Relativistic Doppler effect

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

Figure 1. A source of light waves moving to the right, relative to observers, with velocity 0.7c. The frequency is higher for observers on the right, and lower for observers on the left.

The relativistic Doppler effect is the change in frequency, wavelength and amplitude of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special theory of relativity.

The relativistic Doppler effect is different from the non-relativistic Doppler effect as the equations include the time dilation effect of special relativity and do not involve the medium of propagation as a reference point. They describe the total difference in observed frequencies and possess the required Lorentz symmetry.

Astronomers know of three sources of redshift/blueshift: Doppler shifts; gravitational redshifts (due to light exiting a gravitational field); and cosmological expansion (where space itself stretches). This article concerns itself only with Doppler shifts.

Summary of major results

In the following table, it is assumed that for ${\displaystyle \beta =v/c>0}$ the receiver and the source are moving away from each other, ${\displaystyle v}$ being the relative velocity and ${\displaystyle c}$ the speed of light, and $\gamma =1/\sqrt{1-{\beta }^2}$.

Scenario	Formula	Notes
Relativistic longitudinal Doppler effect	${\displaystyle \frac{{\lambda }_r}{{\lambda }_s}=\frac{f_s}{f_r}=\sqrt{\frac{1+\beta }{1-\beta }}}$
Transverse Doppler effect, geometric closest approach	${\displaystyle f_r=\gamma f_s}$	Blueshift
Transverse Doppler effect, visual closest approach	${\displaystyle f_r=\frac{f_s}{\gamma }}$	Redshift
TDE, receiver in circular motion around source	${\displaystyle f_r=\gamma f_s}$	Blueshift
TDE, source in circular motion around receiver	${\displaystyle f_r=\frac{f_s}{\gamma }}$	Redshift
TDE, source and receiver in circular motion around common center	${\displaystyle \frac{f^{\prime }}{f}={\left(\frac{1-R^2{\omega }^2}{1-R^{\prime 2}{\omega }^2}\right)}^{1/2}}$	No Doppler shift when ${\displaystyle R=R^{\prime }}$
Motion in arbitrary direction measured in receiver frame	${\displaystyle f_r=\frac{f_s}{\gamma \left(1+\beta \cos {\theta }_r\right)}}$
Motion in arbitrary direction measured in source frame	${\displaystyle f_r=\gamma \left(1-\beta \cos {\theta }_s\right)f_s}$

Derivation

Relativistic longitudinal Doppler effect

Relativistic Doppler shift for the longitudinal case, with source and receiver moving directly towards or away from each other, is often derived as if it were the classical phenomenon, but modified by the addition of a time dilation term. This is the approach employed in first-year physics or mechanics textbooks such as those by Feynman or Morin.

Following this approach towards deriving the relativistic longitudinal Doppler effect, assume the receiver and the source are moving away from each other with a relative speed ${\displaystyle v}$ as measured by an observer on the receiver or the source (The sign convention adopted here is that ${\displaystyle v}$ is negative if the receiver and the source are moving towards each other).

Consider the problem in the reference frame of the source.

Suppose one wavefront arrives at the receiver. The next wavefront is then at a distance ${\displaystyle {\lambda }_s=c/f_s}$ away from the receiver (where ${\displaystyle {\lambda }_s}$ is the wavelength, ${\displaystyle f_s}$ is the frequency of the waves that the source emits, and ${\displaystyle c}$ is the speed of light).

The wavefront moves with speed ${\displaystyle c}$, but at the same time the receiver moves away with speed ${\displaystyle v}$ during a time ${\displaystyle t_{r,s}}$, which is the period of light waves impinging on the receiver, as observed in the frame of the source. So,

$${\displaystyle {\lambda }_s+v{t}_{r,s}=c{t}_{r,s}⟺{\lambda }_s=c{t}_{r,s}(1-v/c)⟺t_{r,s}=\frac{1}{f_s(1-\beta )},}$$

where ${\displaystyle \beta =v/c}$ is the speed of the receiver in terms of the speed of light. The corresponding ${\displaystyle f_{r,s}}$, the frequency of at which wavefronts impinge on the receiver in the source's frame, is:

$${\displaystyle f_{r,s}=1/t_{r,s}=f_s(1-\beta ).}$$

Thus far, the equations have been identical to those of the classical Doppler effect with a stationary source and a moving receiver.

