Sam Cottle
I'm a philosopher of science studying the problem of quantum gravity in theoretical physics. I've also made, albeit fairly amateurish, attempts to take on several problems in mathematics, although I consider myself more a hobbyist on the mathematical side of things than an expert. Other interests include, but aren't limited to: literature, history, politics, economics and psychology.
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The first question most readers, I suspect, would like to know the answer to is: ‘what is a theory of quantum gravity?’ The answer is relatively straightforward if you have a rough idea of the terms involved, but to someone who knows nothing about physics at all the answer might be baffling. A theory of quantum gravity is any theory that seeks to explain the force of gravity using quantum mechanical effects. To further unpack what that means requires an explanation of quantum mechanics, and of gravity, which I shall endeavour to give, in brief, in this introduction, as well as in more detail in the larger text.
Quantum mechanics is our theory of the very small. Or, to be more precise, it’s our theory of the smallest things in nature of which we’re aware. The smallest things in nature of which we’re aware are the subatomic particles of the so-called standard model of particle physics, the fermions and the bosons. Therefore, any theory of quantum gravity must use these basic tools, these particles, or ensembles of these particles, in its effort to explain how the force of gravity may be transmitted over large distances such as between the Earth and the Moon. The aspect of quantum theory that I will be invoking (among others later on) is that of quantum tunnelling to explain the force of gravity. In my model of gravity, to put it as simply as I possibly can, particles tunnel long distances through space to transmit forces via bosons (force-carrying particles) which we detect as the force of gravity.
As if quantum mechanics were not already weird enough, gravity (i.e. the force explained by Einstein’s theory of general relativity) also makes many bizarre predictions about the universe. It predicts that, when accelerated towards the speed of light, the hands of a clock will slow down to zero and time will cease to pass. It predicts that there are objects in the universe (black holes) whose gravity is so great that not even light can escape. And it predicts that we may be able to warp the fabric of space and time into a manifold around a spacecraft and travel at speeds faster than the speed of light. In the main, however, it invokes a cosmic speed limit, the speed of light (referred to in physics as c, or roughly 300,000,000 m/s). And I’m sorry to have to disappoint anyone at this point, but this novel theory of mine predicts that wrapping manifolds of spacetime around a ship would not be possible, nor (and, I think, for very good reasons, would time travel).
Building from some of the smallest entities that we’re aware of in the universe (atoms), my model for quantum gravity seeks to explain the large-scale force of gravity as being derived from the minute forces of attraction produced as a result of the gravity of those atoms. When thinking about gravity in relation to atoms one must think first about how, from a quantum-mechanical perspective, it may be possible for them to have gravity at all. The temptation in physics is to begin with general relativity and notions of curved spacetime, however, I propose a different approach, one that looks at the particles tunneling from atoms to regions close enough to the nuclei of other atoms to be able to exert a force of attraction over the protons in those nuclei. As we’re all aware from school, atoms consist of protons and neutrons in the centre (in the nucleus) with electrons orbiting around the nucleus. Electrons don’t exactly orbit the nucleus, but more on that later.
The notion I’m seeking to propound is that electrons from atoms tunnel a great distance from where they’re usually found and make their way inside other atoms to exert a force of attraction. They get close enough to a proton (within the electroweak range of the proton) to exchange a boson with it and it is via these means, taken at a larger scale, that we see the force of gravity emerge within the universe. When I say emerge, some may be tempted to confuse these notions with those of the theoretical physicist Erik Verlinde who proposed a similar model (emergent gravity) based on entangled bits of spacetime information; I propose no such model and propose the electron and electron densities as corresponding to spacetime and that tunneling, rather than entanglement, is the key quantum process underlying this model. That said, my model does bear similarities to many other quantum gravity models and may, in a sense, be considered a derivative of those models, including that of Verlinde; science tends to build on the research that has gone before and I consider this model to be merely the next step on the road to a complete theory of gravity.
