Matter wave

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

Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. At all scales where measurements have been practical, matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave.

The concept that matter behaves like a wave was proposed by French physicist Louis de Broglie (/dəˈbrɔɪ/) in 1924, and so matter waves are also known as de Broglie waves.

The de Broglie wavelength is the wavelength, λ, associated with a particle with momentum p through the Planck constant, h: $${\displaystyle \lambda =\frac{h}{p}.}$$

Wave-like behavior of matter has been experimentally demonstrated, first for electrons in 1927 (independently by Davisson and Germer and George Thomson) and later for other elementary particles, neutral atoms and molecules.

Matter waves have more complex velocity relations than solid objects and they also differ from electromagnetic waves (light). Collective matter waves are used to model phenomena in solid state physics; standing matter waves are used in molecular chemistry.

Matter wave concepts are widely used in the study of materials where different wavelength and interaction characteristics of electrons, neutrons, and atoms are leveraged for advanced microscopy and diffraction technologies.

History

Background

At the end of the 19th century, light was thought to consist of waves of electromagnetic fields which propagated according to Maxwell's equations, while matter was thought to consist of localized particles (see history of wave and particle duality). In 1900, this division was questioned when, investigating the theory of black-body radiation, Max Planck proposed that the thermal energy of oscillating atoms is divided into discrete portions, or quanta. Extending Planck's investigation in several ways, including its connection with the photoelectric effect, Albert Einstein proposed in 1905 that light is also propagated and absorbed in quanta, now called photons. These quanta would have an energy given by the Planck–Einstein relation: $${\displaystyle E=h\nu }$$ and a momentum vector ${\displaystyle \mathbf{p}}$ $${\displaystyle \left|\mathbf{p}\right|=p=\frac{E}{c}=\frac{h}{\lambda },}$$ where ν (lowercase Greek letter nu) and λ (lowercase Greek letter lambda) denote the frequency and wavelength of the light, c the speed of light, and h the Planck constant. In the modern convention, frequency is symbolized by f as is done in the rest of this article. Einstein's postulate was verified experimentally by K. T. Compton and O. W. Richardson and by A. L. Hughes in 1912 then more carefully including a measurement of the Planck constant in 1916 by Robert Millikan.

De Broglie hypothesis

Propagation of de Broglie waves in one dimension – real part of the complex amplitude is blue, imaginary part is green. The probability (shown as the color opacity) of finding the particle at a given point x is spread out like a waveform; there is no definite position of the particle. As the amplitude increases above zero the slope decreases, so the amplitude diminishes again, and vice versa. The result is an alternating amplitude: a wave. Top: plane wave. Bottom: wave packet.

When I conceived the first basic ideas of wave mechanics in 1923–1924, I was guided by the aim to perform a real physical synthesis, valid for all particles, of the coexistence of the wave and of the corpuscular aspects that Einstein had introduced for photons in his theory of light quanta in 1905.

— de Broglie

De Broglie, in his 1924 PhD thesis, proposed that just as light has both wave-like and particle-like properties, electrons also have wave-like properties. His thesis started from the hypothesis, "that to each portion of energy with a proper mass m₀ one may associate a periodic phenomenon of the frequency ν₀, such that one finds: hν₀ = m₀c². The frequency ν₀ is to be measured, of course, in the rest frame of the energy packet. This hypothesis is the basis of our theory." (This frequency is also known as Compton frequency.)

To find the wavelength equivalent to a moving body, de Broglie set the total energy from special relativity for that body equal to hν: $${\displaystyle E=\frac{m{c}^2}{\sqrt{1-\frac{v^2}{c^2}}}=h\nu }$$

(Modern physics no longer uses this form of the total energy; the energy–momentum relation has proven more useful.) De Broglie identified the velocity of the particle, ${\displaystyle v}$, with the wave group velocity in free space: $${\displaystyle v_{\text{g}}\equiv \frac{\mathrm{\partial }\omega }{\mathrm{\partial }k}=\frac{d\nu }{d(1/\lambda )}}$$

(The modern definition of group velocity uses angular frequency ω and wave number k). By applying the differentials to the energy equation and identifying the relativistic momentum: $${\displaystyle p=\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}}}$$

then integrating, de Broglie arrived at his formula for the relationship between the wavelength, λ, associated with an electron and the modulus of its momentum, p, through the Planck constant, h: $${\displaystyle \lambda =\frac{h}{p}.}$$

Schrödinger's (matter) wave equation

Following up on de Broglie's ideas, physicist Peter Debye made an offhand comment that if particles behaved as waves, they should satisfy some sort of wave equation. Inspired by Debye's remark, Erwin Schrödinger decided to find a proper three-dimensional wave equation for the electron. He was guided by William Rowan Hamilton's analogy between mechanics and optics (see Hamilton's optico-mechanical analogy), encoded in the observation that the zero-wavelength limit of optics resembles a mechanical system – the trajectories of light rays become sharp tracks that obey Fermat's principle, an analog of the principle of least action.

In 1926, Schrödinger published the wave equation that now bears his name – the matter wave analogue of Maxwell's equations – and used it to derive the energy spectrum of hydrogen. Frequencies of solutions of the non-relativistic Schrödinger equation differ from de Broglie waves by the Compton frequency since the energy corresponding to the rest mass of a particle is not part of the non-relativistic Schrödinger equation. The Schrödinger equation describes the time evolution of a wavefunction, a function that assigns a complex number to each point in space. Schrödinger tried to interpret the modulus squared of the wavefunction as a charge density. This approach was, however, unsuccessful. Max Born proposed that the modulus squared of the wavefunction is instead a probability density, a successful proposal now known as the Born rule.

Position space probability density of an initially Gaussian state moving in one dimension at minimally uncertain, constant momentum in free space

The following year, 1927, C. G. Darwin (grandson of the famous biologist Charles Darwin) explored Schrödinger's equation in several idealized scenarios. For an unbound electron in free space he worked out the propagation of the wave, assuming an initial Gaussian wave packet. Darwin showed that at time ${\displaystyle t}$ later the position ${\displaystyle x}$ of the packet traveling at velocity ${\displaystyle v}$ would be $${\displaystyle x_0+vt\pm \sqrt{{\sigma }^2+{\left(\frac{ht}{2\pi \sigma m}\right)}^2},}$$ where ${\displaystyle \sigma }$ is the uncertainty in the initial position. This position uncertainty creates uncertainty in velocity (the extra second term in the square root) consistent with Heisenberg's uncertainty relation. The wave packet spreads out as shown in the figure.

Experimental confirmation

In 1927, matter waves were first experimentally confirmed to occur in George Paget Thomson and Alexander Reid's diffraction experiment and the Davisson–Germer experiment, both for electrons.

Original electron diffraction camera made and used by Nobel laureate G P Thomson and his student Alexander Reid in 1925

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

The de Broglie hypothesis and the existence of matter waves has been confirmed for other elementary particles, neutral atoms and even molecules have been shown to be wave-like.

The first electron wave interference patterns directly demonstrating wave–particle duality used electron biprisms (essentially a wire placed in an electron microscope) and measured single electrons building up the diffraction pattern. A close copy of the famous double-slit experiment using electrons through physical apertures gave the movie shown.

