I have worked on this diary entry a long time. I do not mean that it took me a lot of work time, I mean it took a long time to work. I originally started the post to simply say that I hated Schrödinger's cat. Then I found out that I was misguided, because Schrodinger's cat still lives! Yes, it is true that she is 76 years old, but she did not age while in the box (unknown quantum state) until she was released in 2000 by
Serge Haroche. After learning Kittish English, she moved to an unknown location in the US and is working as a fashion photographer. I find now that I have a lot of respect for that cat.
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| SCHRODINGER'S CAT |
However, I still hate
Schrodinger's cat thought experiment. It was a stupid thought (my opinion). Why not a rat? That sounds better, Schrodinger's rat experiment. Why in a box? Why not deep in a cave where you could not hear the poor tormented thing scratching and meowing as it thirsted to death? Why not have the diabolical device just turn on a lamp inside the box? - we would still have to say the lamp was in; an on and an off, quantum state until we looked to see for sure. At least you would not be talking about an uncertain probability state with a dead cat stinking up the room. What was wrong with the 'if a tree falls in the forest' thought experiment anyway?
Schrödinger's original purpose was to bring the quantum level world into the macro level world as a point of contention with the
Copenhagen interpretation of quantum mechanics.
It illustrates what he and others saw as the problems caused by thinking of the wave function as a real entity. I liked the response added by Einstein, "so if the trigger is hooked to dynamite instead of hydrocyanic acid, can the cat be thought of as both alive and blown to pieces"? As I was thinking through my thoughts on this thought experiment, I realized I needed to think some more about what caused Erwin to thunk up such a stupid thought.
That the Copenhagen interpretation became a dominate facet of quantum mechanics was the culmination of the 1927 Solvay Conference, and highlights one of the brightest periods of modern physics.
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| 1927 SOLVAY CONFERENCE ATTENDEES |
The Copenhagen interpretation of quantum physics developed between 1871 and 1927, due to the contributions of a remarkable collection of minds all working around this same time. They theorized a new world of discrete quantities of energy, entities which fit neither the classical idea of particles nor the classical idea of waves. These 'quanta' were not continuous in time, not divisible beyond a certain size, and could only be measured and defined as a state of 'probability'. Physicists were asked to step beyond the world of empirical experiments and pragmatic predictions and accept that the observer became a variable in the equations. According to their interpretation, the act of measurement causes the calculated set of probabilities to "collapse" to the value defined by the measurement. This feature of the mathematics is known as
wavefunction collapse. The concept that quantum mechanics does not yield an objective description of microscopic reality - but deals only with probabilities, and that measurement plays an ineradicable role - is the most significant characteristic of the Copenhagen interpretation.
The Newtonian world had become familiar territory where the physicist felt in control, leading to the famous quote, "There is nothing new to be discovered in physics now. All that remains is more and more precise measurement" (often cited to
William Thompson). However, as pointed out by the same Lord Kelvin, there were "dark clouds" on the horizon even then. The dark clouds he was alluding to were the unsatisfactory explanations that the physics of the time could give for two phenomena: the
Michelson–Morley experiment and
black body radiation. In 1871,
Ludwig Boltzmann and
James Maxwell formulated the
Maxwell–Boltzmann distribution. Boltzmann further identified the logarithmic connection between entropy and probability, which helped usher in the era of modern physics. Stating that the pressure of a gas arises from the force exerted by molecules or atoms impacting on the walls of its container,
kinetic theory developed a statistical probability in a quantized form. This was at a time when most physicists still did not believe in atoms or molecules. Then came a remarkable group of physicists that developed modern physics as we know it, and came together in Solvay, Belgium, in 1927.
Max Karl Ernst Ludwig Planck (April 23, 1858 – October 4, 1947) Won the Nobel Prize in Physics - 1918.
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| PLANCK 1878 |
The grandfather of quantum physics, Max Planck was working on
black body radiation for the power company in 1984. At first, Planck did not include energy quantization, and did not use
statistical mechanics, to which he held an aversion. In November 1900, Planck revised this approach, relying on Boltzmann's statistical interpretation of the second law of thermodynamics as a way of gaining a more fundamental understanding of the principles behind his radiation law. Even though Planck disliked the philosophical and physical implications of Boltzmann's approach, his recourse to them was, "an act of despair ... I was ready to sacrifice any of my previous convictions about physics." He eventually came up with the
Planck postulate, stating that electromagnetic energy could be emitted only in
quantized form, in other words, the energy could only be a multiple of an elementary unit E = hν, where h is
Planck's constant, also known as Planck's action quantum (introduced already in 1899), and ν is the frequency of the radiation.
