyle z\approx \frac{1}{2}{\left(\frac{v_{\perp }}{c}\right)}^2}$  for small ${\displaystyle v_{\perp }}$
Cosmological redshift	FLRW spacetime (expanding Big Bang universe)	${\displaystyle 1+z=\frac{a_{\mathrm{n}\mathrm{o}\mathrm{w}}}{a_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}}}$ Hubble's law: ${\displaystyle z\approx \frac{H_{0}D}{c}}$  for ${\displaystyle D\ll \frac{c}{H_0}}$
Gravitational redshift	any stationary spacetime	${\displaystyle 1+z=\sqrt{\frac{g_{tt}(\text{receiver})}{g_{tt}(\text{source})}}}$ For the Schwarzschild geometry: ${\displaystyle 1+z=\sqrt{\frac{1-\frac{r_S}{r_{\text{receiver}}}}{1-\frac{r_S}{r_{\text{source}}}}}=\sqrt{\frac{1-\frac{2GM}{c^2{r}_{\text{receiver}}}}{1-\frac{2GM}{c^2{r}_{\text{source}}}}}}$ ${\displaystyle z\approx \frac{1}{2}\left(\frac{r_S}{r_{\text{source}}}-\frac{r_S}{r_{\text{receiver}}}\right)}$  for ${\displaystyle r\gg r_S}$ In terms of escape velocity: ${\displaystyle z\approx \frac{1}{2}{\left(\frac{v_{\text{e}}}{c}\right)}_{\text{source}}^2-\frac{1}{2}{\left(\frac{v_{\text{e}}}{c}\right)}_{\text{receiver}}^2}$ for ${\displaystyle v_{\text{e}}\ll c}$

Doppler effect

Main articles: Doppler effect and Relativistic Doppler effect

Doppler effect, yellow (~575 nm wavelength) ball appears greenish (blueshift to ~565 nm wavelength) approaching observer, turns orange (redshift to ~585 nm wavelength) as it passes, and returns to yellow when motion stops. To observe such a change in color, the object would have to be traveling at approximately 5,200 km/s, or about 32 times faster than the speed record for the fastest space probe.

Redshift and blueshift

If a source of the light is moving away from an observer, then redshift (z > 0) occurs; if the source moves towards the observer, then blueshift (z < 0) occurs. This is true for all electromagnetic waves and is explained by the Doppler effect. Consequently, this type of redshift is called the Doppler redshift. If the source moves away from the observer with velocity v, which is much less than the speed of light (v ≪ c), the redshift is given by

${\displaystyle z\approx \frac{v}{c}}$     (since ${\displaystyle \gamma \approx 1}$)

where c is the speed of light. In the classical Doppler effect, the frequency of the source is not modified, but the recessional motion causes the illusion of a lower frequency.

A more complete treatment of the Doppler redshift requires considering relativistic effects associated with motion of sources close to the speed of light. A complete derivation of the effect can be found in the article on the relativistic Doppler effect. In brief, objects moving close to the speed of light will experience deviations from the above formula due to the time dilation of special relativity which can be corrected for by introducing the Lorentz factor γ into the classical Doppler formula as follows (for motion solely in the line of sight):

${\displaystyle 1+z=\left(1+\frac{v}{c}\right)\gamma .}$

This phenomenon was first observed in a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called the Ives–Stilwell experiment.