Matter wave double slit diffraction pattern building up electron by electron. Each white dot represents a single electron hitting a detector; with a statistically large number of electrons interference fringes appear.

Electrons

Further information: Davisson–Germer experiment and Electron diffraction

In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow-moving electrons at a crystalline nickel target. The diffracted electron intensity was measured, and was determined to have a similar angular dependence to diffraction patterns predicted by Bragg for x-rays. At the same time George Paget Thomson and Alexander Reid at the University of Aberdeen were independently firing electrons at thin celluloid foils and later metal films, observing rings which can be similarly interpreted. (Alexander Reid, who was Thomson's graduate student, performed the first experiments but he died soon after in a motorcycle accident and is rarely mentioned.) Before the acceptance of the de Broglie hypothesis, diffraction was a property that was thought to be exhibited only by waves. Therefore, the presence of any diffraction effects by matter demonstrated the wave-like nature of matter. The matter wave interpretation was placed onto a solid foundation in 1928 by Hans Bethe, who solved the Schrödinger equation, showing how this could explain the experimental results. His approach is similar to what is used in modern electron diffraction approaches.

This was a pivotal result in the development of quantum mechanics. Just as the photoelectric effect demonstrated the particle nature of light, these experiments showed the wave nature of matter.

Neutrons

See also: Neutron diffraction

Neutrons, produced in nuclear reactors with kinetic energy of around 1 MeV, thermalize to around 0.025 eV as they scatter from light atoms. The resulting de Broglie wavelength (around 180 pm) matches interatomic spacing and neutrons scatter strongly from hydrogen atoms. Consequently, neutron matter waves are used in crystallography, especially for biological materials. Neutrons were discovered in the early 1930s, and their diffraction was observed in 1936. In 1944, Ernest O. Wollan, with a background in X-ray scattering from his PhD work under Arthur Compton, recognized the potential for applying thermal neutrons from the newly operational X-10 nuclear reactor to crystallography. Joined by Clifford G. Shull, they developed neutron diffraction throughout the 1940s. In the 1970s, a neutron interferometer demonstrated the action of gravity in relation to wave–particle duality. The double-slit experiment was performed using neutrons in 1988.

Atoms

Interference of atom matter waves was first observed by Immanuel Estermann and Otto Stern in 1930, when a Na beam was diffracted off a surface of NaCl. The short de Broglie wavelength of atoms prevented progress for many years until two technological breakthroughs revived interest: microlithography allowing precise small devices and laser cooling allowing atoms to be slowed, increasing their de Broglie wavelength. The double-slit experiment on atoms was performed in 1991.

Advances in laser cooling allowed cooling of neutral atoms down to nanokelvin temperatures. At these temperatures, the de Broglie wavelengths come into the micrometre range. Using Bragg diffraction of atoms and a Ramsey interferometry technique, the de Broglie wavelength of cold sodium atoms was explicitly measured and found to be consistent with the temperature measured by a different method.

Molecules

Recent experiments confirm the relations for molecules and even macromolecules that otherwise might be supposed too large to undergo quantum mechanical effects. In 1999, a research team in Vienna demonstrated diffraction for molecules as large as fullerenes. The researchers calculated a de Broglie wavelength of the most probable C₆₀ velocity as 2.5 pm. More recent experiments prove the quantum nature of molecules made of 810 atoms and with a mass of 10,123 Da. As of 2019, this has been pushed to molecules of 25,000 Da.

In these experiments the build-up of such interference patterns could be recorded in real time and with single molecule sensitivity. Large molecules are already so complex that they give experimental access to some aspects of the quantum-classical interface, i.e., to certain decoherence mechanisms.

Others

Matter waves have been detected in van der Waals molecules, rho mesons, and Bose-Einstein condensate.

Traveling matter waves

Waves have more complicated concepts for velocity than solid objects. The simplest approach is to focus on the description in terms of plane matter waves for a free particle, that is a wave function described by $${\displaystyle \psi (\mathbf{r})=e^{i\mathbf{k}\cdot \mathbf{r}-i\omega t},}$$ where ${\displaystyle \mathbf{r}}$ is a position in real space, ${\displaystyle \mathbf{k}}$ is the wave vector in units of inverse meters, ω is the angular frequency with units of inverse time and ${\displaystyle t}$ is time. (Here the physics definition for the wave vector is used, which is ${\displaystyle 2\pi }$ times the wave vector used in crystallography, see wavevector.) The de Broglie equations relate the wavelength λ to the modulus of the momentum ${\displaystyle |\mathbf{p}|=p}$, and frequency f to the total energy E of a free particle as written above:$${\displaystyle \begin{array}{rl}& \lambda =\frac{2\pi }{|\mathbf{k}|}=\frac{h}{p}\\ & f=\frac{\omega }{2\pi }=\frac{E}{h}\end{array}}$$ where h is the Planck constant. The equations can also be written as $${\displaystyle \begin{array}{rl}& \mathbf{p}=\hslash \mathbf{k}\\ & E=\hslash \omega .\end{array}}$$ Here, ħ = h/2π is the reduced Planck constant. The second equation is also referred to as the Planck–Einstein relation.

Group velocity

In the de Broglie hypothesis, the velocity of a particle equals the group velocity of the matter wave. In isotropic media or a vacuum the group velocity of a wave is defined by: $${\displaystyle {\mathbf{v}}_{\mathbf{g}}=\frac{\mathrm{\partial }\omega (\mathbf{k})}{\mathrm{\partial }\mathbf{k}}}$$ The relationship between the angular frequency and wavevector is called the dispersion relationship. For the non-relativistic case this is: $${\displaystyle \omega (\mathbf{k})\approx \frac{m_0{c}^2}{\hslash }+\frac{\hslash k^2}{2m_0},}$$ where ${\displaystyle m_0}$ is the rest mass. Applying the derivative gives the (non-relativistic) matter wave group velocity: $${\displaystyle {\mathbf{v}}_{\mathbf{g}}=\frac{\hslash \mathbf{k}}{m_0}.}$$ For comparison, the group velocity of light, with a dispersion ${\displaystyle \omega (k)=ck}$, is the speed of light ${\displaystyle c}$.

As an alternative, using the relativistic dispersion relationship for matter waves $${\displaystyle \omega (\mathbf{k})=\sqrt{k^2{c}^2+{\left(\frac{m_0{c}^2}{\hslash }\right)}^2},}$$ then $${\displaystyle {\mathbf{v}}_{\mathbf{g}}=\frac{\mathbf{k}{c}^2}{\omega }.}$$ This relativistic form relates to the phase velocity as discussed below.

