Quantum Gravity (1900s)
It appeared that it would be difficult to reconcile quantum mechanics and Einstein's theory of special relativity in order to develop a quantum mechanical theory of fields. This is because time is defined differently in quantum mechanics to relativity. In quantum mechanics time is a parameter and spatial position is an observable. This is why the energy-time uncertainty relation is different to that of the position-momentum uncertainty relation. This problem can be resolved by either making time an observable and proper time a parameter or by treating position like a parameter. Quantum field theory does the later although both methods will give the same results.
The development of quantum field theory began with Dirac's equations of charged matter in electromagnetic fields, published in 1927 (Dirac, pp.243). Quantum field theory was soon extended to cover the nuclear weak and nuclear strong forces (Kuhlmann, 2006). In quantum field theory, forces are mediated by particles; the electromagnetic force is mediated by an exchange of photons, the weak nuclear force is mediated by intermediate vector bosons and the strong nuclear force is mediated by gluons.
A quantum theory of gravity is needed to describe objects which are small but have a very high mass, such as black holes and other singularities, including the very early universe. Most theories of quantum gravity suggest that the gravitational force is mediated by gravitons, hypothetical particles with no charge or rest mass. However, developing a quantum theory of gravity has proven more difficult than quantum theories of the other three forces.
Quantum field theory suggests that fields are quantised at each point in spacetime. This means that the energy-time uncertainty relationship, which is responsible for quantum tunnelling, will apply to each point and energy must be 'created' here in the same way. On a sufficiently large scale the effects of this energy can be ignored but on a quantum scale, Einstein's spacetime must be full of fluctuating energy. This can appear in the form of particles and antiparticles which immediately annihilate each other. Objects formed in this way are referred to as 'virtual' because they cannot exist for very long, and vacuum energy is sometimes referred to as zero point energy.
In 1948, Dutch physicists Hendrik Casimir and Dirk Polder discovered the Casimir effect (Casimir and Polder, pp.360-372). This shows that if two mirrors are placed opposite each other in a vacuum and then pushed together slightly, they will start to attract each other. This is because when the mirrors are moved together some of this energy is forced out and so the total energy between the mirrors is less than the energy behind them. This effect was first demonstrated by American physicist Steve Lamoreaux in 1996 (Lamoreaux, pp.5-8). In 1981, Soviet physicists Viacheslav Mukhanov and G. Chibisov showed that quantum fluctuations, which occurred 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.
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In 1974, English physicist Stephen Hawking showed that virtual particles can become 'real', meaning that they can continue to exist in time, if they are removed from their anti partner and gain enough energy from an outside source (Hawking, pp.30-31). 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. When the black hole contains more Hawking radiation than matter and energy it will start to evaporate and eventually disappear.
It is possible that a vast amount of vacuum energy can be produced as long as it only persists for a short period of 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 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. There will be many more disordered states than ordered ones, however, and this may make it more likely that the external world we observe is real.
The concept of Boltzmann brains is highly speculative because no one has been able to prove how a theory of quantum gravity will account for vacuum energy. Two popular approaches are loop quantum gravity and string theory. Loop quantum gravity was first suggested by Indian physicist Abhay Ashtekar in 1986 (Ashtekar, pp. 2244-2247) and extended by Italian physicist Carlo Rovelli and American physicist Lee Smolin in 1988. Loop quantum gravity suggests that gravity becomes repulsive at high densities, this prevents singularities from forming and therefore avoids the problem of uniting quantum mechanics and general relativity at this level. This effect also implies that there may have been a time before the big bang. Loop quantum gravity applies quantum theory to the gravitational field but, unlike string theory, it does not try to unite gravity with the other three forces.
String theory was devised in the 1960s by American physicists Geoffrey Chew, Steven Frautschi, Yoichiro Nambu and Leonard Susskind and Danish physicist Holger Bech Nielsen. In 1974, Japanese physicist Tamiaki Yoneya showed that string theory predicts the existence of the graviton (Yoneya, pp. 1907-1920) and shortly after this, American physicist John Schwarz and French physicist Joel Scherk suggested that string theory presents a quantum theory of gravity. String theory suggests that singularities cannot form by replacing the idea that a particle is a point mass with the idea that it is a one dimensional string or a higher dimensional membrane.
String theory relies on the idea that spacetime is composed of at least eleven dimensions, German mathematician Theodor Kaluza had previously added a fifth dimension to general relativity in 1919, after realising that a five dimensional description of gravity describes both gravity and electromagnetism in four dimensions. We cannot see these extra dimensions because they are too small to be noticed. This can be illustrated by the idea that we may not notice the width of a piece of thread, but it will seem wide to an ant walking across it. The different approaches to string theory have been united as M Theory. M theory suggests that our universe, and a vast amount of others, which may have completely different physical laws to our own, are created by collisions between membranes.
References
Ashtekar, A., 1986, 'New variables for classical and quantum gravity', Physical Review Letters, Vol.57
Casimir, H. B. G. and Polder, D., 1948, 'The Influence of Retardation on the London-van der Waals Forces', Physical Review, Vol.73
Dirac, P., 1927, 'The Quantum Theory of the Emission and Absorption of Radiation', Proceedings of the Royal Society of London, Series A, Vol. 114
Hawking, S. W., 1974, 'Black hole explosions?', Nature, Vol.248, pp.30-31
Kuhlmann, M., 2006, 'Quantum Field Theory', Stanford Encyclopedia of Philosophy
Lamoreaux, S. K., 1997, 'Demonstration of the Casimir Force in the 0.6 to 6 um Range', Physical Review Letters, Vol.78
Page, D.N., 2006, 'Return of the Boltzmann brains', Physical Review, Vol.78
Yoneya, T., 1974, 'Connection of Dual Models to Electrodynamics and Gravidynamics', Progress of Theoretical Physics, Vol.51