Psychological egoism

From Wikipedia, the free encyclopedia

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

Psychological egoism is the view that humans are always motivated by self-interest and selfishness, even in what seem to be acts of altruism. It claims that, when people choose to help others, they do so ultimately because of the personal benefits that they expect to obtain, directly or indirectly, from doing so.

This is a descriptive rather than normative view, since it only makes claims about how things are, not how they "ought to be" according to some. It is, however, related to several other normative forms of egoism, such as ethical egoism and rational egoism.

Subtypes of psychological egoism

Psychological hedonism

Main article: Psychological hedonism

A specific form of psychological egoism is psychological hedonism, the view that the ultimate motive for all voluntary human action is the desire to experience pleasure or to avoid pain.

Immediate gratification can be sacrificed for a chance of greater, future pleasure. Further, humans are not motivated strictly to avoid pain and pursue pleasure, but rather humans will endure pain to achieve the greatest net pleasure. Accordingly, all actions are tools for increasing pleasure or decreasing pain, even those defined as altruistic and those that do not cause an immediate change in satisfaction levels.

Elliott Sober argues that psychological egoist, when pressed, often has to resort to hedonism in order to maintain their position, since the supposed pleasure of acting morally can often be the only viable explanation for an altruistic action.

The most famous psychological egoists are Sextus Empiricus, Pierre Bayle, and Bernard Mandeville.

Final cause

Some theorists explain behavior motivated by self-interest without using pleasure and pain as the final causes of behavior.

Foundations

Beginning with ancient philosophy, Epicureanism claims humans live to maximize pleasure. Epicurus argued the theory of human behavior being motivated by pleasure alone is evidenced from infancy to adulthood. Humanity performs altruistic, honorable, and virtuous acts not for the sake of another or because of a moral code but rather to increase the well-being of the self.

In modern philosophy, Jeremy Bentham asserted, like Epicurus, that human behavior is governed by a need to increase pleasure and decrease pain. Bentham explicitly described what types and qualities of pain and pleasure exist, and how human motives are singularly explained using psychological hedonism. Bentham attempted to quantify psychological hedonism. Bentham endeavored to find the ideal human behavior based on hedonic calculus or the measurement of relative gains and losses in pain and pleasure to determine the most pleasurable action a human could choose in a situation.

From an evolutionary perspective, Herbert Spencer, a psychological egoist, argued that all animals primarily seek to survive and protect their lineage. Essentially, the need for the individual and for the individual's immediate family to live supersedes the others' need to live. All species attempt to maximize their own chances of survival and, therefore, well-being. Spencer asserted the best adapted creatures will have their pleasure levels outweigh their pain levels in their environments. Thus, pleasure meant an animal was fulfilling its egoist goal of self survival, and pleasure would always be pursued because species constantly strive for survival.

Contributions to modern psychology

Psychoanalysis

Whether or not Sigmund Freud was a psychological egoist, his concept of the pleasure principle borrowed much from psychological egoism and psychological hedonism in particular. The pleasure principle rules the behavior of the Id which is an unconscious force driving humans to release tension from unfulfilled desires. When Freud introduced Thanatos and its opposing force, Eros, the pleasure principle emanating from psychological hedonism became aligned with the Eros, which drives a person to satiate sexual and reproductive desires. Alternatively, Thanatos seeks the cessation of pain through death and the end of the pursuit of pleasure: thus, hedonism rules Thanatos, but it centers on the complete avoidance of pain rather than psychological hedonist function which pursues pleasure and avoids pain. Therefore, Freud believed in qualitatively different hedonisms where the total avoidance of pain hedonism and the achievement of the greatest net pleasure hedonism are separate and associated with distinct functions and drives of the human psyche. Although Eros and Thanatos are ruled by qualitatively different types of hedonism, Eros remains under the rule of Jeremy Bentham's quantitative psychological hedonism because Eros seeks the greatest net pleasure.

Behaviorism

Traditional behaviorism dictates all human behavior is explained by classical conditioning and operant conditioning. Operant conditioning works through reinforcement and punishment which adds or removes pleasure and pain to manipulate behavior. Using pleasure and pain to control behavior means behaviorists assumed the principles of psychological hedonism could be applied to predicting human behavior. For example, Thorndike's law of effect states that behaviors associated with pleasantness will be learned and those associated with pain will be extinguished. Often, behaviorist experiments using humans and animals are built around the assumption that subjects will pursue pleasure and avoid pain. Although psychological hedonism is incorporated into the fundamental principles and experimental designs of behaviorism, behaviorism itself explains and interprets only observable behavior and therefore does not theorize about the ultimate cause of human behavior. Thus, behaviorism uses but does not strictly support psychological hedonism over other understandings of the ultimate drive of human behavior.

Debate

Psychological egoism is controversial. Proponents cite evidence from introspection: reflection on one's own actions may reveal their motives and intended results to be based on self-interest. Psychological hedonists have found through numerous observations of natural human behavior that behavior can be manipulated through reward and punishment, both of which have direct effects of pain and pleasure. Also, the work of some social scientists has empirically supported this theory. Further, they claim psychological egoism posits a theory that is a more parsimonious explanation than competing theories.

Opponents have argued that psychological egoism is not more parsimonious than other theories. For example, a theory that claims altruism occurs for the sake of altruism explains altruism with less complexity than the egoistic approach. The psychological egoist asserts humans act altruistically for selfish reasons even when cost of the altruistic action is far outweighed by the reward of acting selfishly because altruism is performed to fulfill the desire of a person to act altruistically. Other critics argue that it is false either because it is an over-simplified interpretation of behavior or that there exists empirical evidence of altruistic behaviour. Recently, some have argued that evolutionary theory provides evidence against it.

Critics have stated that proponents of psychological egoism often confuse the satisfaction of their own desires with the satisfaction of their own self-regarding desires. Even though it is true that every human being seeks their own satisfaction, this sometimes may only be achieved via the well-being of their neighbor. An example of this situation could be phoning for an ambulance when a car accident has happened. In this case, the caller desires the well-being of the victim, even though the desire itself is the caller's own.

To counter this critique, psychological egoism asserts that all such desires for the well-being of others are ultimately derived from self-interest. For example, German philosopher Friedrich Nietzsche was a psychological egoist for some of his career, though he is said to have repudiated that later in his campaign against morality. He argues in §133 of The Dawn that in such cases compassionate impulses arise out of the projection of our identity unto the object of our feeling. He gives some hypothetical examples as illustrations to his thesis: that of a person, feeling horrified after witnessing a personal feud, coughing blood, or that of the impulse felt to save a person who is drowning in the water. In such cases, according to Nietzsche, there comes into play unconscious fears regarding our own safety. The suffering of another person is felt as a threat to our own happiness and sense of safety, because it reveals our own vulnerability to misfortunes, and thus, by relieving it, one could also ameliorate those personal sentiments. Essentially, proponents argue that altruism is rooted in self-interest whereas opponents claim altruism occurs for altruism's sake or is caused by a non-selfish reason.