However, due to relativistic effects, clocks on the receiver are time dilated relative to clocks at the source: ${\displaystyle t_r=t_{r,s}/\gamma }$, where $\gamma =1/\sqrt{1-{\beta }^2}$ is the Lorentz factor. In order to know which time is dilated, we recall that ${\displaystyle t_{r,s}}$ is the time in the frame in which the source is at rest. The receiver will measure the received frequency to be

Eq. 1:    ${\displaystyle f_r=f_{r,s}\gamma }$ ${\displaystyle =\frac{1-\beta }{\sqrt{1-{\beta }^2}}{f}_s}$ ${\displaystyle =\sqrt{\frac{1-\beta }{1+\beta }}{f}_s.}$

The ratio

${\displaystyle \frac{f_s}{f_r}=\sqrt{\frac{1+\beta }{1-\beta }}}$

is called the Doppler factor of the source relative to the receiver. (This terminology is particularly prevalent in the subject of astrophysics: see relativistic beaming.)

The corresponding wavelengths are related by

Eq. 2:    ${\displaystyle \frac{{\lambda }_r}{{\lambda }_s}=\frac{f_s}{f_r}=\sqrt{\frac{1+\beta }{1-\beta }},}$

Identical expressions for relativistic Doppler shift are obtained when performing the analysis in the reference frame of the receiver with a moving source. This matches up with the expectations of the principle of relativity, which dictates that the result can not depend on which object is considered to be the one at rest. In contrast, the classic nonrelativistic Doppler effect is dependent on whether it is the source or the receiver that is stationary with respect to the medium.

Transverse Doppler effect

Suppose that a source and a receiver are both approaching each other in uniform inertial motion along paths that do not collide. The transverse Doppler effect (TDE) may refer to (a) the nominal blueshift predicted by special relativity that occurs when the emitter and receiver are at their points of closest approach; or (b) the nominal redshift predicted by special relativity when the receiver sees the emitter as being at its closest approach. The transverse Doppler effect is one of the main novel predictions of the special theory of relativity.

Whether a scientific report describes TDE as being a redshift or blueshift depends on the particulars of the experimental arrangement being related. For example, Einstein's original description of the TDE in 1907 described an experimenter looking at the center (nearest point) of a beam of "canal rays" (a beam of positive ions that is created by certain types of gas-discharge tubes). According to special relativity, the moving ions' emitted frequency would be reduced by the Lorentz factor, so that the received frequency would be reduced (redshifted) by the same factor.

On the other hand, Kündig (1963) described an experiment where a Mössbauer absorber was spun in a rapid circular path around a central Mössbauer emitter. As explained below, this experimental arrangement resulted in Kündig's measurement of a blueshift.

Source and receiver are at their points of closest approach

Figure 2. Source and receiver are at their points of closest approach. (a) Analysis in the frame of the receiver. (b) Analysis in the frame of the source.

In this scenario, the point of closest approach is frame-independent and represents the moment where there is no change in distance versus time. Figure 2 demonstrates that the ease of analyzing this scenario depends on the frame in which it is analyzed.

• Fig. 2a. If we analyze the scenario in the frame of the receiver, we find that the analysis is more complicated than it should be. The apparent position of a celestial object is displaced from its true position (or geometric position) because of the object's motion during the time it takes its light to reach an observer. The source would be time-dilated relative to the receiver, but the redshift implied by this time dilation would be offset by a blueshift due to the longitudinal component of the relative motion between the receiver and the apparent position of the source.
• Fig. 2b. It is much easier if, instead, we analyze the scenario from the frame of the source. An observer situated at the source knows, from the problem statement, that the receiver is at its closest point to him. That means that the receiver has no longitudinal component of motion to complicate the analysis. (i.e. dr/dt = 0 where r is the distance between receiver and source) Since the receiver's clocks are time-dilated relative to the source, the light that the receiver receives is blue-shifted by a factor of gamma. In other words,

Eq. 3:    ${\displaystyle f_r=\gamma f_s}$

Receiver sees the source as being at its closest point

Figure 3. Transverse Doppler shift for the scenario where the receiver sees the source as being at its closest point.

