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How Relevant Is a Theory of Quantum Gravity Today.Docx How relevant is a Theory of Quantum Gravity Today? Quantum mechanics and relativity: the enigma. The interaction of all matter in the universe occurs on the basis of four fundamental forces. These four forces are gravity, electromagnetism, the strong force and the weak force. Gravity, causing the attraction of massive objects; electromagnetism, causing magnets to repel and like charges to repel; the strong force, causing the particles in nuclei to be attracted to one another; and the weak force, causing the emission of radiation from unstable nuclei. Every phenomenon we witness is governed by these distinguished four forces. In the universe which is governed by these four forces, there are two widely accepted theories which agree with experimental evidence in their own fields, and are able to make accurate predictions. The first of these theories is the Theory of Relativity, devised by Einstein in two parts, Special Relativity and General Relativity. His paper on Special Relativity was published in 1905, and was the birth of the famous equation E=mc2, which states the relationship between mass and energy. This paper also made the prediction that as an object’s velocity tended towards the speed of light, then to a stationary observer, a time interval relative to the object would be significantly greater relative to the stationary observer (i.e., if one of two twins went on a rocket at near the speed of light, when they return to Earth the twin from the rocket will have aged less than the twin who stayed on Earth). This was then proven experimentally in the Around-the-World Relativistic Sagnac Experiment. In this experiment, a slowly moving portable atomic clock was moved Eastwards around the earth’s equator once, and was shown to lag an atomic clock on the earth’s surface by about 207.4x10-9 seconds (D. W. Allan, Apr. 5th, 1985). The paper on General Relativity was released in 1916, and predicted the bending of light due to gravity, which was actually observed shortly after the paper was released, when there was an eclipse of the sun, and the positions of stars in the sky shifted to be visible when they were actually hidden directly by the sun (Thompson, 2012, p. 39). However, although many successful predictions were devised from the Theory of Relativity, there are in fact still problems with infinities in the theory. For example, the theory predicts that in two circumstances, the density of matter will become infinite, and hence so will the force of gravity. These circumstances are those in a black hole, and those in the universe’s infancy. For the strength of the gravitational field to be infinite is clearly not a real phenomenon, so perhaps this suggests that the Theory of Relativity is not applicable in all situations, leading to the notion that a new theory must be devised to incorporate the conditions where Relativity breaks down (Smolin, 2007, p. 5). The second of these is Quantum Mechanics, which was also discovered by Einstein in 1905, in his famous paper on the Photoelectric effect. This paper explored the relationship between firing electromagnetic radiation onto a metal surface, and detecting electrons being emitted from that surface. The revolutionary feature of this experiment was the discovery of electromagnetic radiation appearing as discrete quanta instead of as a continuous wave. This was demonstrated experimentally by the measurement of the threshold frequency for different metals, where electron emission from a metal only began after electromagnetic radiation with a certain energy was directed at the metal. This proved that light behaved as discrete quanta, however in other experiments light was proven to act as a wave, and so although quantum mechanics can make accurate predictions, it still includes elements of uncertainty. Quantum mechanics also includes serious issues with infinities, for example when using quantum mechanics to describe the electromagnetic field. As the electromagnetic field has a value at every point in space, then in a finite volume there is an infinite number of points, and so an infinite number of variables. This rapidly leads to predictions of infinite numbers. Infinities suggest that there is a problem with the theory itself, implying that perhaps it is somewhat incomplete. (Smolin, 2007, p. 6) What do we already know? A theory of quantum gravity should incorporate ideas of gravity on a quantum scale, for example the interaction of sub-atomic particles due to their mass. An important question to ask, then, is how do we know that gravity does have such an attractive effect on sub-atomic particles? An extremely sensitive piece of equipment called an X-ray interferometer was developed at Cornell university in 1964 by Ulrich Bonse and Michael Hart. It was originally believed that the interferometer would not work for neutrons, which unlike X-rays have mass, and so it was 10 years later in 1974 when the first neutron