In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), and its direction is perpendicular to the wavefront. In isotropic media, this is also the direction of wave propagation.
A closely related vector is the angular wave vector (or angular wavevector),
with a typical unit being radian per metre. The wave vector and
angular wave vector are related by a fixed constant of proportionality, 2π radians per cycle.
It is common in several fields of physics to refer to the angular wave vector simply as the wave vector, in contrast to, for example, crystallography. It is also common to use the symbol k for whichever is in use.
The terms wave vector and angular wave vector have distinct meanings. Here, the wave vector is denoted by and the wavenumber by . The angular wave vector is denoted by k and the angular wavenumber by k = |k|. These are related by .
ψ is a function of r and t describing the disturbance describing the wave (for example, for an ocean wave, ψ would be the excess height of the water, or for a sound wave, ψ would be the excess air pressure).
A is the amplitude of the wave (the peak magnitude of the oscillation),
ω is the (temporal) angular frequency of the wave, describing how many radians it traverses per unit of time, and related to the periodT by the equation
k is the angular wave vector of the wave, describing how many radians it traverses per unit of distance, and related to the wavelength by the equation
The equivalent equation using the wave vector and frequency is
The direction in which the wave vector points must be distinguished from the "direction of wave propagation". The "direction of wave propagation" is the direction of a wave's energy flow, and the direction that a small wave packet will move, i.e. the direction of the group velocity. For light waves in vacuum, this is also the direction of the Poynting vector. On the other hand, the wave vector points in the direction of phase velocity. In other words, the wave vector points in the normal direction to the surfaces of constant phase, also called wavefronts.
In a losslessisotropic medium such as air, any gas, any liquid, amorphous solids (such as glass), and cubic crystals,
the direction of the wavevector is the same as the direction of wave
propagation. If the medium is anisotropic, the wave vector in general
points in directions other than that of the wave propagation. The wave
vector is always perpendicular to surfaces of constant phase.
A
moving wave surface in special relativity may be regarded as a
hypersurface (a 3D subspace) in spacetime, formed by all the events
passed by the wave surface. A wavetrain (denoted by some variable X) can be regarded as a one-parameter family of such hypersurfaces in spacetime. This variable X
is a scalar function of position in spacetime. The derivative of this
scalar is a vector that characterizes the wave, the four-wavevector.
where the angular frequency is the temporal component, and the wavenumber vector is the spatial component.
Alternately, the wavenumber k can be written as the angular frequency ω divided by the phase-velocityvp, or in terms of inverse period T and inverse wavelength λ.
In the situation where light is being emitted by a fast moving source
and one would like to know the frequency of light detected in an earth
(lab) frame, we would apply the Lorentz transformation as follows. Note
that the source is in a frame Ss and earth is in the observing frame, Sobs.
Applying the Lorentz transformation to the wave vector
and choosing just to look at the component results in
where is the direction cosine of with respect to
So
Source moving away (redshift)
As an example, to apply this to a situation where the source is moving directly away from the observer (), this becomes:
Source moving towards (blueshift)
To apply this to a situation where the source is moving straight towards the observer (θ = 0), this becomes:
The politicization of science for political gain occurs when government, business, or advocacy groups
use legal or economic pressure to influence the findings of scientific
research or the way it is disseminated, reported or interpreted. The
politicization of science may also negatively affect academic and scientific freedom, and as a result it is considered taboo to mix politics with science. Historically, groups have conducted various campaigns to promote their interests in defiance of scientific consensus, and in an effort to manipulate public policy.
Overview
Many factors can act as facets of the politicization of science. These can range, for example, from populistanti-intellectualism and perceived threats to religious belief to postmodernistsubjectivism,
fear for business interests, institutional academic ideological biases
or potentially implicit bias amongst scientific researchers.
Politicization occurs as scientific information is presented with
emphasis on the uncertainty associated with the interpretation of
scientific evidence. The emphasis capitalizes on the lack of consensus,
which influences the way the studies are perceived. Chris Mooney
describes how this point is sometimes intentionally ignored as a part
an "Orwellian tactic." Organizations and politicians seek to disclaim
all discussion on some issues as 'the more probable conclusion is still
uncertain' as opposed to 'conclusions are most scientifically likely' in order to further discredit scientific studies.