Since the Lorentz factor is dependent only on the magnitude of the velocity, this causes the redshift associated with the relativistic correction to be independent of the orientation of the source movement. In contrast, the classical part of the formula is dependent on the projection of the movement of the source into the line-of-sight which yields different results for different orientations. If θ is the angle between the direction of relative motion and the direction of emission in the observer's frame (zero angle is directly away from the observer), the full form for the relativistic Doppler effect becomes:

${\displaystyle 1+z=\frac{1+v\cos (\theta )/c}{\sqrt{1-v^2/c^2}}}$

and for motion solely in the line of sight (θ = 0°), this equation reduces to:

${\displaystyle 1+z=\sqrt{\frac{1+v/c}{1-v/c}}}$

For the special case that the light is moving at right angle (θ = 90°) to the direction of relative motion in the observer's frame, the relativistic redshift is known as the transverse redshift, and a redshift:

${\displaystyle 1+z=\frac{1}{\sqrt{1-v^2/c^2}}}$

is measured, even though the object is not moving away from the observer. Even when the source is moving towards the observer, if there is a transverse component to the motion then there is some speed at which the dilation just cancels the expected blueshift and at higher speed the approaching source will be redshifted.

Expansion of space

Main article: Expansion of the universe

In the earlier part of the twentieth century, Slipher, Wirtz and others made the first measurements of the redshifts and blueshifts of galaxies beyond the Milky Way. They initially interpreted these redshifts and blueshifts as being due to random motions, but later Lemaître (1927) and Hubble (1929), using previous data, discovered a roughly linear correlation between the increasing redshifts of, and distances to, galaxies. Lemaître realized that these observations could be explained by a mechanism of producing redshifts seen in Friedmann's solutions to Einstein's equations of general relativity. The correlation between redshifts and distances is required by all such models that have a metric expansion of space. As a result, the wavelength of photons propagating through the expanding space is stretched, creating the cosmological redshift.

There is a distinction between a redshift in cosmological context as compared to that witnessed when nearby objects exhibit a local Doppler-effect redshift. Rather than cosmological redshifts being a consequence of the relative velocities that are subject to the laws of special relativity (and thus subject to the rule that no two locally separated objects can have relative velocities with respect to each other faster than the speed of light), the photons instead increase in wavelength and redshift because of a global feature of the spacetime through which they are traveling. One interpretation of this effect is the idea that space itself is expanding. Due to the expansion increasing as distances increase, the distance between two remote galaxies can increase at more than 3×10⁸ m/s, but this does not imply that the galaxies move faster than the speed of light at their present location (which is forbidden by Lorentz covariance).

Mathematical derivation

The observational consequences of this effect can be derived using the equations from general relativity that describe a homogeneous and isotropic universe.

To derive the redshift effect, use the geodesic equation for a light wave, which is

${\displaystyle d{s}^2=0=-c^{2}d{t}^2+\frac{a^{2}d{r}^2}{1-k{r}^2}}$

where

• ds is the spacetime interval
• dt is the time interval
• dr is the spatial interval
• c is the speed of light
• a is the time-dependent cosmic scale factor
• k is the curvature per unit area.

For an observer observing the crest of a light wave at a position r = 0 and time t = t_now, the crest of the light wave was emitted at a time t = t_then in the past and a distant position r = R. Integrating over the path in both space and time that the light wave travels yields:

${\displaystyle c{\int }_{t_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}}^{t_{\mathrm{n}\mathrm{o}\mathrm{w}}}\frac{dt}{a}={\int }_R^0\frac{dr}{\sqrt{1-k{r}^2}}.}$

In general, the wavelength of light is not the same for the two positions and times considered due to the changing properties of the metric. When the wave was emitted, it had a wavelength λ_then. The next crest of the light wave was emitted at a time

${\displaystyle t=t_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}+{\lambda }_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}/c.}$

The observer sees the next crest of the observed light wave with a wavelength λ_now to arrive at a time

${\displaystyle t=t_{\mathrm{n}\mathrm{o}\mathrm{w}}+{\lambda }_{\mathrm{n}\mathrm{o}\mathrm{w}}/c.}$

Since the subsequent crest is again emitted from r = R and is observed at r = 0, the following equation can be written:

${\displaystyle c{\int }_{t_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}+{\lambda }_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}/c}^{t_{\mathrm{n}\mathrm{o}\mathrm{w}}+{\lambda }_{\mathrm{n}\mathrm{o}\mathrm{w}}/c}\frac{dt}{a}={\int }_R^0\frac{dr}{\sqrt{1-k{r}^2}}.}$