For non-isotropic media we use the Energy–momentum form instead: $${\displaystyle \begin{array}{rl}{\mathbf{v}}_{\mathrm{g}}& =\frac{\mathrm{\partial }\omega }{\mathrm{\partial }\mathbf{k}}=\frac{\mathrm{\partial }(E/\hslash )}{\mathrm{\partial }(\mathbf{p}/\hslash )}=\frac{\mathrm{\partial }E}{\mathrm{\partial }\mathbf{p}}=\frac{\mathrm{\partial }}{\mathrm{\partial }\mathbf{p}}\left(\sqrt{p^2{c}^2+m_0^2{c}^4}\right)\\ & =\frac{\mathbf{p}{c}^2}{\sqrt{p^2{c}^2+m_0^2{c}^4}}\\ & =\frac{\mathbf{p}{c}^2}{E}.\end{array}}$$

But (see below), since the phase velocity is ${\displaystyle {\mathbf{v}}_{\mathrm{p}}=E/\mathbf{p}=c^2/\mathbf{v}}$, then $${\displaystyle \begin{array}{rl}{\mathbf{v}}_{\mathrm{g}}& =\frac{\mathbf{p}{c}^2}{E}\\ & =\frac{c^2}{{\mathbf{v}}_{\mathrm{p}}}\\ & =\mathbf{v},\end{array}}$$ where ${\displaystyle \mathbf{v}}$ is the velocity of the center of mass of the particle, identical to the group velocity.

Phase velocity

The phase velocity in isotropic media is defined as: $${\displaystyle {\mathbf{v}}_{\mathbf{p}}=\frac{\omega }{\mathbf{k}}}$$ Using the relativistic group velocity above:$${\displaystyle {\mathbf{v}}_{\mathbf{p}}=\frac{c^2}{{\mathbf{v}}_{\mathbf{g}}}}$$ This shows that ${\displaystyle {\mathbf{v}}_{\mathbf{p}}\cdot {\mathbf{v}}_{\mathbf{g}}=c^2}$ as reported by R.W. Ditchburn in 1948 and J. L. Synge in 1952. Electromagnetic waves also obey ${\displaystyle {\mathbf{v}}_{\mathbf{p}}\cdot {\mathbf{v}}_{\mathbf{g}}=c^2}$, as both ${\displaystyle |{\mathbf{v}}_{\mathbf{p}}|=c}$ and ${\displaystyle |{\mathbf{v}}_{\mathbf{g}}|=c}$. Since for matter waves, ${\displaystyle |{\mathbf{v}}_{\mathbf{g}}|<c}$, it follows that ${\displaystyle |{\mathbf{v}}_{\mathbf{p}}|>c}$, but only the group velocity carries information. The superluminal phase velocity therefore does not violate special relativity, as it does not carry information.

For non-isotropic media, then $${\displaystyle {\mathbf{v}}_{\mathrm{p}}=\frac{\omega }{\mathbf{k}}=\frac{E/\hslash }{\mathbf{p}/\hslash }=\frac{E}{\mathbf{p}}.}$$

Using the relativistic relations for energy and momentum yields $${\displaystyle {\mathbf{v}}_{\mathrm{p}}=\frac{E}{\mathbf{p}}=\frac{m{c}^2}{m\mathbf{v}}=\frac{\gamma m_0{c}^2}{\gamma m_0\mathbf{v}}=\frac{c^2}{\mathbf{v}}.}$$ The variable ${\displaystyle \mathbf{v}}$ can either be interpreted as the speed of the particle or the group velocity of the corresponding matter wave—the two are the same. Since the particle speed ${\displaystyle |\mathbf{v}|<c}$ for any particle that has nonzero mass (according to special relativity), the phase velocity of matter waves always exceeds c, i.e., $${\displaystyle |{\mathbf{v}}_{\mathrm{p}}|>c,}$$ which approaches c when the particle speed is relativistic. The superluminal phase velocity does not violate special relativity, similar to the case above for non-isotropic media. See the article on Dispersion (optics) for further details.

Special relativity

Using two formulas from special relativity, one for the relativistic mass energy and one for the relativistic momentum $${\displaystyle \begin{array}{rl}E& =m{c}^2=\gamma m_0{c}^2\\ \mathbf{p}& =m\mathbf{v}=\gamma m_0\mathbf{v}\end{array}}$$ allows the equations for de Broglie wavelength and frequency to be written as $${\displaystyle \begin{array}{rl}& \lambda =\frac{h}{\gamma m_{0}v}=\frac{h}{m_{0}v}\sqrt{1-\frac{v^2}{c^2}}\\ & f=\frac{\gamma m_0{c}^2}{h}=\frac{m_0{c}^2}{h\sqrt{1-\frac{v^2}{c^2}}},\end{array}}$$ where ${\displaystyle v=|\mathbf{v}|}$ is the velocity, ${\displaystyle \gamma }$ the Lorentz factor, and ${\displaystyle c}$ the speed of light in vacuum. This shows that as the velocity of a particle approaches zero (rest) the de Broglie wavelength approaches infinity.

Four-vectors

Main article: Four-vector

Using four-vectors, the de Broglie relations form a single equation: $${\displaystyle \mathbf{P}=\hslash \mathbf{K},}$$ which is frame-independent. Likewise, the relation between group/particle velocity and phase velocity is given in frame-independent form by: $${\displaystyle \mathbf{K}=\left(\frac{{\omega }_0}{c^2}\right)\mathbf{U},}$$ where

• Four-momentum ${\displaystyle \mathbf{P}=\left(\frac{E}{c},\mathbf{p}\right)}$
• Four-wavevector ${\displaystyle \mathbf{K}=\left(\frac{\omega }{c},\mathbf{k}\right)}$
• Four-velocity ${\displaystyle \mathbf{U}=\gamma (c,\mathbf{u})=\gamma (c,v_{\mathrm{g}}\hat{\mathbf{u}})}$

General matter waves

The preceding sections refer specifically to free particles for which the wavefunctions are plane waves. There are significant numbers of other matter waves, which can be broadly split into three classes: single-particle matter waves, collective matter waves and standing waves.

Single-particle matter waves

The more general description of matter waves corresponding to a single particle type (e.g. a single electron or neutron only) would have a form similar to $${\displaystyle \psi (\mathbf{r})=u(\mathbf{r},\mathbf{k})\exp (i\mathbf{k}\cdot \mathbf{r}-iE(\mathbf{k})t/\hslash )}$$ where now there is an additional spatial term ${\displaystyle u(\mathbf{r},\mathbf{k})}$ in the front, and the energy has been written more generally as a function of the wave vector. The various terms given before still apply, although the energy is no longer always proportional to the wave vector squared. A common approach is to define an effective mass which in general is a tensor ${\displaystyle m_{ij}^{\ast }}$ given by $${\displaystyle {m_{ij}^{\ast }}^{-1}=\frac{1}{{\hslash }^2}\frac{{\mathrm{\partial }}^{2}E}{\mathrm{\partial }{k}_i\mathrm{\partial }{k}_j}}$$ so that in the simple case where all directions are the same the form is similar to that of a free wave above.$${\displaystyle E(\mathbf{k})=\frac{{\hslash }^2{\mathbf{k}}^2}{2m^{\ast }}}$$In general the group velocity would be replaced by the probability current $${\displaystyle \mathbf{j}(\mathbf{r})=\frac{\hslash }{2mi}\left({\psi }^{\ast }(\mathbf{r})\mathrm{\nabla }\psi (\mathbf{r})-\psi (\mathbf{r})\mathrm{\nabla }{\psi }^{\ast }(\mathbf{r})\right)}$$ where ${\displaystyle \mathrm{\nabla }}$ is the del or gradient operator. The momentum would then be described using the kinetic momentum operator, $${\displaystyle \mathbf{p}=-i\hslash \mathrm{\nabla }}$$ The wavelength is still described as the inverse of the modulus of the wavevector, although measurement is more complex. There are many cases where this approach is used to describe single-particle matter waves:

• Bloch wave, which form the basis of much of band structure as described in Ashcroft and Mermin, and are also used to describe the diffraction of high-energy electrons by solids.
• Waves with angular momentum such as electron vortex beams.
• Evanescent waves, where the component of the wavevector in one direction is complex. These are common when matter waves are being reflected, particularly for grazing-incidence diffraction.

