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Quantum mechanics, is concerned with the discrete nature of atomic and subatomic phenomena. Quantum mechanics often runs counter to common sense. It is the most successful theory in science and some of it's predictions sound like science fiction. This is a conceptual framework for understanding the microscopic properties of the universe.
Max Planck, was born to an intellectual family in Germany and is considered to be the father of quantum mechanics by many. Quantum mechanics was born in 1900, when Max Planck, put forth a model that was able to explain the full spectrum of thermal radiation. A black body absorbs all of the electromagnetic radiation that falls onto it and emits none. They do not reflect any of the radiation that falls on them. Black body radiation is the emission of light when a black body is heated. The higher the temperature of the black body, the higher the frequency of the emitted radiation. This is Wien's displacement law and it states that as a body becomes heated, it moves from emitting low-frequency red wavelengths to higher frequency blue wavelengths. This is the way astronomers have been able to measure the temperature of deep space. Black body radiation is the way matter absorbs and emits energy as heat and light. This is thermal electromagnetic radiation that is released as a consequence of an object being heated. Thermal radiation, is a kind of electromagnetic radiation, that is released as a consequence of the internal energy of a body. All bodies release electromagnetic radiation over the full frequency range of the spectrum of electromagnetic radiation, and the nature of the radiation depends on the temperature of the body. If a solid is heated to about 700 degrees Celsius, it will begin to glow visibly. Lower temperatures still emit radiation, however, it is not visible. The wavelengths are too weak to be detected by the human eye. As an object becomes heated, it becomes more red. If you keep heating the object, the wavelength of the emitted electromagnetic radiation will become shorter and the frequency higher. Before Planck, the Rayleigh-Jeans law was sufficient to describe low frequencies of thermal radiation. However, the classical mechanics of the 19th century was not sufficient to describe higher frequencies and shorter wavelengths of thermal radiation. This problem was known as the ultraviolet catastrophe. This name came from the fact that the Rayleigh-Jeans law could only make accurate predictions up until the ultraviolet wavelength portion of the spectrum of electromagnetic radiation, where it's predictions begins to diverge from empirical observation. The idea by Max Planck was that the radiation itself was set into equilibrium with a set of harmonic oscillators, that realized energy, in a quantized manner or at a characteristic frequency. These were called "quanta" and were discrete packets of energy. The energy was released in a quantized, well-defined and discrete wavelength. The energy came from the oscillations of individual and discrete atoms. Each oscillator’s energy was proportional to its frequency. The energy of a quantum of radiation was proportional to it's frequency. In Planck's formula, the energy of the quanta at a particular frequency would be the frequency of that particular quanta multiplied by a constant. This constant is known (fittingly) as Planck's constant and is denoted by the symbol h and is a fundamental constant in nature. Planck's constant is the proportionality factor between the frequency of a wave and the minimum amount of energy that it can have. The value of Planck's constant is very small and it only becomes visible and is significant for making measurements at the subatomic scale. In the units of kilograms, meters and seconds, the value of the Planck constant is 6.63 x 10^-34. This remarkable theory took several years to be accepted. Max Planck was not even fully convinced of the applicability or validity of the idea himself initially. Planck thought that what he had discovered was more of a mathematical trick than a valid description of the natural world. He had trouble reconciling himself to the full implications of his new quantum theory. Max Planck won the Nobel prize in 1918 for his discovery of energy quanta. This is also considered to be the mark of the birth of the quantum theory.
Max Planck is considered the father of the quantum theory for his discovery of energy quanta and for creating a full classification of the entire spectrum of thermal radiation.
Planck predicted that the thermal radiation emitted by a black body was emitted in packets or quanta.
The next big step for quantum mechanics will be taken by Albert Einstein, in 1905. Albert Einstein was intrigued by the work of Planck and will follow in his lead. Einstein, proposed that light, occurs in individual packets of energy. This idea is now well accepted and this packet of energy is known as the photon.