The right-hand side of the two integral equations above are identical which means

${\displaystyle c{\int }_{t_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}+{\lambda }_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}/c}^{t_{\mathrm{n}\mathrm{o}\mathrm{w}}+{\lambda }_{\mathrm{n}\mathrm{o}\mathrm{w}}/c}\frac{dt}{a}=c{\int }_{t_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}}^{t_{\mathrm{n}\mathrm{o}\mathrm{w}}}\frac{dt}{a}}$

Using the following manipulation:

${\displaystyle \begin{array}{rl}0& ={\int }_{t_{\mathrm{t}}}^{t_{\mathrm{n}}}\frac{dt}{a}-{\int }_{t_{\mathrm{t}}+{\lambda }_{\mathrm{t}}/c}^{t_{\mathrm{n}}+{\lambda }_{\mathrm{n}}/c}\frac{dt}{a}\\ & ={\int }_{t_{\mathrm{t}}}^{t_{\mathrm{t}}+{\lambda }_{\mathrm{t}}/c}\frac{dt}{a}+{\int }_{t_{\mathrm{t}}+{\lambda }_{\mathrm{t}}/c}^{t_{\mathrm{n}}}\frac{dt}{a}-{\int }_{t_{\mathrm{t}}+{\lambda }_{\mathrm{t}}/c}^{t_{\mathrm{n}}+{\lambda }_{\mathrm{n}}/c}\frac{dt}{a}\\ & ={\int }_{t_{\mathrm{t}}}^{t_{\mathrm{t}}+{\lambda }_{\mathrm{t}}/c}\frac{dt}{a}-\left({\int }_{t_{\mathrm{n}}}^{t_{\mathrm{t}}+{\lambda }_{\mathrm{t}}/c}\frac{dt}{a}+{\int }_{t_{\mathrm{t}}+{\lambda }_{\mathrm{t}}/c}^{t_{\mathrm{n}}+{\lambda }_{\mathrm{n}}/c}\frac{dt}{a}\right)\\ & ={\int }_{t_{\mathrm{t}}}^{t_{\mathrm{t}}+{\lambda }_{\mathrm{t}}/c}\frac{dt}{a}-{\int }_{t_{\mathrm{n}}}^{t_{\mathrm{n}}+{\lambda }_{\mathrm{n}}/c}\frac{dt}{a}\end{array}}$

we find that:

${\displaystyle {\int }_{t_{\mathrm{n}}}^{t_{\mathrm{n}}+{\lambda }_{\mathrm{n}}/c}\frac{dt}{a}={\int }_{t_{\mathrm{t}}}^{t_{\mathrm{t}}+{\lambda }_{\mathrm{t}}/c}\frac{dt}{a}.}$

For very small variations in time (over the period of one cycle of a light wave) the scale factor is essentially a constant (a = a_n today and a = a_t previously). This yields

${\displaystyle \frac{t_{\mathrm{n}\mathrm{o}\mathrm{w}}+{\lambda }_{\mathrm{n}\mathrm{o}\mathrm{w}}/c}{a_{\mathrm{n}\mathrm{o}\mathrm{w}}}-\frac{t_{\mathrm{n}\mathrm{o}\mathrm{w}}}{a_{\mathrm{n}\mathrm{o}\mathrm{w}}}=\frac{t_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}+{\lambda }_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}/c}{a_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}}-\frac{t_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}}{a_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}}}$

which can be rewritten as

${\displaystyle \frac{{\lambda }_{\mathrm{n}\mathrm{o}\mathrm{w}}}{{\lambda }_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}}=\frac{a_{\mathrm{n}\mathrm{o}\mathrm{w}}}{a_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}}.}$

Using the definition of redshift provided above, the equation

${\displaystyle 1+z=\frac{a_{\mathrm{n}\mathrm{o}\mathrm{w}}}{a_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}}}}$

is obtained. In an expanding universe such as the one we inhabit, the scale factor is monotonically increasing as time passes, thus, z is positive and distant galaxies appear redshifted.