Collective matter waves

See also: List of quasiparticles

Other classes of matter waves involve more than one particle, so are called collective waves and are often quasiparticles. Many of these occur in solids – see Ashcroft and Mermin. Examples include:

• In solids, an electron quasiparticle is an electron where interactions with other electrons in the solid have been included. An electron quasiparticle has the same charge and spin as a "normal" (elementary particle) electron and, like a normal electron, it is a fermion. However, its effective mass can differ substantially from that of a normal electron. Its electric field is also modified, as a result of electric field screening.
• A hole is a quasiparticle which can be thought of as a vacancy of an electron in a state; it is most commonly used in the context of empty states in the valence band of a semiconductor. A hole has the opposite charge of an electron.
• A polaron is a quasiparticle where an electron interacts with the polarization of nearby atoms.
• An exciton is an electron and hole pair which are bound together.
• A Cooper pair is two electrons bound together so they behave as a single matter wave.

Standing matter waves

See also: Standing wave

Some trajectories of a particle in a box according to Newton's laws of classical mechanics (A), and matter waves (B–F). In (B–F), the horizontal axis is position, and the vertical axis is the real part (blue) and imaginary part (red) of the wavefunction. The states (B,C,D) are energy eigenstates, but (E,F) are not.

The third class are matter waves which have a wavevector, a wavelength and vary with time, but have a zero group velocity or probability flux. The simplest of these, similar to the notation above would be $${\displaystyle \cos (\mathbf{k}\cdot \mathbf{r}-\omega t)}$$ These occur as part of the particle in a box, and other cases such as in a ring. This can, and arguably should be, extended to many other cases. For instance, in early work de Broglie used the concept that an electron matter wave must be continuous in a ring to connect to the Bohr–Sommerfeld condition in the early approaches to quantum mechanics. In that sense atomic orbitals around atoms, and also molecular orbitals are electron matter waves.

Matter waves vs. electromagnetic waves (light)

Schrödinger applied Hamilton's optico-mechanical analogy to develop his wave mechanics for subatomic particles. Consequently, wave solutions to the Schrödinger equation share many properties with results of light wave optics. In particular, Kirchhoff's diffraction formula works well for electron optics and for atomic optics. The approximation works well as long as the electric fields change more slowly than the de Broglie wavelength. Macroscopic apparatus fulfill this condition; slow electrons moving in solids do not.

Beyond the equations of motion, other aspects of matter wave optics differ from the corresponding light optics cases.

Sensitivity of matter waves to environmental condition. Many examples of electromagnetic (light) diffraction occur in air under many environmental conditions. Obviously visible light interacts weakly with air molecules. By contrast, strongly interacting particles like slow electrons and molecules require vacuum: the matter wave properties rapidly fade when they are exposed to even low pressures of gas. With special apparatus, high velocity electrons can be used to study liquids and gases. Neutrons, an important exception, interact primarily by collisions with nuclei, and thus travel several hundred feet in air.

Dispersion. Light waves of all frequencies travel at the same speed of light while matter wave velocity varies strongly with frequency. The relationship between frequency (proportional to energy) and wavenumber or velocity (proportional to momentum) is called a dispersion relation. Light waves in a vacuum have linear dispersion relation between frequency: ${\displaystyle \omega =ck}$. For matter waves the relation is non-linear: $${\displaystyle \omega (k)\approx \frac{m_0{c}^2}{\hslash }+\frac{\hslash k^2}{2m_0}.}$$ This non-relativistic matter wave dispersion relation says the frequency in vacuum varies with wavenumber (${\displaystyle k=1/\lambda }$) in two parts: a constant part due to the de Broglie frequency of the rest mass (${\displaystyle \hslash {\omega }_0=m_0{c}^2}$) and a quadratic part due to kinetic energy. The quadratic term causes rapid spreading of wave packets of matter waves.

Coherence The visibility of diffraction features using an optical theory approach depends on the beam coherence, which at the quantum level is equivalent to a density matrix approach. As with light, transverse coherence (across the direction of propagation) can be increased by collimation. Electron optical systems use stabilized high voltage to give a narrow energy spread in combination with collimating (parallelizing) lenses and pointed filament sources to achieve good coherence. Because light at all frequencies travels the same velocity, longitudinal and temporal coherence are linked; in matter waves these are independent. For example, for atoms, velocity (energy) selection controls longitudinal coherence and pulsing or chopping controls temporal coherence.

Optically shaped matter waves Optical manipulation of matter plays a critical role in matter wave optics: "Light waves can act as refractive, reflective, and absorptive structures for matter waves, just as glass interacts with light waves." Laser light momentum transfer can cool matter particles and alter the internal excitation state of atoms.

Multi-particle experiments While single-particle free-space optical and matter wave equations are identical, multiparticle systems like coincidence experiments are not.

Applications of matter waves

The following subsections provide links to pages describing applications of matter waves as probes of materials or of fundamental quantum properties. In most cases these involve some method of producing travelling matter waves which initially have the simple form ${\displaystyle \exp (i\mathbf{k}\cdot \mathbf{r}-i\omega t)}$, then using these to probe materials.

As shown in the table below, matter wave mass ranges over 6 orders of magnitude and energy over 9 orders but the wavelengths are all in the picometre range, comparable to atomic spacings. (Atomic diameters range from 62 to 520 pm, and the typical length of a carbon–carbon single bond is 154 pm.) Reaching longer wavelengths requires special techniques like laser cooling to reach lower energies; shorter wavelengths make diffraction effects more difficult to discern. Therefore, many applications focus on material structures, in parallel with applications of electromagnetic waves, especially X-rays. Unlike light, matter wave particles may have mass, electric charge, magnetic moments, and internal structure, presenting new challenges and opportunities.

Various matter wave wavelengths

matter	mass	kinetic energy	wavelength	reference
Electron	1/1823 Da	54 eV	167 pm	Davisson–Germer experiment
Electron	1/1823 Da	5×104 eV	5 pm	Tonomura et al.
He atom, H2 molecule	4 Da		50 pm	Estermann and Stern
Neutron	1 Da	0.025 eV	181 pm	Wollan and Shull
Sodium atom	23 Da		20 pm	Moskowitz et al.
Helium	4 Da	0.065 eV	56 pm	Grisenti et al.
Na2	23 Da	0.00017 eV	459 pm	Chapman et al.
C60 fullerene	720 Da	0.2 eV	5 pm	Arndt et al.
C70 fullerene	841 Da	0.2 eV	2 pm	Brezger et al.
polypeptide, Gramicidin A	1860 Da		360 fm	Shayeghi et al.
functionalized oligoporphyrins	25000 Da	17 eV	53 fm	Fein et al.