Tactics such as shifting conversation, failing to acknowledge
facts, and capitalizing on doubt of scientific consensus have been used
to gain more attention for views that have been undermined by scientific
evidence. "Merchants of Doubt,"
ideology-based interest groups that claim expertise on scientific
issues, have run successful "disinformation campaigns" in which they
highlight the inherent uncertainty of science to cast doubt on
scientific issues such as human-caused climate change, even though the
scientific community has reached virtual consensus that humans play a
role in climate change.
William R. Freudenburg and colleagues have written about
politicization of science as a rhetorical technique and states that it
is an attempt to shift the burden of proof in an argument. He offers the example of cigarette lobbyists
opposing laws that would discourage smoking. The lobbyists trivialize
evidence as uncertain, emphasizing lack of conclusion. Freudenberg
concludes that politicians and lobby groups are too often able to make
"successful efforts to argue for full 'scientific certainty' before a
regulation can be said to be 'justified' and maintain that what is
needed is a balanced approach that carefully considers the risks of both
Type 1 and Type 2 errors in a situation while noting that scientific
conclusions are always tentative.
Politicization by advocacy groups
A
political tactic, sometimes used to delay the implementation of
legislation to control potentially harmful activities, is the
"Scientific Certainty Argumentation Method" (SCAM). In many cases, there
is a degree of uncertainty in scientific findings and this can be
exploited to delay action, perhaps for many years, by demanding more
"certainty" before action is taken.
Democrats and Republicans have long differed in views of climate change, with the gap widening in the late 2010s, and Democrats three times more likely to view it as human-caused.
The
sharp divide over the existence of and responsibility for global
warming and climate change falls largely along political lines. Overall, 60% of Americans surveyed said oil and gas companies were "completely or mostly responsible" for climate change.
Opinion
about human causation of climate change increased substantially with
education among Democrats, but not among Republicans.
Conversely, opinions favoring becoming carbon neutral declined
substantially with age among Republicans, but not among Democrats.
National
political divides on the seriousness of climate change consistently
correlate with political ideology, with right-wing opinion being more
negative.
In 1991, a US corporate coalition including the National Coal Association, the Western Fuels Association and Edison Electrical Institute created a public relations organization called the "Information Council on the Environment"
(ICE). ICE launched a $500,000 advertising campaign to, in ICE's own
words, "reposition global warming as theory (not fact)." Critics of
industry groups have charged that the claims about a global warming
controversy are part of a deliberate effort to reduce the impact any
international treaty, such as the Kyoto Protocol, might have on their business interests.
In 2006, Guardian columnist George Monbiot
reported that according to data found in official Exxon documents, 124
organizations have taken money from ExxonMobil or worked closely with
those that have, and that "These organizations take a consistent line on
climate change: that the science is contradictory, the scientists are
split, environmentalists are charlatans, liars or lunatics, and if
governments took action to prevent global warming, they would be
endangering the global economy for no good reason. The findings these
organisations dislike are labelled 'junk science'. The findings they welcome are labelled 'sound science'." The "selective use of data", cherry picking, is identified as a notable form of scientific abuse by the Pacific Institute,
an organization created to provide independent research and policy
analysis on issues at the intersection of development, environment, and
security.
The intelligent design movement associated with the Discovery Institute, attempts to "defeat [the] materialistworld view" represented by the theory of evolution in favor of "a science consonant with Christian and theistic convictions".
The Discovery Institute portrays evolution as a "theory in crisis" with
scientists criticizing evolution and that "fairness" and "equal time"
requires educating students about "the controversy."
A cornerstone of modern scientific biological theory is that all
forms of life on Earth are related by common descent with modification.
