title: Planck's law

text: Planck's law describes the unique and characteristic spectral distribution for electromagnetic radiation in thermodynamic equilibrium, when there is no net flow of matter or energy. Its physics is most easily understood by considering the radiation in a cavity with rigid opaque walls. Motion of the walls can affect the radiation. If the walls are not opaque, then the thermodynamic equilibrium is not isolated. It is of interest to explain how the thermodynamic equilibrium is attained. There are two main cases: (a) when the approach to thermodynamic equilibrium is in the presence of matter, when the walls of the cavity are imperfectly reflective for every wavelength or when the walls are perfectly reflective while the cavity contains a small black body (this was the main case considered by Planck); or (b) when the approach to equilibrium is in the absence of matter, when the walls are perfectly reflective for all wavelengths and the cavity contains no matter. For matter not enclosed in such a cavity, thermal radiation can be approximately explained by appropriate use of Planck's law.


title: Planck's law

text: Classical physics led, via the equipartition theorem, to the ultraviolet catastrophe, a prediction that the total blackbody radiation intensity was infinite. If supplemented by the classically unjustifiable assumption that for some reason the radiation is finite, classical thermodynamics provides an account of some aspects of the Planck distribution, such as the Stefan–Boltzmann law, and the Wien displacement law. For the case of the presence of matter, quantum mechanics provides a good account, as found below in the section headed Einstein coefficients. This was the case considered by Einstein, and is nowadays used for quantum optics. For the case of the absence of matter, quantum field theory is necessary, because non-relativistic quantum mechanics with fixed particle numbers does not provide a sufficient account.


title: Planck's law

text: Quantum theoretical explanation of Planck's law views the radiation as a gas of massless, uncharged, bosonic particles, namely photons, in thermodynamic equilibrium. Photons are viewed as the carriers of the electromagnetic interaction between electrically charged elementary particles. Photon numbers are not conserved. Photons are created or annihilated in the right numbers and with the right energies to fill the cavity with the Planck distribution. For a photon gas in thermodynamic equilibrium, the internal energy density is entirely determined by the temperature; moreover, the pressure is entirely determined by the internal energy density. This is unlike the case of thermodynamic equilibrium for material gases, for which the internal energy is determined not only by the temperature, but also, independently, by the respective numbers of the different molecules, and independently again, by the specific characteristics of the different molecules. For different material gases at given temperature, the pressure and internal energy density can vary independently, because different molecules can carry independently different excitation energies.


title: Planck's law

text: Planck's law arises as a limit of the Bose–Einstein distribution, the energy distribution describing non-interactive bosons in thermodynamic equilibrium. In the case of massless bosons such as photons and gluons, the chemical potential is zero and the Bose–Einstein distribution reduces to the Planck distribution. There is another fundamental equilibrium energy distribution: the Fermi–Dirac distribution, which describes fermions, such as electrons, in thermal equilibrium. The two distributions differ because multiple bosons can occupy the same quantum state, while multiple fermions cannot. At low densities, the number of available quantum states per particle is large, and this difference becomes irrelevant. In the low density limit, the Bose–Einstein and the Fermi–Dirac distribution each reduce to the Maxwell–Boltzmann distribution.


title: Planck's law

text: Kirchhoff's law of thermal radiation is a succinct and brief account of a complicated physical situation. The following is an introductory sketch of that situation, and is very far from being a rigorous physical argument. The purpose here is only to summarize the main physical factors in the situation, and the main conclusions.


title: Planck's law

text: There is a difference between conductive heat transfer and radiative heat transfer. Radiative heat transfer can be filtered to pass only a definite band of radiative frequencies.


title: Planck's law

text: In a cavity in an opaque body with rigid walls that are not perfectly reflective at any frequency, in thermodynamic equilibrium, there is only one temperature, and it must be shared in common by the radiation of every frequency.


title: Planck's law

text: One may imagine two such cavities, each in its own isolated radiative and thermodynamic equilibrium. One may imagine an optical device that allows radiative heat transfer between the two cavities, filtered to pass only a definite band of radiative frequencies. If the values of the spectral radiances of the radiations in the cavities differ in that frequency band, heat may be expected to pass from the hotter to the colder. One might propose to use such a filtered transfer of heat in such a band to drive a heat engine. If the two bodies are at the same temperature, the second law of thermodynamics does not allow the heat engine to work. It may be inferred that for a temperature common to the two bodies, the values of the spectral radiances in the pass-band must also be common. This must hold for every frequency band. This became clear to Balfour Stewart and later to Kirchhoff. Balfour Stewart found experimentally that of all surfaces, one of lamp-black emitted the greatest amount of thermal radiation for every quality of radiation, judged by various filters.


title: Planck's law

text: Thinking theoretically, Kirchhoff went a little further, and pointed out that this implied that the spectral radiance, as a function of radiative frequency, of any such cavity in thermodynamic equilibrium must be a unique universal function of temperature. He postulated an ideal black body that interfaced with its surrounds in just such a way as to absorb all the radiation that falls on it. By the Helmholtz reciprocity principle, radiation from the interior of such a body would pass unimpeded, directly to its surrounds without reflection at the interface. In thermodynamic equilibrium, the thermal radiation emitted from such a body would have that unique universal spectral radiance as a function of temperature. This insight is the root of Kirchhoff's law of thermal radiation.


title: Planck's law

text: One may imagine a small homogeneous spherical material body labeled at a temperature , lying in a radiation field within a large cavity with walls of material labeled at a temperature . The body emits its own thermal radiation. At a particular frequency , the radiation emitted from a particular cross-section through the centre of in one sense in a direction normal to that cross-section may be denoted , characteristically for the material of . At that frequency , the radiative power from the walls into that cross-section in the opposite sense in that direction may be denoted , for the wall temperature . For the material of , defining the absorptivity as the fraction of that incident radiation absorbed by , that incident energy is absorbed at a rate .


title: Planck's law

text: The rate of accumulation of energy in one sense into the cross-section of the body can then be expressed


title: Planck's law

text: Kirchhoff's seminal insight, mentioned just above, was that, at thermodynamic equilibrium at temperature , there exists a unique universal radiative distribution, nowadays denoted , that is independent of the chemical characteristics of the materials and , that leads to a very valuable understanding of the radiative exchange equilibrium of any body at all, as follows.


title: Planck's law

text: When there is thermodynamic equilibrium at temperature , the cavity radiation from the walls has that unique universal value, so that . Further, one may define the emissivity of the material of the body just so that at thermodynamic equilibrium at temperature , one has .


title: Planck's law

text: When thermal equilibrium prevails at temperature , the rate of accumulation of energy vanishes so that . It follows that in thermodynamic equilibrium, when ,


title: Planck's law

text: Introducing the special notation for the absorptivity of material at thermodynamic equilibrium at temperature (justified by a discovery of Einstein, as indicated below), one further has the equality


title: Planck's law

text: The equality of absorptivity and emissivity here demonstrated is specific for thermodynamic equilibrium at temperature and is in general not to be expected to hold when conditions of thermodynamic equilibrium do not hold. The emissivity and absorptivity are each separately properties of the molecules of the material but they depend differently upon the distributions of states of molecular excitation on the occasion, because of a phenomenon known as "stimulated emission", that was discovered by Einstein. On occasions when the material is in thermodynamic equilibrium or in a state known as local thermodynamic equilibrium, the emissivity and absorptivity become equal. Very strong incident radiation or other factors can disrupt thermodynamic equilibrium or local thermodynamic equilibrium. Local thermodynamic equilibrium in a gas means that molecular collisions far outweigh light emission and absorption in determining the distributions of states of molecular excitation.


title: Planck's law

text: Kirchhoff pointed out that he did not know the precise character of , but he thought it important that it should be found out. Four decades after Kirchhoff's insight of the general principles of its existence and character, Planck's contribution was to determine the precise mathematical expression of that equilibrium distribution .


title: Planck's law

text: In physics, one considers an ideal black body, here labeled , defined as one that completely absorbs all of the electromagnetic radiation falling upon it at every frequency (hence the term "black"). According to Kirchhoff's law of thermal radiation, this entails that, for every frequency , at thermodynamic equilibrium at temperature , one has , so that the thermal radiation from a black body is always equal to the full amount specified by Planck's law. No physical body can emit thermal radiation that exceeds that of a black body, since if it were in equilibrium with a radiation field, it would be emitting more energy than was incident upon it.


title: Planck's law

text: Though perfectly black materials do not exist, in practice a black surface can be accurately approximated. As to its material interior, a body of condensed matter, liquid, solid, or plasma, with a definite interface with its surroundings, is completely black to radiation if it is completely opaque. That means that it absorbs all of the radiation that penetrates the interface of the body with its surroundings, and enters the body. This is not too difficult to achieve in practice. On the other hand, a perfectly black interface is not found in nature. A perfectly black interface reflects no radiation, but transmits all that falls on it, from either side. The best practical way to make an effectively black interface is to simulate an 'interface' by a small hole in the wall of a large cavity in a completely opaque rigid body of material that does not reflect perfectly at any frequency, with its walls at a controlled temperature. Beyond these requirements, the component material of the walls is unrestricted. Radiation entering the hole has almost no possibility of escaping the cavity without being absorbed by multiple impacts with its walls.


title: Planck's law

text: As explained by Planck, a radiating body has an interior consisting of matter, and an interface with its contiguous neighbouring material medium, which is usually the medium from within which the radiation from the surface of the body is observed. The interface is not composed of physical matter but is a theoretical conception, a mathematical two-dimensional surface, a joint property of the two contiguous media, strictly speaking belonging to neither separately. Such an interface can neither absorb nor emit, because it is not composed of physical matter; but it is the site of reflection and transmission of radiation, because it is a surface of discontinuity of optical properties. The reflection and transmission of radiation at the interface obey the Stokes–Helmholtz reciprocity principle.