Electrons

Electron diffraction patterns emerge when energetic electrons reflect or penetrate ordered solids; analysis of the patterns leads to models of the atomic arrangement in the solids.

They are used for imaging from the micron to atomic scale using electron microscopes, in transmission, using scanning, and for surfaces at low energies.

The measurements of the energy they lose in electron energy loss spectroscopy provides information about the chemistry and electronic structure of materials. Beams of electrons also lead to characteristic X-rays in energy dispersive spectroscopy which can produce information about chemical content at the nanoscale.

Quantum tunneling explains how electrons escape from metals in an electrostatic field at energies less than classical predictions allow: the matter wave penetrates of the work function barrier in the metal.

Scanning tunneling microscope leverages quantum tunneling to image the top atomic layer of solid surfaces.

Electron holography, the electron matter wave analog of optical holography, probes the electric and magnetic fields in thin films.

Neutrons

Neutron diffraction complements x-ray diffraction through the different scattering cross sections and sensitivity to magnetism.

Small-angle neutron scattering provides way to obtain structure of disordered systems that is sensitivity to light elements, isotopes and magnetic moments.

Neutron reflectometry is a neutron diffraction technique for measuring the structure of thin films.

Neutral atoms

Atom interferometers, similar to optical interferometers, measure the difference in phase between atomic matter waves along different paths.

Atom optics mimic many light optic devices, including mirrors, atom focusing zone plates.

Scanning helium microscopy uses He atom waves to image solid structures non-destructively.

Quantum reflection uses matter wave behavior to explain grazing angle atomic reflection, the basis of some atomic mirrors.

Quantum decoherence measurements rely on Rb atom wave interference.

Molecules

Quantum superposition revealed by interference of matter waves from large molecules probes the limits of wave–particle duality and quantum macroscopicity.

Matter-wave interfererometers generate nanostructures on molecular beams that can be read with nanometer accuracy and therefore be used for highly sensitive force measurements, from which one can deduce a plethora of properties of individualized complex molecules.

Serengeti

From Wikipedia, the free encyclopedia

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

An umbrella thorn silhouetted by the setting sun near Seronera Camp

The Serengeti (/ˌsɛrənˈɡɛti/ SERR-ən-GHET-ee) ecosystem is a geographical region in Africa, spanning the Mara and Arusha Regions of Tanzania. The protected area within the region includes approximately 30,000 km² (12,000 sq mi) of land, including the Serengeti National Park and several game reserves. The Serengeti hosts one of the world's largest land animal migration (in terms of total body weight), which helps secure it as one of the Seven Natural Wonders of Africa.

The Serengeti is also renowned for its large lion population and is one of the best places to observe prides in their natural environment. Approximately 70 large mammal and 500 bird species are found there. This high diversity is a function of diverse habitats, including riverine forests, swamps, kopjes, grasslands, and woodlands. Blue wildebeest, gazelles, zebras, and buffalos are some of the commonly found large mammals in the region. The Serengeti also contains the Serengeti District of Tanzania.

The name "Serengeti" is often said to be derived from the word "seringit" in the Maasai language, Maa, meaning "endless plains". This etymology does not appear in Maa dictionaries.

History

Map of Tanzania showing the country's national parks, including the Serengeti National Park

For eons, African wildlife have roamed freely across the vast rolling plains of the Serengeti, which was sparsely inhabited by humans. This changed when nomadic pastoralists of the Maasai began to migrate to the area in the early 1800s.

The Maasai, however, were struck by drought and disease. Thousands died in the 1880s from a cholera epidemic and in 1892 from smallpox. Making matters worse, their cattle were wiped out by Rinderpest (a bovine viral disease). Later in the 20th century the Tanzanian government re-settled the Maasai around the Ngorongoro Crater. Poaching, and the absence of fires (which had been caused by humans), allowed dense woodlands and thickets to develop over the next 30–50 years. Tsetse fly populations now prevented any significant human settlement in the area.

By the mid-1970s, wildebeest and Cape buffalo populations had recovered and were increasingly cropping the grass, reducing the amount of fuel available for fires. The reduced intensity of fires has allowed acacia to once again become established.

In the 21st century, mass rabies vaccination programmes for domestic dogs in the Serengeti have not only indirectly prevented hundreds of human deaths, but also protected wildlife species such as the endangered African wild dog.

Great migration

Migrating wildebeest.

Each year around the same time, the circular great wildebeest migration begins in the Ngorongoro Conservation Area of the southern Serengeti in Tanzania and loops clockwise through the Serengeti National Park and north towards the Masai Mara reserve in Kenya. This migration is naturally caused by the availability of grazing. The initial phase lasts from about January to March, when the calving season begins – a time when there is plenty of rain-ripened grass available for the 260,000 zebras that precede 1.7 million wildebeest and the following hundreds of thousands of other plains game, including around 470,000 gazelles.

Wildebeest crossing the river during the Serengeti migration.

During February, the wildebeest are on the short grass plains of the southeast part of the ecosystem, grazing and giving birth to approximately 500,000 calves in 2 to 3 weeks. Few calves are born ahead of time and of these, hardly any survive, largely because very young calves are more noticeable to predators when mixed with older calves from the previous year. As the rains end in May, the animals start moving northwest into the areas around the Grumeti River, where they typically remain until late June. The crossings of the Grumeti and Mara rivers beginning in July are a popular safari attraction because crocodiles are lying in wait. The herds arrive in Kenya in late July / August, where they stay for the rest of the dry season, except that the Thomson's and Grant's gazelles move only east/west. In early November, with the start of the short rains, the migration starts moving south again, to the short grass plains of the southeast, usually arriving in December in plenty of time for calving in February.

About 250,000 wildebeests die during the journey from Tanzania to the Maasai Mara National Reserve in southwestern Kenya, of 800 kilometres (500 mi). Death is usually from thirst, hunger, exhaustion, or predation, including by big cats.

Ecology

River and the Serengeti plains

The Serengeti has some of East Africa's finest game areas. Besides being known for the great migration, the Serengeti is also famous for its abundant large predators. The ecosystem is home to over 3,000 lions, 1,000 African leopards, and 7,700 to 8,700 spotted hyenas (Crocuta crocuta). The East African cheetah is also present in Serengeti.

African wild dogs are relatively scarce in much of the Serengeti. This is particularly true in places such as Serengeti National Park (where they became extinct in 1992), in which lions and spotted hyenas, predators that steal wild dog kills and are a direct cause of wild dog mortality, are abundant.

The Serengeti is also home to a diversity of grazers, including Cape buffalo, African elephant, warthog, Grant's gazelle, eland, waterbuck, and topi. The Serengeti can support this remarkable variety of grazers only because each species, even those closely related, has a different diet. For example, wildebeests prefer to consume shorter grasses, while plains zebras prefer taller grasses. Similarly, dik-diks eat the lowest leaves of a tree, impalas eat the leaves that are higher up, and giraffes eat leaves that are even higher.

Giraffes in Eastern Serengeti

The governments of Tanzania and Kenya maintain a number of protected areas, including national parks, conservation areas, and game reserves, that give legal protection to over 80 percent of the Serengeti. Despite this, the ecosystem is now just 60 per cent of its original size, due to human encroachment.

