Posts Tagged ‘DIRAC

Dirac, Majorana and the others

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Searching for an equation

S. Esposito
We review the non-trivial issue of the relativistic description of a quantum mechanical system that, contrary to a common belief, kept theoreticians busy from the end of 1920s to (at least) mid 1940s.

Starting by the well-known works by Klein-Gordon and Dirac, we then give an account of the main results achieved by a variety of different authors, ranging from de Broglie to Proca, Majorana, Fierz-Pauli, Kemmer, Rarita-Schwinger and many others.

A particular interest comes out for the general problem of the description of particles with arbitrary spin, introduced (and solved) by Majorana as early as 1932, and later reconsidered, within a different approach, by Dirac in 1936 and by Fierz-Pauli in 1939.

The final settlement of the problem in 1945 by Bhabha, who came back to the general ideas introduced by Majorana in 1932, is discussed as well, and, by making recourse also to unpublished documents by Majorana, we are able to reconstruct the line of reasoning behind the Majorana and the Bhabha equations, as well as its evolution.

Intriguingly enough, such an evolution was identical in the two authors, the difference being just the period of time required for that: probably few weeks in one case (Majorana), while more than ten years in the other one (Bhabha), with the contribution of several intermediate authors.

Majorana’s paper of 1932, in fact, contrary to the more complicated Dirac-Fierz-Pauli formalism, resulted to be very difficult to fully understand (probably for its pregnant meaning and latent physical and mathematical content): as is clear from his letters, even Pauli (who suggested its reading to Bhabha) took about one year in 1940-1 to understand it.

This just testifies for the difficulty of the problem, and for the depth of Majorana’s reasoning and results…..

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Written by physicsgg

November 1, 2011 at 6:56 pm

Posted in High Energy Physics

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Solving the Dirac Equation

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Alternative Discrete Energy Solutions to the Free Particle Dirac Equation
Thomas Edward Brennan
 The usual method of solving the free particle Dirac equation results in the so called continuum energy solutions. Here, we take a different approach and find a set of solutions with quantized energies which are proportional to the total angular momentum……
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Written by physicsgg

October 28, 2011 at 11:46 am

Posted in High Energy Physics, MATHEMATICS

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Why antimatter should matter to us

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The news that scientists can capture and store antimatter could have a profound effect on our understanding of the universe, says Tom Chivers.

The birth of a star: the ability to capture antimatter means that we can begin to 'study the animal in captivity' rather than document its destruction

Sixteen minutes is not a particularly long time. It’s enough time for a cup of tea, or to run two miles, if you’re in good shape. But if you have a few atoms of antimatter, it may be enough time to learn about the birth of the universe.

On Sunday, scientists at the European Organization for Nuclear Research (Cern) generated excited headlines worldwide when it was announced that they had created and stored antimatter – the elusive “mirror image” of everything we see around us – in a stable state for the first time. They have managed to keep atoms of antihydrogen – the antimatter equivalent of hydrogen, the simplest element – trapped for 1,000 seconds, or 16 minutes and 40 seconds. Their previous record stood at just 172 milliseconds, or rather less than a fifth of a second. It’s an exciting breakthrough, but one that may have been hard to grasp for those of us without a physics degree.

To understand it, we first need to know what matter and antimatter really are. The universe is made of subatomic particles – electrons, protons and neutrons being the best known. In 1928, the English physicist Paul Dirac, a pioneer of quantum mechanics, created a detailed mathematical model of the subatomic world – but he realised that, for his equations to work, he required a particle with the same mass as an electron, but with the opposite, “positive” charge. In 1932, an American, Carl Anderson, observed such a particle, which became known as a positron. Later, it became clear to physicists that every particle of matter had an associated antiparticle. In 1955, researchers at the University of California at Berkeley identified an antineutron and antiproton.

But studying this antimatter was not easy. When an antiparticle of any kind meets its matter counterpart, the pair annihilate each other in a small but fierce burst of energy. An atom of antihydrogen, consisting of a positron and an antiproton, would instantly vanish upon contact with any matter. The only way to store antimatter, then, is to keep it in a magnetic field.

Until very recently, that meant that only subatomic antiparticles could be stored and studied because only charged antiparticles, antiprotons and positrons, can be manipulated by a magnetic field. Whole atoms do not have an electric charge and so magnets were of limited use.
Last December, however, the Antihydrogen Laser Physics Apparatus (Alpha) team at Cern managed a world first: to make and trap whole atoms of antihydrogen using magnetic fields. At very low temperatures, anti-atoms will behave like minuscule magnets. Only when they are close to absolute zero are anti-atoms sluggish enough to be guided, even with powerful superconducting magnets. It was a remarkable technical feat, but a short-lived one: the team only held the antihydrogen for a few microseconds, before turning off the fields and allowing the anti-atoms to annihilate with matter. They then observed the resulting bursts with their detectors.