While many valid criticisms to the theory of evolution have existed
throughout time, often certain ideological proponents seek to expand the
scope of these disagreements in order to draw doubt onto the entire
theory. For example, in the United States, there is a legal precedent of
those who sought to discredit the teaching of evolution in classrooms
by emphasizing so-called flaws in the theory of evolution or
disagreements within the scientific community. Others insist that
teachers have absolute freedom within their classrooms and cannot be
disciplined for teaching non-scientific "alternatives" to evolution. A
number of bills require that students be taught to "critically analyze"
evolution or to understand "the controversy." But there is no
significant controversy within the mainstream scientific community about
the validity of the main pillars of theory of evolution at this time.
The current controversy surrounding the teaching of evolution is thus
not primarily a scientific one. The 2005 ruling in the Dover trial, Kitzmiller v. Dover Area School District, where the claims of intelligent design proponents were considered by a United States federal court
concluded that intelligent design is not science, that it "cannot
uncouple itself from its creationist, and thus religious, antecedents",
and concluded that the school district's promotion of it therefore
violated the Establishment Clause of the First Amendment to the U.S. Constitution.
Tobacco and cancer
By the mid-1950s there was a scientific consensus that smoking promotes lung cancer, but the tobacco industry fought the findings, both in the public eye and within the scientific community. Tobacco companies funded think tanks
and lobbying groups, started health reassurance campaigns, ran
advertisements in medical journals, and researched alternate
explanations for lung cancer, such as pollution, asbestos
and even pet birds. Denying the case against tobacco was "closed," they
called for more research as a tactic to delay regulation.
John Horgan, notes a rhetoric tactic that has been used by tobacco
companies. It is summarized in a line that appeared in a confidential
memo from a tobacco company, in 1969, when they sought to cast doubt on
evidence that supports smoking causes cancer. It read, "Doubt is our
product since it is the best means of competing with the 'body of fact'
that exists in the mind of the general public. It is also the means of
establishing a controversy."
Nazi Germany under Adolf Hitler was well known for eugenics programs which attempted to maintain a "pure" German race through a series of programs that ran under the banner of racial hygiene.
The Nazis manipulated scientific research in Germany, by forcing some
scholars to emigrate, and by allocating funding for research based on
ideological rather than scientific merit.
In the early 20th century, Eugenics enjoyed substantial
international support, from leading politicians and scientists. The
First International Congress of Eugenics in 1912 was supported by many
prominent persons, including its president Leonard Darwin, the son of Charles Darwin; honorary vice-president Winston Churchill, then First Lord of the Admiralty and future Prime Minister of the United Kingdom; Auguste Forel, famous Swiss pathologist; Alexander Graham Bell, the inventor of the telephone; among other prominent people.
The level of support for eugenics research by the Nazis prompted
an American eugenics advocate to seek an expansion of the American
program, with the complaint that "the Germans are beating us at our own
game".
There was a strong connection between American and Nazi eugenics research. Nazis based their eugenics program on the United States' programs of forced sterilization, especially on the eugenics laws that had been enacted in California.
Social justice
Some critics argue that science has been politicized by social justice advocates. David Randall, director of research at the politically conservative advocacy group the National Association of Scholars,said that the emphasis on pursuing social justice and political
activism "threatens the very definition of science as primarily a search
for truth". In October 2021, The New York Times
reported a rise in calls for "citational justice" within academic
communities, which the article defines as an effort by professors and
graduate students "to cite more Black, Latino, Asian and Native American
scholars and in some cases refuse to acknowledge in footnotes the
research of those who hold distasteful views."
Some researchers have defended these efforts against the charge of
politicization, arguing that science has always been inherently
political.
In the Soviet Union, scientific research was under strict political control. A number of research areas were declared "bourgeois pseudoscience" and forbidden. This has led to significant setbacks for the Soviet science, notably in biology due to ban on genetics (see "Lysenkoism") and in computer science, which drastically influenced the Soviet economy and technology.