title: Planck's law

text: At any point in the interior of a black body located inside a cavity in thermodynamic equilibrium at temperature the radiation is homogeneous, isotropic and unpolarized. A black body absorbs all and reflects none of the electromagnetic radiation incident upon it. According to the Helmholtz reciprocity principle, radiation from the interior of a black body is not reflected at its surface, but is fully transmitted to its exterior. Because of the isotropy of the radiation in the body's interior, the spectral radiance of radiation transmitted from its interior to its exterior through its surface is independent of direction.


title: Planck's law

text: This is expressed by saying that radiation from the surface of a black body in thermodynamic equilibrium obeys Lambert's cosine law. This means that the spectral flux from a given infinitesimal element of area of the actual emitting surface of the black body, detected from a given direction that makes an angle with the normal to the actual emitting surface at , into an element of solid angle of detection centred on the direction indicated by , in an element of frequency bandwidth , can be represented as


title: Planck's law

text: where denotes the flux, per unit area per unit frequency per unit solid angle, that area would show if it were measured in its normal direction .


title: Planck's law

text: The factor is present because the area to which the spectral radiance refers directly is the projection, of the actual emitting surface area, onto a plane perpendicular to the direction indicated by . This is the reason for the name "cosine law".


title: Planck's law

text: Taking into account the independence of direction of the spectral radiance of radiation from the surface of a black body in thermodynamic equilibrium, one has and so


title: Planck's law

text: Thus Lambert's cosine law expresses the independence of direction of the spectral radiance of the surface of a black body in thermodynamic equilibrium.


title: Planck's law

text: The total power emitted per unit area at the surface of a black body () may be found by integrating the black body spectral flux found from Lambert's law over all frequencies, and over the solid angles corresponding to a hemisphere () above the surface.


title: Planck's law

text: The equation of radiative transfer describes the way in which radiation is affected as it travels through a material medium. For the special case in which the material medium is in thermodynamic equilibrium in the neighborhood of a point in the medium, Planck's law is of special importance.


title: Planck's law

text: For simplicity, we can consider the linear steady state, without scattering. The equation of radiative transfer states that for a beam of light going through a small distance , energy is conserved: The change in the (spectral) radiance of that beam () is equal to the amount removed by the material medium plus the amount gained from the material medium. If the radiation field is in equilibrium with the material medium, these two contributions will be equal. The material medium will have a certain emission coefficient and absorption coefficient.


title: Planck's law

text: The absorption coefficient is the fractional change in the intensity of the light beam as it travels the distance , and has units of length. It is composed of two parts, the decrease due to absorption and the increase due to stimulated emission. Stimulated emission is emission by the material body which is caused by and is proportional to the incoming radiation. It is included in the absorption term because, like absorption, it is proportional to the intensity of the incoming radiation. Since the amount of absorption will generally vary linearly as the density of the material, we may define a "mass absorption coefficient" which is a property of the material itself. The change in intensity of a light beam due to absorption as it traverses a small distance will then be


title: Planck's law

text: The "mass emission coefficient" is equal to the radiance per unit volume of a small volume element divided by its mass (since, as for the mass absorption coefficient, the emission is proportional to the emitting mass) and has units of power⋅solid angle⋅frequency⋅density. Like the mass absorption coefficient, it too is a property of the material itself. The change in a light beam as it traverses a small distance will then be


title: Planck's law

text: If the radiation field is in equilibrium with the material medium, then the radiation will be homogeneous (independent of position) so that and:


title: Planck's law

text: which is another statement of Kirchhoff's law, relating two material properties of the medium, and which yields the radiative transfer equation at a point around which the medium is in thermodynamic equilibrium:


title: Planck's law

text: The principle of detailed balance states that, at thermodynamic equilibrium, each elementary process is equilibrated by its reverse process.


title: Planck's law

text: In 1916, Albert Einstein applied this principle on an atomic level to the case of an atom radiating and absorbing radiation due to transitions between two particular energy levels, giving a deeper insight into the equation of radiative transfer and Kirchhoff's law for this type of radiation. If level 1 is the lower energy level with energy , and level 2 is the upper energy level with energy , then the frequency of the radiation radiated or absorbed will be determined by Bohr's frequency condition:


title: Planck's law

text: If and are the number densities of the atom in states 1 and 2 respectively, then the rate of change of these densities in time will be due to three processes:


title: Planck's law

text: where is the spectral energy density of the radiation field. The three parameters , and , known as the Einstein coefficients, are associated with the photon frequency produced by the transition between two energy levels (states). As a result, each line in a spectra has its own set of associated coefficients. When the atoms and the radiation field are in equilibrium, the radiance will be given by Planck's law and, by the principle of detailed balance, the sum of these rates must be zero:


title: Planck's law

text: Since the atoms are also in equilibrium, the populations of the two levels are related by the Boltzmann factor:


title: Planck's law

text: where and are the multiplicities of the respective energy levels. Combining the above two equations with the requirement that they be valid at any temperature yields two relationships between the Einstein coefficients:


title: Planck's law

text: so that knowledge of one coefficient will yield the other two. For the case of isotropic absorption and emission, the emission coefficient () and absorption coefficient () defined in the radiative transfer section above, can be expressed in terms of the Einstein coefficients. The relationships between the Einstein coefficients will yield the expression of Kirchhoff's law expressed in the "Radiative transfer" section above, namely that


title: Planck's law

text: The reason for this is that, as mentioned above, one cannot go from (for example) to simply by substituting by . In addition, one must also multiply the result of the substitution by


title: Planck's law

text: This factor shifts the peak of the distribution to higher energies. These peaks are the "mode" energy of a photon, when binned using equal-size bins of frequency or wavelength, respectively. Meanwhile, the "average" energy of a photon from a blackbody is


title: Planck's law

text: where formula_45 is the Riemann zeta function. Dividing by this energy expression gives the wavelength of the peak. For this one can use = .


title: Planck's law

text: The radiance increases as the square of the frequency, illustrating the ultraviolet catastrophe. In the limit of high frequencies (i.e. small wavelengths) Planck's law tends to the Wien approximation:


title: Planck's law

text: Both approximations were known to Planck before he developed his law. He was led by these two approximations to develop a law which incorporated both limits, which ultimately became Planck's law.


title: Planck's law

text: Wien's displacement law in its stronger form states that the shape of Planck's law is independent of temperature. It is therefore possible to list the percentile points of the total radiation as well as the peaks for wavelength and frequency, in a form which gives the wavelength when divided by temperature . The second row of the following table lists the corresponding values of , that is, those values of for which the wavelength is micrometers at the radiance percentile point given by the corresponding entry in the first row.


title: Planck's law

text: That is, 0.01% of the radiation is at a wavelength below  µm, 20% below , etc. The wavelength and frequency peaks are in bold and occur at 25.0% and 64.6% respectively. The 41.8% point is the wavelength-frequency-neutral peak (i.e. the peak in power per unit change in logarithm of wavelength or frequency). These are the points at which the respective Planck-law functions , and , respectively, divided by attain their maxima. The much smaller gap in ratio of wavelengths between 0.1% and 0.01% (1110 is 22% more than 910) than between 99.9% and 99.99% (113374 is 120% more than 51613) reflects the exponential decay of energy at short wavelengths (left end) and polynomial decay at long.


title: Planck's law

text: Which peak to use depends on the application. The conventional choice is the wavelength peak at 25.0% given by Wien's displacement law in its weak form. For some purposes the median or 50% point dividing the total radiation into two-halves may be more suitable. The latter is closer to the frequency peak than to the wavelength peak because the radiance drops exponentially at short wavelengths and only polynomially at long. The neutral peak occurs at a shorter wavelength than the median for the same reason.


title: Planck's law

text: For the Sun, is 5778 K, allowing the percentile points of the Sun's radiation, in nanometers, to be tabulated as follows when modeled as a black body radiator, to which the Sun is a fair approximation. For comparison a planet modeled as a black body radiating at a nominal 288 K (15 °C) as a representative value of the Earth's highly variable temperature has wavelengths more than twenty times that of the Sun, tabulated in the third row in micrometers (thousands of nanometers).


title: Planck's law

text: That is, only 1% of the Sun's radiation is at wavelengths shorter than 251 nm, and only 1% at longer than 3961 nm. Expressed in micrometers this puts 98% of the Sun's radiation in the range from 0.251 to 3.961 µm. The corresponding 98% of energy radiated from a 288 K planet is from 5.03 to 79.5 µm, well above the range of solar radiation (or below if expressed in terms of frequencies instead of wavelengths ).


title: Planck's law

text: A consequence of this more-than-order-of-magnitude difference in wavelength between solar and planetary radiation is that filters designed to pass one and block the other are easy to construct. For example, windows fabricated of ordinary glass or transparent plastic pass at least 80% of the incoming 5778 K solar radiation, which is below 1.2 µm in wavelength, while blocking over 99% of the outgoing 288 K thermal radiation from 5 µm upwards, wavelengths at which most kinds of glass and plastic of construction-grade thickness are effectively opaque.


title: Planck's law

text: The Sun's radiation is that arriving at the top of the atmosphere (TOA). As can be read from the table, radiation below 400 nm, or ultraviolet, is about 12%, while that above 700 nm, or infrared, starts at about the 49% point and so accounts for 51% of the total. Hence only 37% of the TOA insolation is visible to the human eye. The atmosphere shifts these percentages substantially in favor of visible light as it absorbs most of the ultraviolet and significant amounts of infrared.


title: Planck's law

text: Consider a cube of side with conducting walls filled with electromagnetic radiation in thermal equilibrium at temperature . If there is a small hole in one of the walls, the radiation emitted from the hole will be characteristic of a perfect black body. We will first calculate the spectral energy density within the cavity and then determine the spectral radiance of the emitted radiation.