Max Stirner

Stencil drawing of Max Stirner

Philosopher Max Stirner was an advocate for people striving towards ownness, however he rejected the concept of psychological egoism because he believed most people are slaves to a 'spook'- a framework for moral behaviour that can delude our self-interest. Examples of spooks include society and natural rights.

Stirner also uses the example of Juliet from Romeo and Juliet to counter psychological egoism. Juliet kills herself as a sacrifice for others' betterment. She is in love, and knows that by doing this she will leave her self-will unsatisfied, nevertheless she subjects herself to a higher power and prohibits herself from having what she truly wants. This demonstrates how it is possible for a person to act without satisfying one's self-interest.

Problem of apparent altruism

David Hume once wrote, "What interest can a fond mother have in view, who loses her health by assiduous attendance on her sick child, and afterwards languishes and dies of grief, when freed, by its death [the child's], from the slavery of that attendance?". It seems incorrect to describe such a mother's goal as self-interested.

Psychological egoists, however, respond that helping others in such ways is ultimately motivated by some form of self-interest, such as non-sensory satisfaction, the expectation of reciprocation, the desire to gain respect or reputation, or by the expectation of a reward in a putative afterlife. The helpful action is merely instrumental to these ultimately selfish goals.

In the ninth century, Mohammed Ibn Al-Jahm Al-Barmaki (محمد بن الجـَهْم البَرمَكي) has been quoted saying:

"No one deserves thanks from another about something he has done for him or goodness he has done, he is either willing to get a reward from God, therefore he wanted to serve himself, or he wanted to get a reward from people, therefore, he has done that to get profit for himself, or to be mentioned and praised by people, therefore, to it is also for himself, or due to his mercy and tenderheartedness, so he has simply done that goodness to pacify these feelings and treat himself."

This sort of explanation appears to be close to the view of La Rochefoucauld (and perhaps Hobbes).

According to psychological hedonism, the ultimate egoistic motive is to gain good feelings of pleasure and avoid bad feelings of pain. Other, less restricted forms of psychological egoism may allow the ultimate goal of a person to include such things as avoiding punishments from oneself or others (such as guilt or shame) and attaining rewards (such as pride, self-worth, power or reciprocal beneficial action).

Some psychologists explain empathy in terms of psychological hedonism. According to the "merge with others hypothesis", empathy increases the more an individual feels like they are one with another person, and decreases accordingly. Therefore, altruistic actions emanating from empathy, and empathy itself, are caused by making others' interests our own, and the satisfaction of their desires becomes our own, not just theirs. Both cognitive studies and neuropsychological experiments have provided evidence for this theory: as humans increase our oneness with others, our empathy increases, and as empathy increases, so too does our inclination to act altruistically. Neuropsychological studies have linked mirror neurons to humans experiencing empathy. Mirror neurons are activated both when a human (or animal) performs an action and when they observe another human (or animal) perform the same action. Researchers have found that the more these mirror neurons fire the more human subjects report empathy. From a neurological perspective, scientists argue that when a human empathizes with another, the brain operates as if the human is actually participating in the actions of the other person. Thus, when performing altruistic actions motivated by empathy, humans experience someone else's pleasure of being helped. Therefore, in performing acts of altruism, people act in their own self-interest even at a neurological level.

Criticism

Circularity

Psychological egoism has been accused of being circular: "If a person willingly performs an act, that means he derives personal enjoyment from it; therefore, people only perform acts that give them personal enjoyment." In particular, seemingly altruistic acts must be performed because people derive enjoyment from them and are therefore, in reality, egoistic. This statement is circular because its conclusion is identical to its hypothesis: it assumes that people only perform acts that give them personal enjoyment, and concludes that people only perform acts that give them personal enjoyment. This objection was tendered by William Hazlitt and Thomas Macaulay in the 19th century, and has been restated many times since. An earlier version of the same objection was made by Joseph Butler in the Fifteen Sermons.

Joel Feinberg, in his 1958 paper "Psychological Egoism", embraces a similar critique by drawing attention to the infinite regress of psychological egoism. He expounds it in the following cross-examination:

"All men desire only satisfaction."

"Satisfaction of what?"

"Satisfaction of their desires."

"Their desires for what?"

"Their desires for satisfaction."

"Satisfaction of what?"

"Their desires."

"For what?"

"For satisfaction"—etc., ad infinitum.

Evolutionary argument

In their 1998 book, Unto Others, Sober and Wilson detailed an evolutionary argument based on the likelihood for egoism to evolve under the pressures of natural selection. Specifically, they focus on the human behavior of parental care. To set up their argument, they propose two potential psychological mechanisms for this. The hedonistic mechanism is based on a parent's ultimate desire for pleasure or the avoidance of pain and a belief that caring for its offspring will be instrumental to that. The altruistic mechanism is based on an altruistic ultimate desire to care for its offspring.

Sober and Wilson argue that when evaluating the likelihood of a given trait to evolve, three factors must be considered: availability, reliability and energetic efficiency. The genes for a given trait must first be available in the gene pool for selection. The trait must then reliably produce an increase in fitness for the organism. The trait must also operate with energetic efficiency to not limit the fitness of the organism. Sober and Wilson argue that there is neither reason to suppose that an altruistic mechanism should be any less available than a hedonistic one nor reason to suppose that the content of thoughts and desires (hedonistic vs. altruistic) should impact energetic efficiency. As availability and energetic efficiency are taken to be equivalent for both mechanisms it follows that the more reliable mechanism will then be the more likely mechanism.

For the hedonistic mechanism to produce the behavior of caring for offspring, the parent must believe that the caring behavior will produce pleasure or avoidance of pain for the parent. Sober and Wilson argue that the belief also must be true and constantly reinforced, or it would not be likely enough to persist. If the belief fails then the behavior is not produced. The altruistic mechanism does not rely on belief; therefore, they argue that it would be less likely to fail than the alternative, i.e. more reliable.