Near Lake Victoria, floodplains have developed from ancient lakebeds.

In the far northwest, acacia woodlands are replaced by broadleaved Terminalia-Combretum woodlands, caused by a change in geology. This area has the highest rainfall in the system and forms a refuge for the migrating ungulates at the end of the dry season.

Altitudes in the Serengeti range from 920 to 1,850 metres (3,020 to 6,070 ft) with mean temperatures varying from 15 to 25 °C (59 to 77 °F). Although the climate is usually warm and dry, rainfall occurs in two rainy seasons: March to May, and a shorter season in October and November. Rainfall amounts vary from a low of 508 millimetres (20 in) in the lee of the Ngorongoro highlands to a high of 1,200 millimetres (47 in) on the shores of Lake Victoria.

Lioness on a kopje, or rock outcropping

The area is also home to the Ngorongoro Conservation Area, which contains Ngorongoro Crater and the Olduvai Gorge, where some of the oldest hominin fossils have been found.

In media

• In 1993, soft rock artist Dan Fogelberg recorded a song titled "Serengeti Moon" for his studio album River of Souls. It is an African-themed love song about a couple making love underneath the Serengeti moon.
• Canadian guitarist Sonny Greenwich recorded a song titled "Serengeti" on his 1994 album Hymn to the Earth with vocals by Ernie Nelson.
• Serengeti, a six-episode BBC series, chronicles the life of some of the animals in the Serengeti.
• The 1982 song "Africa" by the American rock band Toto, originally released on their album Toto IV, includes a reference to the Serengeti. The song inaccurately describes Mount Kilimanjaro as "ris(ing) like Olympus above the Serengeti"; Kilimanjaro is actually located hundreds of miles to the east of the Serengeti.
• The American rock band the Grateful Dead included the track "Serengetti", an instrumental dual drum solo, on their 1978 album Shakedown Street, interrupting the disco and soft rock-inspired sound with a tribal jam.

Domain (biology)

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Domain_(biology) 

The hierarchy of biological classification's eight major taxonomic ranks. Life is divided into domains, which are subdivided into further groups. Intermediate minor rankings are not shown.

In biological taxonomy, a domain (/dəˈmeɪn/ or /doʊˈmeɪn/) (Latin: regio or dominium), also dominion, superkingdom, realm, or empire, is the highest taxonomic rank of all organisms taken together. It was introduced in the three-domain system of taxonomy devised by Carl Woese, Otto Kandler and Mark Wheelis in 1990.

According to the domain system, the tree of life consists of either three domains, Archaea, Bacteria, and Eukarya, or two domains, Archaea and Bacteria, with Eukarya included in Archaea. In the three-domain model, the first two are prokaryotes, single-celled microorganisms without a membrane-bound nucleus. All organisms that have a cell nucleus and other membrane-bound organelles are included in Eukarya and called eukaryotes.

Non-cellular life, most notably the viruses, is not included in this system. Alternatives to the three-domain system include the earlier two-empire system (with the empires Prokaryota and Eukaryota), and the eocyte hypothesis (with two domains of Bacteria and Archaea, with Eukarya included as a branch of Archaea).

Terminology

The term domain was proposed by Carl Woese, Otto Kandler, and Mark Wheelis (1990) in a three-domain system.

Development of the domain system

Carl Linnaeus made the classification "domain" popular in the famous taxonomy system he created in the middle of the eighteenth century. This system was further improved by the studies of Charles Darwin later on but could not classify bacteria easily, as they have very few observable features to compare to the other domains.

The mycologist Royall T. Moore proposed the similar term dominion (Lat. dominium) in 1974, but this was not widely adopted. His proposed system had three dominions: Virus, Prokaryota, and Eukaryota.

Carl Woese made a revolutionary breakthrough when, in 1977, he compared the nucleotide sequences of the 16s ribosomal RNA and discovered that the rank "domain" contained three branches, not two as scientists had previously thought. Initially, due to their physical similarities, Archaea and Bacteria were classified together and called "archaebacteria". However, scientists now know that these two domains are hardly similar and are internally distinctly different.

Characteristics of the three domains

A speculatively rooted tree for RNA genes, showing major branches Bacteria, Archaea, and Eukaryota

The three-domain tree and the eocyte hypothesis (two-domain tree), 2008.

Phylogenetic tree showing the relationship between the eukaryotes and other forms of life, 2006. Eukaryotes are colored red, archaea green, and bacteria blue.

Main article: Three-domain system

Each of these three domains contains unique ribosomal RNA. This forms the basis of the three-domain system. While the presence of a nuclear membrane differentiates the Eukarya from the Archaea and Bacteria, both of which lack a nuclear envelope, the Archaea and Bacteria are distinct from each other due to differences in the biochemistry of their cell membranes and RNA markers.

Archaea

Further information: Archaea

Archaea are prokaryotic cells, typically characterized by membrane lipids that are branched hydrocarbon chains attached to glycerol by ether linkages. The presence of these ether linkages in Archaea adds to their ability to withstand extreme temperatures and highly acidic conditions, but many archaea live in mild environments. Halophiles (organisms that thrive in highly salty environments) and hyperthermophiles (organisms that thrive in extremely hot environments) are examples of Archaea.

Archaea are relatively small. They range from 0.1 μm to 15 μm diameter and up to 200 μm long, about the size of bacteria and the mitochondria found in eukaryotic cells. Members of the genus Thermoplasma are the smallest Archaea.

Bacteria

Further information: Bacteria

Cyanobacteria and mycoplasmas are two examples of bacteria. Even though bacteria are prokaryotic cells like Archaea, their cell membranes are instead made of phospholipid bilayers, with none of the ether linkages that Archaea have. Internally, bacteria have different RNA structures in their ribosomes, hence they are grouped into a different category. In the two- and three-domain systems, this puts them into a separate domain.

There is a great deal of diversity in the domain Bacteria. That diversity is further confounded by the exchange of genes between different bacterial lineages. The occurrence of duplicate genes between otherwise distantly-related bacteria makes it nearly impossible to distinguish bacterial species, count the bacterial species on the Earth, or organize them into a tree-like structure (unless the structure includes cross-connections between branches, making it a "network" instead of a "tree").

Eukarya

Further information: Eukaryote

Members of the domain Eukarya—called eukaryotes—have membrane-bound organelles (including a nucleus containing genetic material) and are represented by five kingdoms: Plantae, Protozoa, Animalia, Chromista, and Fungi.

Exclusion of viruses and prions

Main article: Non-cellular life

Further information: Virus and Prion

The three-domain system includes no form of non-cellular life. Stefan Luketa proposed a five-dominion system in 2012, adding Prionobiota (acellular and without nucleic acid) and Virusobiota (acellular but with nucleic acid) to the traditional three domains.