This proposal was able to explain the photoelectric effect, which is a phenomenon where, light is shone onto a material and electrons are emitted. This is the emission of electricity when light illuminates a charged surface. Einstein predicted that light was made of particles to explain this phenomenon.
The photoelectric effect was first observed by Heinrich Hertz in 1887. Hertz was working to prove James Clerk Maxwell's theory of electromagnetism and in-so-doing, noticed this phenomenon:
Light is shone onto a negatively charged metal plate.
Electrons can be knocked off the surface of the plate.
This is the ejection of electrons from a surface by the action of light.
The problem was observed first in 1902 by Phillip Lenard: the energy of the ejected electrons was proportional to the frequency of the light and not to the intensity. This is a problem because if light was a wave and not composed of particles, there should not be this discrepancy. There was a cutoff frequency, beyond which, electrons were not emitted. The intensity didn't make a difference as the classical theory of light would suggest. Another problem was that there was no observed lag time for the electrons to be ejected. In the classical theory, the electrons would need more time to absorb enough energy to be ejected, especially, if the intensity of the light was more feeble. The electrons would be emitted instantly when light hit the negatively charged surface.
Albert Einstein, in 1905, published a quantum solution to the photoelectric effect: a phenomenon where photons are shone onto a metal plate and they emit electrons. He also predicted the existence of photons and that light was quantized and existed in these discrete packets of energy.
Arthur Compton
Einstein predicted that light was made of particles to explain the phenomenon of the photoelectric effect. This idea will later be proved by the experiments of Arthur Compton in 1923. Compton will prove that photons have momentum. Compton shot a beam of X-rays of a specific frequency at a block of graphite and observed that the scattered radiation was of a lower frequency. According to Compton, this drop in frequency was a consequence of the particle-nature of light. Compton needed a particle description of light to explain it's scattering from electrons. It will also be proposed that photons have no mass since they move at light speed.
This work confirmed the particle-like nature of light.
About 8 years later, in 1913, Niels Bohr, is going to propose a new model of the atom that reconciled Ernest Rutherford's idea of an atomic nucleus with electrons in a surrounding orbit with the work by Max Planck on quantization. Niels Bohr was a Danish physicist and was regarded by many to be the most influential scientist of the 20th century. Bohr is also regarded by many to be the father of the quantum theory as it is currently understood.
The atom, for Bohr, is going to have quantized electron orbits, where, they are only permitted to orbit at certain distances from the nucleus. Bohr proposed that the angular momentum of the orbiting electrons was quantized. Electrons orbit the nucleus in discrete shells. The distance of these electron shells to the nucleus will determine their energy. This is different than in the Newtonian view, where the electrons could orbit the nucleus in any arbitrary fashion. Electrons could transmit from one orbit to another, however, not without emitting a photon. This is not the modern view of the atom, however, it sufficed to explain the stability of the electron orbits. It is also still taught in schools to this day. That being said, the full model of the atom didn't come until about a decade later after more work was done on the quantum theory.
Prior to Bohr's proposal of the first quantum model of the atom in 1913, it was known that the atom consisted of a tiny dense nucleus, surrounded by even tinier electrons. This was known from the alpha-scattering experiments of Ernest Rutherford.
Niels Bohr, in 1913, proposed a model of the atom, where electrons orbit the nucleus in a discrete manner.
Bohr won the Nobel Prize in 1922 for his work.
1922, Otto Stern and Walther Gerlach detect discrete patterns of angular momentum for atoms passing through an inhomogeneous magnetic field. This led to the discovery of electron spin. The proposal that electrons spin about an axis will be proposed 3 years later (see below).
In 1922, was proposed the Stern-Gerlach experiment.
Silver atoms are shot through an inhomogeneous magnetic field.
They were either deflected up or down, implying that their angular momentum was quantized.