This scenario is equivalent to the receiver looking at a direct right angle to the path of the source. The analysis of this scenario is best conducted from the frame of the receiver. Figure 3 shows the receiver being illuminated by light from when the source was closest to the receiver, even though the source has moved on. Because the source's clock is time dilated as measured in the frame of the receiver, and because there is no longitudinal component of its motion, the light from the source, emitted from this closest point, is redshifted with frequency

Eq. 4:    ${\displaystyle f_r=\frac{f_s}{\gamma }}$

In the literature, most reports of transverse Doppler shift analyze the effect in terms of the receiver pointed at direct right angles to the path of the source, thus seeing the source as being at its closest point and observing a redshift.

Point of null frequency shift

Figure 4. Null frequency shift occurs for a pulse that travels the shortest distance from source to receiver.

Given that, in the case where the inertially moving source and receiver are geometrically at their nearest approach to each other, the receiver observes a blueshift, whereas in the case where the receiver sees the source as being at its closest point, the receiver observes a redshift, there obviously must exist a point where blueshift changes to a redshift. In Fig. 2, the signal travels perpendicularly to the receiver path and is blueshifted. In Fig. 3, the signal travels perpendicularly to the source path and is redshifted.

As seen in Fig. 4, null frequency shift occurs for a pulse that travels the shortest distance from source to receiver. When viewed in the frame where source and receiver have the same speed, this pulse is emitted perpendicularly to the source's path and is received perpendicularly to the receiver's path. The pulse is emitted slightly before the point of closest approach, and it is received slightly after.

One object in circular motion around the other

Figure 5. Transverse Doppler effect for two scenarios: (a) receiver moving in a circle around the source; (b) source moving in a circle around the receiver.

Fig. 5 illustrates two variants of this scenario. Both variants can be analyzed using simple time dilation arguments. Figure 5a is essentially equivalent to the scenario described in Figure 2b, and the receiver observes light from the source as being blueshifted by a factor of ${\displaystyle \gamma }$. Figure 5b is essentially equivalent to the scenario described in Figure 3, and the light is redshifted.

The only seeming complication is that the orbiting objects are in accelerated motion. An accelerated particle does not have an inertial frame in which it is always at rest. However, an inertial frame can always be found which is momentarily comoving with the particle. This frame, the momentarily comoving reference frame (MCRF), enables application of special relativity to the analysis of accelerated particles. If an inertial observer looks at an accelerating clock, only the clock's instantaneous speed is important when computing time dilation.

The converse, however, is not true. The analysis of scenarios where both objects are in accelerated motion requires a somewhat more sophisticated analysis. Not understanding this point has led to confusion and misunderstanding.

Source and receiver both in circular motion around a common center

Figure 6. Source and receiver are placed on opposite ends of a rotor, equidistant from the center.

Suppose source and receiver are located on opposite ends of a spinning rotor, as illustrated in Fig. 6. Kinematic arguments (special relativity) and arguments based on noting that there is no difference in potential between source and receiver in the pseudogravitational field of the rotor (general relativity) both lead to the conclusion that there should be no Doppler shift between source and receiver.

In 1961, Champeney and Moon conducted a Mössbauer rotor experiment testing exactly this scenario, and found that the Mössbauer absorption process was unaffected by rotation. They concluded that their findings supported special relativity.

This conclusion generated some controversy. A certain persistent critic of relativity maintained that, although the experiment was consistent with general relativity, it refuted special relativity, his point being that since the emitter and absorber were in uniform relative motion, special relativity demanded that a Doppler shift be observed. The fallacy with this critic's argument was, as demonstrated in section Point of null frequency shift, that it is simply not true that a Doppler shift must always be observed between two frames in uniform relative motion. Furthermore, as demonstrated in section Source and receiver are at their points of closest approach, the difficulty of analyzing a relativistic scenario often depends on the choice of reference frame. Attempting to analyze the scenario in the frame of the receiver involves much tedious algebra. It is much easier, almost trivial, to establish the lack of Doppler shift between emitter and absorber in the laboratory frame.

As a matter of fact, however, Champeney and Moon's experiment said nothing either pro or con about special relativity. Because of the symmetry of the setup, it turns out that virtually any conceivable theory of the Doppler shift between frames in uniform inertial motion must yield a null result in this experiment.