(14 March 1879 – 18 April 1955) Won the Nobel Prize in Physics - 1921.
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| EINSTEIN 1905 |
As a young physicist, Einstein was convinced that Newtonian mechanics was no longer enough to reconcile the laws of classical mechanics with the laws of the
electromagnetic field. On 30 April 1905, Einstein completed his thesis and was awarded a PhD by the University of Zurich. His dissertation was entitled "A New Determination of Molecular Dimensions". Einstein published four additional papers in the
Annalen der Physik scientific journal that year. 1905 was Einstein's
annus mirabilis or "miracle year", and these papers could arguably mark the post-Newtonian age of physics. These four articles contributed substantially to the foundation of modern physics and changed views on space, time, and matter. (
1)
"On a Heuristic Viewpoint Concerning the Production and Transformation of Light", received March 18 and published June 9, proposed the idea of energy quanta. This idea, motivated by Max Planck's earlier derivation of the law of black body radiation, assumes that luminous energy can be absorbed or emitted only in discrete amounts, called quanta. (
2)
"On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat" received May 11 and published July 18, delineated a stochastic model of Brownian motion. Using the kinetic theory of fluids, this paper cemented the reality of the atom, and formalized the value of statistical mechanics. (
3)
"On the Electrodynamics of Moving Bodies" was received on June 30 and published September 26. It reconciles Maxwell's equations for electricity and magnetism with the laws of mechanics, by introducing major changes to mechanics close to the speed of light. This later became known as Einstein's special theory of relativity. (
4)
"Does the Inertia of a Body Depend Upon Its Energy Content?" was received on September 27 and published November 21. In this paper Einstein developed an argument for arguably the most famous equation in the field of physics:
E = mc2. Einstein considered the energy-matter equivalency equation to be of paramount importance because it showed that a massive particle possesses an energy, the "rest energy", distinct from its classical kinetic and potential energies.
Other important papers include;
- In 1907 and again in 1911, Einstein developed the first quantum theory of specific heats by generalizing Planck's law. His theory resolved a paradox of 19th-century physics that specific heats were often smaller than could be explained by any classical theory. His work was also the first to show that Planck's quantum mechanical law E=hν was a fundamental law of physics, and not merely special to blackbody radiation.
- Between 1907 and 1915, Einstein developed the theory of general relativity, a classical field theory of gravitation that provides the cornerstone for modern astrophysics and cosmology. General relativity is based on the surprising idea that time and space dynamically interact with matter and energy, and has been checked experimentally in many ways, confirming its predictions of matter affecting the flow of time, frame dragging, black holes, and gravitational waves.
- In 1917, Einstein published the idea for the Einstein-Brillouin-Keller method for finding the quantum mechanical version of a classical system. The famous Bohr model of the hydrogen atom is a simple example, but the EBK method also gives accurate predictions for more complicated systems, such as the dinuclear cations H2+ and HeH2+.
- In 1918, Einstein developed a general theory of the process by which atoms emit and absorb electromagnetic radiation (his A and B coefficients), which is the basis of lasers (stimulated emission) and shaped the development of modern quantum electrodynamics, the best-validated physical theory at present.
- In 1924, together with Satyendra Nath Bose, Einstein developed the theory of Bose-Einstein statistics and Bose-Einstein condensates, which form the basis for superfluidity, superconductivity, and other phenomena.
- In 1935, together with Boris Podolsky and Nathan Rosen, Einstein put forward what is now known as the EPR paradox, and argued that the quantum-mechanical wave function must be an incomplete description of the physical world.