title: Planck's law

text: At the walls of the cube, the parallel component of the electric field and the orthogonal component of the magnetic field must vanish. Analogous to the wave function of a particle in a box, one finds that the fields are superpositions of periodic functions. The three wavelengths , , and , in the three directions orthogonal to the walls can be:


title: Planck's law

text: where the are positive integers. For each set of integers there are two linearly independent solutions (known as modes). According to quantum theory, the energy levels of a mode are given by:


title: Planck's law

text: The quantum number can be interpreted as the number of photons in the mode. The two modes for each set of correspond to the two polarization states of the photon which has a spin of 1. For the energy of the mode is not zero. This vacuum energy of the electromagnetic field is responsible for the Casimir effect. In the following we will calculate the internal energy of the box at absolute temperature .


title: Planck's law

text: According to statistical mechanics, the equilibrium probability distribution over the energy levels of a particular mode is given by:


title: Planck's law

text: which is the energy of a single photon. As explained here, the average energy in a mode can be expressed in terms of the partition function:


title: Planck's law

text: This formula, apart from the first vacuum energy term, is a special case of the general formula for particles obeying Bose–Einstein statistics. Since there is no restriction on the total number of photons, the chemical potential is zero.


title: Planck's law

text: If we measure the energy relative to the ground state, the total energy in the box follows by summing over all allowed single photon states. This can be done exactly in the thermodynamic limit as approaches infinity. In this limit, becomes continuous and we can then integrate over this parameter. To calculate the energy in the box in this way, we need to evaluate how many photon states there are in a given energy range. If we write the total number of single photon states with energies between and as , where is the density of states (which is evaluated below), then we can write:


title: Planck's law

text: For every vector with integer components larger than or equal to zero, there are two photon states. This means that the number of photon states in a certain region of -space is twice the volume of that region. An energy range of corresponds to shell of thickness in -space. Because the components of have to be positive, this shell spans an octant of a sphere. The number of photon states , in an energy range , is thus given by:


title: Planck's law

text: From this equation one can derive the spectral energy density as a function of frequency and as a function of wavelength :


title: Planck's law

text: This is also a spectral energy density function with units of energy per unit wavelength per unit volume. Integrals of this type for Bose and Fermi gases can be expressed in terms of polylogarithms. In this case, however, it is possible to calculate the integral in closed form using only elementary functions. Substituting


title: Planck's law

text: This is not the Stefan–Boltzmann law (which provides the total energy "radiated" by a black body per unit surface area per unit time), but it can be written more compactly using the Stefan–Boltzmann constant , giving


title: Planck's law

text: Since the radiation is the same in all directions, and propagates at the speed of light (), the spectral radiance of radiation exiting the small hole is


title: Planck's law

text: Dimensional analysis shows that the unit of steradians, shown in the denominator of the right hand side of the equation above, is generated in and carried through the derivation but does not appear in any of the dimensions for any element on the left-hand-side of the equation.


title: Planck's law

text: In 1858, Balfour Stewart described his experiments on the thermal radiative emissive and absorptive powers of polished plates of various substances, compared with the powers of lamp-black surfaces, at the same temperature. Stewart chose lamp-black surfaces as his reference because of various previous experimental findings, especially those of Pierre Prevost and of John Leslie. He wrote "Lamp-black, which absorbs all the rays that fall upon it, and therefore possesses the greatest possible absorbing power, will possess also the greatest possible radiating power."


title: Planck's law

text: Stewart measured radiated power with a thermo-pile and sensitive galvanometer read with a microscope. He was concerned with selective thermal radiation, which he investigated with plates of substances that radiated and absorbed selectively for different qualities of radiation rather than maximally for all qualities of radiation. He discussed the experiments in terms of rays which could be reflected and refracted, and which obeyed the Helmholtz reciprocity principle (though he did not use an eponym for it). He did not in this paper mention that the qualities of the rays might be described by their wavelengths, nor did he use spectrally resolving apparatus such as prisms or diffraction gratings. His work was quantitative within these constraints. He made his measurements in a room temperature environment, and quickly so as to catch his bodies in a condition near the thermal equilibrium in which they had been prepared by heating to equilibrium with boiling water. His measurements confirmed that substances that emit and absorb selectively respect the principle of selective equality of emission and absorption at thermal equilibrium.


title: Planck's law

text: Stewart offered a theoretical proof that this should be the case separately for every selected quality of thermal radiation, but his mathematics was not rigorously valid. According to historian D. M. Siegel: "He was not a practitioner of the more sophisticated techniques of nineteenth-century mathematical physics; he did not even make use of the functional notation in dealing with spectral distributions." He made no mention of thermodynamics in this paper, though he did refer to conservation of "vis viva". He proposed that his measurements implied that radiation was both absorbed and emitted by particles of matter throughout depths of the media in which it propagated. He applied the Helmholtz reciprocity principle to account for the material interface processes as distinct from the processes in the interior material. He concluded that his experiments showed that, in the interior of an enclosure in thermal equilibrium, the radiant heat, reflected and emitted combined, leaving any part of the surface, regardless of its substance, was the same as would have left that same portion of the surface if it had been composed of lamp-black. He did not mention the possibility of ideally perfectly reflective walls; in particular he noted that highly polished real physical metals absorb very slightly.


title: Planck's law

text: In 1859, not knowing of Stewart's work, Gustav Robert Kirchhoff reported the coincidence of the wavelengths of spectrally resolved lines of absorption and of emission of visible light. Importantly for thermal physics, he also observed that bright lines or dark lines were apparent depending on the temperature difference between emitter and absorber.


title: Planck's law

text: Kirchhoff then went on to consider bodies that emit and absorb heat radiation, in an opaque enclosure or cavity, in equilibrium at temperature .


title: Planck's law

text: Here is used a notation different from Kirchhoff's. Here, the emitting power denotes a dimensioned quantity, the total radiation emitted by a body labeled by index at temperature . The total absorption ratio of that body is dimensionless, the ratio of absorbed to incident radiation in the cavity at temperature . (In contrast with Balfour Stewart's, Kirchhoff's definition of his absorption ratio did not refer in particular to a lamp-black surface as the source of the incident radiation.) Thus the ratio of emitting power to absorption ratio is a dimensioned quantity, with the dimensions of emitting power, because is dimensionless. Also here the wavelength-specific emitting power of the body at temperature is denoted by and the wavelength-specific absorption ratio by . Again, the ratio of emitting power to absorption ratio is a dimensioned quantity, with the dimensions of emitting power.


title: Planck's law

text: In a second report made in 1859, Kirchhoff announced a new general principle or law for which he offered a theoretical and mathematical proof, though he did not offer quantitative measurements of radiation powers. His theoretical proof was and still is considered by some writers to be invalid. His principle, however, has endured: it was that for heat rays of the same wavelength, in equilibrium at a given temperature, the wavelength-specific ratio of emitting power to absorption ratio has one and the same common value for all bodies that emit and absorb at that wavelength. In symbols, the law stated that the wavelength-specific ratio has one and the same value for all bodies, that is for all values of index . In this report there was no mention of black bodies.


title: Planck's law

text: In 1860, still not knowing of Stewart's measurements for selected qualities of radiation, Kirchhoff pointed out that it was long established experimentally that for total heat radiation, of unselected quality, emitted and absorbed by a body in equilibrium, the dimensioned total radiation ratio , has one and the same value common to all bodies, that is, for every value of the material index . Again without measurements of radiative powers or other new experimental data, Kirchhoff then offered a fresh theoretical proof of his new principle of the universality of the value of the wavelength-specific ratio at thermal equilibrium. His fresh theoretical proof was and still is considered by some writers to be invalid.


title: Planck's law

text: But more importantly, it relied on a new theoretical postulate of "perfectly black bodies", which is the reason why one speaks of Kirchhoff's law. Such black bodies showed complete absorption in their infinitely thin most superficial surface. They correspond to Balfour Stewart's reference bodies, with internal radiation, coated with lamp-black. They were not the more realistic perfectly black bodies later considered by Planck. Planck's black bodies radiated and absorbed only by the material in their interiors; their interfaces with contiguous media were only mathematical surfaces, capable neither of absorption nor emission, but only of reflecting and transmitting with refraction.


title: Planck's law

text: Kirchhoff's proof considered an arbitrary non-ideal body labeled as well as various perfect black bodies labeled . It required that the bodies be kept in a cavity in thermal equilibrium at temperature . His proof intended to show that the ratio was independent of the nature of the non-ideal body, however partly transparent or partly reflective it was.


title: Planck's law

text: His proof first argued that for wavelength and at temperature , at thermal equilibrium, all perfectly black bodies of the same size and shape have the one and the same common value of emissive power , with the dimensions of power. His proof noted that the dimensionless wavelength-specific absorption ratio of a perfectly black body is by definition exactly 1. Then for a perfectly black body, the wavelength-specific ratio of emissive power to absorption ratio is again just , with the dimensions of power. Kirchhoff considered, successively, thermal equilibrium with the arbitrary non-ideal body, and with a perfectly black body of the same size and shape, in place in his cavity in equilibrium at temperature . He argued that the flows of heat radiation must be the same in each case. Thus he argued that at thermal equilibrium the ratio was equal to , which may now be denoted , a continuous function, dependent only on at fixed temperature , and an increasing function of at fixed wavelength , at low temperatures vanishing for visible but not for longer wavelengths, with positive values for visible wavelengths at higher temperatures, which does not depend on the nature of the arbitrary non-ideal body. (Geometrical factors, taken into detailed account by Kirchhoff, have been ignored in the foregoing.)


title: Planck's law

text: Thus Kirchhoff's law of thermal radiation can be stated: "For any material at all, radiating and absorbing in thermodynamic equilibrium at any given temperature ', for every wavelength ', the ratio of emissive power to absorptive ratio has one universal value, which is characteristic of a perfect black body, and is an emissive power which we here represent by ""." (For our notation , Kirchhoff's original notation was simply .)


