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### Dayton Miller - Wikipedia

Ralph Fowlerhis research supervisor, had received a proof copy of an exploratory paper by Werner Heisenberg in the framework of the old quantum theory of Bohr and Sommerfeld. Heisenberg leaned heavily on Bohr's correspondence principle but changed the equations so that they involved directly observable quantities, leading to the matrix formulation of quantum mechanics. Fowler sent Heisenberg's paper on to Dirac, who was on vacation in Bristol, asking him to look into this paper carefully.

Dirac's attention was drawn to a mysterious mathematical relationship, at first sight unintelligible, that Heisenberg had reached.

Several weeks later, back in Cambridge, Dirac suddenly recognised that this mathematical form had the same structure as the Poisson brackets that occur in the classical dynamics of particle motion. From this thought, he quickly developed a quantum theory that was based on non-commuting dynamical variables. This led him to a more profound and significant general formulation of quantum mechanics than was achieved by any other worker in this field.

For this work, [55] published inDirac received a PhD from Cambridge. Dirac was famously not bothered by issues of interpretation in quantum theory. In fact, in a paper published in a book in his honour, he wrote: I want to deal with more fundamental things.

Dirac's equation also contributed to explaining the origin of quantum spin as a relativistic phenomenon. Thus reinterpreted, in by Werner Heisenbergas a quantum field equation accurately describing all elementary matter particles — today quarks and leptons — this Dirac field equation is as central to theoretical physics as the MaxwellYang—Mills and Einstein field equations.

Dirac is regarded as the founder of quantum electrodynamicsbeing the first to use that term. He also introduced the idea of vacuum polarisation in the early s. This work was key to the development of quantum mechanics by the next generation of theorists, in particular SchwingerFeynmanSin-Itiro Tomonaga and Dyson in their formulation of quantum electrodynamics. Dirac's The Principles of Quantum Mechanicspublished inis a landmark in the history of science.

It quickly became one of the standard textbooks on the subject and is still used today. The book also introduced the delta function.

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Following his article, [60] he also included the bra—ket notation in the third edition of his book, [61] thereby contributing to its universal use nowadays. Magnetic monopoles InDirac proposed that the existence of a single magnetic monopole in the universe would suffice to explain the quantisation of electrical charge. Inhe proposed a speculative cosmological model based on the so-called large numbers hypothesis. During World War II, he conducted important theoretical and experimental research on uranium enrichment by gas centrifuge.

Dirac's quantum electrodynamics QED made predictions that were — more often than not — infinite and therefore unacceptable. A workaround known as renormalisation was developed, but Dirac never accepted this. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it is small — not neglecting it just because it is infinitely great and you do not want it! However, from his once rejected notes he managed to work on putting quantum electrodynamics on "logical foundations" based on Hamiltonian formalism that he formulated.

He found a rather novel way of deriving the anomalous magnetic moment "Schwinger term" and also the Lamb shiftafresh inusing the Heisenberg picture and without using the joining method used by Weisskopf and French, and by the two pioneers of modern QED, Schwinger and Feynman.

Weisskopf and French FW were the first to obtain the correct result for the Lamb shift and the anomalous magnetic moment of the electron. At first FW results did not agree with the incorrect but independent results of Feynman and Schwinger.

After having relocated to Florida to be near his elder daughter, Mary, Dirac spent his last fourteen years of both life and physics research at the University of Miami in Coral Gables, Floridaand Florida State University in Tallahassee, Florida. In the s in his search for a better QED, Paul Dirac developed the Hamiltonian theory of constraints [70] based on lectures that he delivered at the International Mathematical Congress in Canada.

## Werner Heisenberg

The Hamiltonian of constrained systems is one of Dirac's many masterpieces. They showed that the successful formula Kramers had developed earlier could not be based on Bohr orbits, because the transition frequencies are based on level spacings which are not constant. The frequencies which occur in the Fourier transform of sharp classical orbits, by contrast, are equally spaced. But these results could be explained by a semi-classical virtual state model: In a subsequent paper Heisenberg showed that this virtual oscillator model could also explain the polarization of fluorescent radiation.

These two successes, and the continuing failure of the Bohr-Sommerfeld model to explain the outstanding problem of the anomalous Zeeman effect, led Heisenberg to use the virtual oscillator model to try to calculate spectral frequencies.

The method proved too difficult to immediately apply to realistic problems, so Heisenberg turned to a simpler example, the anharmonic oscillator. The dipole oscillator consists of a simple harmonic oscillatorwhich is thought of as a charged particle on a spring, perturbed by an external force, like an external charge.

The motion of the oscillating charge can be expressed as a Fourier series in the frequency of the oscillator. Heisenberg solved for the quantum behavior by two different methods. First, he treated the system with the virtual oscillator method, calculating the transitions between the levels that would be produced by the external source.