Equivocation

In philosopher Derek Parfit's 2011 book On What Matters, Volume 1, Parfit presents an argument against psychological egoism that centers around an apparent equivocation between different senses of the word "want":

The word desire often refers to our sensual desires or appetites, or to our being attracted to something, by finding the thought of it appealing. I shall use ‘desire’ in a wider sense, which refers to any state of being motivated, or of wanting something to happen and being to some degree disposed to make it happen, if we can. The word want already has both these senses.

According to Parfit, the argument for psychological egoism fails, because it uses the word want first in the wide sense and then in the narrow sense. If I voluntarily gave up my life to save the lives of several strangers, my act would not be selfish, though I would be doing what in the wide sense I wanted to do.

Barriers to pro-environmental behaviour

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Barriers_to_pro-environmental_behaviour

Pro-environmental behaviour is behaviour that people consciously choose in order to minimize the negative impact of their actions on the environment. Barriers to pro-environmental behaviour are the numerous factors that hinder individuals when they try to adjust their behaviours toward living more sustainable lifestyles.

Generally, these barriers can be separated into larger categories: psychological, social/cultural, financial and structural. Psychological barriers are considered internal, where an individual's knowledge, beliefs and thoughts affect their behaviour. Social and cultural barriers are contextual, where an individual's behaviour is affected by their surroundings (e.g. neighbourhood, town, city, etc.). Financial barriers are simply a lack of funds to move toward more sustainable behaviour (e.g. new technologies, electric cars). Structural barriers are external and often impossible for an individual to control, such as lack of governmental action, or locality of residence that promotes car dependency as opposed to public transit.

Internal/psychological barriers

Further information: Media coverage of climate change

Identifying psychological barriers to pro-environmental behaviour is key to the design of successful behaviour change interventions. Scholars have identified several different categories of psychological barriers to pro-environmental action. A known researcher in the field, environmental psychologist Robert Gifford, has identified 33 of these barriers, barriers that he has termed "The Dragons of Inaction." The Dragons are separated into seven categories: Limited Cognition, Ideologies, Social Comparison, Sunk Costs, Discredence, Perceived Risks, and Limited Behaviour. Below are the seven categories, integrated with additional barriers identified by other researchers. Other psychologists have argued that the attempt to identify psychological barriers to environmental behavior is problematic when used to explain societal inaction on climate change.

Limited cognition

See also: Agnotology

Limited cognition barriers are barriers that arise from a lack of knowledge and awareness about environmental issues. For example, with a key environmental issue like climate change, a person might not engage in pro-environmental behaviour because they are: unaware that climate change is occurring; or aware that climate change is an issue, but are ill-informed about the science of climate change; or lacking information about how they could address the issue.

For those who are aware of current environmental issues, self-efficacy is an important barrier to action, where individuals often feel powerless in achieving large goals such as mitigating global climate change. Moreover, lack of motivation to change one's behaviour is correlated with the belief that individuals are incapable of performing effective pro-environmental actions.

Ideologies

Climate denial billboard

Ideological barriers are created by pre-conceived ideas and the way an individual thinks about the world. Ideologies that can create barriers to pro-environmental behaviour can include a strong belief in free-enterprise capitalism, a fatalistic belief that a higher power is in control, and a belief that technology can solve all environmental issues. Accordingly, tactics such as environmental policies have prompted a tendency to struggle against perceived threats to one's freedom and comfortable lifestyle. This barrier is namely present in Western countries where individuals enjoy comparatively high levels of objective and subjective wellbeing due to socioeconomic status. It has been noted that to live within environmental limits, there is a need to make changes to the comfortable aspects of Western lifestyles, for example, reducing meat consumption, the use of airplanes, and use of electronic gadgets with short life-spans. Western cultural norms associate meat consumption with wealth, status and luxury, and meat consumption per capita in the richest 15 nations of the world is 750% higher than in the poorest 24 nations. A shift in values may be difficult, as people's life goals are formed by their ideas of social progress, personal status, and success through careers, higher incomes and consumption.

Moreover, there exist deep structural and cultural roots that couple the macro-level of financial, property or labour institutions to the micro-level of individualistic, utilitarian values. These roots are linked to the current economic growth paradigm, which can be defined as a worldview that maintains that economic growth is both good and necessary.

Social comparison

North Hills East truck dealer. The Ford F-150 truck has been the best selling vehicle in the United States for some time achieving less than 30mpg on average.

Social comparison barriers include the comparison of actions with those of others to determine the "correct" behaviour, whether it be beneficial or harmful for the environment. This means that social comparison barriers can also facilitate pro-environmental behaviour. For example, people will alter their energy consumption to replicate the reported usage of their neighbours. Moreover, if individuals believe those around them are not actively engaging in pro-environmental behaviour, they are less likely to engage in it themselves because they believe this to be unfair.

Sunk costs

See also: Cognitive inertia

Sunk cost barriers are the investments (not necessarily financial) of an individual that in turn restrict alternative possibilities for change, or in this circumstance, for pro-environmental behaviour. One example of a financial investment is car ownership, where the individual will be less likely to use alternative modes of transportation. Habits are considered a Sunk Costs Dragon as well because they are very difficult to change (e.g. eating habits). Individuals are also deeply invested in their life goals and aspirations, even if achieving them will harm the environment. Place attachment is considered here as well, where an individual who feels no place attachment to their home will be less likely to act pro-environmentally in that place than one who loves where they live.

Additional barriers are inconvenience and time-related pressures, which are suggested as reasons why individuals go back to unsustainable habits. An individual may find it annoying and inconvenient to compost if they do not have access to municipal composting, for example, and if one is pressed for time they may choose to use their car rather than wait for public transit.

Discredence

See also: Conspiracy theories

Discredence barriers generally involve disbelief in environmental issues and/or distrust in government officials and scientists. Complete denial of climate change and other environmental issues is becoming less prominent, but it continues to persist. Skepticism is still apparent in countries where there are efforts to shape public opinion through mediums such as conservative think tanks and media outlets. Moreover, mass media is the primary source of information on climate change in many countries, therefore depending on the individual, they will either trust or ignore the information they receive which will vary from one media outlet to the next based on different views.

Distrust in government has become a prevalent issue recently. In the United States for example, Americans have been polled every year about their confidence in their country's institutions (e.g. the Supreme Court, Congress, the Presidency, and the health-care establishment), and there has been a reported collapse in trust over time (12% in 2017). From an environmental standpoint, the first Trump administration has significantly diminished regulations that were put in place by the former administration to meet environmental standards. Examples of policy changes include pulling out of the Paris Agreement, loosening regulations on toxic air pollution, and issuing an executive order that called for a 30% increase in logging on public lands. There is a 97% scientific consensus on anthropogenic climate change, yet there is still not enough being done to meet global temperature targets of staying below a 1.5 degrees Celsius increase (see Paris Agreement).