Alternative classifications

Taxonomical root node	Two superdomains (controversial)	Two empires	Three domains	Five Dominiums	Five kingdoms	Six kingdoms	Eocyte hypothesis
Biota / Vitae / Life	Acytota / Aphanobionta non-cellular life			Virusobiota (Viruses, Viroids)
				Prionobiota (Prions)
	Cytota cellular life	Prokaryota / Procarya (Monera)	Bacteria	Bacteria	Monera	Eubacteria	Bacteria
			Archaea	Archaea		Archaebacteria	Archaea including eukaryotes
		Eukaryota / Eukarya			Protista
					Fungi
					Plantae
					Animalia

Alternative classifications of life include:

• The two-empire system or superdomain system, proposed by Mayr (1998), with top-level groupings of Prokaryota (or Monera) and Eukaryota.
• The eocyte hypothesis, proposed by Lake et al. (1984), which posits two domains, Bacteria and Archaea, with Eukaryota included as a subordinate clade branching from Archaea.

North American Man/Boy Love Association

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/North_American_Man/Boy_Love_Association 

 

North American Man/Boy Love Association

A NAMBLA logo. The capital M and lowercase b symbolize a man and a boy.
Founded	December 2, 1978
Founder	David Thorstad
Type	Unincorporated association
Focus	Pedophilia and pederasty activism
Location	New York City and San Francisco
Area served	North America
Method	Removing age-of-consent laws

The North American Man/Boy Love Association (NAMBLA, stylized as NAMbLA) is a pedophilia and pederasty advocacy organization in the United States. It works to abolish age-of-consent laws criminalizing adult sexual involvement with minors and campaigns for the release of men who have been jailed for sexual contacts with minors that did not involve what it considers coercion.

The group no longer holds regular national meetings, and as of the late 1990s—to avoid local police infiltration—the organization discouraged the formation of local chapters. Around 1995, an undercover detective discovered there were 1,100 people on the organization's rolls. NAMBLA was the largest group in International Pedophile and Child Emancipation (IPCE), an international pro-pedophile activist organization. Since then, the organization has dwindled to only a handful of people, with many members joining online pedophile networks, according to Xavier Von Erck, director of operations at the anti-pedophile organization Perverted-Justice. As of 2005, a newspaper report stated that NAMBLA was based in New York and San Francisco.

History

Events such as Anita Bryant's 1977 "Save Our Children" campaign and a police raid of a Toronto-area newspaper, The Body Politic, for publishing an article by Gerald Hannon sympathetic to "boy-love" set the stage for the founding of NAMBLA.

In December 1977, police raided a house in the Boston suburb Revere. Twenty-four men were arrested and indicted on over 100 felony counts of the statutory rape of boys aged eight to fifteen. Suffolk County district attorney Garrett H. Byrne found the men had used drugs and video games to lure the boys into a house, where they photographed them as they engaged in sexual activity. The men were members of a "sex ring"; Byrne said the arrest was "the tip of the iceberg". Commenting on this issue, Boston magazine described NAMBLA as "the most despised group of men in America", which was "founded mostly by eccentric, boy-loving leftists". The "Boston-Boise Committee", a gay rights organization, was formed in response to these events (which they termed the "Boston witch-hunt"), allegedly in order to promote solidarity amongst gay men, saying in an official leaflet that: "The closet is weak. There is strength in unity and openness." NAMBLA's founding was inspired by this organization. It was co-founded by gay-rights activist and socialist David Thorstad.

In 1982, a NAMBLA member was falsely linked to the disappearance of Etan Patz. Although the accusation was groundless, the negative publicity was disastrous to the organization. NAMBLA published a book A Witchhunt Foiled: The FBI vs. NAMBLA, which documented these events. In testimony before the United States Senate, NAMBLA was exonerated from criminal activities; it said, "It is the pedophile with no organized affiliations who is the real threat to children".

Mike Echols, the author of I Know My First Name Is Steven, infiltrated NAMBLA and recorded his observations in his book, which was published in 1991. Echols published the names, addresses and telephone numbers of eighty suspected NAMBLA members on his website, which led to death threats being made to people who were not members of the organization.

Onell R. Soto, a San Diego Union-Tribune writer, wrote in February 2005, "Law enforcement officials and mental health professionals say that while NAMBLA's membership numbers are small, the group has a dangerous ripple effect through the Internet by sanctioning the behavior of those who would abuse children".

ILGA controversy

Main article: ILGA consultative status controversy

In 1993, the International Lesbian and Gay Association (ILGA) achieved United Nations consultative status. NAMBLA's membership in ILGA drew heavy criticism and caused the suspension of ILGA. Many gay organizations called for the ILGA to dissolve ties with NAMBLA. Republican Senator Jesse Helms proposed a bill to withhold US$119 million in UN contributions until U.S. President Bill Clinton could certify that no UN agency grants any official status to organizations that condoned pedophilia. The bill was unanimously approved by Congress and signed into law by Clinton in April 1994.

In 1994, ILGA expelled NAMBLA—the first U.S.-based organization to be a member—as well as Vereniging Martijn and Project Truth, because they were judged to be "organizations with a predominant aim of supporting or promoting pedophilia". Although ILGA removed NAMBLA, the UN reversed its decision to grant ILGA special consultative status. Repeated attempts by ILGA to regain special status with the UN succeeded in 2006.

Partially in response to the NAMBLA situation, Gregory King of the Human Rights Campaign later said, "NAMBLA is not a gay organization ... they are not part of our community and we thoroughly reject their efforts to insinuate that pedophilia is an issue related to gay and lesbian civil rights". NAMBLA said, "man/boy love is by definition homosexual", that "the Western homosexual tradition from Socrates to Wilde to Gide ... [and] many non Western homo sexualities from New Guinea and Persia to the Zulu and the Japanese" were formed by pederasty, that "man/boy lovers are part of the gay movement and central to gay history and culture", and that "homosexuals denying that it is 'not gay' to be attracted to adolescent boys are just as ludicrous as heterosexuals saying it's 'not heterosexual' to be attracted to adolescent girls".

Curley v. NAMBLA

Main article: Curley v. NAMBLA

In 2000, a Boston couple, Robert and Barbara Curley, sued NAMBLA for the wrongful death of their son. According to the suit, defendants Charles Jaynes and Salvatore Sicari, who were convicted of murdering the Curleys' son Jeffrey, "stalked ... tortured, murdered and mutilated [his] body on or about October 1, 1997. Upon information and belief immediately prior to said acts, Charles Jaynes accessed NAMBLA's website at the Boston Public Library." The lawsuit said, "NAMBLA serves as a conduit for an underground network of pedophiles in the United States who use their NAMBLA association and contacts therein and the Internet to obtain and promote pedophile activity". Jaynes wrote in his diary, "This was a turning point in discovery of myself ... NAMBLA's Bulletin helped me to become aware of my own sexuality and acceptance of it ... ".

Citing cases in which NAMBLA members were convicted of sexual offenses against children, Larry Frisoli, the attorney representing the Curleys, said the organization is a "training ground" for adults who wish to seduce children, in which men exchange strategies to find and groom child sex partners. Frisoli also said NAMBLA has sold on its website "The Rape and Escape Manual", which gave details about the avoidance of capture and prosecution. The American Civil Liberties Union (ACLU) stepped in to defend NAMBLA as a free speech matter; it won a dismissal because NAMBLA is organized as an unincorporated association rather than a corporation. John Reinstein, director of the ACLU Massachusetts, said although NAMBLA "may extol conduct which is currently illegal", there was nothing on its website that "advocated or incited the commission of any illegal acts, including murder or rape".

