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sâmbătă, 13 aprilie 2013

From Fields and Forces to Boltzmann Brain

A field describes something that varies continuously through space and time, like a wave, and creates a "condition in space" whereby a particle will "feel" a force (Feynman, 1963). Field theories describe how forces interact with matter.

A field that permeates space was introduced to physics in the 18th century in order to describe Newtonian gravity. This field described the gravitational force felt by a mass at any point in space. Field theory was next applied in the 19th century to electromagnetism. British physicist Michael Faraday coined the term 'field' in order to describe these interactions in 1849. Maxwell discovered that waves in these fields travel at a finite speed. At first, Maxwell did not think of a field as a fundamental entity and suggested that the electromagnetic field propagated through the aether.

Fields were not thought of as independent entities until after German-American physicist Albert Einstein's theory of special relativity in 1905. Until this point it was thought that the force of gravity could be felt instantaneously over vast distances. Einstein showed that the force of gravity travelled at the speed of light - if the Sun suddenly disappeared we would feel the effect at the same time as it gets dark, not eight minutes before.

Quantum field theories were invented to explain how forces work taking into account both quantum mechanics and special relativity. In the 1900s it was shown that there are at least four fundamental forces; the electromagnetic force, the strong nuclear force, the weak nuclear force and the force of gravity. It was shown that forces are actually 'transmitted' by particles, the fundamental bosons; photons, gluons and Z and W bosons.

The Electromagnetic Force
The first quantum field theory described the electromagnetic field and is known as quantum electrodynamics (QED). All charged particles, like protons and electrons, interact via the electromagnetic force, the force that conveys electric charge. The electromagnetic force is about 10^40 (100 thousand billion billion billion billion) times stronger than the force of gravity but often doesn't effect large objects because most things have charges that cancel making them neutral, whereas gravity always effects everything with mass.

British physicist Paul Dirac coined the term QED in 1927 when he provided a quantum theory of the electromagnetic field which explained how an atom can decay to a lower and therefore less energetic state, and still follow the laws of the conservation of energy. It does this by emitting the excess energy in the form of a photon. Dirac showed this by treating the electromagnetic field as if it was a gas made up of photons which act as harmonic oscillators. Within a year, he published his relativistic theory of the electron which combined quantum mechanics with special relativity. This showed that the electron has a spin of plus or minus 1/2 and not only predicted the existence of the anti-electron - an electron with a negative energy, and therefore an opposite spin and charge - but that all particles have corresponding anti-particles. Matter and antimatter annihilate each other upon contact and the entire rest mass of the particles is converted to kinetic energy in accordance with special relativity.

In 1932, within four years of Dirac's prediction, American physicist Carl Anderson discovered antielectrons, which he named positrons, from tracks produced by cosmic rays inside of a cloud chamber. That same year British physicist Patrick Blackett and Italian physicist Giuseppe "Beppo" Occhialini showed that photons can produce positrons and electrons in pairs if they are energetic enough. They did this by improving the efficiency of cloud chamber records by linking the chamber to Geiger counters that triggered the camera when a particle arrived.

In the 1930s other physicists including Austrian physicist Wolfgang Pauli, Hungarian-American physicist Eugene Wigner, German physicists Pascual Jordan and Werner Heisenberg and Italian physicist Enrico Fermi helped extend Dirac's idea to form the basis for modern QED theory.

QED not only describes how light and matter interact but how all charged particles interact with one another. Whilst photons can be thought of as both particles and waves, QED treats them as particles that 'carry' the electromagnetic force. Charged particles interact by emitting and absorbing photons. Photons do not experience the electromagnetic force themselves and so they do not interact with each other but the effects of electromagnetism are produced by the energy and momentum they carry.

The photons that carry force are 'virtual' particles. Virtual particles are created in the instant a particle emits or absorbs a photon, the total energy and momentum of the system is the same before and after, but Heisenberg's uncertainty principle allows for 'extra' energy to exist in the form of a particle for a very brief period of time. Each virtual particle can be thought of as a harmonic oscillator, the strength of the field given by the displacement from its rest position.

Virtual particles exist for such a short period of time that they are essentially invisible and can only be detected by the effect they have on the particle that emits or absorbs them. Force carrying photons are therefore different from photons produced by other means, like in nuclear fusion, which could potentially exist forever.

By 1939 however American physicist Robert Oppenheimer, Swiss physicist Felix Bloch and American physicists Arnold Nordsieck and Victor Weisskopf had all shown that this version of QED could not be correct. This is because it led to the prediction that the energy, mass and charge of a single electron was infinite, which clearly did not match observations.

By 1940 American physicists Willis Lamb and Robert Retherford had found another problem with QED. Lamb and Retherford measured hydrogen lines in the microwave spectrum in order to study the difference in energy between the S and P states. It was predicted that the two states should have equal energy but a magnetic field could induce an energy difference between them. Lamb and Retherford measured this difference and then calculated what the difference would be if there was no magnetic field. To their surprise it was not zero. The two states did not have equal energy after all. This difference is known as the Lamb shift and could not be explained by QED.

In the 1947 'Shelter Island Conference on Quantum Mechanics', which took place in Long Island, New York, over 20 physicists - including Lamb, Oppenheimer, German-American physicist Hans Beth and American physicists Julian Schwinger, Richard Feynman and David Bohm - discussed whether QED could solve these problems.