Rather than being equidistant from the center, suppose the emitter and absorber were at differing distances from the rotor's center. For an emitter at radius ${\displaystyle R^{\prime }}$ and the absorber at radius ${\displaystyle R}$ anywhere on the rotor, the ratio of the emitter frequency, ${\displaystyle f^{\prime },}$ and the absorber frequency, ${\displaystyle f,}$ is given by

Eq. 5:    ${\displaystyle \frac{f^{\prime }}{f}={\left(\frac{1-R^2{\omega }^2}{1-R^{\prime 2}{\omega }^2}\right)}^{1/2}}$

where ${\displaystyle \omega }$ is the angular velocity of the rotor. The source and emitter do not have to be 180° apart, but can be at any angle with respect to the center.

Motion in an arbitrary direction

Figure 7. Doppler shift with source moving at an arbitrary angle with respect to the line between source and receiver.

The analysis used in section Relativistic longitudinal Doppler effect can be extended in a straightforward fashion to calculate the Doppler shift for the case where the inertial motions of the source and receiver are at any specified angle. Fig. 7 presents the scenario from the frame of the receiver, with the source moving at speed ${\displaystyle v}$ at an angle ${\displaystyle {\theta }_r}$ measured in the frame of the receiver. The radial component of the source's motion along the line of sight is equal to ${\displaystyle v\cos {\theta }_r.}$

The equation below can be interpreted as the classical Doppler shift for a stationary and moving source modified by the Lorentz factor ${\displaystyle \gamma :}$

Eq. 6:    ${\displaystyle f_r=\frac{f_s}{\gamma \left(1+\beta \cos {\theta }_r\right)}.}$

In the case when ${\displaystyle {\theta }_r={90}^{\circ }}$, one obtains the transverse Doppler effect:

${\displaystyle f_r=\frac{f_s}{\gamma }.}$

In his 1905 paper on special relativity, Einstein obtained a somewhat different looking equation for the Doppler shift equation. After changing the variable names in Einstein's equation to be consistent with those used here, his equation reads

Eq. 7:    ${\displaystyle f_r=\gamma \left(1-\beta \cos {\theta }_s\right)f_s.}$

The differences stem from the fact that Einstein evaluated the angle ${\displaystyle {\theta }_s}$ with respect to the source rest frame rather than the receiver rest frame. ${\displaystyle {\theta }_s}$ is not equal to ${\displaystyle {\theta }_r}$ because of the effect of relativistic aberration. The relativistic aberration equation is:

Eq. 8:    ${\displaystyle \cos {\theta }_r=\frac{\cos {\theta }_s-\beta }{1-\beta \cos {\theta }_s}}$

Substituting the relativistic aberration equation Equation 8 into Equation 6 yields Equation 7, demonstrating the consistency of these alternate equations for the Doppler shift.

Setting ${\displaystyle {\theta }_r=0}$ in Equation 6 or ${\displaystyle {\theta }_s=0}$ in Equation 7 yields Equation 1, the expression for relativistic longitudinal Doppler shift.

A four-vector approach to deriving these results may be found in Landau and Lifshitz (2005).

In electromagetic waves both the electric and the magnetic field amplitudes E and B transform in a similar manner as the frequency:

${\displaystyle E_r=\gamma \left(1-\beta \cos {\theta }_s\right)E_s}$

${\displaystyle B_r=\gamma \left(1-\beta \cos {\theta }_s\right)B_s.}$

Visualization

Figure 8. Comparison of the relativistic Doppler effect (top) with the non-relativistic effect (bottom).

Fig. 8 helps us understand, in a rough qualitative sense, how the relativistic Doppler effect and relativistic aberration differ from the non-relativistic Doppler effect and non-relativistic aberration of light. Assume that the observer is uniformly surrounded in all directions by yellow stars emitting monochromatic light of 570 nm. The arrows in each diagram represent the observer's velocity vector relative to its surroundings, with a magnitude of 0.89 c.