---

Using a model of the expansion of the universe, redshift can be related to the age of an observed object, the so-called cosmic time–redshift relation. Denote a density ratio as Ω₀:

${\displaystyle {\mathrm{\Omega }}_0=\frac{\rho }{{\rho }_{\text{crit}}},}$

with ρ_crit the critical density demarcating a universe that eventually crunches from one that simply expands. This density is about three hydrogen atoms per cubic meter of space. At large redshifts, 1 + z > Ω₀⁻¹, one finds:

${\displaystyle t(z)\approx \frac{2}{3H_0{{\mathrm{\Omega }}_0}^{1/2}(1+z{)}^{3/2}},}$

where H₀ is the present-day Hubble constant, and z is the redshift.

There are websites for calculating light-travel distance from redshift.

Distinguishing between cosmological and local effects

For cosmological redshifts of z < 0.01 additional Doppler redshifts and blueshifts due to the peculiar motions of the galaxies relative to one another cause a wide scatter from the standard Hubble Law. The resulting situation can be illustrated by the Expanding Rubber Sheet Universe, a common cosmological analogy used to describe the expansion of space. If two objects are represented by ball bearings and spacetime by a stretching rubber sheet, the Doppler effect is caused by rolling the balls across the sheet to create peculiar motion. The cosmological redshift occurs when the ball bearings are stuck to the sheet and the sheet is stretched.

The redshifts of galaxies include both a component related to recessional velocity from expansion of the universe, and a component related to peculiar motion (Doppler shift). The redshift due to expansion of the universe depends upon the recessional velocity in a fashion determined by the cosmological model chosen to describe the expansion of the universe, which is very different from how Doppler redshift depends upon local velocity. Describing the cosmological expansion origin of redshift, cosmologist Edward Robert Harrison said, "Light leaves a galaxy, which is stationary in its local region of space, and is eventually received by observers who are stationary in their own local region of space. Between the galaxy and the observer, light travels through vast regions of expanding space. As a result, all wavelengths of the light are stretched by the expansion of space. It is as simple as that..." Steven Weinberg clarified, "The increase of wavelength from emission to absorption of light does not depend on the rate of change of a(t) [here a(t) is the Robertson–Walker scale factor] at the times of emission or absorption, but on the increase of a(t) in the whole period from emission to absorption."

Popular literature often uses the expression "Doppler redshift" instead of "cosmological redshift" to describe the redshift of galaxies dominated by the expansion of spacetime, but the cosmological redshift is not found using the relativistic Doppler equation which is instead characterized by special relativity; thus v ≥ c is impossible while, in contrast, v ≥ c is possible for cosmological redshifts because the space which separates the objects (for example, a quasar from the Earth) can expand faster than the speed of light. More mathematically, the viewpoint that "distant galaxies are receding" and the viewpoint that "the space between galaxies is expanding" are related by changing coordinate systems. Expressing this precisely requires working with the mathematics of the Friedmann–Robertson–Walker metric.

If the universe were contracting instead of expanding, we would see distant galaxies blueshifted by an amount proportional to their distance instead of redshifted.

Gravitational redshift

Main article: Gravitational redshift

In the theory of general relativity, there is time dilation within a gravitational well. This is known as the gravitational redshift or Einstein Shift. The theoretical derivation of this effect follows from the Schwarzschild solution of the Einstein equations which yields the following formula for redshift associated with a photon traveling in the gravitational field of an uncharged, nonrotating, spherically symmetric mass:

${\displaystyle 1+z=\frac{1}{\sqrt{1-\frac{2GM}{r{c}^2}}},}$

where

• G is the gravitational constant,
• M is the mass of the object creating the gravitational field,
• r is the radial coordinate of the source (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate), and
• c is the speed of light.