title: Planck's law

text: Kirchhoff announced that the determination of the function was a problem of the highest importance, though he recognized that there would be experimental difficulties to be overcome. He supposed that like other functions that do not depend on the properties of individual bodies, it would be a simple function. That function has occasionally been called 'Kirchhoff's (emission, universal) function', though its precise mathematical form would not be known for another forty years, till it was discovered by Planck in 1900. The theoretical proof for Kirchhoff's universality principle was worked on and debated by various physicists over the same time, and later. Kirchhoff stated later in 1860 that his theoretical proof was better than Balfour Stewart's, and in some respects it was so. Kirchhoff's 1860 paper did not mention the second law of thermodynamics, and of course did not mention the concept of entropy which had not at that time been established. In a more considered account in a book in 1862, Kirchhoff mentioned the connection of his law with "Carnot's principle", which is a form of the second law.


title: Planck's law

text: According to Helge Kragh, "Quantum theory owes its origin to the study of thermal radiation, in particular to the "blackbody" radiation that Robert Kirchhoff had first defined in 1859–1860."


title: Planck's law

text: In 1860, Kirchhoff predicted experimental difficulties for the empirical determination of the function that described the dependence of the black-body spectrum as a function only of temperature and wavelength. And so it turned out. It took some forty years of development of improved methods of measurement of electromagnetic radiation to get a reliable result.


title: Planck's law

text: In 1865, John Tyndall described radiation from electrically heated filaments and from carbon arcs as visible and invisible. Tyndall spectrally decomposed the radiation by use of a rock salt prism, which passed heat as well as visible rays, and measured the radiation intensity by means of a thermopile.


title: Planck's law

text: In 1880, André-Prosper-Paul Crova published a diagram of the three-dimensional appearance of the graph of the strength of thermal radiation as a function of wavelength and temperature. He determined the spectral variable by use of prisms. He analyzed the surface through what he called "isothermal" curves, sections for a single temperature, with a spectral variable on the abscissa and a power variable on the ordinate. He put smooth curves through his experimental data points. They had one peak at a spectral value characteristic for the temperature, and fell either side of it towards the horizontal axis. Such spectral sections are widely shown even today.


title: Planck's law

text: In a series of papers from 1881 to 1886, Langley reported measurements of the spectrum of heat radiation, using diffraction gratings and prisms, and the most sensitive detectors that he could make. He reported that there was a peak intensity that increased with temperature, that the shape of the spectrum was not symmetrical about the peak, that there was a strong fall-off of intensity when the wavelength was shorter than an approximate cut-off value for each temperature, that the approximate cut-off wavelength decreased with increasing temperature, and that the wavelength of the peak intensity decreased with temperature, so that the intensity increased strongly with temperature for short wavelengths that were longer than the approximate cut-off for the temperature.


title: Planck's law

text: Having read Langley, in 1888, Russian physicist V.A. Michelson published a consideration of the idea that the unknown Kirchhoff radiation function could be explained physically and stated mathematically in terms of "complete irregularity of the vibrations of ... atoms". At this time, Planck was not studying radiation closely, and believed in neither atoms nor statistical physics. Michelson produced a formula for the spectrum for temperature:


title: Planck's law

text: where denotes specific radiative intensity at wavelength and temperature , and where and are empirical constants.


title: Planck's law

text: In 1898, Otto Lummer and Ferdinand Kurlbaum published an account of their cavity radiation source. Their design has been used largely unchanged for radiation measurements to the present day. It was a platinum box, divided by diaphragms, with its interior blackened with iron oxide. It was an important ingredient for the progressively improved measurements that led to the discovery of Planck's law. A version described in 1901 had its interior blackened with a mixture of chromium, nickel, and cobalt oxides.


title: Planck's law

text: The importance of the Lummer and Kurlbaum cavity radiation source was that it was an experimentally accessible source of black-body radiation, as distinct from radiation from a simply exposed incandescent solid body, which had been the nearest available experimental approximation to black-body radiation over a suitable range of temperatures. The simply exposed incandescent solid bodies, that had been used before, emitted radiation with departures from the black-body spectrum that made it impossible to find the true black-body spectrum from experiments.


title: Planck's law

text: Theoretical and empirical progress enabled Lummer and Pringsheim to write in 1899 that available experimental evidence was approximately consistent with the specific intensity law where and denote empirically measurable constants, and where and denote wavelength and temperature respectively. For theoretical reasons, Planck at that time accepted this formulation, which has an effective cut-off of short wavelengths.


title: Planck's law

text: Gustav Kirchhoff was Max Planck's teacher and surmised that there was a universal law for blackbody radiation and this was called "Kirchhoff's challenge". Planck, a theorist, believed that Wilhelm Wien had discovered this law and Planck expanded on Wien's work presenting it in 1899 to the meeting of the German Physical Society. Experimentalists Otto Lummer, Ferdinand Kurlbaum, Ernst Pringsheim Sr., and Heinrich Rubens did experiments that appeared to support Wien's law especially at higher frequency short wavelengths which Planck so wholly endorsed at the German Physical Society that it began to be called the Wien-Planck Law. However, by September 1900, the experimentalists had proven beyond a doubt that the Wien-Planck law failed at the longer wavelengths. They would present their data on October 19. Planck was informed by his friend Rubens and quickly created a formula within a few days. In June of that same year, Lord Raleigh had created a formula that would work for short lower frequency wavelengths based on the widely accepted theory of equipartition. So Planck submitted a formula combining both Raleigh's Law (or a similar equipartition theory) and Wien's law which would be weighted to one or the other law depending on wavelength to match the experimental data. However, although this equation worked, Planck himself said unless he could explain the formula derived from a "lucky intuition" into one of "true meaning" in physics, it did not have true significance. Planck explained that thereafter followed the hardest work of his life. Planck did not believe in atoms, nor did he think the second law of thermodynamics should be statistical because probability does not provide an absolute answer, and Boltzmann's entropy law rested on the hypothesis of atoms and was statistical. But Planck was unable to find a way to reconcile his Blackbody equation with continuous laws such as Maxwell's wave equations. So in what Planck called "an act of desperation", he turned to Boltzmann's atomic law of entropy as it was the only one that made his equation work. Therefore, he used the Boltzmann constant "k" and his new constant "h" to explain the blackbody radiation law which became widely known through his published paper.


title: Planck's law

text: Max Planck produced his law on 19 October 1900 as an improvement upon the Wien approximation, published in 1896 by Wilhelm Wien, which fit the experimental data at short wavelengths (high frequencies) but deviated from it at long wavelengths (low frequencies). In June 1900, based on heuristic theoretical considerations, Rayleigh had suggested a formula that he proposed might be checked experimentally. The suggestion was that the Stewart–Kirchhoff universal function might be of the form . This was not the celebrated Rayleigh–Jeans formula , which did not emerge until 1905, though it did reduce to the latter for long wavelengths, which are the relevant ones here. According to Klein, one may speculate that it is likely that Planck had seen this suggestion though he did not mention it in his papers of 1900 and 1901. Planck would have been aware of various other proposed formulas which had been offered. On 7 October 1900, Rubens told Planck that in the complementary domain (long wavelength, low frequency), and only there, Rayleigh's 1900 formula fitted the observed data well.


title: Planck's law

text: For long wavelengths, Rayleigh's 1900 heuristic formula approximately meant that energy was proportional to temperature, . It is known that and this leads to and thence to for long wavelengths. But for short wavelengths, the Wien formula leads to and thence to for short wavelengths. Planck perhaps patched together these two heuristic formulas, for long and for short wavelengths, to produce a formula


title: Planck's law

text: Planck sent this result to Rubens, who compared it with his and Kurlbaum's observational data and found that it fitted for all wavelengths remarkably well. On 19 October 1900, Rubens and Kurlbaum briefly reported the fit to the data, and Planck added a short presentation to give a theoretical sketch to account for his formula. Within a week, Rubens and Kurlbaum gave a fuller report of their measurements confirming Planck's law. Their technique for spectral resolution of the longer wavelength radiation was called the residual ray method. The rays were repeatedly reflected from polished crystal surfaces, and the rays that made it all the way through the process were 'residual', and were of wavelengths preferentially reflected by crystals of suitably specific materials.


title: Planck's law

text: Once Planck had discovered the empirically fitting function, he constructed a physical derivation of this law. His thinking revolved around entropy rather than being directly about temperature. Planck considered a cavity with perfectly reflective walls; inside the cavity, there are finitely many distinct but identically constituted resonant oscillatory bodies of definite magnitude, with several such oscillators at each of finitely many characteristic frequencies. These hypothetical oscillators were for Planck purely imaginary theoretical investigative probes, and he said of them that such oscillators do not need to "really exist somewhere in nature, provided their existence and their properties are consistent with the laws of thermodynamics and electrodynamics.". Planck did not attribute any definite physical significance to his hypothesis of resonant oscillators but rather proposed it as a mathematical device that enabled him to derive a single expression for the black body spectrum that matched the empirical data at all wavelengths. He tentatively mentioned the possible connection of such oscillators with atoms. In a sense, the oscillators corresponded to Planck's speck of carbon; the size of the speck could be small regardless of the size of the cavity, provided the speck effectively transduced energy between radiative wavelength modes.