Wave-particle duality is the proposal that matter, also, can exhibit wave-like properties, and, vice versa. The first way that the wave behavior of matter was observed was in electrons, which exhibit diffraction, much like a water wave would. Neither the classical concept of “wave” nor of “particle” can successfully describe entities at the quantum scale. Louis de Broglie, won the Nobel Prize in 1924 for his prediction that matter can also act as a wave. He proposed that you could even calculate the wavelength of a particle. This wavelength would be inversely proportional to the mass of that particle. The wavelengths depended on their momentum. However, this wavelength phenomenon would only be measurable on the subatomic scale.
Wave-particle duality can be demonstrated by the double-slit experiment. The double slit experiment is a classic example of the strange behavior of quantum mechanics. This experiment demonstrates that individual particles have wavelike properties. These particles give an interference pattern on a screen after being passed through two narrow slits. It was the same result even when they were sent through one at a time. A beam of light is shot at a piece of paper or film with two slits carved into them. There is also a screen behind the "slitted" plate to detect the pattern. What was found was that there is an interference pattern of both light and dark bands on the screen.
The double slit experiment demonstrates the wavelike property of light:
Electrons are passed through a dual-slit apparatus.
What is expected would be two narrow illuminated bands on the other side.
However, since particles also have a wave-like nature: there will be an interference and a banded pattern will be produced.
Wolfgang Pauli, in 1924, proposes his Pauli-exclusion principle. This is a quantum mechanical rule that applies to fermions. Fermions are the particles of the Standard Model that have a spin of 1/2 integer. These are the particles like the quarks and the electron. The rule began for electrons, that they cannot all occupy the same lowest energy orbit in the atom, however, these electrons must stack up and organize themselves according to their energy and spin, in successively higher orbits. This explains:
the rigidity of matter.
why a star as small as the Sun, when it runs out of nuclear fuel, will not collapse into a black hole.
According to the Pauli-exclusion principle, no two fermions, can occupy the same quantum state, at the same time. It is a theoretical limit on their number per volume, or, spatial density. It is impossible for two particles in the same system to be in the same quantum state at the same time. To explain the electron shells of the periodic table, Pauli proposed that an electron can be defined by 4 quantum numbers:
1. Orbital
2. Shape
3. Inclination
4. Spin
This new property of spin will separate the classification of subatomic particles into 2 families: fermions and bosons. Fermions are all matter particles and have a half-integer spin, while the bosons, are the force carrying particles with an integer value spin.
Wolfgang Pauli proposed his exclusion principle in 1924. This explains some properties of the periodic table, such as how electrons occupy orbits inside the atoms. This would account for how an electron orbital could be full and no longer be able to hold other electrons. More than one electron cannot exist in the same quantum state. This explains why matter has its rigidity and why electrons can't be pushed all the way into the atomic nucleus. Only fermions, the particles with a 1/2 integer value spin obey this principle. The bosons, which have an integer value spin of 1, do not obey this principle and are able to occupy the same quantum state.
Wolfgang Pauli was the first to propose the property of spin, however, did not name it. In 1925, there was a proposal by George Uhlenbeck, Samuel Goudsmit and Ralph Kronig that electrons have spin around their own axis.
Pauli proposed that spin should be quantized (although he and Heisenberg originally disliked the idea). The electron could either be in a state of "up" or "down" spin.
Another consequence of the exclusion principle is the phenomenon of quantum entanglement. This is when physical information in one place can seemingly be transferred to another place instantaneously. Two quantum particles can be correlated that the action of one will affect the behavior of the other. Albert Einstein referred to this phenomenon as "spooky action at a distance." Particles may initially be acting independent from one another, however, upon interacting may become entangled. This means that even after they are separated, measurements on one particle, will affect the other entangled particle instantly. These entangled particles operate as one.
The EPR paradox, was a 1935 thought experiment by Albert Einstein, Boris Podolsky and Nathan Rosen. This is a famous example of entanglement phenomenon. It involves two particles created from a common source. These correlated particles were sent off in opposing directions. The idea was that this thought experiment would prove that the wave function does not accurately describe the natural world and that the Copenhagen interpretation of quantum mechanics could not be a complete description of reality. The paradox assumed two properties:
They assumed that local realism was valid. Local realism is a combination of the principle of locality (that an object is only directly influenced by it's immediate surroundings) with the assumption that a particle must have a pre-existing value before a measurement is made. They also thought that there would have to be hidden parameters to explain how the measurement of one particle could affect the other. The combination of these two proposals led to what is known as the "principle of local action".