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| BOHR ~1920 |
In 1912, Bohr went to work for Ernest Rutherford at Manchester University. By 1914, experiments by physicists Ernest Rutherford, Henry Moseley, James Franck, and Gustav Hertz had largely established the structure of an atom as a dense nucleus of positive charge surrounded by lower-mass electrons. Working with Rutherford's model, Bohr further postulated that electrons resided in quantized energy states, with the energy determined by the angular momentum of the electron's orbits about the nucleus. The electrons could move between these states, or orbits, by the emission or absorption of photons at specific frequencies. By means of these quantized orbits, he accurately explained the spectral lines of the hydrogen atom.This became a basis for quantum theory. Bohr also conceived the principle of complementarity: that items could be separately analyzed as having several contradictory properties. For example, Bohr concluded that light behaves either as a wave or a stream of particles depending on the experimental framework — two apparently mutually exclusive properties — on the basis of this principle. Bohr continued to be a champion of the Copenhagen interpretation throughout his life.
Werner Karl Heisenberg (5 December 1901 – 1 February 1976) Won the Nobel Prize in Physics - 1932.
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| HEISENBERG - 1927 |
On 1 May 1926, Heisenberg began his appointment as university lecturer and assistant to Bohr in Copenhagen. It was in Copenhagen, in 1927, that Heisenberg developed his
uncertainty principle, while working on the mathematical foundations of quantum mechanics. On 23 February, Heisenberg first described his theory in a letter to fellow physicist Wolfgang Pauli. Published in 1927, the principle implies that it is impossible to simultaneously both measure the present position while "determining" the future momentum of an electron or any other particle with an arbitrary degree of accuracy and certainty. This is not a statement about researchers' ability to measure one quantity while determining the other quantity. Rather, it is a statement about the laws of physics. That is, a system cannot be defined to simultaneously measure one value while determining the future value of these pairs of quantities. The principle states that a minimum exists for the product of the uncertainties in these properties that is equal to or greater than one half of ħ the reduced Planck constant (ħ = h/2π). For me the uncertainty principle is the basis of my life - the more information that I know about a subject, the less I understand - and this occurs at about the same ratio as Heisenberg's theory.
Louis-Victor-Pierre-Raymond, 7th duc de Broglie (15 August 1892 – 19 March 1987) Won the Nobel Prize in Physics - 1929.
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| DE BROGLIE ~ 1929 |
Broglie's, "Research on the Theory of the Quanta", was published in 1924 and introduced his theory of electron waves. This included the wave-particle duality theory of matter, based on the work of Max Planck and Albert Einstein on light. This research culminated in the de Broglie hypothesis stating that any moving particle or object had an associated wave. De Broglie thus created a new field in physics, the mécanique ondulatoire, or wave mechanics, uniting the physics of energy (wave) and matter (particle).
The concept of the particle creating the wave was supported by Einstein, confirmed by the
electron diffraction experiments of Davisson and Germer, and generalized by the work of Schrödinger (although unlike Schrödinger, de Broglie considered the wave to be real, not statististical).
Erwin Rudolf Josef Alexander Schrödinger (12 August 1887 – 4 January 1961) Won the Nobel Prize in Physics - 1933.
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| SCHRODINGER ~ 1927 |
In January 1926, Schrödinger published in Annalen der Physik the paper "Quantisierung als Eigenwertproblem" (
Quantization as an Eigenvalue Problem) on wave mechanics and what is now known as the
Schrödinger equation. In this paper he gave a "derivation" of the wave equation for time independent systems, and showed that it gave the correct energy eigenvalues for the hydrogen-like atom. This paper has been universally celebrated as one of the most important achievements of the twentieth century, and created a revolution in quantum mechanics, and indeed of all physics and chemistry. A second paper was submitted just four weeks later that solved the quantum harmonic oscillator, the rigid rotor and the diatomic molecule, and gives a new derivation of the Schrödinger equation. A third paper in May showed the equivalence of his approach to that of Heisenberg and gave the treatment of the
Stark effect. A fourth paper in this most remarkable series showed how to treat problems in which the system changes with time, as in scattering problems. These papers were the central achievement of his career and were at once recognized as having great significance by the physics community.
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| DIRAC - 1933 |
Dirac's "
Principles of Quantum Mechanics", published in 1930, is a landmark in the history of science. It quickly became one of the standard textbooks on the subject and is still used today. In that book, Dirac incorporated the previous work of Werner Heisenberg on matrix mechanics, and of Erwin Schrödinger on wave mechanics, into a single mathematical formalism that associates measurable quantities to operators acting on the
Hilbert space of vectors that describe the state of a physical system. The book also introduced the
delta function. He proposed the
Dirac equation as a relativistic equation of motion for the wavefunction of the electron. This work led Dirac to predict the existence of the
positron, the electron's antiparticle, which he interpreted in terms of what came to be called the
Dirac sea. Dirac's equation also contributed to explaining the origin of
quantum spin as a relativistic phenomenon.