A crucial element of any theory seeking to align a theory of gravity (as it’s currently understood) with a theory of quantum mechanics is that it needs to explain how gravity, via quantum particles, affects light. In the relativistic universe described by Albert Einstein the path of light through space is curved by the presence of masses (i.e. objects with mass) so therefore, as a candidate particle for a gravity particle that can affect light, I selected the electron due to what we know from quantum electrodynamics about the behaviour seen when particles of light (i.e. photons) interact with electrons. An electron will always reflect an incoming photon at an angle of 31 degrees, and from this, considering a cosmic background filled with electrons, it’s not so hard to imagine where the phenomena of the wave properties of light come from! As for the way that light particles come to be curved around massive objects, the answer is a little more convoluted, although I will endeavour to give a full explanation of this in due course.
The number of cosmic and astrophysical situations to which this model may be applied are enormous, and one of the striking things about this model is its versatility. There is one problem with too much versatility in science, however; if a theory is capable of explaining too many phenomena or is, in a sense, too complete, it runs the risk of becoming impossible to disprove, and hence becomes unscientific. It is the crucial quality of being possible to disprove, or falsify, that makes a hypothesis scientific and I thought I’d devote this last paragraph of the introduction to demonstrating possible means of falsifying this hypothesis. One way would be to analyse the data on neutrinos coming from supernovae which, against general relativity, arrive on Earth some time before light arrives on Earth. Another means of testing this hypothesis could be to construct a neutrino detector somewhere in the Solar System to measure for neutrinos being deflected by the Sun. If none are, i.e. if none follow the curved trajectories predicted in my model, then my hypothesis would be vindicated. Early on, too many things lined-up perfectly (it seemed) with this way of looking at the world for me to abandon it. So I continued my pursuit. In spite of a great deal of resistance from the mainstream community of theoretical physics I have produced this essay to summarise my idea and its implications. I hope the reader finds it informative and enjoys reading it as much as I did writing it.
This book is also about a very special ratio, and that is the number 4.17 x 10⁴² , the ratio between the force of electrostatic repulsion and the force of gravitational attraction that I recommend we call the gravito-electric fine-structure constant or , there are equations in this book, although I feel they’re simple enough for a lay audience to understand. I am a citizen scientist/philosopher of science and this book is my phenomenological theory on the phenomenon of quantum gravity.
I give easy-reading, whistle-stop tours of quantum mechanics, general relativity and quantum field theory before also giving an overview of popular approaches to quantum gravity are discussed.
The first question most readers, I suspect, would like to know the answer to is: ‘what is a theory of quantum gravity?’ The answer is relatively straightforward if you have a rough idea of the terms involved, but to someone who knows nothing about physics at all the answer might be baffling. A theory of quantum gravity is any theory that seeks to explain the force of gravity using quantum mechanical effects. To further unpack what that means requires an explanation of quantum mechanics, and of gravity, which I shall endeavour to give, in brief, in this introduction, as well as in more detail in the larger text.
Quantum mechanics is our theory of the very small. Or, to be more precise, it’s our theory of the smallest things in nature of which we’re aware. The smallest things in nature of which we’re aware are the subatomic particles of the so-called standard model of particle physics, the fermions and the bosons. Therefore, any theory of quantum gravity must use these basic tools, these particles, or ensembles of these particles, in its effort to explain how the force of gravity may be transmitted over large distances such as between the Earth and the Moon. The aspect of quantum theory that I will be invoking (among others later on) is that of quantum tunnelling to explain the force of gravity. In my model of gravity, to put it as simply as I possibly can, particles tunnel long distances through space to transmit forces via bosons (force-carrying particles) which we detect as the force of gravity.
As if quantum mechanics were not already weird enough, gravity (i.e. the force explained by Einstein’s theory of general relativity) also makes many bizarre predictions about the universe. It predicts that, when accelerated towards the speed of light, the hands of a clock will slow down to zero and time will cease to pass. It predicts that there are objects in the universe (black holes) whose gravity is so great that not even light can escape. And it predicts that we may be able to warp the fabric of space and time into a manifold around a spacecraft and travel at speeds faster than the speed of light. In the main, however, it invokes a cosmic speed limit, the speed of light (referred to in physics as c, or roughly 300,000,000 m/s). And I’m sorry to have to disappoint anyone at this point, but this novel theory of mine predicts that wrapping manifolds of spacetime around a ship would not be possible, nor (and, I think, for very good reasons, would time travel).