They proposed that unless momentum and position were real properties that can be understood at the same time (unlike in the Heisenberg uncertainty principle, which is central to the Copenhagen interpretation of quantum mechanics) than quantum mechanics would predict non-locality.
That was the paradox. However, physicists today have shown that it is theoretically consistent for quantum particles to remain entangled despite their vast distance from one another.
Charles H. Bennett
Gilles Brassard
Quantum teleportation was discovered by Charles H. Bennett (who coined the term) and Gilles Brassard in 1993.
These IBM scientists, making use of the EPR experiment, showed that it was physically possible to teleport objects at the atomic level. They showed that you could teleport all of the information contained within a particle.
Ever since this discovery, it has been shown that photons and even atoms (cesium and rubidium) can be teleported.
Quantum teleportation could have a theoretical explanation. The quantum information, which is the exact state of the particle, can be transmitted. This would involve entanglement between the sending and receiving locations. Two or more particles can be quantum entangled and could theoretically be moved from place to place.
It has been proven to be physically possible to transport qubits (unit of quantum information) between entangled particles.
However, the teleportation of humans raises ethical questions. This is because, the original copy, in quantum teleportation has to be destroyed. Despite an exact copy being produced of the teleporter, one would die in the process. Such teleportation may or may not be possible in the future. The answer is not yet clear.
Another possible application of quantum entanglement is quantum cryptography. The idea is that, in quantum mechanics, the idea of measuring a system disturbs it. Thus, if a third party or eavesdropper were attempting to see a private message, this eavesdropping could be detected by the disturbance that its observation created on the quantum system. Observations of quanta change their behavior. For example, in the Heisenberg uncertainty principle, examining the velocity changes the position and vice-versa of a particle. Also, because of the no-cloning theorem, it would be impossible for the eavesdropper to make a copy of the unknown quantum state. This disturbance would be able to be detected.
Erwin Schrodinger, in 1926, published his equation, which famously became known as the "Schrodinger equation." This is building on the work of de Broglie (who inspired Schrodinger) on wave-particle duality. Schrodinger proposes that you can actually know the wavefunction of a particle. The wavefunction is the distribution of the particle's energy in space. The wavefunction is the solution to the Schrodinger equation and contains all of the information about a quantum system that can be known.
The wavefunction is not a directly observable quantity. The wavefunction is an abstract mathematical entity. However, physically meaningful information can be deduced from the wavefunction. The square of the wavefunction is known as the probability density. The probability density is a measurable value and it can be used to measure the probability of locating an electron at a specific point in space.
The Schrodinger equation is going to express how quantum mechanical systems change with time. This equation, will describe the behavior of a quantum mechanical wave. The Schrodinger equation essentially defines two properties of the quantum system:
It defines the system's permitted stationary states. Schrodinger proposed that electrons could only have orbits where a whole number of the electron's associated waves can fit. If it lay in between these states, where the orbits could contain a fractional number of wavelengths than it was not allowed.
It describes how the state of a quantum mechanical system changes with time.
Erwin Schrodinger
The wave is described by a function called a wave function. According to Erwin Schrodinger, the purpose of the wave function was to be used to predict the probability of certain results being measured. It did not only apply to electrons, however, to all subatomic particles. This was not the description of the motion of particles, as in Newtonian mechanics. However, this was wave mechanics: a description of the propagation of waves.
In quantum mechanics, we are only able to make predictions about the probability of certain particle behavior. This is the way nature behaves at the subatomic level: it is probabilistic. An electron's associated probability wave will determine the location that that electron will most likely be located.
Erwin Schrodinger, an Austrian physicist, in 1926, publishes his Schrodinger equation, which describes how quantum mechanical systems change in time.