title: Planck's law

text: Partly following a heuristic method of calculation pioneered by Boltzmann for gas molecules, Planck considered the possible ways of distributing electromagnetic energy over the different modes of his hypothetical charged material oscillators. This acceptance of the probabilistic approach, following Boltzmann, for Planck was a radical change from his former position, which till then had deliberately opposed such thinking proposed by Boltzmann. In Planck's words, "I considered the [quantum hypothesis] a purely formal assumption, and I did not give it much thought except for this: that I had obtained a positive result under any circumstances and at whatever cost." Heuristically, Boltzmann had distributed the energy in arbitrary merely mathematical quanta , which he had proceeded to make tend to zero in magnitude, because the finite magnitude had served only to allow definite counting for the sake of mathematical calculation of probabilities, and had no physical significance. Referring to a new universal constant of nature, , Planck supposed that, in the several oscillators of each of the finitely many characteristic frequencies, the total energy was distributed to each in an integer multiple of a definite physical unit of energy, , not arbitrary as in Boltzmann's method, but now for Planck, in a new departure, characteristic of the respective characteristic frequency. His new universal constant of nature, , is now known as the Planck constant.


title: Planck's law

text: Planck explained further that the respective definite unit, , of energy should be proportional to the respective characteristic oscillation frequency of the hypothetical oscillator, and in 1901 he expressed this with the constant of proportionality :


title: Planck's law

text: Planck did not propose that light propagating in free space is quantized. The idea of quantization of the free electromagnetic field was developed later, and eventually incorporated into what we now know as quantum field theory.


title: Planck's law

text: In 1906, Planck acknowledged that his imaginary resonators, having linear dynamics, did not provide a physical explanation for energy transduction between frequencies. Present-day physics explains the transduction between frequencies in the presence of atoms by their quantum excitability, following Einstein. Planck believed that in a cavity with perfectly reflecting walls and with no matter present, the electromagnetic field cannot exchange energy between frequency components. This is because of the linearity of Maxwell's equations. Present-day quantum field theory predicts that, in the absence of matter, the electromagnetic field obeys nonlinear equations and in that sense does self-interact. Such interaction in the absence of matter has not yet been directly measured because it would require very high intensities and very sensitive and low-noise detectors, which are still in the process of being constructed. Planck believed that a field with no interactions neither obeys nor violates the classical principle of equipartition of energy, and instead remains exactly as it was when introduced, rather than evolving into a black body field. Thus, the linearity of his mechanical assumptions precluded Planck from having a mechanical explanation of the maximization of the entropy of the thermodynamic equilibrium thermal radiation field. This is why he had to resort to Boltzmann's probabilistic arguments.


title: Planck's law

text: Some recent proposals in the possible physical explanation of the Planck constant suggest that, following de Broglie's spirit of wave-particle duality, if, regarding the radiation as a wave packet, the Planck constant is determined by the physical properties of the vacuum and a critical amount of disturbance in the electromagnetic field.


title: Planck's law

text: Planck's law may be regarded as fulfilling the prediction of Gustav Kirchhoff that his law of thermal radiation was of the highest importance. In his mature presentation of his own law, Planck offered a thorough and detailed theoretical proof for Kirchhoff's law, theoretical proof of which until then had been sometimes debated, partly because it was said to rely on unphysical theoretical objects, such as Kirchhoff's perfectly absorbing infinitely thin black surface.


title: Planck's law

text: It was not until five years after Planck made his heuristic assumption of abstract elements of energy or of action that Albert Einstein conceived of really existing quanta of light in 1905 as a revolutionary explanation of black-body radiation, of photoluminescence, of the photoelectric effect, and of the ionization of gases by ultraviolet light. In 1905, "Einstein believed that Planck's theory could not be made to agree with the idea of light quanta, a mistake he corrected in 1906." Contrary to Planck's beliefs of the time, Einstein proposed a model and formula whereby light was emitted, absorbed, and propagated in free space in energy quanta localized in points of space. As an introduction to his reasoning, Einstein recapitulated Planck's model of hypothetical resonant material electric oscillators as sources and sinks of radiation, but then he offered a new argument, disconnected from that model, but partly based on a thermodynamic argument of Wien, in which Planck's formula played no role. Einstein gave the energy content of such quanta in the form . Thus Einstein was contradicting the undulatory theory of light held by Planck. In 1910, criticizing a manuscript sent to him by Planck, knowing that Planck was a steady supporter of Einstein's theory of special relativity, Einstein wrote to Planck: "To me it seems absurd to have energy continuously distributed in space without assuming an aether."


title: Planck's law

text: According to Thomas Kuhn, it was not till 1908 that Planck more or less accepted part of Einstein's arguments for physical as distinct from abstract mathematical discreteness in thermal radiation physics. Still in 1908, considering Einstein's proposal of quantal propagation, Planck opined that such a revolutionary step was perhaps unnecessary. Until then, Planck had been consistent in thinking that discreteness of action quanta was to be found neither in his resonant oscillators nor in the propagation of thermal radiation. Kuhn wrote that, in Planck's earlier papers and in his 1906 monograph, there is no "mention of discontinuity, [nor] of talk of a restriction on oscillator energy, [nor of] any formula like ." Kuhn pointed out that his study of Planck's papers of 1900 and 1901, and of his monograph of 1906, had led him to "heretical" conclusions, contrary to the widespread assumptions of others who saw Planck's writing only from the perspective of later, anachronistic, viewpoints. Kuhn's conclusions, finding a period till 1908, when Planck consistently held his 'first theory', have been accepted by other historians.


title: Planck's law

text: In the second edition of his monograph, in 1912, Planck sustained his dissent from Einstein's proposal of light quanta. He proposed in some detail that absorption of light by his virtual material resonators might be continuous, occurring at a constant rate in equilibrium, as distinct from quantal absorption. Only emission was quantal. This has at times been called Planck's "second theory".


title: Planck's law

text: It was not till 1919 that Planck in the third edition of his monograph more or less accepted his 'third theory', that both emission and absorption of light were quantal.


title: Planck's law

text: The colourful term "ultraviolet catastrophe" was given by Paul Ehrenfest in 1911 to the paradoxical result that the total energy in the cavity tends to infinity when the equipartition theorem of classical statistical mechanics is (mistakenly) applied to black-body radiation. But this had not been part of Planck's thinking, because he had not tried to apply the doctrine of equipartition: when he made his discovery in 1900, he had not noticed any sort of "catastrophe". It was first noted by Lord Rayleigh in 1900, and then in 1901 by Sir James Jeans; and later, in 1905, by Einstein when he wanted to support the idea that light propagates as discrete packets, later called 'photons', and by Rayleigh and by Jeans.


title: Planck's law

text: In 1913, Bohr gave another formula with a further different physical meaning to the quantity . In contrast to Planck's and Einstein's formulas, Bohr's formula referred explicitly and categorically to energy levels of atoms. Bohr's formula was where and denote the energy levels of quantum states of an atom, with quantum numbers and . The symbol denotes the frequency of a quantum of radiation that can be emitted or absorbed as the atom passes between those two quantum states. In contrast to Planck's model, the frequency formula_79 has no immediate relation to frequencies that might describe those quantum states themselves.


title: Planck's law

text: Later, in 1924, Satyendra Nath Bose developed the theory of the statistical mechanics of photons, which allowed a theoretical derivation of Planck's law. The actual word 'photon' was invented still later, by G.N. Lewis in 1926, who mistakenly believed that photons were conserved, contrary to Bose–Einstein statistics; nevertheless the word 'photon' was adopted to express the Einstein postulate of the packet nature of light propagation. In an electromagnetic field isolated in a vacuum in a vessel with perfectly reflective walls, such as was considered by Planck, indeed the photons would be conserved according to Einstein's 1905 model, but Lewis was referring to a field of photons considered as a system closed with respect to ponderable matter but open to exchange of electromagnetic energy with a surrounding system of ponderable matter, and he mistakenly imagined that still the photons were conserved, being stored inside atoms.


title: Planck's law

text: Ultimately, Planck's law of black-body radiation contributed to Einstein's concept of quanta of light carrying linear momentum, which became the fundamental basis for the development of quantum mechanics.


title: Planck's law

text: The above-mentioned linearity of Planck's mechanical assumptions, not allowing for energetic interactions between frequency components, was superseded in 1925 by Heisenberg's original quantum mechanics. In his paper submitted on 29 July 1925, Heisenberg's theory accounted for Bohr's above-mentioned formula of 1913. It admitted non-linear oscillators as models of atomic quantum states, allowing energetic interaction between their own multiple internal discrete Fourier frequency components, on the occasions of emission or absorption of quanta of radiation. The frequency of a quantum of radiation was that of a definite coupling between internal atomic meta-stable oscillatory quantum states. At that time, Heisenberg knew nothing of matrix algebra, but Max Born read the manuscript of Heisenberg's paper and recognized the matrix character of Heisenberg's theory. Then Born and Jordan published an explicitly matrix theory of quantum mechanics, based on, but in form distinctly different from, Heisenberg's original quantum mechanics; it is the Born and Jordan matrix theory that is today called matrix mechanics. Heisenberg's explanation of the Planck oscillators, as non-linear effects apparent as Fourier modes of transient processes of emission or absorption of radiation, showed why Planck's oscillators, viewed as enduring physical objects such as might be envisaged by classical physics, did not give an adequate explanation of the phenomena.


title: Planck's law

text: Nowadays, as a statement of the energy of a light quantum, often one finds the formula , where , and denotes angular frequency, and less often the equivalent formula . This statement about a really existing and propagating light quantum, based on Einstein's, has a physical meaning different from that of Planck's above statement about the abstract energy units to be distributed amongst his hypothetical resonant material oscillators.


title: United States embargo against Cuba

text: The United States embargo against Cuba prevents American businesses, and businesses organized under U.S. law or majority-owned by American citizens, from conducting trade with Cuban interests. It is the most enduring trade embargo in modern history. The US first imposed an embargo on the sale of arms to Cuba on March 14, 1958, during the Fulgencio Batista regime. Again on October 19, 1960, almost two years after the Cuban Revolution had led to the deposition of the Batista regime, the US placed an embargo on exports to Cuba except for food and medicine after Cuba nationalized the US-owned Cuban oil refineries without compensation. On February 7, 1962, the embargo was extended to include almost all exports. The United Nations General Assembly has passed a resolution every year since 1992 demanding the end of the US economic embargo on Cuba, with the US and Israel being the only nations to consistently vote against the resolutions.