Building from some of the smallest entities that we’re aware of in the universe (atoms), my model for quantum gravity seeks to explain the large-scale force of gravity as being derived from the minute forces of attraction produced as a result of the gravity of those atoms. When thinking about gravity in relation to atoms one must think first about how, from a quantum-mechanical perspective, it may be possible for them to have gravity at all. The temptation in physics is to begin with general relativity and notions of curved spacetime, however, I propose a different approach, one that looks at the particles tunneling from atoms to regions close enough to the nuclei of other atoms to be able to exert a force of attraction over the protons in those nuclei. As we’re all aware from school, atoms consist of protons and neutrons in the centre (in the nucleus) with electrons orbiting around the nucleus. Electrons don’t exactly orbit the nucleus, but more on that later.
The notion I’m seeking to propound is that electrons from atoms tunnel a great distance from where they’re usually found and make their way inside other atoms to exert a force of attraction. They get close enough to a proton (within the electroweak range of the proton) to exchange a boson with it and it is via these means, taken at a larger scale, that we see the force of gravity emerge within the universe. When I say emerge, some may be tempted to confuse these notions with those of the theoretical physicist Erik Verlinde who proposed a similar model (emergent gravity) based on entangled bits of spacetime information; I propose no such model and propose the electron and electron densities as corresponding to spacetime and that tunneling, rather than entanglement, is the key quantum process underlying this model. That said, my model does bear similarities to many other quantum gravity models and may, in a sense, be considered a derivative of those models, including that of Verlinde; science tends to build on the research that has gone before and I consider this model to be merely the next step on the road to a complete theory of gravity.
A crucial element of any theory seeking to align a theory of gravity (as it’s currently understood) with a theory of quantum mechanics is that it needs to explain how gravity, via quantum particles, affects light. In the relativistic universe described by Albert Einstein the path of light through space is curved by the presence of masses (i.e. objects with mass) so therefore, as a candidate particle for a gravity particle that can affect light, I selected the electron due to what we know from quantum electrodynamics about the behaviour seen when particles of light (i.e. photons) interact with electrons. An electron will always reflect an incoming photon at an angle of 31 degrees, and from this, considering a cosmic background filled with electrons, it’s not so hard to imagine where the phenomena of the wave properties of light come from! As for the way that light particles come to be curved around massive objects, the answer is a little more convoluted, although I will endeavour to give a full explanation of this in due course.
The number of cosmic and astrophysical situations to which this model may be applied are enormous, and one of the striking things about this model is its versatility. There is one problem with too much versatility in science, however; if a theory is capable of explaining too many phenomena or is, in a sense, too complete, it runs the risk of becoming impossible to disprove, and hence becomes unscientific. It is the crucial quality of being possible to disprove, or falsify, that makes a hypothesis scientific and I thought I’d devote this last paragraph of the introduction to demonstrating possible means of falsifying this hypothesis. One way would be to analyse the data on neutrinos coming from supernovae which, against general relativity, arrive on Earth some time before light arrives on Earth. Another means of testing this hypothesis could be to construct a neutrino detector somewhere in the Solar System to measure for neutrinos being deflected by the Sun. If none are, i.e. if none follow the curved trajectories predicted in my model, then my hypothesis would be vindicated. Early on, too many things lined-up perfectly (it seemed) with this way of looking at the world for me to abandon it. So I continued my pursuit. In spite of a great deal of resistance from the mainstream community of theoretical physics I have produced this essay to summarise my idea and its implications. I hope the reader finds it informative and enjoys reading it as much as I did writing it.
This book is also about a very special ratio, and that is the number 4.17 x 10⁴² , the ratio between the force of electrostatic repulsion and the force of gravitational attraction that I recommend we call the gravito-electric fine-structure constant or , there are equations in this book, although I feel they’re simple enough for a lay audience to understand. I am a citizen scientist/philosopher of science and this book is my phenomenological theory on the phenomenon of quantum gravity.
I give easy-reading, whistle-stop tours of quantum mechanics, general relativity and quantum field theory before also giving an overview of popular approaches to quantum gravity are discussed.