Schrodinger's cat is a thought experiment devised by Schrodinger himself in 1935. This was to point out a problem with the Copenhagen interpretation of quantum mechanics. While the box is not opened, the cat lies in an undetermined state of being either alive or dead. The cat can be said to be in a superposition of two different states: alive or dead.
Heisenberg is going to build on the work of Schrodinger and of the notion of the wavefunction of a particle. Werner Heisenberg realized that the wavefunction of a particle implied that particles could not perfectly be localized to a specific position in space and be known to have a definite wavelength at the same time. This will give way to the Heisenberg Uncertainty principle, which is well known, however, frequently misunderstood. The Heisenberg Uncertainty principle is a limit to the precision, that certain pairs of properties can be known at the same time. A wave has no definite location in space. Indeed, the uncertainty principle was proposed by Werner Heisenberg in 1927. It was originally dubbed the "principle of indeterminacy." The best way to understand this is to consider the position (x) and momentum (p) of a particle. The more accurately one is known at a single time, the less accurately the other can be determined at the same time. In quantum mechanics, a wave has no definite location in space. This principle also applies to other pairs of quantities such as: energy and time.
Heisenberg is also known for:
Developing matrix mechanics to calculate electron energy levels.
the Copenhagen interpretation of quantum mechanics.
German nuclear project
Werner Heisenberg proposed his Uncertainty principle in 1927.
An example of an implication of the uncertainty principle (as well as wave-particle duality) is a phenomenon known as quantum tunneling. Quantum tunneling is also known as barrier penetration. This is one of the more bizarre results of quantum mechanics. This is when particles can borrow energy from their surroundings, thus, allowing particles to tunnel through walls or barriers. The energy also must be given back by a specified time.
These are actual particles tunneling through potential energy barriers. These are barriers that classical entities can't move through. Without quantum tunneling, atomic nuclei could never decay by emitting alpha particles. This was proposed by George Gamow in 1928. The alpha particle has a small (however, non-zero) probability of tunneling through and escaping the nucleus.
Indeed, according to the Heisenberg uncertainty principle, there is a limit to the precision that certain pairs of particle properties can be known at the same time. The example I gave above is position and momentum. A more general interpretation of this idea will be formulated by Bohr in 1928.
Niels Bohr formulated this "principle of complementarity" in 1928. These are complementary properties that cannot both be known precisely at the same time. Examples of complementary phenomenon are:
Position and momentum
Wave and particle
Energy and duration
Entanglement and coherence
Paul Dirac, in 1928, is going to extend the work of Pauli, his so called Pauli equation. The Pauli equation, describes the spin of electrons. Dirac extended the equation, indeed, to account for special relativity. Thus, the Dirac wave equation, was a "relativistic wave equation." The equation is consistent, both with quantum mechanics and special relativity. The Dirac equation could also describe all massive spin-1/2 particles, such as quarks and the electron. The idea was that the equation could describe electrons that orbit the atomic nucleus at significant fractions of the speed of light.
Paul Dirac
Another interesting result emerged from this work by Dirac. When the results would yield negative for the value of energy of the electron, Dirac thought fast. He proposed a solution, the existence of an antimatter counterpart to the electron: the positron. Every elementary particle has a corresponding antiparticle. Antiparticles have the same mass as their normal particle counterpart, however, opposite electric charge. When a particle and it's antiparticle meet, they are both destroyed in a burst of energy known as annihilation. Indeed, the relativistic Dirac wave equation, predicted the existence of antimatter. Antimatter was experimentally confirmed to exist in 1932 by Carl D. Anderson.
Paul Dirac, in 1928, proposed a relativistic wave equation, known as the Dirac equation, to describe electron orbits at significant fractions of the speed of light. In so doing, Dirac predicted the existence of antimatter.
These are some of the tenets of the Copenhagen interpretation of quantum mechanics:
A wave function, will be the state of some system. It is all the known information about a system in quantum mechanics.
Due to the Heisenberg uncertainty principle, some properties of a system, can not both be understood with precision, at the same time.