Even in a stable constitutional republic, a cynical or unmoored citizenry presents an opportunity for demagogues and populists. As much as stagnant wages in former manufacturing regions, glaring economic inequality, or white backlash after the Obama Presidency, the country's disillusionment with institutions enabled Donald Trump's election.

— The New Yorker

Perceived risk

Risk perception barriers include worrying about whether financial or temporal investments will pay off. An example of a financial investment is solar panels which are initially costly. A temporal investment can simply be spending the time to do research on the topic instead of doing something else.

There exists the concept of psychological distance, where people tend to discount future risks when making trade-offs between cost and benefits, and instead prioritize immediate day-to-day concerns. Spatial distance allows individuals to disregard any risks, and instead consider them more likely for other people and places than for themselves. This barrier can simply be thought of as "out of sight, out of mind." Additionally, people typically underestimate the likelihood of being affected by natural disasters, as well as the degree to which others are concerned about environmental issues. Furthermore, the human brain privileges experience over analysis: personal experiences with extreme weather events can influence risk perceptions, beliefs, behaviour and policy support, whereas statistical information by itself means very little to most people.

It has been hypothesised many times that no matter how strong the climate knowledge provided by risk analysts, experts and scientists is, risk perception determines agents' ultimate response in terms of mitigation. However, recent literature reports conflicting evidence about the actual impact of risk perception on agents’ climate response. Rather, a no-direct perception-response link with the mediation and moderation of many other factors and a strong dependency on the context analysed is shown. Some moderation factors considered as such in the specialised literature include communication and social norms. Yet, conflicting evidence of the disparity between public communication about climate change and the lack of behavioural change has also been observed in the general public. Likewise, doubts are raised about the observance of social norms as an influencing predominant factor that affects action on climate change. What is more, disparate evidence also showed that even agents highly engaged in mitigation (engagement is a mediation factor) actions fail ultimately to respond.

Limited behaviour

Limited behaviour barriers may include people choosing easier, yet less effective, pro-environmental behavioural changes (e.g. recycling, metal straws), and the rebound effect, which occurs when a positive environmental behaviour is followed by one that negates it (e.g. saving money with an electric car to then buy a plane ticket).

Contextual barriers

Social and cultural factors

Research has also shown that how people support and engage in pro-environmental behaviour is also affected by contextual factors (i.e. social, economic, and cultural); people with diverse cultural backgrounds have different perspectives and priorities, and thus, they may respond to the same policies and interventions in different ways with regionally differentiated world views playing an important role. This means that people will use different excuses for their behaviours depending on contextual factors. Research has shown that information has a greater impact on behaviour if it is tailored to the personal situations of consumers and resonates with their important values. This suggests that, for example, policies developed to reduce and mitigate climate change would be more effective if they were developed specifically for the people whose behaviour they were targeting.

People are social beings who respond to group norms: behaviour and decision-making has been shown to be affected by social norms and contexts.

Demographic variables like age, gender and education, can have a variety of effects on pro-environmental behaviour, depending on the issue and context. However, when considering the effects of socio-demographics on individual perceptions of climate change, a recent study reported a meta-analysis which found that the largest demographic correlation with the belief of human-caused climate change is political affiliation (e.g. conservative views often mean less support for climate mitigation).

Economic factors

The cost of sustainable alternatives and financial measures used to support new technologies can also be a barrier to pro-environmental behaviour. Households may have severe budgetary constraints that discourage them from investing in energy-efficient measures. In addition, individuals may fear that project costs will not be recovered prior to a future sale of a property. Economic factors are not just barriers to pro-environmental behaviour for individual households but are also a barrier on the international scale. Developing countries that rely on coal and fossil fuels may not have the funding or infrastructure to switch to more sustainable energy sources. Therefore, help from developed countries, with regards to cost, may be needed. As nations become more prosperous, their citizens are less concerned with the economic battle for survival and are free to pursue postmaterialistic ideals such as political freedom, personal fulfillment, and environmental conservation. In other cases however, environment-friendly behaviours may be undertaken for non-environmental reasons, such as to save money or to improve health (e.g. biking or walking instead of driving).

Structural barriers

Structural barriers are large-scale systemic barriers that may be perceived as being objective and external, and can be highly influential and near impossible to control, even when one wishes to adopt more pro-environmental behaviour. For example, lack of organizational and governmental action on sustainability is considered a barrier for individuals looking to participate in sustainable practices. Further examples of structural barriers include: low problem awareness at the local level caused by a low priority for adaptation at higher institutional levels, and missing leadership by certain key actors leading to an absence of appropriate decision-making routines. Other structural barriers reported from a Vancouver-based study include: term limits imposed on politicians that affect council's ability to make long-term decisions; budgetary cycles that force planning based on three year terms, rather than long-term planning; and hierarchical systems that inhibit flexibility and innovation.

Research has shown that individuals may not behave in accordance with environmental sustainability when they have little control over the outcome of a situation. An example of a structural choice that can influence an individual's use of high carbon transport, occurs when cities governments allow sprawling neighbourhoods to develop without associated public transit infrastructure.

The concept of barriers has also been defined in relation to adaptive capacity, the ability of a system to respond to environmental changes; a barrier can either be a reason for potential adaptive capacity not being translated into action, or a reason for the existence of low adaptive capacity.

Einstein–Podolsky–Rosen paradox

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox

Albert Einstein

The Einstein–Podolsky–Rosen (EPR) paradox is a thought experiment proposed by physicists 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. Resolutions of the paradox have important implications for the interpretation of quantum mechanics.

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 were 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 impossible according to the theory of relativity. They invoked a principle, later known as the "EPR criterion of reality", which posited 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.

The "Paradox" paper

The term "Einstein–Podolsky–Rosen paradox" or "EPR" arose from a paper written in 1934 after Einstein joined the Institute for Advanced Study, having fled the rise of Nazi Germany. The original paper purports to describe what must happen to "two systems I and II, which we permit to interact", and after some time "we suppose that there is no longer any interaction between the two parts." The EPR description involves "two particles, A and B, [which] interact briefly and then move off in opposite directions." According to Heisenberg's uncertainty principle, it is impossible to measure both the momentum and the position of particle B exactly; however, it is possible to measure the exact position of particle A. By calculation, therefore, with the exact position of particle A known, the exact position of particle B can be known. Alternatively, the exact momentum of particle A can be measured, so the exact momentum of particle B can be worked out. As Manjit Kumar writes, "EPR argued that they had proved that ... [particle] B can have simultaneously exact values of position and momentum. ... Particle B has a position that is real and a momentum that is real. EPR appeared to have contrived a means to establish the exact values of either the momentum or the position of B due to measurements made on particle A, without the slightest possibility of particle B being physically disturbed."