• In the relativistic case, the light ahead of the observer is blueshifted to a wavelength of 137 nm in the far ultraviolet, while light behind the observer is redshifted to 2400 nm in the short wavelength infrared. Because of the relativistic aberration of light, objects formerly at right angles to the observer appear shifted forwards by 63°.
• In the non-relativistic case, the light ahead of the observer is blueshifted to a wavelength of 300 nm in the medium ultraviolet, while light behind the observer is redshifted to 5200 nm in the intermediate infrared. Because of the aberration of light, objects formerly at right angles to the observer appear shifted forwards by 42°.
• In both cases, the monochromatic stars ahead of and behind the observer are Doppler-shifted towards invisible wavelengths. If, however, the observer had eyes that could see into the ultraviolet and infrared, he would see the stars ahead of him as brighter and more closely clustered together than the stars behind, but the stars would be far brighter and far more concentrated in the relativistic case.

Real stars are not monochromatic, but emit a range of wavelengths approximating a black body distribution. It is not necessarily true that stars ahead of the observer would show a bluer color. This is because the whole spectral energy distribution is shifted. At the same time that visible light is blueshifted into invisible ultraviolet wavelengths, infrared light is blueshifted into the visible range. Precisely what changes in the colors one sees depends on the physiology of the human eye and on the spectral characteristics of the light sources being observed.

Doppler effect on intensity

Further information: Black-body radiation § Doppler effect

The Doppler effect (with arbitrary direction) also modifies the perceived source intensity: this can be expressed concisely by the fact that source strength divided by the cube of the frequency is a Lorentz invariant. This implies that the total radiant intensity (summing over all frequencies) is multiplied by the fourth power of the Doppler factor for frequency.

As a consequence, since Planck's law describes the black-body radiation as having a spectral intensity in frequency proportional to ${\displaystyle \frac{f^3}{e^{\frac{hf}{kT}}-1}}$ (where ${\displaystyle T}$ is the source temperature and ${\displaystyle f}$ the frequency), we can draw the conclusion that a black body spectrum seen through a Doppler shift (with arbitrary direction) is still a black body spectrum with a temperature multiplied by the same Doppler factor as frequency.

This result provides one of the pieces of evidence that serves to distinguish the Big Bang theory from alternative theories proposed to explain the cosmological redshift.

Experimental verification

Main article: Ives–Stilwell-, Mössbauer rotor-, and Spectroscopy tests of time dilation

Since the transverse Doppler effect is one of the main novel predictions of the special theory of relativity, the detection and precise quantification of this effect has been an important goal of experiments attempting to validate special relativity.

Ives and Stilwell-type measurements

Figure 9. Why it is difficult to measure the transverse Doppler effect accurately using a transverse beam.

Einstein (1907) had initially suggested that the TDE might be measured by observing a beam of "canal rays" at right angles to the beam. Attempts to measure TDE following this scheme proved it to be impractical, since the maximum speed of particle beam available at the time was only a few thousandths of the speed of light.

Fig. 9 shows the results of attempting to measure the 4861 Angstrom line emitted by a beam of canal rays (a mixture of H1+, H2+, and H3+ ions) as they recombine with electrons stripped from the dilute hydrogen gas used to fill the Canal ray tube. Here, the predicted result of the TDE is a 4861.06 Angstrom line. On the left, longitudinal Doppler shift results in broadening the emission line to such an extent that the TDE cannot be observed. The middle figures illustrate that even if one narrows one's view to the exact center of the beam, very small deviations of the beam from an exact right angle introduce shifts comparable to the predicted effect.

Rather than attempt direct measurement of the TDE, Ives and Stilwell (1938) used a concave mirror that allowed them to simultaneously observe a nearly longitudinal direct beam (blue) and its reflected image (red). Spectroscopically, three lines would be observed: An undisplaced emission line, and blueshifted and redshifted lines. The average of the redshifted and blueshifted lines would be compared with the wavelength of the undisplaced emission line. The difference that Ives and Stilwell measured corresponded, within experimental limits, to the effect predicted by special relativity.

Various of the subsequent repetitions of the Ives and Stilwell experiment have adopted other strategies for measuring the mean of blueshifted and redshifted particle beam emissions. In some recent repetitions of the experiment, modern accelerator technology has been used to arrange for the observation of two counter-rotating particle beams. In other repetitions, the energies of gamma rays emitted by a rapidly moving particle beam have been measured at opposite angles relative to the direction of the particle beam. Since these experiments do not actually measure the wavelength of the particle beam at right angles to the beam, some authors have preferred to refer to the effect they are measuring as the "quadratic Doppler shift" rather than TDE.