A wave function, upon it's measurement, collapses, from a probability amplitude of several potential eigenstates or potential outcomes, to a single and definite eigenstate.
1927, Solvay Conference: Brussels, Belgium
The Copenhagen interpretation of quantum mechanics is the standard way to explain the bizarre behavior of quantum mechanics. It was put together at Bohr's institute in Copenhagen in the 1920s.
It also should be noted that the nature of the wave-function is probabilistic and it expresses wave-particle duality. The future cannot be measured with absolute certainty, however, statistical behavior can be determined from the behavior of many quantum systems. At the quantum level, nothing really exists until it is observed. Until observation, an electron, is just a wave of probability.
Other interpretations of quantum mechanics:
Richard Feynman
In 1947, Richard Feynman developed an alternative interpretation to quantum mechanics. This is known as the "path integral" or "sum over histories" method. In this interpretation, a particle can follow all possible paths at the same time! An implication of this interpretation was that a particle in the double-slit experiment goes through both slits at once. The particle will follow two paths at the same time. The electron in the double-slit experiment, according to the path integral method, will follow all possible paths from the source to the screen. The final observed position of the particle is the combination of all the possible paths. The most paradoxical part of this interpretation is that the particle remains point-like the entire time. There is no matter wave nor is there a wave of probability. Even more alarming is that the results of this interpretation come out identical to the results yielded from the Copenhagen interpretation (which instead, uses waves of probability).
If you are ever discouraged and feel that you are having trouble understanding the quantum theory, keep in mind the words of the American physicist Richard Feynman:
"I think I can safely say that nobody understands quantum mechanics."
David Bohm
In 1952, David Bohm, will publish two papers on quantum mechanics. Bohm proposed an alternate explanation and extension of the wavefunction that involved the particles having an actual configuration, even when not observed. This is opposed to, in the Copenhagen interpretation, where, nothing really exists until it is observed. The idea was that particles must exist whether or not they are being observed. Bohm reinterpreted the wave function by doing away with the notion of wave-particle duality. The particles remained particles. For example, in the double-slit experiment the electron would only pass through one of the slits. It's path would be guided by something called a quantum potential. The quantum potential was a kind of energy field which would emerge from the wavefunction. The quantum potential will influence the way the particles move and will result in the observed interference pattern. The quantum mechanics of Bohm is rejected by many and is considered by some to only be another kind of weirdness and not a better substitute or alternative to the Copenhagen interpretation of quantum mechanics.
Hugh Everett
In 1957, Hugh Everett proposed the Many-worlds interpretation of quantum mechanics. Instead of the measurement of a quantum system reducing the system from a number of potential outcomes to one definite outcome, the entire Universe will split into a number of parallel realities equal to the number of potential outcomes.
In the Many-world's interpretation of quantum mechanics, we will observe one outcome in our universe, however, all other possible outcomes will be viewed in another universe that exists parallel to ours. Some physicists favor this view, while others find it hard to accept.
H. Dieter Zeh
The Many-worlds interpretation of quantum mechanics can be understood further by using a fundamental of the quantum theory known as "decoherence". Quantum decoherence was discovered in 1970 by H. Dieter Zeh. According to quantum decoherence, the alternate universes created in the MWI will never be accessible to us. This is because:
once their is a measurement done, the measured system is entangled with both the observer and with a large number of other particles.
some of these other particles are photons moving at the speed of light.
to prove that the wave-function did not collapse, one would have to bring all of these particles back and measure them again.
In quantum mechanics, an electron can be described by it's wavefunction as having different probabilities of being measured to be in different locations. There even exists a probability that the electron can exist in more than one state at once. Decoherence can explain why these superpositions are not measured in observation. Quantum decoherence can be understood as the loss of a system's information into it's environment. A quantum system can become too entangled to it's surroundings and some of it's quantum properties can leak out of the system. A quantum system will lose relevant quantum properties through this decay of coherence. For example, when an electron interacts with other particles, or is observed, the probability of it existing in more than place disappears.
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