title: United States embargo against Cuba

text: , the embargo is enforced mainly through the Trading with the Enemy Act of 1917, the Foreign Assistance Act of 1961, the Cuban Assets Control Regulations of 1963, the Cuban Democracy Act of 1992, the Helms–Burton Act of 1996, and the Trade Sanctions Reform and Export Enhancement Act of 2000. The stated purpose of the Cuban Democracy Act of 1992 is to maintain sanctions on Cuba as long as the Cuban government refuses to move toward "democratization and greater respect for human rights." The Helms-Burton Act further restricted United States citizens from doing commerce in or with Cuba, and mandated restrictions on giving public or private assistance to any successor government in Havana unless and until certain claims against the Cuban government were met. In 1999, President Bill Clinton expanded the trade embargo by also disallowing foreign subsidiaries of U.S. companies to trade with Cuba. In 2000, Clinton authorized the sale of food and humanitarian products to Cuba.


title: United States embargo against Cuba

text: William M. LeoGrande summarized that the embargo against Cuba is "the oldest and most comprehensive US economic sanctions regime against any country in the world" imposed over half a century ago. According to LeoGrande, "the embargo has never been effective at achieving its principal purpose: forcing Cuba's revolutionary regime out of power or bending it to Washington's will."


title: United States embargo against Cuba

text: In Cuba, the embargo is called (the blockade), despite there being no naval blockade of the country by the United States since the end of the Cuban Missile Crisis. The Cuban government frequently blames the US embargo for the economic problems of Cuba. The United States has threatened to stop financial aid to other countries if they trade non-food items with Cuba. The US's attempts to do so have been vocally condemned by the United Nations General Assembly as an extraterritorial measure that contravenes "the sovereign equality of States, non-intervention in their internal affairs and freedom of trade and navigation as paramount to the conduct of international affairs".Despite the existence of the embargo, Cuba can, and does, conduct international trade with many countries, including many US allies; however, US-based companies, and companies that do business with the US, which trade in Cuba do so at the risk of US sanctions. Cuba has been a member of the World Trade Organization since 1995. The European Union is Cuba's largest trading partner, and the United States is the fifth-largest exporter to Cuba (6.6% of Cuba's imports come from the US). The Cuban government must, however, pay cash for all food imports from the United States, as credit is not allowed.


title: United States embargo against Cuba

text: Beyond criticisms of human rights in Cuba, the United States holds $6 billion worth of financial claims against the Cuban government. The pro-embargo position is that the U.S. embargo is, in part, an appropriate response to these unaddressed claims. The Latin America Working Group argues that pro-embargo Cuban-American exiles, whose votes are crucial in the U.S. state of Florida, have swayed many politicians to adopt views similar to their own. Some business leaders, including James E. Perrella, Dwayne O. Andreas, and Peter Blyth, have opposed the Cuban-American views, arguing that trading freely would be good for Cuba and the United States.


title: United States embargo against Cuba

text: Human-rights groups including Amnesty International, Human Rights Watch, and the Inter-American Commission on Human Rights have also been critical of the embargo. Critics of the embargo often refer to it as a "blockade" and say that the respective laws are too harsh, citing the fact that violations can result in up to 10 years in prison.


title: United States embargo against Cuba

text: The United States imposed an arms embargo on Cuba on March 14, 1958, during the armed conflict of 1953-1958 between rebels led by Fidel Castro and the Fulgencio Batista régime. Arms sales violated U.S. policy which had permitted the sale of weapons to Latin-American countries which had signed the 1947 Inter-American Treaty of Reciprocal Assistance (Rio Treaty) as long as the weapons were not used for hostile purposes. The arms embargo had more of an impact on Batista than on the rebels. After the Castro socialist government came to power on January 1, 1959, relations were initially friendly between Castro and the Dwight D. Eisenhower administration but became strained after the Agricultural Reform confiscated land owned by many American businesses and Cuba continued to sponsor revolutionary movements in other parts of the Caribbean. By March 1960 the US government began making plans to help overthrow the Castro administration. Congress did not want to lift the embargo.


title: United States embargo against Cuba

text: In April 1960, the US Department of State issued a memorandum from Deputy Assistant Secretary of State for Inter-American Affairs Lester D. Mallory to his immediate superior, Roy Rubottom, acknowledging majority support within Cuba for the Castro administration, the fast spread of communism within the country, and the lack of an effective political opposition. The memorandum stated that the "only foreseeable means of alienating internal support is through disenchantment and disaffection based on economic dissatisfaction and hardship." It recommended a policy that would be "adroit and inconspicuous as possible" while aiming to deny "money and supplies to Cuba, to decrease monetary and real wages, to bring about hunger, desperation and overthrow of government."


title: United States embargo against Cuba

text: In May 1960 the Cuban government began regularly and openly purchasing armaments from the Soviet Union, citing the US arms embargo. In July 1960 the United States reduced the import quota of brown sugar from Cuba to 700,000 tons under the "Sugar Act of 1948"; and the Soviet Union responded by agreeing to purchase the sugar instead.


title: United States embargo against Cuba

text: In June 1960 a key incident occurred: Eisenhower's government refused to export oil to the island, leaving Cuba reliant on Soviet crude oil, which the American companies in Cuba refused to refine. This led the Cuban government to nationalize all three American-owned oil refineries in Cuba in response. The refinery owners were not compensated for the nationalization of their property. The refineries became part of the state-run company, Unión Cuba-Petróleo. This prompted the Eisenhower administration to launch the first trade embargo—a prohibition against selling all products to Cuba except food and medicine. In October 1960 the Cuban administration responded by nationalizing all American businesses and most American privately owned properties on the island. No compensation was given for the seizures, and a number of diplomats were expelled from Cuba.


title: United States embargo against Cuba

text: The second wave of nationalizations prompted the Eisenhower administration, in one of its last actions, to sever all diplomatic relations with Cuba in January 1961. The U.S. partial trade embargo with Cuba continued under the "Trading with the Enemy Act 1917".


title: United States embargo against Cuba

text: After the Bay of Pigs Invasion in April 1961, which had been largely planned under the Eisenhower administration, but which Kennedy had been informed of and approved during the months preceding his presidency and in his first few months as president, the Cuban government declared that it now considered itself Marxist and socialist, and aligned with the Soviet Union. On September 4, 1961, partly in response, Congress passed the "Foreign Assistance Act", a Cold War Act (among many other measures) that prohibited aid to Cuba and authorized the President to impose a complete trade embargo against Cuba.


title: United States embargo against Cuba

text: On January 21, 1962, Cuba was suspended by the Organization of American States (OAS), by a vote of 14 in favor, one (Cuba) against with six abstentions. (See Cuba–OAS relations.) Mexico and Ecuador, two abstaining members, argued that the expulsion was not authorized in the OAS Charter. Multilateral sanctions were imposed by OAS on July 26, 1964, which were later rescinded on July 29, 1975. Cuban relations with OAS have since improved, and the suspension of membership was lifted on June 3, 2009.


title: United States embargo against Cuba

text: President John F. Kennedy extended measures by Executive order, first widening the scope of the trade restrictions on February 8, 1962 (announced on February 3 and again on March 23, 1962). These measures expanded the embargo to include all imports of products containing Cuban goods, even if the final products had been made or assembled outside Cuba. On August 3, 1962, the "Foreign Assistance Act" was amended to prohibit aid to any country that provides assistance to Cuba. On September 7, 1962, Kennedy formally expanded the Cuban embargo to include all Cuban trade, except for the non-subsidized sale of food and medicines.


title: United States embargo against Cuba

text: Following the Cuban Missile Crisis (October 1962), Kennedy imposed travel restrictions on February 8, 1963, and the "Cuban Assets Control Regulations" were issued on July 8, 1963, again under the "Trading with the Enemy Act" in response to Cubans hosting Soviet nuclear weapons. Under these restrictions, Cuban assets in the U.S. were frozen and existing restrictions were consolidated.


title: United States embargo against Cuba

text: The restrictions on U.S. citizens traveling to Cuba lapsed on March 19, 1977; the regulation was renewable every six months, but President Jimmy Carter did not renew it and the regulation on spending U.S. dollars in Cuba was lifted shortly afterwards. President Ronald Reagan reinstated the trade embargo on April 19, 1982, though it was now only restricted to business and tourist travel and did not apply to travel by U.S.


title: United States embargo against Cuba

text: engaging in professional research, or persons visiting their close relatives. This has been modified subsequently with the present regulation, effective June 30, 2004, being the Cuban Assets Control Regulations, 31 C.F.R. part 515.


title: United States embargo against Cuba

text: The current regulation does not prohibit travel by U.S. citizens to Cuba "per se", but it makes it illegal for U.S. citizens to have transactions (spend money or receive gifts) in Cuba under most circumstances without a US government Office of Foreign Assets Control issued license. Since even paying unavoidable airfare ticket taxes into a Cuban airport would violate this transaction law, it is effectively impossible for ordinary tourists to visit Cuba without breaking the monetary transaction rule.


title: United States embargo against Cuba

text: The embargo was reinforced in October 1992 by the "Cuban Democracy Act" (the "Torricelli Law") and in 1996 by the "Cuban Liberty and Democracy Solidarity Act" (known as the Helms–Burton Act) which penalizes foreign companies that do business in Cuba by preventing them from doing business in the U.S. Justification provided for these restrictions was that these companies were trafficking in stolen U.S. properties, and should, thus, be excluded from the United States. President Obama tried to lift the embargo, but congress did not allow it.