Direct measurement of transverse Doppler effect

The advent of particle accelerator technology has made possible the production of particle beams of considerably higher energy than was available to Ives and Stilwell. This has enabled the design of tests of the transverse Doppler effect directly along the lines of how Einstein originally envisioned them, i.e. by directly viewing a particle beam at a 90° angle. For example, Hasselkamp et al. (1979) observed the Hα line emitted by hydrogen atoms moving at speeds ranging from 2.53×10⁸ cm/s to 9.28×10⁸ cm/s, finding the coefficient of the second order term in the relativistic approximation to be 0.52±0.03, in excellent agreement with the theoretical value of 1/2.

Other direct tests of the TDE on rotating platforms were made possible by the discovery of the Mössbauer effect, which enables the production of exceedingly narrow resonance lines for nuclear gamma ray emission and absorption. Mössbauer effect experiments have proven themselves easily capable of detecting TDE using emitter-absorber relative velocities on the order of 2×10⁴ cm/s. These experiments include ones performed by Hay et al. (1960), Champeney et al. (1965), and Kündig (1963).

Time dilation measurements

The transverse Doppler effect and the kinematic time dilation of special relativity are closely related. All validations of TDE represent validations of kinematic time dilation, and most validations of kinematic time dilation have also represented validations of TDE. An online resource, "What is the experimental basis of Special Relativity?" has documented, with brief commentary, many of the tests that, over the years, have been used to validate various aspects of special relativity. Kaivola et al. (1985) and McGowan et al. (1993) are examples of experiments classified in this resource as time dilation experiments. These two also represent tests of TDE. These experiments compared the frequency of two lasers, one locked to the frequency of a neon atom transition in a fast beam, the other locked to the same transition in thermal neon. The 1993 version of the experiment verified time dilation, and hence TDE, to an accuracy of 2.3×10⁻⁶.

Relativistic Doppler effect for sound and light

Figure 10. The relativistic Doppler shift formula is applicable to both sound and light.

First-year physics textbooks almost invariably analyze Doppler shift for sound in terms of Newtonian kinematics, while analyzing Doppler shift for light and electromagnetic phenomena in terms of relativistic kinematics. This gives the false impression that acoustic phenomena requires a different analysis than light and radio waves.

The traditional analysis of the Doppler effect for sound represents a low speed approximation to the exact, relativistic analysis. The fully relativistic analysis for sound is, in fact, equally applicable to both sound and electromagnetic phenomena.

Consider the spacetime diagram in Fig. 10. Worldlines for a tuning fork (the source) and a receiver are both illustrated on this diagram. The tuning fork and receiver start at O, at which point the tuning fork starts to vibrate, emitting waves and moving along the negative x-axis while the receiver starts to move along the positive x-axis. The tuning fork continues until it reaches A, at which point it stops emitting waves: a wavepacket has therefore been generated, and all the waves in the wavepacket are received by the receiver with the last wave reaching it at B. The proper time for the duration of the packet in the tuning fork's frame of reference is the length of OA while the proper time for the duration of the wavepacket in the receiver's frame of reference is the length of OB. If ${\displaystyle n}$ waves were emitted, then ${\displaystyle f_s=\frac{n}{|OA|}}$, while ${\displaystyle f_r=\frac{n}{|OB|}}$; the inverse slope of AB represents the speed of signal propagation (i.e. the speed of sound) to event B. We can therefore write:

${\displaystyle c_s=\frac{x_B-x_A}{t_B-t_A}}$ (speed of sound)

${\displaystyle v_s=-\frac{x_A}{t_A}}$        ${\displaystyle v_r=\frac{x_B}{t_B}}$      (speeds of source and receiver)

${\displaystyle |OA|=\sqrt{t_A^2-(x_A/c{)}^2}}$

${\displaystyle |OB|=\sqrt{t_B^2-(x_B/c{)}^2}}$

${\displaystyle v_s}$ and ${\displaystyle v_r}$ are assumed to be less than ${\displaystyle c_s,}$ since otherwise their passage through the medium will set up shock waves, invalidating the calculation. Routine algebra gives the ratio of frequencies:

Eq. 9:    ${\displaystyle \frac{f_r}{f_s}=\frac{|OA|}{|OB|}}$ ${\displaystyle =\frac{1-v_r/c_s}{1+v_s/c_s}\sqrt{\frac{1-(v_s/c{)}^2}{1-(v_r/c{)}^2}}}$

If ${\displaystyle v_r}$ and ${\displaystyle v_s}$ are small compared with ${\displaystyle c}$, the above equation reduces to the classical Doppler formula for sound.