United States
The
General Social Survey (GSS) of 1974 recorded that conservatives had the
highest rates of trust in science between the three major political
demographics: conservatives, liberals, and moderates. This study was
repeated annually between 1972 and 1994, and biannually from 1994 until
2010. In 2010, when the same study was repeated, conservatives' trust
rates had decreased from 49% to 38%, moderates' trust rates from 45% to
40%, and liberals' trust rates staying relatively stable, rising
slightly from 48% to 50%.
The study by Gordon Gauchat, which investigates time trends in
the public trust of science in the United States, suggests that the
increase of distrust of conservatives can be attributed to two cultural
shifts. The first was during the post-Reagan era when the New Right emerged, and the second during the G.W. Bush era when the NR intensified and conservatives commenced the "war on science".
Barack Obama and other politicians, since Bush's presidency, have
expressed their concerns with the politicization of science in both the
public and government sphere. In 2011, during his State of the Union
speech, Obama discussed his dissatisfaction of the relationships between
organized science, private economic interests, and the government.
A 2024 analysis found that 100 U.S. Representatives and 23 U.S.
Senators—23% of the 535 members of Congress—were climate change deniers. All were Republicans.
George W. Bush administration
In 2004, The Denver Post reported that the George W. Bush administration
"has installed more than 100 top officials who were once lobbyists,
attorneys or spokespeople for the industries they oversee." At least 20
of these former industry advocates helped their agencies write, shape or
push for policy shifts that benefit their former industries. "They knew
which changes to make because they had pushed for them as industry
advocates."
Also in 2004, the scientific advocacy group Union of Concerned Scientists issued a report, Scientific Integrity in Policymaking: An Investigation into the Bush Administration's Misuse of Science which charged the following:
A
growing number of scientists, policy makers, and technical specialists
both inside and outside the government allege that the current Bush
administration has suppressed or distorted the scientific analyses of
federal agencies to bring these results in line with administration
policy. In addition, these experts contend that irregularities in the
appointment of scientific advisors and advisory panels are threatening
to upset the legally mandated balance of these bodies.
A petition, signed on February 18, 2004, by more than 9,000 scientists, including 49 Nobel laureates and 63 National Medal of Science recipients, followed the report. The petition stated:
When
scientific knowledge has been found to be in conflict with its
political goals, the administration has often manipulated the process
through which science enters into its decisions. This has been done by
placing people who are professionally unqualified or who have clear
conflicts of interest in official posts and on scientific advisory
committees; by disbanding existing advisory committees; by censoring and
suppressing reports by the government's own scientists; and by simply
not seeking independent scientific advice. Other administrations have,
on occasion, engaged in such practices, but not so systematically nor on
so wide a front. Furthermore, in advocating policies that are not
scientifically sound, the administration has sometimes misrepresented
scientific knowledge and misled the public about the implications of its
policies.
The same year, Francesca Grifo, executive director of the Union of
Concerned Scientists' Scientific Integrity Program, stated "We have
reports that stay in draft form and don't get out to the public. We have
reports that are changed. We have reports that are ignored and
overwritten."
In response to criticisms, President Bush in 2006 unveiled a campaign in his State of the Union Address
to promote scientific research and education to ensure American
competitiveness in the world, vowing to "double the federal commitment
to the most critical basic research programs in the physical sciences
over the next 10 years."
"Anything that doesn't fit into the political appointees'
ideological, theological or political agenda is often ignored,
marginalized or simply buried," Carmona testified.
Although he did not make personal accusations, the Washington Post reported on July 29 that the official who blocked at least one of Carmona's reports was William R. Steiger.
Food and Drug Administration
In
July 2006 the Union of Concerned Scientists (UCS) released survey
results that demonstrate pervasive political influence of science at the
Food and Drug Administration (FDA).
Of the 997 FDA scientists who responded to the survey, nearly one fifth
(18 percent) said that they "have been asked, for non-scientific
reasons, to inappropriately exclude or alter technical information or
their conclusions in a FDA scientific document." This is the third
survey Union of Concerned Scientists has conducted to examine
inappropriate interference with science at federal agencies.