EPR tried to set up a paradox to question the range of true application of quantum mechanics: quantum theory predicts that both values cannot be known for a particle, and yet the EPR thought experiment purports to show that they must both have determinate values. The EPR paper says: "We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete." The EPR paper ends by saying: "While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible." The 1935 EPR paper condensed the philosophical discussion into a physical argument. The authors claim that given a specific experiment, in which the outcome of a measurement is known before the measurement takes place, there must exist something in the real world, an "element of reality", that determines the measurement outcome. They postulate that these elements of reality are, in modern terminology, local, in the sense that each belongs to a certain point in spacetime. Each element may, again in modern terminology, only be influenced by events that are located in the backward light cone of its point in spacetime (i.e. in the past). These claims are thus founded on assumptions about nature that constitute what is now known as local realism.

Article headline regarding the EPR paradox paper in the May 4, 1935, issue of The New York Times

Though the EPR paper has often been taken as an exact expression of Einstein's views, it was primarily authored by Podolsky, based on discussions at the Institute for Advanced Study with Einstein and Rosen. Einstein later expressed to Erwin Schrödinger that, "it did not come out as well as I had originally wanted; rather, the essential thing was, so to speak, smothered by the formalism." Einstein would later go on to present an individual account of his local realist ideas. Shortly before the EPR paper appeared in the Physical Review, The New York Times ran a news story about it, under the headline "Einstein Attacks Quantum Theory". The story, which quoted Podolsky, irritated Einstein, who wrote to the Times, "Any information upon which the article 'Einstein Attacks Quantum Theory' in your issue of May 4 is based was given to you without authority. It is my invariable practice to discuss scientific matters only in the appropriate forum and I deprecate advance publication of any announcement in regard to such matters in the secular press."

The Times story also sought out comment from physicist Edward Condon, who said, "Of course, a great deal of the argument hinges on just what meaning is to be attached to the word 'reality' in physics." The physicist and historian Max Jammer later noted, "[I]t remains a historical fact that the earliest criticism of the EPR paper – moreover, a criticism that correctly saw in Einstein's conception of physical reality the key problem of the whole issue – appeared in a daily newspaper prior to the publication of the criticized paper itself."

Bohr's reply

The publication of the paper prompted a response by Niels Bohr, which he published in the same journal (Physical Review), in the same year, using the same title. (This exchange was only one chapter in a prolonged debate between Bohr and Einstein about the nature of quantum reality.) He argued that EPR had reasoned fallaciously. Bohr said measurements of position and of momentum are complementary, meaning the choice to measure one excludes the possibility of measuring the other. Consequently, a fact deduced regarding one arrangement of laboratory apparatus could not be combined with a fact deduced by means of the other, and so, the inference of predetermined position and momentum values for the second particle was not valid. Bohr concluded that EPR's "arguments do not justify their conclusion that the quantum description turns out to be essentially incomplete."

Einstein's own argument

In his own publications and correspondence, Einstein indicated that he was not satisfied with the EPR paper and that Podolsky had authored most of it. He later used a different argument to insist that quantum mechanics is an incomplete theory. He explicitly de-emphasized EPR's attribution of "elements of reality" to the position and momentum of particle B, saying that "I couldn't care less" whether the resulting states of particle B allowed one to predict the position and momentum with certainty.

For Einstein, the crucial part of the argument was the demonstration of nonlocality, that the choice of measurement done in particle A, either position or momentum, would lead to two different quantum states of particle B. He argued that, because of locality, the real state of particle B could not depend on which kind of measurement was done in A and that the quantum states therefore cannot be in one-to-one correspondence with the real states. Einstein struggled unsuccessfully for the rest of his life to find a theory that could better comply with his idea of locality.

Later developments

Bohm's variant

In 1951, David Bohm proposed a variant of the EPR thought experiment in which the measurements have discrete ranges of possible outcomes, unlike the position and momentum measurements considered by EPR. The EPR–Bohm thought experiment can be explained using electron–positron pairs. Suppose we have a source that emits electron–positron pairs, with the electron sent to destination A, where there is an observer named Alice, and the positron sent to destination B, where there is an observer named Bob. According to quantum mechanics, we can arrange our source so that each emitted pair occupies a quantum state called a spin singlet. The particles are thus said to be entangled. This can be viewed as a quantum superposition of two states, which we call state I and state II. In state I, the electron has spin pointing upward along the z-axis (+z) and the positron has spin pointing downward along the z-axis (−z). In state II, the electron has spin −z and the positron has spin +z. Because it is in a superposition of states, it is impossible without measuring to know the definite state of spin of either particle in the spin singlet.

The EPR thought experiment, performed with electron–positron pairs. A source (center) sends particles toward two observers, electrons to Alice (left) and positrons to Bob (right), who can perform spin measurements.

Alice now measures the spin along the z-axis. She can obtain one of two possible outcomes: +z or −z. Suppose she gets +z. Informally speaking, the quantum state of the system collapses into state I. The quantum state determines the probable outcomes of any measurement performed on the system. In this case, if Bob subsequently measures spin along the z-axis, there is 100% probability that he will obtain −z. Similarly, if Alice gets −z, Bob will get +z. There is nothing special about choosing the z-axis: according to quantum mechanics the spin singlet state may equally well be expressed as a superposition of spin states pointing in the x direction.

Whatever axis their spins are measured along, they are always found to be opposite. In quantum mechanics, the x-spin and z-spin are "incompatible observables", meaning the Heisenberg uncertainty principle applies to alternating measurements of them: a quantum state cannot possess a definite value for both of these variables. Suppose Alice measures the z-spin and obtains +z, so that the quantum state collapses into state I. Now, instead of measuring the z-spin as well, Bob measures the x-spin. According to quantum mechanics, when the system is in state I, Bob's x-spin measurement will have a 50% probability of producing +x and a 50% probability of -x. It is impossible to predict which outcome will appear until Bob actually performs the measurement. Therefore, Bob's positron will have a definite spin when measured along the same axis as Alice's electron, but when measured in the perpendicular axis its spin will be uniformly random. It seems as if information has propagated (faster than light) from Alice's apparatus to make Bob's positron assume a definite spin in the appropriate axis.