If the speed of signal propagation ${\displaystyle c_s}$ approaches ${\displaystyle c}$, it can be shown that the absolute speeds ${\displaystyle v_s}$ and ${\displaystyle v_r}$ of the source and receiver merge into a single relative speed independent of any reference to a fixed medium. Indeed, we obtain Equation 1, the formula for relativistic longitudinal Doppler shift.

Analysis of the spacetime diagram in Fig. 10 gave a general formula for source and receiver moving directly along their line of sight, i.e. in collinear motion.

Figure 11. A source and receiver are moving in different directions and speeds in a frame where the speed of sound is independent of direction.

Fig. 11 illustrates a scenario in two dimensions. The source moves with velocity ${\displaystyle {\mathbf{v}}_{\mathbf{s}}}$ (at the time of emission). It emits a signal which travels at velocity ${\displaystyle \mathbf{C}}$ towards the receiver, which is traveling at velocity ${\displaystyle {\mathbf{v}}_{\mathbf{r}}}$ at the time of reception. The analysis is performed in a coordinate system in which the signal's speed ${\displaystyle |\mathbf{C}|}$ is independent of direction.

The ratio between the proper frequencies for the source and receiver is

Eq. 10:    ${\displaystyle \frac{f_r}{f_s}=\frac{1-\frac{|{\mathbf{v}}_{\mathbf{r}}|}{\mathbf{|}\mathbf{C}\mathbf{|}}\cos ({\theta }_{\mathbf{C}\mathbf{,}{\mathbf{v}}_{\mathbf{r}}})}{1-\frac{|{\mathbf{v}}_{\mathbf{s}}|}{\mathbf{|}\mathbf{C}\mathbf{|}}\cos ({\theta }_{\mathbf{C}\mathbf{,}{\mathbf{v}}_{\mathbf{s}}})}\sqrt{\frac{1-(v_s/c{)}^2}{1-(v_r/c{)}^2}}}$

The leading ratio has the form of the classical Doppler effect, while the square root term represents the relativistic correction. If we consider the angles relative to the frame of the source, then ${\displaystyle v_s=0}$ and the equation reduces to Equation 7, Einstein's 1905 formula for the Doppler effect. If we consider the angles relative to the frame of the receiver, then ${\displaystyle v_r=0}$ and the equation reduces to Equation 6, the alternative form of the Doppler shift equation discussed previously.

Schadenfreude

From Wikipedia, the free encyclopedia

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

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

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

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

Etymology

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

Psychological causes

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

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

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

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

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

Synonyms

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

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

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

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

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

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

Related emotions or concepts

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

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

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

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

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

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

Neologisms and variants

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

Literary usage and philosophical analysis

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

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

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

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

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

During the seventeenth century, Robert Burton wrote:

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

— The Anatomy of Melancholy

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

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

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

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

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

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

Scientific studies

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

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

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

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

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

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

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

Mental health in education

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

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

Primary school children in classroom

Prevalence of mental health issues in adolescents

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

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

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

Common disorder's effects on academics and school life

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

Anxiety

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

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

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

Depression

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

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

Attention deficit hyperactivity disorder

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

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

Other common struggles for adolescents

Alcoholism

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

Suicide

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

Reaching Out For Help

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

Covid-19 and mental health

Early Covid-19 Predictions

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

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

Current Covid-19 Effects

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

Policies in public schools

United States

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

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

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

Canada

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

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

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

Bhutan

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

Gross national happiness

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

United Kingdom

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

Singapore

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

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

Mexico

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

Japan and China

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

South Korea

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

Alleviation and fostering adjustment

Prevention

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

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

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

Belonging

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

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