title: United States embargo against Cuba

text: The European Union resented the Helms-Burton Act because it felt that the U.S. was dictating how other nations ought to conduct their trade and challenged it on that basis. The EU eventually dropped its challenge in favor of negotiating a solution.


title: United States embargo against Cuba

text: After Cuba shot down two "Hermanos al Rescate" (Brothers to the Rescue) planes in 1996, killing three Americans and a U.S. resident, a bi-partisan coalition in the United States Congress approved the Helms-Burton Act. The Title III of this law also states that any non-U.S. company that "knowingly trafficks in property in Cuba confiscated without compensation from a U.S. person" can be subjected to litigation and that company's leadership can be barred from entry into the United States. Sanctions may also be applied to non-U.S. companies trading with Cuba. This restriction also applies to maritime shipping, as ships docking at Cuban ports are not allowed to dock at U.S. ports for six months. It's important to note that this title includes waiver authority, so that the President might suspend its application. This waiver must be renewed every six months and traditionally it has been.


title: United States embargo against Cuba

text: In response to pressure from some American farmers and agribusiness, the embargo was relaxed by the Trade Sanctions Reform and Export Enhancement Act, which was passed by the Congress in October 2000 and signed by President Bill Clinton. The relaxation allowed the sale of agricultural goods and medicine to Cuba for humanitarian reasons. Although Cuba initially declined to engage in such trade (having even refused U.S. food aid in the past, seeing it as a half-measure serving U.S. interests), the Cuban government began to allow the purchase of food from the U.S. as a result of Hurricane Michelle in November 2001. These purchases have grown since then, even though all sales are made in cash. In 2007, the U.S. was the largest food supplier of Cuba, and its fifth largest trading partner.


title: United States embargo against Cuba

text: In some tourist spots across the island, American brands such as Coca-Cola can be purchased. Ford tankers refuel planes in airports and some computers use Microsoft software. The origin of the financing behind such goods is not always clear. The goods often come from third parties based in countries outside the U.S., even if the product being dealt originally has U.S. shareholders or investors. This can be seen, for example, with Nestlé products (which have a 10% US ownership) that can be bought in Cuba with Cuban convertible pesos (CUCs). These CUC pesos are hard currency that are traded in foreign exchange against the US dollar, Euro and other currencies.


title: United States embargo against Cuba

text: On April 13, 2009, President Barack Obama eased the travel ban, allowing Cuban-Americans to travel freely to Cuba; and on January 14, 2011, he further eased the ban, by allowing students and religious missionaries to travel to Cuba if they meet certain restrictions.


title: United States embargo against Cuba

text: On July 16, 2012, the "Ana Cecilia" became the first officially sanctioned direct ship to sail from Miami to Cuba. It carried food, medicine and personal hygiene goods sent by Cuban-Americans to family members.


title: United States embargo against Cuba

text: In 2014, the Obama administration announced its intention to re-establish relations with Cuba. In January 2015, the Administration lightened restrictions on U.S. citizen travel to Cuba. While restrictions on travel for missionary work and education have been loosened, visits for tourism remain banned. President Obama and President Raúl Castro of Cuba met on April 11, 2015, which was the first meeting between distinct leaders of the two countries in over fifty years. In May 2015, several American companies reported they had been granted licenses to establish ferry travel between Florida and Cuba, with a U.S. Department of Treasury spokeswoman confirming they had begun issuing licenses. So far the general ban on travel to Cuba remains in effect for Americans, so the ferry service will not be accessible to Americans who have not received special approval for travel to Cuba.


title: United States embargo against Cuba

text: On September 21, 2015, the Commerce and Treasury Departments took additional coordinated actions in support of the President's Cuba policy. These actions included a rule published by the Commerce Department's Bureau of Industry and Security (BIS) that amended the terms of existing license exceptions that are available for Cuba, increased the number of license exception provisions that are available for Cuba, created a new Cuba licensing policy to help ensure the safety of civil aviation and the safe operation of commercial passenger aircraft, and made the deemed export and deemed reexport license requirements for Cuba consistent with other sanctioned destinations.


title: United States embargo against Cuba

text: In February 2016, the U.S. Government allowed two American men from Alabama to build a factory that will assemble as many as 1,000 small tractors a year for sale to private farmers in Cuba. The $5 million to $10 million plant would be the first significant U.S. business investment on Cuban soil since 1959. The deal was not authorized by Cuban authorities later that year because one of the owners had recently obtained Cuban citizenship. Factory ownership is still illegal in Cuba.


title: United States embargo against Cuba

text: In concert with a prisoner exchange with Cuba, Presidents Barack Obama and Raúl Castro announced moves on December 17, 2014, to reestablish diplomatic relations and to loosen travel and economic policies. Cuba released Alan Gross, an American prisoner, on humanitarian grounds and exchanged an unnamed American spy for the three remaining members of the Cuban Five. Obama also announced a review of Cuba's status as a terrorist state and an intention to ask Congress to remove the embargo entirely. Cuba agreed to release 53 political prisoners and to allow Red Cross and UN human-rights investigators access. On May 29, 2015, according to the U.S. State Department, "Cuba's designation as a state sponsor of terrorism was rescinded".


title: United States embargo against Cuba

text: Under the announced changes by President Obama, there will be an increased ability to transact with Cuban nationals and businesses, including Cuban financial institutions. Additionally, permitted U.S. banks will now be able to open accredited accounts in Cuban banks.


title: United States embargo against Cuba

text: On January 12, 2017, President Barack Obama announced the immediate cessation of the wet feet, dry feet policy, eight days before his term ended. The Cuban government agreed to accept the return of Cuban nationals. Beginning in 2014, anticipation of the end of the policy had led to increased numbers of Cuban immigrants.


title: United States embargo against Cuba

text: On November 8, 2017, it was announced that President Donald Trump's Administration had enacted new rules which would re-enforce the business and travel restrictions which were loosened by the Obama Administration and would go into effect on November 9.


title: United States embargo against Cuba

text: In July 2021, under President Joe Biden, the United States imposed sanctions on Cuba's police force and on two of Cuba's leaders in response to the 2021 Cuban protests.


title: United States embargo against Cuba

text: The embargo has been criticized for its effects on food, clean water, medicine, and other economic needs of the Cuban population. Criticism has come from both Fidel Castro and Raúl Castro, citizens and groups from within Cuba, and international organizations and leaders.


title: United States embargo against Cuba

text: American diplomat Lester D. Mallory wrote an internal memo on April 6, 1960, arguing in favor of an embargo to "to decrease monetary and real wages, to bring about hunger, desperation and overthrow of government".


title: United States embargo against Cuba

text: Some medical scholars, outside Cuba, have linked the embargo to shortages of medical supplies and soap which have resulted in a series of medical crises and heightened levels of infectious diseases. Medical scholars have also linked the embargo to epidemics of specific diseases, including neurological disorders and blindness caused by poor nutrition. An article written in 1997 suggests malnutrition and disease resulting from increased food and medicine prices have affected men and the elderly in particular, due to Cuba's rationing system which gives preferential treatment to women and children.


title: United States embargo against Cuba

text: Although since 2000 the embargo has explicitly excluded the acquisition of food and medicines, a 1997 study by the American Association for World Health (AAWH) and a 1996 article in "The Lancet" by Anthony F Kirkpatrick of the University of South Florida College of Medicine showed that while the Cuban Democracy Act was amended to allow the "de jure" export of food and medicines into the country, the "de facto" application and implications of the act's enforcement significantly restricted the accessibility of both within Cuba. The AAWH stated that "a humanitarian catastrophe has been averted only because the Cuban government has maintained a high level of budgetary support for a healthcare system designed to deliver primary and preventive healthcare to all of its citizens." The AAWH found that travel restrictions embedded in the embargo have limited the amount of medical information that flows into Cuba from the United States.


title: United States embargo against Cuba

text: Writing in 2021, in the context of the 2021 Cuban protests, according to Pavel Vidal, a former Central Bank of Cuba economist who teaches at Javeriana University in Colombia, reforms in Cuba "do not depend on the embargo, and the embargo should be eliminated unilaterally, independently from reforms in Cuba. Both cause problems."


title: United States embargo against Cuba

text: The U.S. sanctions on Cuba and their economic impacts can be traced back to when they were first implemented in the 1960s.


title: United States embargo against Cuba

text: In 2012, an economic panel of experts from the Initiative on Global Markets at the University of Chicago Booth School of Business, were asked whether they agree or disagree that "Cuba's low per-capita income growth — 1.2 percent per year since 1960 —has more to do with Cuba's own economic policies than with the U.S. embargo on trade and tourism." The poll found that 49% of economic experts "strongly agree" with the statement, another 49% "agree", 1% were "uncertain", and 0% "disagree" or "strongly disagree" with the statement.


title: United States embargo against Cuba

text: Between 1954 and 1959, trade between Cuba and the United States was at a higher level than what it was in 2003, according to a BA dissertation submitted to the Teresa Lozano Long Institute of Latin American Studies, with 65% of Cuba's total exports sent to the United States while American imports totaled 74% percent of Cuba's international purchases. After the formal implementation of the embargo and the passage of Proclamation 3355, there was a 95% decrease in Cuba's sugar quota, which canceled roughly 700,000 tons of the 3,119,655 tons previously allotted to the United States. A year later, Cuba's sugar quota was reduced to zero when President Eisenhower issued Proclamation 3383. This substantially affected Cuba's total exports, as Cuba was one of the world's leading sugar exporters at the time.


title: United States embargo against Cuba

text: In 1989, with the collapse of the Soviet bloc, Cuba witnessed its most devastating economic crises. Cuba's GDP plummeted 34% and trade between the nations apart from the Council of Mutual Economic Assistance (CMEA) declined by 56%. Between 1989 and 1992, the termination of traditional trade partnerships with the Soviet bloc caused the total value of Cuba's exports to fall by 61% and imports to drop by approximately 72%. This period is known as the Special Period. Supporters of the embargo and many international economists believed that the dissolution of the Soviet Union and the resultant economic crisis would lead to the downfall of Fidel Castro's government. However, Cuba's government instituted a campaign of macroeconomic adjustment and liberalization, which provided significant economic recovery.