Bell's theorem

Main article: Bell's theorem

In 1964, John Stewart Bell published a paper investigating the puzzling situation at that time: on one hand, the EPR paradox purportedly showed that quantum mechanics was nonlocal, and suggested that a hidden-variable theory could heal this nonlocality. On the other hand, David Bohm had recently developed the first successful hidden-variable theory, but it had a grossly nonlocal character. Bell set out to investigate whether it was indeed possible to solve the nonlocality problem with hidden variables, and found out that first, the correlations shown in both EPR's and Bohm's versions of the paradox could indeed be explained in a local way with hidden variables, and second, that the correlations shown in his own variant of the paradox couldn't be explained by any local hidden-variable theory. This second result became known as the Bell theorem.

To understand the first result, consider the following toy hidden-variable theory introduced later by J.J. Sakurai: in it, quantum spin-singlet states emitted by the source are actually approximate descriptions for "true" physical states possessing definite values for the z-spin and x-spin. In these "true" states, the positron going to Bob always has spin values opposite to the electron going to Alice, but the values are otherwise completely random. For example, the first pair emitted by the source might be "(+z, −x) to Alice and (−z, +x) to Bob", the next pair "(−z, −x) to Alice and (+z, +x) to Bob", and so forth. Therefore, if Bob's measurement axis is aligned with Alice's, he will necessarily get the opposite of whatever Alice gets; otherwise, he will get "+" and "−" with equal probability.

Bell showed, however, that such models can only reproduce the singlet correlations when Alice and Bob make measurements on the same axis or on perpendicular axes. As soon as other angles between their axes are allowed, local hidden-variable theories become unable to reproduce the quantum mechanical correlations. This difference, expressed using inequalities known as "Bell's inequalities", is in principle experimentally testable. After the publication of Bell's paper, a variety of experiments to test Bell's inequalities were carried out, notably by the group of Alain Aspect in the 1980s; all experiments conducted to date have found behavior in line with the predictions of quantum mechanics. The present view of the situation is that quantum mechanics flatly contradicts Einstein's philosophical postulate that any acceptable physical theory must fulfill "local realism". The fact that quantum mechanics violates Bell inequalities indicates that any hidden-variable theory underlying quantum mechanics must be non-local; whether this should be taken to imply that quantum mechanics itself is non-local is a matter of continuing debate.

Steering

Main article: Quantum steering

Inspired by Schrödinger's treatment of the EPR paradox back in 1935, Howard M. Wiseman et al. formalised it in 2007 as the phenomenon of quantum steering. They defined steering as the situation where Alice's measurements on a part of an entangled state steer Bob's part of the state. That is, Bob's observations cannot be explained by a local hidden state model, where Bob would have a fixed quantum state in his side, which is classically correlated but otherwise independent of Alice's.

Locality

Locality has several different meanings in physics. EPR describe the principle of locality as asserting that physical processes occurring at one place should have no immediate effect on the elements of reality at another location. At first sight, this appears to be a reasonable assumption to make, as it seems to be a consequence of special relativity, which states that energy can never be transmitted faster than the speed of light without violating causality; however, it turns out that the usual rules for combining quantum mechanical and classical descriptions violate EPR's principle of locality without violating special relativity or causality. Causality is preserved because there is no way for Alice to transmit messages (i.e., information) to Bob by manipulating her measurement axis. Whichever axis she uses, she has a 50% probability of obtaining "+" and 50% probability of obtaining "−", completely at random; according to quantum mechanics, it is fundamentally impossible for her to influence what result she gets. Furthermore, Bob is able to perform his measurement only once: there is a fundamental property of quantum mechanics, the no-cloning theorem, which makes it impossible for him to make an arbitrary number of copies of the electron he receives, perform a spin measurement on each, and look at the statistical distribution of the results. Therefore, in the one measurement he is allowed to make, there is a 50% probability of getting "+" and 50% of getting "−", regardless of whether or not his axis is aligned with Alice's.

As a summary, the results of the EPR thought experiment do not contradict the predictions of special relativity. Neither the EPR paradox nor any quantum experiment demonstrates that superluminal signaling is possible; however, the principle of locality appeals powerfully to physical intuition, and Einstein, Podolsky and Rosen were unwilling to abandon it. Einstein derided the quantum mechanical predictions as "spooky action at a distance". The conclusion they drew was that quantum mechanics is not a complete theory.

Mathematical formulation

Bohm's variant of the EPR paradox can be expressed mathematically using the quantum mechanical formulation of spin. The spin degree of freedom for an electron is associated with a two-dimensional complex vector space V, with each quantum state corresponding to a vector in that space. The operators corresponding to the spin along the x, y, and z direction, denoted S_x, S_y, and S_z respectively, can be represented using the Pauli matrices:$${\displaystyle S_x=\frac{\hslash }{2}\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right],S_y=\frac{\hslash }{2}\left[\begin{array}{cc}0& -i\\ i& 0\end{array}\right],S_z=\frac{\hslash }{2}\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right],}$$ where ${\displaystyle \hslash }$ is the reduced Planck constant (or the Planck constant divided by 2π).

The eigenstates of S_z are represented as $${\displaystyle |+z⟩\leftrightarrow \left[\begin{array}{c}1\\ 0\end{array}\right],|-z⟩\leftrightarrow \left[\begin{array}{c}0\\ 1\end{array}\right]}$$ and the eigenstates of S_x are represented as $${\displaystyle |+x⟩\leftrightarrow \frac{1}{\sqrt{2}}\left[\begin{array}{c}1\\ 1\end{array}\right],|-x⟩\leftrightarrow \frac{1}{\sqrt{2}}\left[\begin{array}{c}1\\ -1\end{array}\right].}$$

The vector space of the electron-positron pair is ${\displaystyle V\otimes V}$, the tensor product of the electron's and positron's vector spaces. The spin singlet state is $${\displaystyle |\psi ⟩=\frac{1}{\sqrt{2}}(|+z⟩\otimes |-z⟩-|-z⟩\otimes |+z⟩),}$$ where the two terms on the right hand side are what we have referred to as state I and state II above.

From the above equations, it can be shown that the spin singlet can also be written as $${\displaystyle |\psi ⟩=-\frac{1}{\sqrt{2}}(|+x⟩\otimes |-x⟩-|-x⟩\otimes |+x⟩),}$$ where the terms on the right hand side are what we have referred to as state Ia and state IIa.