This gravitational redshift result can be derived from the assumptions of special relativity and the equivalence principle; the full theory of general relativity is not required.

The effect is very small but measurable on Earth using the Mössbauer effect and was first observed in the Pound–Rebka experiment. However, it is significant near a black hole, and as an object approaches the event horizon the red shift becomes infinite. It is also the dominant cause of large angular-scale temperature fluctuations in the cosmic microwave background radiation (see Sachs–Wolfe effect).

Observations in astronomy

The redshift observed in astronomy can be measured because the emission and absorption spectra for atoms are distinctive and well known, calibrated from spectroscopic experiments in laboratories on Earth. When the redshift of various absorption and emission lines from a single astronomical object is measured, z is found to be remarkably constant. Although distant objects may be slightly blurred and lines broadened, it is by no more than can be explained by thermal or mechanical motion of the source. For these reasons and others, the consensus among astronomers is that the redshifts they observe are due to some combination of the three established forms of Doppler-like redshifts. Alternative hypotheses and explanations for redshift such as tired light are not generally considered plausible.

Spectroscopy, as a measurement, is considerably more difficult than simple photometry, which measures the brightness of astronomical objects through certain filters. When photometric data is all that is available (for example, the Hubble Deep Field and the Hubble Ultra Deep Field), astronomers rely on a technique for measuring photometric redshifts. Due to the broad wavelength ranges in photometric filters and the necessary assumptions about the nature of the spectrum at the light-source, errors for these sorts of measurements can range up to δz = 0.5, and are much less reliable than spectroscopic determinations. However, photometry does at least allow a qualitative characterization of a redshift. For example, if a Sun-like spectrum had a redshift of z = 1, it would be brightest in the infrared(1000nm) rather than at the blue-green(500nm) color associated with the peak of its blackbody spectrum, and the light intensity will be reduced in the filter by a factor of four, (1 + z)². Both the photon count rate and the photon energy are redshifted. (See K correction for more details on the photometric consequences of redshift.)

Local observations

In nearby objects (within our Milky Way galaxy) observed redshifts are almost always related to the line-of-sight velocities associated with the objects being observed. Observations of such redshifts and blueshifts have enabled astronomers to measure velocities and parametrize the masses of the orbiting stars in spectroscopic binaries, a method first employed in 1868 by British astronomer William Huggins. Similarly, small redshifts and blueshifts detected in the spectroscopic measurements of individual stars are one way astronomers have been able to diagnose and measure the presence and characteristics of planetary systems around other stars and have even made very detailed differential measurements of redshifts during planetary transits to determine precise orbital parameters. Finely detailed measurements of redshifts are used in helioseismology to determine the precise movements of the photosphere of the Sun. Redshifts have also been used to make the first measurements of the rotation rates of planets, velocities of interstellar clouds, the rotation of galaxies, and the dynamics of accretion onto neutron stars and black holes which exhibit both Doppler and gravitational redshifts. Additionally, the temperatures of various emitting and absorbing objects can be obtained by measuring Doppler broadening—effectively redshifts and blueshifts over a single emission or absorption line. By measuring the broadening and shifts of the 21-centimeter hydrogen line in different directions, astronomers have been able to measure the recessional velocities of interstellar gas, which in turn reveals the rotation curve of our Milky Way. Similar measurements have been performed on other galaxies, such as Andromeda. As a diagnostic tool, redshift measurements are one of the most important spectroscopic measurements made in astronomy.

Extragalactic observations

The most distant objects exhibit larger redshifts corresponding to the Hubble flow of the universe. The largest-observed redshift, corresponding to the greatest distance and furthest back in time, is that of the cosmic microwave background radiation; the numerical value of its redshift is about z = 1089 (z = 0 corresponds to present time), and it shows the state of the universe about 13.8 billion years ago, and 379,000 years after the initial moments of the Big Bang.