title: United States embargo against Cuba

text: Cuba was estimated to have lost over $28.6 billion in trade, according to a 1992 study published by the Cuban Central Planning Board's Institute of Economic Research.


title: United States embargo against Cuba

text: In November 1991 speech to the UN General Assembly, the Cuban ambassador Ricardo Alarcón cited 27 recent cases of trade contracts interrupted by US pressure. The British journal "Cuba Business" claimed that British Petroleum was seemingly dissuaded by US authorities from investing in offshore oil exploration in Cuba despite being initially keenly interested. The Petroleum economist claimed in September 1992 that the US State Department vigorously discouraged firms like Royal Dutch Shell and Clyde Petroleum from investing in Cuba; this pressure did not work in all cases. According to the Mexican newspaper "El Financiero", the US ambassador to Mexico John Negroponte travelled to meet two Mexican business men who had signed a textile deal with Cuba on October 17, 1992. Despite the representation, the deal went ahead and was eventually worth $500 million in foreign capital. All of this happened before the signing of the Cuban Democracy Act.


title: United States embargo against Cuba

text: The 1998 U.S. State Department report "Zenith and Eclipse: A Comparative Look at Socio-Economic Conditions in Pre-Castro and Present Day Cuba" attributed Cuba's economic penury not as a result of the embargo, but instead the lack of foreign currency due to the unwillingness of Cuba to liberalize its economy and diversify its export base during the years of abundant Soviet aid. Cuba also amassed substantial debts owed to its Japanese, European, and Latin American trading partners during the years of abundant Soviet aid.


title: United States embargo against Cuba

text: According to a 2001 U.S. International Trade Commission report in response to a request made by the U.S. House of Representatives, the total value of U.S. exports of selected agricultural products, intermediate goods, and manufactured goods to Cuba in the absence of U.S. sanctions was estimated to be at $146 and $658 million for U.S. imports from Cuba between 1996 and 1998.


title: United States embargo against Cuba

text: In 2002, the Cuba Policy Foundation estimated that the embargo costs the U.S. economy $3.6 billion per year in economic output.


title: United States embargo against Cuba

text: In 2007, the United States Commerce's Bureau of Industry and Security (BIS) has become more lenient with some of the sanctions imposed upon Cuba by introducing new streamlined procedures to expedite processing of license applications for exporting eligible agricultural commodities to Cuba. As a result, annual U.S. exports to Cuba have risen from $6 million to about $350 million between 2000 and 2006. Over this period, U.S. exports to Cuba have totaled more than $1.5 billion. As of 2006, agricultural products comprised 98% of total U.S. exports to Cuba.


title: United States embargo against Cuba

text: In 2009, the U.S. Chamber of Commerce estimated that the embargo costs the U.S. economy $1.2 billion per year in lost sales and exports, while the Cuban government estimates that the embargo has cost the island itself $753.69 billion. The Cuba Policy Foundation (CPF) has provided more extreme data; its estimates put the cost of the embargo at $4.84 billion per year while costing Cuba $685 million per year.


title: United States embargo against Cuba

text: According to critics of the embargo, one of the major problems with the embargo is that the United States is the only major country that has such an embargo against Cuba in place. Cuba still receives tourists and trade from other countries, making the embargo appear both illegitimate and pointless.


title: United States embargo against Cuba

text: A 2015 report in Al Jazeera estimated that the embargo had cost the Cuban economy $1.1 trillion in the 55 years since its inception,


title: United States embargo against Cuba

text: Under the Cuban Assets Control Regulations persons subject to U.S. jurisdiction must obtain a license to engage in any travel-related transactions pursuant to travel to, from, and within Cuba. Transactions related solely to tourist travel are not licensable.


title: United States embargo against Cuba

text: Spurred by a burgeoning interest in the assumed untapped product demand in Cuba, a growing number of free-marketers in Congress, backed by Western and Great Plains lawmakers who represent agribusiness, have tried each year since 2000 to water down or lift regulations preventing Americans from traveling to Cuba. Four times over that time period the United States House of Representatives has adopted language lifting the travel ban, and in 2003 the U.S. Senate followed suit for the first time. Each time President George W. Bush threatened to veto the bill. Faced with a veto threat, each year Congress dropped its attempt to lift the travel ban before sending legislation to the president.


title: United States embargo against Cuba

text: Some United States nationals circumvent the ban by traveling to Cuba from a different country, such as Mexico, The Bahamas, Canada or Costa Rica. Cuban immigration authorities do not routinely stamp passports, instead stamping a Cuban visa page which is provided, and not permanently affixed to the passport. However, the practice still opens U.S. citizens to a risk of prosecution and fines by the U.S. government if discovered. Until July 20, 2015, there was no U.S. Embassy or consulate in Cuba and United States representation was limited to a United States Interests Section.


title: United States embargo against Cuba

text: The United States Treasury Department's Office of Foreign Assets Control (OFAC) considers any visit of more than one day to be "prima facie" proof of violation. OFAC also holds that U.S. citizens may not receive goods or services for free from any Cuban national, eliminating any attempts to circumvent the regulation based on that premise. On July 25, 2011, OFAC declared that the "people to people" relaxation of restrictions on travel conceded by the Obama administration should not be mistakenly interpreted as promoting tourism.


title: United States embargo against Cuba

text: On October 10, 2006, the United States announced the creation of a task force will pursue more aggressively violations of the U.S. trade embargo against Cuba, with severe penalties. The regulations are still in force and are administered by OFAC. Criminal penalties for violating the embargo range up to ten years in prison, $1 million in corporate fines, and $250,000 in individual fines; civil penalties up to $55,000 per violation.


title: United States embargo against Cuba

text: In September 2016, "Newsweek" reported that then future President Donald Trump's hotel company violated the embargo, spending a minimum of $68,000 for its 1998 foray into Cuba without U.S. government approval. With Trump's knowledge, executives funneled the cash for the Cuba trip through an American consulting firm called Seven Arrows Investment and Development Corp. Once the business consultants traveled to Cuba and incurred the expenses for the venture, Seven Arrows instructed senior officers with Trump's company—then called Trump Hotels & Casino Resorts—how to make it appear legal by linking it after the fact to a charitable effort.


title: United States embargo against Cuba

text: The embargo does not block food and medicine goods to Cuba from the United States. In 2020, $176.8 million worth of goods were exported to Cuba from the US and $14.9 million imported to the US from Cuba.


title: United States embargo against Cuba

text: Since 1992, the UN General Assembly has passed a nonbinding resolution every year, except for 2020, condemning the ongoing impact of the embargo and declaring it in violation of the Charter of the United Nations and of international law. There was no voting on this issue in 2020 due to the COVID-19 pandemic.<ref name="A/71/L.3"></ref> Israel is the only country that routinely joins the U.S. in voting against the resolution as did Palau every year from 2004 to 2008. In 2010, the General Assembly condemned the embargo, 187 to 2 with 3 abstentions. Israel sided with the U.S., while Marshall Islands, Palau and Micronesia abstained. In 2014, out of the 193-nation assembly, 188 countries voted in favour of the resolution, the United States and Israel voted against, and the Pacific Island nations Palau, Marshall Islands and Micronesia abstained. The United Nations General Assembly voted in favour of a resolution demanding an end to the embargo in both 2021 and 2022. 184 countries voted in favour of the resolution in 2021, while 185 voted in favour in 2022. The United States and Israel voted against in both years. Brazil and Ukraine abstained in both years, while Colombia abstained in 2021.


title: United States embargo against Cuba

text: On May 1, 2009, Venezuelan President Hugo Chávez, while speaking about his meeting U.S. President Barack Obama at a summit days earlier, stated "if President Obama does not dismantle this savage blockade of the Cuban people, then it is all a lie, it will all be a great farce and the U.S. empire will be alive and well, threatening us."


title: United States embargo against Cuba

text: The Helms-Burton Act has been the target of criticism from Canadian and European governments in particular, who object to what they say is the extraterritorial pretensions of a piece of legislation aimed at punishing non-U.S. corporations and non-U.S. investors who have economic interests in Cuba. In the House of Commons of Canada, Helms-Burton was mocked by the introduction of the Godfrey-Milliken Bill, which called for the return of property of United Empire Loyalists seized by the American government as a result of the American Revolution (the bill never became law). The European Council has stated that it:


title: United States embargo against Cuba

text: Some critics of the embargo say that the embargo helps the Cuban government more than it hurts it, by providing it with a bogeyman for all of Cuba's misfortunes. Hillary Clinton publicly shared the view that the embargo helps the Castros, saying that "It is my personal belief that the Castros do not want to see an end to the embargo and do no want to see normalization with the United States, because they would lose all of their excuses for what hasn't happened in Cuba in the last 50 years." Clinton said in the same interview that "we're open to changing with them."


title: United States embargo against Cuba

text: In a 2005 interview, George P. Shultz, who served as Secretary of State under Reagan, called the embargo "insane". Daniel Griswold, director of the Cato Institute's Center for Trade Policy Studies, criticized the embargo in a June 2009 article:


title: United States embargo against Cuba

text: In June 2009, Venezuela commentator Moisés Naím wrote in "Newsweek": "The embargo is the perfect example used by anti-Americans everywhere to expose the hypocrisy of a superpower that punishes a small island while cozying to dictators elsewhere."


title: United States embargo against Cuba

text: Some American business leaders openly call for an end to the embargo. They argue, as long as the embargo continues, non-U.S. foreign businesses in Cuba that violate the embargo, do not have to compete with U.S. businesses, and thus, will have a head start when and if the embargo is lifted.