The Department of Health and Human Services also conducted a survey addressing the same topic which generated similar findings. According to USA Today, a survey of Food and Drug Administration scientists by Public Employees for Environmental Responsibility
and the Union of Concerned Scientists found that many scientists have
been pressured to approve or reject new drugs despite their scientific
findings concerns.
In July 2006, the Union of Concerned Scientists released survey results
that they said "demonstrate pervasive political influence of science"
at the Food and Drug Administration.
On May 1, 2007, deputy assistant secretary at the United States Department of the InteriorJulie MacDonald
resigned after the Interior Department Inspector General, Honorable
Earl E. Devaney, reported that MacDonald broke federal rules by giving
non-public, internal government documents to oil industry and property
rights groups, and manipulated scientific findings to favor Bush policy
goals and assist land developers.
On November 29, 2007, another report by Devaney found that MacDonald
could have also benefitted financially from a decision she was involved
with to remove the Sacramento splittail fish from the federal endangered species list.
MacDonald's conduct violated the Code of Federal Regulations (CFR) under 5 C.F.R. § 2635.703, Use of nonpublic information, and 5 C.F.R. § 2635.101, Basic obligation of public service.
MacDonald resigned a week before a House congressional oversight
committee was to hold a hearing on accusations that she had "violated
the Endangered Species Act, censored science and mistreated staff of the
U.S. Fish and Wildlife Service."
Climate change
In December 2007, the Christian Science Monitor reported that at least since 2003, and especially after Hurricane Katrina, the George W. Bush administration broadly attempted to control which climate scientists could speak with reporters, as well as edited scientists' congressional testimony on climate science and key legal opinions.
Those who have studied organizations that set up to delay action and
manufacture uncertainty about the well-established scientific consensus
have divided their tactics into three steps: first, deny that there is a
problem, second, make the case that there are benefits involved, and,
third, insist that there is nothing that can be done.
In a study, "The legitimacy of environmental scientists in the
public sphere" by Gordon Gauchat, Timothy O'Brien, and Oriol Mirosa, the
researchers conclude that attitudes about environmental scientists as
policy advisers are highly politicized. Their results demonstrate that,
to be perceived by the public as a reputable policy advisor, the
public's perception of their integrity and understanding weigh more
strongly than their agreement with scientific consensus.
Waxman report
In August 2003, United States, Democratic Congressman Henry A. Waxman and the staff of the Government Reform Committee released a report concluding that the administration of George W. Bush had politicized science and sex education.
The report accuses the administration of modifying performance measures
for abstinence-based programs to make them look more effective. The
report also found that the Bush administration had appointed Dr. Joseph
McIlhaney, a prominent advocate of abstinence-only program, to the
Advisory Committee to the director of the Centers for Disease Control. According to the report, information about comprehensive sex education was removed from the CDC's website.
Other issues considered for removal included agricultural pollution, the Arctic National Wildlife Refuge and breast cancer; the report found that a National Cancer Institute website has been changed to reflect the administration view that there may be a risk of breast cancer associated with abortions. The website was updated after protests and now holds that no such risk has been found in recent, well-designed studies.
The abortion-breast cancer hypothesis is the belief that induced abortions increase the risk of developing breast cancer.
This belief is in contrast to the scientific consensus that there is no
evidence suggesting that abortions can cause breast cancer. Despite the scientific community rejecting the hypothesis, many anti-abortion
advocates continue to argue that a link between abortions and breast
cancer exists, in an effort to influence public policy and opinion to
further restrict abortions and discourage women from having abortions. While historically a controversial hypothesis, the debate now is almost entirely political rather than scientific.
The most notable example of the politicization of this topic was
the modification of the National Cancer Institute (NCI) fact sheet by
the George W. Bush administration from concluding no link to a more
ambiguous assessment regarding the abortion-breast cancer hypothesis, despite the NCI's scientifically based assessment to the contrary.
United States House Science Subcommittee on Oversight
In January 2007, the U.S. House Committee on Science, Space and Technology announced the formation of a new subcommittee, the Science Subcommittee on Oversight, which handles investigative and oversight activities on matters covering the committee's entire jurisdiction.