Wolfgang Ernst Pauli (25 April 1900 – 15 December 1958) Won the Nobel Prize in Physics - 1945.
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| PAULI - 1945 |
Pauli made many important contributions in his career as a physicist, primarily in the field of
quantum mechanics. He seldom published papers, preferring lengthy correspondences with colleagues such as
Niels Bohr and
Werner Heisenberg, with whom he had close friendships. Many of his ideas and results were never published and appeared only in his letters, which were often copied and circulated by their recipients. Pauli was apparently unconcerned that much of his work thus went uncredited.
Pauli proposed in 1924 a new quantum degree of freedom (or
quantum number) with two possible values, in order to resolve inconsistencies between observed molecular spectra and the developing theory of quantum mechanics. He formulated the Pauli exclusion principle, perhaps his most important work, which stated that no two electrons could exist in the same quantum state, identified by four quantum numbers including his new two-valued degree of freedom. In 1926, shortly after Heisenberg published the matrix theory of modern quantum mechanics, Pauli used it to derive the observed spectrum of the hydrogen atom. This result was important in securing credibility for Heisenberg's theory.
Pauli introduced the 2 × 2
Pauli matrices as a basis of spin operators, thus solving the nonrelativistic theory of spin. This work is sometimes said to have influenced
Paul Dirac in his creation of the
Dirac equation for the relativistic electron. In 1930, Pauli considered the problem of beta decay. In a letter of 4 December to
Lise Meitner et al., beginning, "Dear radioactive ladies and gentlemen", he proposed the existence of a hitherto unobserved neutral particle with a small mass, no greater than 1% the mass of a proton, in order to explain the continuous spectrum of beta decay. In 1934,
Enrico Fermi incorporated the particle, which he called a
neutrino, into his theory of beta decay. The neutrino was first confirmed experimentally in 1956.
In 1940, he proved the
spin-statistics theorem, a critical result of quantum field theory which states that particles with half-integer spin are
fermions, while particles with integer spin are
bosons.
In 1949, he published a paper on
Pauli–Villars regularization: regularization is the term for techniques which modify infinite mathematical integrals to make them finite during calculations, so that one can identify whether the intrinsically infinite quantities in the theory (mass, charge, wavefunction) form a finite and hence calculable set which can be redefined in terms of their experimental values, which criterion is termed
renormalization, and which removes infinities from quantum field theories, but also importantly allows the calculation of higher order corrections in perturbation theory.
Max Born (11 December 1882 – 5 January 1970) Won the Nobel Prize in Physics - 1954.
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| BORN ~ 1912 |
In 1921, Born formulated the now-standard interpretation of the
probability density function for ψ*ψ in the Schrödinger equation of quantum mechanics. Up until this time, matrices were seldom used by physicists; they were considered to belong to the realm of pure mathematics. Born had used them in his work on the lattices theory of crystals in 1921. While matrices were used in these cases, the algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics. In 1925, Born and Werner Heisenberg formulated the matrix mechanics representation of quantum mechanics. On 9 July, Heisenberg gave Born a paper to review and submit for publication. In the paper, Heisenberg formulated quantum theory avoiding the concrete but unobservable representations of electron orbits by using parameters such as transition probabilities for quantum jumps, which necessitated using two indexes corresponding to the initial and final states. When Born read the paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices, which he had learned from his study under Jakob Rosanes at Breslau University. Born, with the help of his assistant and former student Pascual Jordan, began immediately to make the transcription and extension, and they submitted their results for publication; the paper was received for publication just 60 days after Heisenberg’s paper (Hiesenberg won the Nobel Prize for this work in 1932). Heisenberg wrote a letter to Born in which he said he had been delayed in writing due to a “bad conscience” that he alone had received the Prize “for work done in Göttingen in collaboration — you, Jordan and I.” Heisenberg went on to say that Born and Jordan’s contribution to quantum mechanics cannot be changed by “a wrong decision from the outside.” In 1954, Heisenberg wrote an article honoring Max Planck for his insight in 1900. In the article, Heisenberg credited Born and Jordan for the final mathematical formulation of matrix mechanics and Heisenberg went on to stress how great their contributions were to quantum mechanics, which were not “adequately acknowledged in the public eye.”