To illustrate the paradox, we need to show that after Alice's measurement of S_z (or S_x), Bob's value of S_z (or S_x) is uniquely determined and Bob's value of S_x (or S_z) is uniformly random. This follows from the principles of measurement in quantum mechanics. When S_z is measured, the system state ${\displaystyle |\psi ⟩}$ collapses into an eigenvector of S_z. If the measurement result is +z, this means that immediately after measurement the system state collapses to $${\displaystyle |+z⟩\otimes |-z⟩=|+z⟩\otimes \frac{|+x⟩-|-x⟩}{\sqrt{2}}.}$$

Similarly, if Alice's measurement result is −z, the state collapses to $${\displaystyle |-z⟩\otimes |+z⟩=|-z⟩\otimes \frac{|+x⟩+|-x⟩}{\sqrt{2}}.}$$ The left hand side of both equations show that the measurement of S_z on Bob's positron is now determined, it will be −z in the first case or +z in the second case. The right hand side of the equations show that the measurement of S_x on Bob's positron will return, in both cases, +x or −x with probability 1/2 each.

Stern–Gerlach experiment

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment 

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 quantum physics, the Stern–Gerlach experiment demonstrated that the spatial orientation of angular momentum is quantized. Thus an atomic-scale system was shown to have intrinsically quantum properties. In the original experiment, silver atoms were sent through a spatially-varying magnetic field, which deflected them before they struck a detector screen, such as a glass slide. Particles with non-zero magnetic moment were deflected, owing to the magnetic field gradient, from a straight path. The screen revealed discrete points of accumulation, rather than a continuous distribution, owing to their quantized spin. Historically, this experiment was decisive in convincing physicists of the reality of angular-momentum quantization in all atomic-scale systems.

After its conception by Otto Stern in 1921, the experiment was first successfully conducted with Walther Gerlach in early 1922.

Description

See also: Spin quantum number

The Stern–Gerlach experiment involves sending silver atoms through an inhomogeneous magnetic field and observing their deflection. Silver atoms were evaporated using an electric furnace in a vacuum. Using thin slits, the atoms were guided into a flat beam and the beam sent through an inhomogeneous magnetic field before colliding with a metallic plate. The laws of classical physics predict that the collection of condensed silver atoms on the plate should form a thin solid line in the same shape as the original beam. However, the inhomogeneous magnetic field caused the beam to split in two separate directions, creating two lines on the metallic plate.

The results show that particles possess an intrinsic angular momentum that is closely analogous to the angular momentum of a classically spinning object, but that takes only certain quantized values. Another important result is that only one component of a particle's spin can be measured at one time, meaning that the measurement of the spin along the z-axis destroys information about a particle's spin along the x and y axis.

The experiment is normally conducted using electrically neutral particles such as silver atoms. This avoids the large deflection in the path of a charged particle moving through a magnetic field and allows spin-dependent effects to dominate.

If the particle is treated as a classical spinning magnetic dipole, it will precess in a magnetic field because of the torque that the magnetic field exerts on the dipole (see torque-induced precession). If it moves through a homogeneous magnetic field, the forces exerted on opposite ends of the dipole cancel each other out and the trajectory of the particle is unaffected. However, if the magnetic field is inhomogeneous then the force on one end of the dipole will be slightly greater than the opposing force on the other end, so that there is a net force which deflects the particle's trajectory. If the particles were classical spinning objects, one would expect the distribution of their spin angular momentum vectors to be random and continuous. Each particle would be deflected by an amount proportional to the dot product of its magnetic moment with the external field gradient, producing some density distribution on the detector screen. Instead, the particles passing through the Stern–Gerlach apparatus are deflected either up or down by a specific amount. This was a measurement of the quantum observable now known as spin angular momentum, which demonstrated possible outcomes of a measurement where the observable has a discrete set of values or point spectrum.

Although some discrete quantum phenomena, such as atomic spectra, were observed much earlier, the Stern–Gerlach experiment allowed scientists to directly observe separation between discrete quantum states for the first time.

Theoretically, quantum angular momentum of any kind has a discrete spectrum, which is sometimes briefly expressed as "angular momentum is quantized".

Experiment using particles with +1/2 or −1/2 spin

If the experiment is conducted using charged particles like electrons, there will be a Lorentz force that tends to bend the trajectory in a circle. This force can be cancelled by an electric field of appropriate magnitude oriented transverse to the charged particle's path.

Spin values for fermions

Electrons are spin-1/2 particles. These have only two possible spin angular momentum values measured along any axis, ${\displaystyle +\frac{\hslash }{2}}$ or ${\displaystyle -\frac{\hslash }{2}}$, a purely quantum mechanical phenomenon. Because its value is always the same, it is regarded as an intrinsic property of electrons, and is sometimes known as "intrinsic angular momentum" (to distinguish it from orbital angular momentum, which can vary and depends on the presence of other particles). If one measures the spin along a vertical axis, electrons are described as "spin up" or "spin down", based on the magnetic moment pointing up or down, respectively.

To mathematically describe the experiment with spin-1/2 particles, it is easiest to use Dirac's bra–ket notation. As the particles pass through the Stern–Gerlach device, they are deflected either up or down, and observed by the detector which resolves to either spin up or spin down. These are described by the angular momentum quantum number ${\displaystyle j}$, which can take on one of the two possible allowed values, either +1/2 or -1/2. The act of observing (measuring) the momentum along the ${\displaystyle z}$ axis corresponds to the ${\displaystyle z}$-axis angular momentum operator, often denoted ${\displaystyle J_z}$. In mathematical terms, the initial state of the particles is

${\displaystyle |\psi ⟩=c_1|{\psi }_{j=+\frac{1}{2}}⟩+c_2|{\psi }_{j=-\frac{1}{2}}⟩}$

where constants ${\displaystyle c_1}$ and ${\displaystyle c_2}$ are complex numbers. This initial state spin can point in any direction. The squares of the absolute values ${\displaystyle |c_1{|}^2}$ and ${\displaystyle |c_2{|}^2}$ are respectively the probabilities for a system in the state ${\displaystyle |\psi ⟩}$ to be found in ${\displaystyle |{\psi }_{j=+\frac{1}{2}}⟩}$ and ${\displaystyle |{\psi }_{j=-\frac{1}{2}}⟩}$ after the measurement along ${\displaystyle z}$ axis is made. The constants ${\displaystyle c_1}$ and ${\displaystyle c_2}$ must also be normalized in order that the probability of finding either one of the values be unity, that is we must ensure that ${\displaystyle |c_1{|}^2+|c_2{|}^2=1}$. However, this information is not sufficient to determine the values of ${\displaystyle c_1}$ and ${\displaystyle c_2}$, because they are complex numbers. Therefore, the measurement yields only the squared magnitudes of the constants, which are interpreted as probabilities.