The luminous point-like cores of quasars were the first "high-redshift" (z > 0.1) objects discovered before the improvement of telescopes allowed for the discovery of other high-redshift galaxies.

For galaxies more distant than the Local Group and the nearby Virgo Cluster, but within a thousand megaparsecs or so, the redshift is approximately proportional to the galaxy's distance. This correlation was first observed by Edwin Hubble and has come to be known as Hubble's law. Vesto Slipher was the first to discover galactic redshifts, in about the year 1912, while Hubble correlated Slipher's measurements with distances he measured by other means to formulate his Law. In the widely accepted cosmological model based on general relativity, redshift is mainly a result of the expansion of space: this means that the farther away a galaxy is from us, the more the space has expanded in the time since the light left that galaxy, so the more the light has been stretched, the more redshifted the light is, and so the faster it appears to be moving away from us. Hubble's law follows in part from the Copernican principle. Because it is usually not known how luminous objects are, measuring the redshift is easier than more direct distance measurements, so redshift is sometimes in practice converted to a crude distance measurement using Hubble's law.

Gravitational interactions of galaxies with each other and clusters cause a significant scatter in the normal plot of the Hubble diagram. The peculiar velocities associated with galaxies superimpose a rough trace of the mass of virialized objects in the universe. This effect leads to such phenomena as nearby galaxies (such as the Andromeda Galaxy) exhibiting blueshifts as we fall towards a common barycenter, and redshift maps of clusters showing a fingers of god effect due to the scatter of peculiar velocities in a roughly spherical distribution. This added component gives cosmologists a chance to measure the masses of objects independent of the mass-to-light ratio (the ratio of a galaxy's mass in solar masses to its brightness in solar luminosities), an important tool for measuring dark matter.

The Hubble law's linear relationship between distance and redshift assumes that the rate of expansion of the universe is constant. However, when the universe was much younger, the expansion rate, and thus the Hubble "constant", was larger than it is today. For more distant galaxies, then, whose light has been travelling to us for much longer times, the approximation of constant expansion rate fails, and the Hubble law becomes a non-linear integral relationship and dependent on the history of the expansion rate since the emission of the light from the galaxy in question. Observations of the redshift-distance relationship can be used, then, to determine the expansion history of the universe and thus the matter and energy content.^{[citation needed]}

While it was long believed that the expansion rate has been continuously decreasing since the Big Bang, observations beginning in 1988 of the redshift-distance relationship using Type Ia supernovae have suggested that in comparatively recent times the expansion rate of the universe has begun to accelerate.

Highest redshifts

See also: List of most distant objects by type

Plot of distance (in giga light-years) vs. redshift according to the Lambda-CDM model. d_H (in solid black) is the proper distance from Earth to the location with the Hubble redshift z while ct_LB (in dotted red) is the speed of light multiplied by the lookback time to Hubble redshift z. The proper distance is the physical space-like distance between here and the distant location, asymptoting to the size of the observable universe at some 47 billion light-years. The lookback time is the distance a photon traveled from the time it was emitted to now divided by the speed of light, with a maximum distance of 13.8 billion light-years corresponding to the age of the universe. There are websites for calculating light-travel distance from redshift.

Currently, the objects with the highest known redshifts are galaxies and the objects producing gamma ray bursts. The most reliable redshifts are from spectroscopic data, and the highest-confirmed spectroscopic redshift of a galaxy is that of GN-z11, with a redshift of z = 11.1, corresponding to 400 million years after the Big Bang. The previous record was held by UDFy-38135539 at a redshift of z = 8.6, corresponding to 600 million years after the Big Bang. Slightly less reliable are Lyman-break redshifts, the highest of which is the lensed galaxy A1689-zD1 at a redshift z = 7.5 and the next highest being z = 7.0. The most distant-observed gamma-ray burst with a spectroscopic redshift measurement was GRB 090423, which had a redshift of z = 8.2. The most distant-known quasar, ULAS J1342+0928, is at z = 7.54. The highest-known redshift radio galaxy (TGSS1530) is at a redshift z = 5.72 and the highest-known redshift molecular material is the detection of emission from the CO molecule from the quasar SDSS J1148+5251 at z = 6.42.