On the train ride home Bethe suggested that the infinite values could be removed in a process known as renormalisation, where most of the infinities cancel out leaving just the measured values. This theory was developed in the late 1940s by Schwinger and Feynman and Japanese physicist Tomonaga Shin'ichiro. British-American physicist Freeman Dyson later showed that the two approaches were equivalent. The problem of Lamb shift was solved with the realisation that different corrections were needed for S and P states as they differ in their average distance from the nucleus.

The possible ways in which charged particles can interact by exchanging virtual photons are represented by Feynman diagrams. These were devised by Feynman in the 1940s and 1950s. They show a plot of time and space with straight lines used to depict fermions like electrons and wavy lines to depict bosons like virtual photons. Antiparticles are represented as normal particles that are moving backwards in time.


1) Feynman diagram showing how an electron changes trajectory when it emits a photon.
2) Feynman diagram showing one electron emitting a photon and a second electron absorbing it, this exchange of energy is reflected in the electrons new trajectories.
Image credit: Encyclopaedia Britannica

Illustration of the Casimir effect
Image credit: Wiki commons


Quantum field theories state that all fundamental fields must be quantized at each point in space - which means that they can be thought of as virtual particles coming in and out of existence almost everywhere. The temporary change in the amount of energy in a point in space is known as a quantum fluctuation. All of this excess energy - known as zero-point energy or vacuum energy - should add to the energy density of the universe. If space is infinitely divisible then it should produce an infinite amount of energy yet this does not seem to be the case and we will probably not understand how vacuum energy effects the energy density of the universe until we have quantum field theories of the gravitational force.

In 1948 Dutch physicists Hendrik Casimir and Dirk Polder discovered the Casimir effect which demonstrates measurable forces possibly arising from vacuum energy. Casimir and Polder showed that if two uncharged metal plates are placed close enough together in a vacuum, and are then pushed together slightly, they will start to attract each other.

This is because the vacuum energy between the plates contains contributions from all whole wavelengths that fit in the gap between the plates. As they are pushed together more wavelengths are excluded and the radiation pressure between the plates decreases. This change in energy pulls the plates together. This effect becomes the dominant force if the plates are less than a micrometre (one-thousandth of a millimetre) apart and was first demonstrated by American physicist Steve Lamoreaux in 1997. In 1961 Russian physicists Igor Ekhiel'evich Dzyaloshinskii, Evgeny Mikhailovich Lifshitz and Lev Petrovich Pitaveskii predicted that some materials can be made to repel each other via the Casimir effect, if the medium between them is not a vacuum, and this was shown experimentally in 2009.

Some argue that the Casimir effect does not provide evidence for vacuum energy as it can also be explained in terms of relativistic van der Waals forces - the forces between neutral atoms - which were given a quantum description by German physicist Fritz London in 1930. Quantum van der Waals forces occur because the negative charge of the electrons in an atom and the positive charge of the nuclei are not always in the same place relative to each other. The fluctuation of charge can result in attractive forces between atoms, in this case the atoms that make up the metal plates.

The theoretical evidence for vacuum energy is still extremely strong. The strongest evidence comes from the problem of spontaneous symmetry breaking.

In 1981 Soviet physicists Viacheslav Mukhanov and G. Chibisov showed that quantum fluctuations that were present during the inflationary epoch of the early universe can explain the asymmetry in spacetime which led objects to becoming gravitationally bound, creating structure in the universe.

Virtual particles are usually created with an antimatter partner and they annihilate each other almost instantly but a virtual particle can become 'real' if it is removed from its anti-partner and gains the required amount of energy from an outside source. In 1974 British physicist Stephen Hawking showed that this is what happens at the edge of black holes. To an observer on either side, the constant production of particles would make it seem as if the black hole was emitting radiation and so this effect is known as Hawking radiation. Hawking argued that black holes will start to evaporate and eventually disappear when they contain more Hawking radiation than matter and energy.

Black holes only have mass and sometimes charge and angular momentum but they retain no information about the matter that formed them. If black holes existed forever then this information would be thought of as existing within the black hole. If they evaporate by emitting Hawking radiation then the information appears to be lost forever.

In quantum mechanics information loss violates unitarity which is another way of saying that it violates the conservation of probability because it makes the sum of probabilities of all possible quantum outcomes different from 1. This may mean breaking the laws of energy conservation. The question whether information is truly lost in black holes is known as the black hole information paradox.

It is possible that a vast amount of vacuum energy can be produced as long as it persists for a short enough time. In 2006 Canadian physicist Don Page popularised the idea that every possible object could be created and, if we accept a material theory of the mind, then this includes conscious beings. These are known as Boltzmann brains because it was Austrian physicist Ludwig Boltzmann who first suggested that macroscopic objects could arise as the result of random interactions. If the universe continues to evolve in the way that we predict then there will be a point when there are no more biological minds and it is suggested that in this time, Boltzmann brains will outnumber all other observers who have ever existed. This implies that it is more likely we are a Boltzmann brain than the product of a biological mind, and so it is unlikely that the external world exists in the way that we think. Few Boltzmann brains will become 'real' and so the past is more likely to be an illusion than to have actually happened, although this theory is still extremely controversial.

References
 
Feynman, R.P., 1963, 'The Feynman Lectures on Physics Volume 1', Caltech, pp.2–4

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