## Louis de Broglie

He then solved the same problem by treating the anharmonic potential term as a perturbation to the harmonic oscillator and using the perturbation methods that he and Born had developed. Both methods led to the same results for the first and the very complicated second order correction terms.

This suggested that behind the very complicated calculations lay a consistent scheme. So Heisenberg set out to formulate these results without any explicit dependence on the virtual oscillator model. To do this, he replaced the Fourier expansions for the spatial coordinates by matrices, matrices which corresponded to the transition coefficients in the virtual oscillator method.

He justified this replacement by an appeal to Bohr's correspondence principle and the Pauli doctrine that quantum mechanics must be limited to observables. On 9 July, Heisenberg gave Born this paper to review and submit for publication. When Born read the paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices, [36] which he had learned from his study under Jakob Rosanes [37] at Breslau University.

Born, with the help of his assistant and former student Pascual Jordanbegan 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. Gustav Mie had used them in a paper on electrodynamics in and Born had used them in his work on the lattice theory of crystals in 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.

As applied in the university environment, political factors took priority over the historically applied concept of scholarly ability, [48] even though its two most prominent supporters were the Nobel Laureates in Physics Philipp Lenard [49] and Johannes Stark.

His attempt to be appointed as the successor to Arnold Sommerfeld failed because of opposition by the Deutsche Physik movement. However, Sommerfeld stayed in his chair during the selection process for his successor, which took until 1 December The process was lengthy due to academic and political differences between the Munich Faculty's selection and that of the Reichserziehungsministerium REM, Reich Education Ministry and the supporters of Deutsche Physikwhich was anti-Semitic and had a bias against theoretical physicsespecially quantum mechanics and the theory of relativity.

Inthe Munich Faculty drew up a list of candidates to replace Sommerfeld as ordinarius professor of theoretical physics and head of the Institute for Theoretical Physics at the University of Munich. The three candidates had all been former students of Sommerfeld: The Munich Faculty was firmly behind these candidates, with Heisenberg as their first choice. However, supporters of Deutsche Physik and elements in the REM had their own list of candidates, and the battle dragged on for over four years.

During this time, Heisenberg came under vicious attack by the Deutsche Physik supporters. In this, Heisenberg was called a "White Jew" i. Heisenberg fought back with an editorial and a letter to Himmler, in an attempt to resolve this matter and regain his honour.

At one point, Heisenberg's mother visited Himmler's mother. The two women knew each other, as Heisenberg's maternal grandfather and Himmler's father were rectors and members of a Bavarian hiking club. In the letter to Heydrich, Himmler said Germany could not afford to lose or silence Heisenberg, as he would be useful for teaching a generation of scientists. To Heisenberg, Himmler said the letter came on recommendation of his family and he cautioned Heisenberg to make a distinction between professional physics research results and the personal and political attitudes of the involved scientists.

The most influential of the three was Johannes Juilfs. During their investigation, they had become supporters of Heisenberg as well as his position against the ideological policies of the Deutsche Physik movement in theoretical physics and academia.

On 15 Julyhe was attacked in a journal of the SS. However, Heisenberg refused an invitation to emigrate to the United States. The project had its first meeting on 16 September Most of the energy released is in the form of the kinetic velocities of the fission products and the neutrons.

The trouble with Professor Einstein is that he knows nothing about my results. He wrote to me in November suggesting this. I am not so simple as to make no allowance for temperature.

### Paul Dirac - Wikipedia

During the s a number of experiments, both interferometry based, as in Miller's experiment, and others using entirely different techniques, were conducted and these returned a null result as well.

Even at the time, Miller's work was increasingly considered to be a statistical anomaly, an opinion that remains true today, [12] given an ever-growing body of negative results. Kuerti performed a re-analysis of Miller's results.

**Aportes a la física por Albert Einstein**

Shanklandwho led the report, noted that the "signal" that Miller observed in is actually composed of points that are an average of several hundred measurements each, and the magnitude of the signal is more than 10 times smaller than the resolution with which the measurements were recorded. Miller's extraction of a single value for the measurement is statistically impossible, the data is too variable to say "this" number is any better than "that"—the data, from Shankland's position, supports a null result as equally as Miller's positive.

Shankland concluded that Miller's observed signal was partly due to statistical fluctuations and partly due to local temperature conditions and, also, suggested that the results of Miller were due to a systematic error rather than an observed existence of aether.

In particular he felt that Miller did not take enough care in guarding against thermal gradients in the room where the experiment took place, as, unlike most interferometry experiments, Miller conducted his in a room where the apparatus was deliberately left open to the elements to some degree. In Shankland's analysis, no statistically significant signal for the existence of aether was found. Shankland concluded that Miller's observed signal was spurious, due mainly to uncontrolled temperature effects rather than to the observed existence of an aether.