A NAMBLA founder said the case would "break our backs, even if we win, which we will". Media reports from 2006 said that for practical purposes the group no longer exists and that it consists only of a website maintained by a few enthusiasts. The Curleys continued the suit as a wrongful death action against individual NAMBLA members, some of whom were active in the group's leadership. Targets of the wrongful death suits included NAMBLA co-founder David Thorstad. The lawsuit was dropped in April 2008 after a judge ruled that a key witness was not competent to testify.

Support

Allen Ginsberg, poet and father of the Beat Generation, was an affiliated member of NAMBLA. Claiming to have joined the organization "in defense of free speech", Ginsberg said: "Attacks on NAMBLA stink of politics, witchhunting for profit, humorlessness, vanity, anger and ignorance ... I'm a member of NAMBLA because I love boys too—everybody does, who has a little humanity". He appeared in Chicken Hawk: Men Who Love Boys, produced and directed by Adi Sideman, a documentary in which members of NAMBLA gave interviews and presented defenses of the organization.

Pat Califia argued that politics played an important role in the gay community's rejection of NAMBLA. Califia has since withdrawn much of his earlier support for the association while still maintaining that discussing an issue does not constitute criminal activity.

Camille Paglia, feminist academic and social critic, signed a manifesto supporting the group in 1993. In 1994, Paglia supported lowering the legal age of consent to fourteen. She noted in a 1995 interview with pro-pedophile activist Bill Andriette "I fail to see what is wrong with erotic fondling with any age." In a 1997 Salon column, Paglia expressed the view that male pedophilia correlates with the heights of a civilization, stating "I have repeatedly protested the lynch-mob hysteria that dogs the issue of man-boy love. In Sexual Personae, I argued that male pedophilia is intricately intertwined with the cardinal moments of Western civilization." Paglia noted in several interviews, as well as Sexual Personae, that she supports the legalization of certain forms of child pornography. She later had a change of heart on the matter. In an interview for Radio New Zealand's Saturday Morning show, conducted on April 28, 2018, by Kim Hill, Paglia was asked, "Are you a libertarian on the issue of pedophilia?", to which she replied

In terms of the present day, I think it's absolutely impossible to think we could reproduce the Athenian code of pedophilia, of boy-love, that was central to culture at that time. ... We must protect children, and I feel that very very strongly. The age of consent for sexual interactions between a boy and an older man is obviously disputed, at what point that should be. I used to think that fourteen (the way it is in some places in the world) was adequate. I no longer think that. I think young people need greater protection than that. ... This is one of those areas that we must confine to the realm of imagination and the history of the arts.

Feigned support

See also: Anti-LGBTQ rhetoric § Conflation with pedophilia, and Societal attitudes toward homosexuality § Association with child abuse and pedophilia

In a 2017 protest at Columbia University against Mike Cernovich, an unidentified individual raised a pro-pedophilia banner showing logos from NAMBLA and some leftist organizations (all denying knowledge of any such cooperation). Fact-checking organizations consider this a false flag operation as alt-right personalities were quick to repost the photo without caveat and because NAMBLA had largely ceased operation by 2016. A similar 4chan hoax in 2018 connected NAMBLA with TED, following a controversial TEDx presentation—notably unvetted by the TED organization—referring to pedophilia as an "unchangeable sexual orientation".

Opposition

The first documented opposition to NAMBLA from LGBTQ organizations occurred at the conference that organized the first gay march on Washington in 1979.

In 1980, a group called the Lesbian Caucus distributed a flyer urging women to split from the annual New York City Gay Pride March, because according to the group, the organizing committee had been dominated by NAMBLA and its supporters. The next year, after some lesbians threatened to picket, the Cornell University group Gay People at Cornell (Gay PAC) rescinded its invitation to NAMBLA co-founder David Thorstad to be the keynote speaker at the annual May Gay Festival. In the following years, gay rights groups tried to block NAMBLA's participation in gay pride parades, prompting leading gay rights figure Harry Hay to wear a sign proclaiming "NAMBLA walks with me" as he participated in a 1986 gay pride march in Los Angeles.^[42]

By the mid-1980s, NAMBLA was virtually alone in its positions and found itself politically isolated.^[43] Support for "groups perceived as being on the fringe of the gay community," such as NAMBLA, vanished in the process.^[43]

In 1994, Stonewall 25, a New York LGBTQ rights group, voted to ban NAMBLA from its international march on the United Nations in June of that year.^[44] The same year, NAMBLA was again banned from the march commemorating Stonewall. Instead, members of NAMBLA and the Gay Liberation Front formed their own competing march called "The Spirit of Stonewall". The Gay & Lesbian Alliance Against Defamation (GLAAD) adopted a document called "Position Statement Regarding NAMBLA", which said GLAAD "deplores the North American Man Boy Love Association's (NAMBLA) goals, which include advocacy for sex between adult men and boys and the removal of legal protections for children. These goals constitute a form of child abuse and are repugnant to GLAAD."

That year, the Board of Directors of the National Gay and Lesbian Task Force (NGLTF) adopted a resolution on NAMBLA that said, "NGLTF condemns all abuse of minors, both sexual and any other kind, perpetrated by adults. Accordingly, NGLTF condemns the organizational goals of NAMBLA and any other such organization."

In 2000 in New York, a teacher was fired for his association with NAMBLA. There were no criminal charges or complaints about his conduct in class.

In April 2013, the hacktivist group Anonymous prevented NAMBLA's website from being accessed as part of an operation dubbed "Operation Alice Day". The timing of the attack coincided with Alice Day, a Pedophilia Pride Day celebrated by a small group of pedophiles and their supporters on April 25.

Associated individuals

Allen Ginsberg was a member of NAMBLA

• Bill Andriette, journalist. He joined NAMBLA at the age of 15 and edited the NAMBLA Bulletin for six years.
• Allen Ginsberg was a defender of NAMBLA and a member.
• Harry Hay, prominent LGBTQ rights activist. Hay supported NAMBLA's inclusion in gay pride parades and publicly addressed their meetings in support of the organization.
• Alan J. Horowitz, MD, convicted sex offender, ordained Orthodox rabbi, and psychiatrist. He specialized in working with adolescents, graduated magna cum laude from Harvard University, and earned a Ph.D. and medical degree from Duke University. Infamous for being the subject of a worldwide manhunt, Horowitz was known as "NAMBLA Rabbi".
• David Thorstad, founding member.
• Walter Breen, convicted sex offender. He wrote a book, Greek Love, and published a journal, The International Journal of Greek Love, both under the pseudonym "J.Z. Eglinton". As "Eglinton", he spoke at NAMBLA's founding convention.

In popular culture

• In the South Park episode "Cartman Joins NAMBLA", which first aired on June 21, 2000, Eric Cartman is convinced to become a poster boy for the organization after befriending older men online.
• In the Law and Order: Special Victims Unit episode "Angels", which aired on November 1, 2002, the body of a battered young boy found in a luggage compartment of an airport shuttle bus sends the detectives to his guardian who was discovered to be a pedophile only to find his corpse in bed with his genitals removed. The subsequent investigation leads them to a travel agency specializing in exotic trips for sexual predators, some of whom were NAMBLA members.