Extremely red objects (EROs) are astronomical sources of radiation that radiate energy in the red and near infrared part of the electromagnetic spectrum. These may be starburst galaxies that have a high redshift accompanied by reddening from intervening dust, or they could be highly redshifted elliptical galaxies with an older (and therefore redder) stellar population. Objects that are even redder than EROs are termed hyper extremely red objects (HEROs).

The cosmic microwave background has a redshift of z = 1089, corresponding to an age of approximately 379,000 years after the Big Bang and a proper distance of more than 46 billion light-years. The yet-to-be-observed first light from the oldest Population III stars, not long after atoms first formed and the CMB ceased to be absorbed almost completely, may have redshifts in the range of 20 < z < 100. Other high-redshift events predicted by physics but not presently observable are the cosmic neutrino background from about two seconds after the Big Bang (and a redshift in excess of z > 10¹⁰) and the cosmic gravitational wave background emitted directly from inflation at a redshift in excess of z > 10²⁵.

In June 2015, astronomers reported evidence for Population III stars in the Cosmos Redshift 7 galaxy at z = 6.60. Such stars are likely to have existed in the very early universe (i.e., at high redshift), and may have started the production of chemical elements heavier than hydrogen that are needed for the later formation of planets and life as we know it.

Redshift surveys

Rendering of the 2dFGRS data

Main article: Redshift survey

With advent of automated telescopes and improvements in spectroscopes, a number of collaborations have been made to map the universe in redshift space. By combining redshift with angular position data, a redshift survey maps the 3D distribution of matter within a field of the sky. These observations are used to measure properties of the large-scale structure of the universe. The Great Wall, a vast supercluster of galaxies over 500 million light-years wide, provides a dramatic example of a large-scale structure that redshift surveys can detect.

The first redshift survey was the CfA Redshift Survey, started in 1977 with the initial data collection completed in 1982. More recently, the 2dF Galaxy Redshift Survey determined the large-scale structure of one section of the universe, measuring redshifts for over 220,000 galaxies; data collection was completed in 2002, and the final data set was released 30 June 2003. The Sloan Digital Sky Survey (SDSS), is ongoing as of 2013 and aims to measure the redshifts of around 3 million objects. SDSS has recorded redshifts for galaxies as high as 0.8, and has been involved in the detection of quasars beyond z = 6. The DEEP2 Redshift Survey uses the Keck telescopes with the new "DEIMOS" spectrograph; a follow-up to the pilot program DEEP1, DEEP2 is designed to measure faint galaxies with redshifts 0.7 and above, and it is therefore planned to provide a high-redshift complement to SDSS and 2dF.

Effects from physical optics or radiative transfer

The interactions and phenomena summarized in the subjects of radiative transfer and physical optics can result in shifts in the wavelength and frequency of electromagnetic radiation. In such cases, the shifts correspond to a physical energy transfer to matter or other photons rather than being by a transformation between reference frames. Such shifts can be from such physical phenomena as coherence effects or the scattering of electromagnetic radiation whether from charged elementary particles, from particulates, or from fluctuations of the index of refraction in a dielectric medium as occurs in the radio phenomenon of radio whistlers. While such phenomena are sometimes referred to as "redshifts" and "blueshifts", in astrophysics light-matter interactions that result in energy shifts in the radiation field are generally referred to as "reddening" rather than "redshifting" which, as a term, is normally reserved for the effects discussed above.

In many circumstances scattering causes radiation to redden because entropy results in the predominance of many low-energy photons over few high-energy ones (while conserving total energy). Except possibly under carefully controlled conditions, scattering does not produce the same relative change in wavelength across the whole spectrum; that is, any calculated z is generally a function of wavelength. Furthermore, scattering from random media generally occurs at many angles, and z is a function of the scattering angle. If multiple scattering occurs, or the scattering particles have relative motion, then there is generally distortion of spectral lines as well.