OK, so back to the cat, so one day Mrs Schrodinger calls her husband at work and says, "Erwin, have you seen the cat?"
The purpose of all of this is to try to understand how physicists reached the point we are now (and I want to focus on the time element). The people at the 1927 Solvay conference conceived quantum mechanics, and were, (it could be said 'still are') the ones that have explained it to the rest of us. These were the ring-leaders. They took away Newton and replaced it with uncertainty. Well, the
Copenhagen interpretation (subjective interpretation) divided the physics world into two major camps (each with many factions). Bohr, Born, and Heisenberg were leaders of the subjective interpretation of quantum mechanics. All versions of the Copenhagen interpretation include at least a formal or methodological version of
wave function collapse, in which unobserved
eigenvalues are removed from further consideration. The strictly subjective interpretation is that nothing at atomic scale is real, that a system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system. They believe that the observer brings reality through the act of observing. The Copenhagen interpretation rejects questions like "where was the particle before I measured its position?" as meaningless. The measurement process randomly picks out exactly one of the many possibilities allowed for by the state's wave function in a manner consistent with the well-defined probabilities that are assigned to each possible state. According to the interpretation, the interaction of an observer or apparatus that is external to the quantum system is the cause of wave function collapse, thus according to Heisenberg "reality is in the observations, not in the electron".
The other dissenting interpretation from Copenhagen was that quantum mechanics was not a complete theory (championed by Einstein, Schrodinger, and Pauli). It is unrealistic to make the tool into something more than a tool. So, the wavefunction, and probability are describing only a part of nature - mathematically. The current usage of "realism" and "completeness" originated in the 1935 paper in which Einstein and others proposed the
EPR paradox In that paper the authors proposed the concepts "element of reality" and the "completeness" of a physical theory. They characterised "element of reality" as a quantity whose value can be predicted with certainty before measuring or otherwise disturbing it, and defined a "complete physical theory" as one in which every element of physical reality is accounted for by the theory. In a semantic view of interpretation, an interpretation is complete if every element of the interpreting structure is present in the mathematics. Realism is also a property of each of the elements of the maths; an element is real if it corresponds to something in the interpreting structure. For example, in some interpretations of quantum mechanics (such as the many-worlds interpretation) the key vector associated to the system state is said to correspond to an element of physical reality, while in other interpretations it is not.
The state of physics changed completely within the period of about 15 years. In 1905 when Einstein published his first paper, Newtonian physics ruled the landscape. He was finally recognized for his work on light quanta in 1922 (he won the 1921 Nobel, the following year). By the time of the Solvay conference in 1927, quantum mechanics was nearly fully formed. We have made tremendous progress in the last 80 years, but we are still divided by the Copenhagen interpretation. It seems a handful of physicists took it the first 90% and all other physicists have been filling the remaining 10% since then.
Several of the other interpretations that still have a following are as follows;
Incomplete Theory: Classification adopted by Einstein
Main article:
Grand Unified Theory
The Copenhagen interpretation
Main article:
Copenhagen interpretation
Many worlds
Main article:
Many-worlds interpretation
Consistent histories
Main article:
Consistent histories
Ensemble interpretation, or statistical interpretation
Main article:
Ensemble interpretation
de Broglie–Bohm theory
Main article:
de Broglie–Bohm theory
Relational quantum mechanics
Main article:
Relational quantum mechanics
Transactional interpretation
Main article:
Transactional interpretation
Stochastic mechanics
Main article:
Stochastic interpretation
Objective collapse theories
Main article:
Objective collapse theory
von Neumann/Wigner interpretation: consciousness causes the collapse
Main article:
Quantum mind/body problem
Many minds
Main article:
Many-minds interpretation
Quantum logic
Main article:
Quantum logic
Other interpretations
Main article:
Minority interpretations of quantum mechanics
Time-symmetric theories
Main article:
RetrocausalityStudent: "What's the meaning of it all?"
Professor: "Shut up and calculate!"
The term 'wave' is not well defined. One person's interpretation of a wave will certainly conflict with another. When a surfer says 'he caused the wave to collapse', it is not the same as a quantum wave collapse.