interferometer was operated, by Ulrich Bonse, Helmut Rauch and W. Triemer. The neutron interferometer was an apparatus which can detect the phase difference of neutron waves over very small distances. It is made out of a single crystal up to 10cm in length, which must be free of any misalignments and faults in the regular crystalline structure. (Greenberger & Overhauser, 1980) The neutron interferometer sensitive enough to detect the change in wavelength of a neutron beam of wavelength approximate to 10-8cm of 0.5λ in relation to the other beam. Furthermore, the microscopic effect this has on the amplitude of the neutron wave due to the change in phase of the wave can be translated into the macroscopic change in the relative counting rate of the detectors. (Greenberger & Overhauser, 1980) The importance of this device was massive in measuring the effect of gravity on the phase of a neutron wave. Before the effect of gravity was directly measured in 1975, in the COW experiment, physicists were already aware of the effect gravity caused neutrons to fall, no different to any other object which possessed mass. However, this was understood on a classical basis, not quantized, which is the problem I mentioned in the introduction: we are trying to explain gravity in a quantized theory, in order to extend quantum mechanics to involve the fourth force of nature. The importance of this experiment was that it could demonstrate the effect of gravity on the wave nature of a neutron. To do this, the interferometer was rotated about the incident beam, to give a difference in the gravitational potentials of the split beam. What the experiment demonstrated, was that as the height difference increased, the difference in phase of the neutron waves increased. (Greenberger & Overhauser, 1980 p 71) state that this phase difference had to be separated from a classical side effect of gravity. Hence, the COW experiment proves that a weak gravitational field can shift the phase of a neutron wave, which shows that gravity appears in Schrödinger’s equation like any other force would. (Greenberger & Overhauser, 1980) Although this experimental evidence does prove directly the existence of gravity influencing quantum mechanical properties, we are looking for a theory which always holds. Gravity can already be perturbatively quantized, quantized meaning understood on a quantum, discrete level; and a perturbative theory is an approximation of the original equation, which may be too complicated to solve. The issue becomes apparent when calculations are made at very high energies, exceeding the Planck energy. The theory really has no predictive power at these high energies. Hence, the theory is unsatisfactory as it does not describe all phenomenon, and so cannot be considered a fundamental theory. (Hossenfelder, 2015) The reason that we can’t use experiments to directly understand the effects of quantum gravity is that the conditions where general relativity and quantum mechanics both essentially crossover is at the Planck length~10-33cm, and the Planck energy~1019GeV (Ashtekar, 2005). In comparison to this figure, the current most powerful particle accelerator, the Large Hadron Collider in Geneva, can generate collisions at 13TeV, which is approximately ≈104GeV, so the Planck Energy is roughly 1015 times greater than the energy the Large Hadron Collider can collide particles with. However, there are future plans for new particle accelerators, for example the Future Circular Collider, which would have a circumference of 100km (the circumference of the Large Hadron Collider is 27km), allowing particles to reach energies of 100TeV, roughly 10 times greater than the energies reached in the Large Hadron Collider. Although this would be a major improvement compared to the Large Hadron Collider, it would not bring us much closer to the Planck energy. (Anon., 2021) So, to conclude, gravity can have an effect on quantum mechanical events, which has been demonstrated by the neutron interferometer, by shifting their phases when the two neutron beams were at different heights. However, the quantized theory of gravity which we currently have breaks down at the Planck energy. To understand gravity completely in a quantized manner would solve the conundrum of the different realities which quantum mechanics and general relativity both paints. This new theory must either be an extension of the first, or a new theory entirely. Already, there is an outstanding new theory which has potential to unify physics, but lacks any experimental evidence to show any legitimacy. This theory is called String Theory, which will be a topic of later discussion. Introduction to theories of everything Throughout human history, we have sought reason for the occurring phenomena which transpire in the world around us, some of those explanations being Theories of Everything. It could be argued that some of the first Theories of Everything were fashioned in mythological culture.
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