Amazing as this was, there is only so much we can learn about antimatter from such experiments. We want to watch its existence, not just document its destruction. As Tom Whyntie, a physicist at Cern, said: “It’s the difference between observing an animal’s tracks or droppings, and studying it in captivity.” And it is the latest breakthrough that may make such observation possible. Professor Jeffrey Hangst, a spokesman for the Alpha team, explained: “1,000 seconds is long enough to begin to study [antihydrogen atoms] – even with the small number that we can catch so far.”

We need to look back to the start of the universe, 13.7 billion years ago, to explain why this is important. In the moments after the Big Bang, the universe – according to our understanding – consisted of equal parts matter and antimatter. If that is the case, we should expect that the two would annihilate each other, but they did not. Almost all the antimatter in the universe is long gone, but somehow, we were left with enough matter to create a working universe.

That would make sense if there were some difference between antimatter and matter which meant that antimatter disappeared more readily. But it is a fundamental feature of modern physics, stretching back to Dirac’s equations, that antimatter and matter are symmetrical. “Any hint of symmetry-breaking would require a serious rethink of our understanding of nature,” says Prof Hangst. “But half of the universe has gone missing, so some kind of rethink is on the agenda.” Indeed, the very fact of our existence is one of the greatest mysteries facing modern physics.

A key goal of antimatter physics, then, is to find out what the asymmetry – or difference between matter and antimatter – is. There are two obvious starting points: first, does antihydrogen react to light in the same way as ordinary hydrogen; and second, does it interact with gravity in the usual fashion. Later this year, experiments will begin to determine both.

The first involves spectroscopy and is similar to the methods used to determine the chemical make-up of distant stars. By bombarding an atom with lasers or microwaves, scientists can see what frequencies the atom absorbs, and so learn more about its nature. “If you hit the trapped antihydrogen atoms with the right microwave frequency, they will escape the trap, and we can detect the annihilation – even for just a single atom,” explains Prof Hangst. “This would provide the first ever look inside the structure of antihydrogen – element number one on the anti-periodic table.” The second experiment, known as Aegis (Antimatter Experiment: Gravity, Interferometry, Spectroscopy), will determine whether antimatter falls to Earth in the same way as matter.

Will scientists find any evidence of asymmetry? It’s not clear, just as it’s not clear what it will mean if they do or don’t. Prof Hangst says: “If we find no difference, that just means that in this system, to this degree of accuracy, we can’t find a difference. You get that a lot in this kind of physics. But finding a difference would be really interesting. There is no model for what it would mean, and nothing, a priori, to suggest what we might find. It’s not obvious that it would point you towards what happened in the first moments of the universe. But it would mean that we haven’t understood everything.”

For now, though, simply being able to produce and capture the exotic anti-stuff is achievement enough. It may lead to profound breakthroughs at the very edge of physics. Or it may not. But there is only one way to find out – as Prof Hangst says: “My philosophy is, if you get hold of some antimatter, you should take the chance to look long and hard at it.”

Catching atoms

British physicist Paul Dirac, winner of the Nobel Prize for physics in 1933, first predicted the existence of an antimatter particle

• What is antimatter?

The universe is made up of subatomic particles, most famously the electron, proton and neutron. Every kind of particle has an associated antiparticle with the opposite electrical charge – electron and positron; proton and antiproton etc.

• Who discovered it?

The English physicist Paul Dirac, one of the fathers of quantum mechanics, realised in 1928 that for his equations to work, an antiparticle must exist. In 1932, the American Carl Anderson confirmed Dirac’s prediction.

• Where did it come from?

At the birth of the universe, matter and antimatter were created in equal amounts. One of the great unsolved mysteries of modern physics is why antimatter was almost entirely destroyed.

Powering starships and planting bombs: antimatter has featured in (left to right) Star Trek, Star Wars and Avatar.

Star Trek (1969)

Annihilation of matter and antimatter fuels the Starship Enterprise’s warp engines

Star Wars (1977-2005) The Jedi Interceptor hyperdrive rings utilise antimatter to provide density for the starship to remain in hyperspace

Angels & Demons (2009)

Terrorists plant an antimatter bomb underneath the Vatican

Avatar 2009

Mile-long interstellar spaceships cruise at 670 million miles per hour courtesy of hybrid antimatter fusion engines
Read also “Future is bright for CERN antimatter physicists

Written by physicsgg

June 7, 2011 at 11:15 am

Posted in High Energy Physics

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