The subcommittee has authority to look into a whole range of important
issues, particularly those concerning manipulation of scientific data at
Federal agencies.
In an interview, subcommittee chairman Rep. Brad Miller pledged
to investigate scientific integrity concerns under the Bush
Administration. Miller noted that there were multiple reports in the
media of the Bush Administration's manipulation of science to advance
his political agenda, corrupt advisory panels, and minimize scientific
research with federal funds. Miller, as part of the House Committee of
Science and Technology, collected evidence of interference with
scientific integrity by Bush's political appointees.
The
Trump administration marginalized the role of science in policy making,
halted numerous research projects, and saw the departure of scientists
who said their work was marginalized or suppressed. It was the first administration since 1941 not to name a Science Advisor to the President. In July 2018, Trump nominated meteorologist Kelvin Droegemeier for the position, and Droegemeier was confirmed by the Senate on January 2, 2019, the final day of the 115th United States Congress. He was sworn in by Vice President Mike Pence on February 11, 2019. While preparing for talks with Kim Jong-un, the White House did so without the assistance of a White House science adviser or senior counselor trained in nuclear physics.
The position of chief scientist in the State Department or the
Department of Agriculture was not filled. The administration nominated Sam Clovis to be chief scientist in the United States Department of Agriculture, but he had no scientific background and the White House later withdrew the nomination. The United States Department of the Interior, the National Oceanic and Atmospheric Administration, and the Food and Drug Administration disbanded advisory committees.
Climate change
Global warming
The people that gave you global warming are the same people that gave you ObamaCare!
Tweet of Donald Trump Nov. 23, 2013
The issue of politicized science surfaced during the 2016 United States presidential campaign by then Republican candidate Donald Trump. Trump stated his intention to strip NASA's
Earth Science division of its funding, a move that "would mean the
elimination of NASA's world-renowned research into temperature, ice,
clouds and other climate phenomena". Subsequently, the Trump administration successfully nominated Jim Bridenstine, who had no background in science and rejected the scientific consensus on climate change, to lead NASA. Under the Trump administration, the Department of Energy prohibited the use of the term "climate change". In March 2020 The New York Times
reported that an official at the Interior Department has repeatedly
inserted climate change-denying language into the agency's scientific
reports, such as those that affect water and mineral rights.
Health
During the 2020 COVID-19 pandemic, the Trump administration replaced career public affairs staff at the Department of Health and Human Services with political appointees, including Michael Caputo, who interfered with weekly Centers for Disease Control scientific reports and attempted to silence the government's most senior infectious disease expert, Anthony Fauci,
"sowing distrust of the FDA at a time when health leaders desperately
need people to accept a vaccine in order to create the immunity
necessary to defeat the novel coronavirus."
One day after President Donald Trump noted that he might dismiss an FDA
proposal to improve standards for emergency use of a coronavirus
vaccine, the Presidents of the National Academies
of Sciences and Medicine issued a statement expressing alarm at
political interference in science during a pandemic, "particularly the
overriding of evidence and advice from public health officials and
derision of government scientists".
The administration reportedly sent a list to the CDC on words that the agency was prohibited from using in its official communications, including "transgender", "fetus", "evidence-based", "science-based", "vulnerable", "entitlement", and "diversity". The Director of the CDC denied these reports.
Biden administration
As part of an effort to "refresh and reinvigorate our national science and technology strategy," President-elect Joe Biden announced, before taking office, that he will elevate the role of Director of the Office of Science and Technology Policy to a cabinet level position.
The
politicization of science is a subset of a broader topic, the politics
of science, which has been studied by scholars in a variety of fields,
including most notably Science and Technology Studies; history of science;
political science; and the sociology of science, knowledge, and
technology. Increasingly in recent decades, these fields have examined
the process through which science and technology are shaped. Some of the
scholarly work in this area is reviewed in The Handbook of Science & Technology Studies (1995, 2008), a collection of literature reviews published by the Society for Social Studies of Science.
There is an annual award for books relevant to the politics of science
given by the Society for Social Studies of Science called the Rachel Carson Prize.