In interstellar astronomy, visible spectra can appear redder due to scattering processes in a phenomenon referred to as interstellar reddening—similarly Rayleigh scattering causes the atmospheric reddening of the Sun seen in the sunrise or sunset and causes the rest of the sky to have a blue color. This phenomenon is distinct from redshifting because the spectroscopic lines are not shifted to other wavelengths in reddened objects and there is an additional dimming and distortion associated with the phenomenon due to photons being scattered in and out of the line of sight.

Blueshift

"Blueshift" redirects here. For the term as used in photochemistry, see hypsochromic shift. For the political phenomenon, see blue shift (politics). For other uses of "blueshift" or "blue shift", see Blueshift (disambiguation).

The opposite of a redshift is a blueshift. A blueshift is any decrease in wavelength (increase in energy), with a corresponding increase in frequency, of an electromagnetic wave. In visible light, this shifts a color towards the blue end of the spectrum.

Doppler blueshift

Doppler redshift and blueshift

Doppler blueshift is caused by movement of a source towards the observer. The term applies to any decrease in wavelength and increase in frequency caused by relative motion, even outside the visible spectrum. Only objects moving at near-relativistic speeds toward the observer are noticeably bluer to the naked eye, but the wavelength of any reflected or emitted photon or other particle is shortened in the direction of travel.

Doppler blueshift is used in astronomy to determine relative motion:

• The Andromeda Galaxy is moving toward our own Milky Way galaxy within the Local Group; thus, when observed from Earth, its light is undergoing a blueshift.
• Components of a binary star system will be blueshifted when moving towards Earth
• When observing spiral galaxies, the side spinning toward us will have a slight blueshift relative to the side spinning away from us (see Tully–Fisher relation).
• Blazars are known to propel relativistic jets toward us, emitting synchrotron radiation and bremsstrahlung that appears blueshifted.
• Nearby stars such as Barnard's Star are moving toward us, resulting in a very small blueshift.
• Doppler blueshift of distant objects with a high z can be subtracted from the much larger cosmological redshift to determine relative motion in the expanding universe.

Gravitational blueshift

Main article: Gravitational blueshift

Matter waves (protons, electrons, photons, etc.) falling into a gravity well become more energetic and undergo observer-independent blueshifting.

Unlike the relative Doppler blueshift, caused by movement of a source towards the observer and thus dependent on the received angle of the photon, gravitational blueshift is absolute and does not depend on the received angle of the photon:

Photons climbing out of a gravitating object become less energetic. This loss of energy is known as a "redshifting", as photons in the visible spectrum would appear more red. Similarly, photons falling into a gravitational field become more energetic and exhibit a blueshifting. ... Note that the magnitude of the redshifting (blueshifting) effect is not a function of the emitted angle or the received angle of the photon—it depends only on how far radially the photon had to climb out of (fall into) the potential well.

It is a natural consequence of conservation of energy and mass–energy equivalence, and was confirmed experimentally in 1959 with the Pound–Rebka experiment. Gravitational blueshift contributes to cosmic microwave background (CMB) anisotropy via the Sachs–Wolfe effect: when a gravitational well evolves while a photon is passing, the amount of blueshift on approach will differ from the amount of gravitational redshift as it leaves the region.

Blue outliers

There are faraway active galaxies that show a blueshift in their [O III] emission lines. One of the largest blueshifts is found in the narrow-line quasar, PG 1543+489, which has a relative velocity of -1150 km/s. These types of galaxies are called "blue outliers".

Cosmological blueshift

In a hypothetical universe undergoing a runaway Big Crunch contraction, a cosmological blueshift would be observed, with galaxies further away being increasingly blueshifted—the exact opposite of the actually observed cosmological redshift in the present expanding universe.