Sequential experiments

If we link multiple Stern–Gerlach apparatuses (the rectangles containing S-G), we can clearly see that they do not act as simple selectors, i.e. filtering out particles with one of the states (pre-existing to the measurement) and blocking the others. Instead they alter the state by observing it (as in light polarization). In the figure below, x and z name the directions of the (inhomogenous) magnetic field, with the x-z-plane being orthogonal to the particle beam. In the three S-G systems shown below, the cross-hatched squares denote the blocking of a given output, i.e. each of the S-G systems with a blocker allows only particles with one of two states to enter the next S-G apparatus in the sequence.

Exp. 1 - Notice that no z- neutrons are detected at the second S-G analyzer

Experiment 1

The top illustration shows that when a second, identical, S-G apparatus is placed at the exit of the first apparatus, only z+ is seen in the output of the second apparatus. This result is expected since all particles at this point are expected to have z+ spin, as only the z+ beam from the first apparatus entered the second apparatus.

Exp. 2 - The z-spin is known, now measuring the x-spin.

Experiment 2

The middle system shows what happens when a different S-G apparatus is placed at the exit of the z+ beam resulting of the first apparatus, the second apparatus measuring the deflection of the beams on the x axis instead of the z axis. The second apparatus produces x+ and x- outputs. Now classically we would expect to have one beam with the x characteristic oriented + and the z characteristic oriented +, and another with the x characteristic oriented - and the z characteristic oriented +.

Exp. 3 - Neutrons thought to have only z+ spin are measured again, finding that the z-spin has been 'reset'.

Experiment 3

The bottom system contradicts that expectation. The output of the third apparatus which measures the deflection on the z axis again shows an output of z- as well as z+. Given that the input to the second S-G apparatus consisted only of z+, it can be inferred that a S-G apparatus must be altering the states of the particles that pass through it. This experiment can be interpreted to exhibit the uncertainty principle: since the angular momentum cannot be measured on two perpendicular directions at the same time, the measurement of the angular momentum on the x direction destroys the previous determination of the angular momentum in the z direction. That's why the third apparatus measures renewed z+ and z- beams like the x measurement really made a clean slate of the z+ output.

History

A plaque at the Frankfurt institute commemorating the experiment

The Stern–Gerlach experiment was conceived by Otto Stern in 1921 and performed by him and Walther Gerlach in Frankfurt in 1922. At the time of the experiment, the most prevalent model for describing the atom was the Bohr-Sommerfeld model, which described electrons as going around the positively charged nucleus only in certain discrete atomic orbitals or energy levels. Since the electron was quantized to be only in certain positions in space, the separation into distinct orbits was referred to as space quantization. The Stern–Gerlach experiment was meant to test the Bohr–Sommerfeld hypothesis that the direction of the angular momentum of a silver atom is quantized.

The experiment was first performed with an electromagnet that allowed the non-uniform magnetic field to be turned on gradually from a null value. When the field was null, the silver atoms were deposited as a single band on the detecting glass slide. When the field was made stronger, the middle of the band began to widen and eventually to split into two, so that the glass-slide image looked like a lip-print, with an opening in the middle, and closure at either end. In the middle, where the magnetic field was strong enough to split the beam into two, statistically half of the silver atoms had been deflected by the non-uniformity of the field.

Note that the experiment was performed several years before George Uhlenbeck and Samuel Goudsmit formulated their hypothesis about the existence of electron spin in 1925. Even though the result of the Stern−Gerlach experiment has later turned out to be in agreement with the predictions of quantum mechanics for a spin-1/2 particle, the experimental result was also consistent with the Bohr–Sommerfeld theory.

In 1927, T.E. Phipps and J.B. Taylor reproduced the effect using hydrogen atoms in their ground state, thereby eliminating any doubts that may have been caused by the use of silver atoms. However, in 1926 the non-relativistic scalar Schrödinger equation had incorrectly predicted the magnetic moment of hydrogen to be zero in its ground state. To correct this problem Wolfgang Pauli considered a spin-1/2 version of the Schrödinger equation using the 3 Pauli matrices which now bear his name, which was later shown by Paul Dirac in 1928 to be a consequence of his relativistic Dirac equation.

In the early 1930s Stern, together with Otto Robert Frisch and Immanuel Estermann improved the molecular beam apparatus sufficiently to measure the magnetic moment of the proton, a value nearly 2000 times smaller than the electron moment. In 1931, theoretical analysis by Gregory Breit and Isidor Isaac Rabi showed that this apparatus could be used to measure nuclear spin whenever the electronic configuration of the atom was known. The concept was applied by Rabi and Victor W. Cohen in 1934 to determine the ${\displaystyle 3/2}$ spin of sodium atoms.

In 1938 Rabi and coworkers inserted an oscillating magnetic field element into their apparatus, inventing nuclear magnetic resonance spectroscopy. By tuning the frequency of the oscillator to the frequency of the nuclear precessions they could selectively tune into each quantum level of the material under study. Rabi was awarded the Nobel Prize in 1944 for this work.

Importance

The Stern–Gerlach experiment was the first direct evidence of angular-momentum quantization in quantum mechanics, and it strongly influenced later developments in modern physics:

• In the decade that followed, scientists showed using similar techniques, that the nuclei of some atoms also have quantized angular momentum. It is the interaction of this nuclear angular momentum with the spin of the electron that is responsible for the hyperfine structure of the spectroscopic lines.
• Norman F. Ramsey later modified the Rabi apparatus to improve its sensitivity (using the separated oscillatory field method). In the early sixties, Ramsey, H. Mark Goldenberg, and Daniel Kleppner used a Stern–Gerlach system to produce a beam of polarized hydrogen as the source of energy for the hydrogen maser. This led to developing an extremely stable clock based on a hydrogen maser. From 1967 until 2019, the second was defined based on 9,192,631,770 Hz hyperfine transition of a cesium-133 atom; the atomic clock which is used to set this standard is an application of Ramsey's work.
• The Stern–Gerlach experiment has become a prototype for quantum measurement, demonstrating the observation of a discrete value (eigenvalue) of a physical property, previously assumed to be continuous. Entering the Stern–Gerlach magnet, the direction of the silver atom's magnetic moment is indefinite, but when the atom is registered at the screen, it is observed to be at either one spot or the other, and this outcome cannot be predicted in advance. Because the experiment illustrates the character of quantum measurements, The Feynman Lectures on Physics use idealized Stern–Gerlach apparatuses to explain the basic mathematics of quantum theory.