dorsal/arxiv
View SchemaA microscopic derivation of Special Relativity: simple harmonic oscillations of a moving space-time lattice
| Authors | Lieu, Richard |
|---|---|
| Categories | |
| ArXiv ID | physics/0004007 |
| URL | https://arxiv.org/abs/physics/0004007 |
Abstract
The starting point of the theory of Special Relativity$^1$ is the Lorentz transformation, which in essence describes the lack of absolute measurements of space and time. These effects came about when one applies the Second Relativity Postulate to inertial observers. Here I demonstrate that there is a very elegant way of explaining how exactly nature enforces Special Relativity, which compels us to conclude that Einstein's great theory has already revealed quantization of space and time. The model proposes that microscopically the structure of space-time is analogous to a crystal which consists of lattice points or `tickmarks' (for measurements) connected by identical `elastic springs'. When at rest the `springs' are at their natural states. When set in motion and used to measure objects at rest, however, the lattice effectively vibrates in a manner described by Einstein's theory of the heat capacity of solids, with consequent widening of the `tickmarks' because the root-mean-square separation now increases. I associate a vibration temperature $T$ with the speed of motion $v$ via the fundamental postulate of this theory, viz. the relation $\frac{v^2}{c^2} = e^{-\frac{\epsilon}{kT}}$ where $\epsilon$ is a quantum of energy of the lattice harmonic oscillator. A moving observer who measures distances with such a vibrating lattice obtains results which are precisely those given by the Lorentz transformation. Apart from its obvious beauty, this approach provides many new prospects in understanding space and time. For example, a consequence of the model is that space-time, like mass, can in principle be converted to energy.
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"abstract": "The starting point of the theory of Special Relativity$^1$ is the Lorentz\ntransformation, which in essence describes the lack of absolute measurements of\nspace and time. These effects came about when one applies the Second Relativity\nPostulate to inertial observers. Here I demonstrate that there is a very\nelegant way of explaining how exactly nature enforces Special Relativity, which\ncompels us to conclude that Einstein\u0027s great theory has already revealed\nquantization of space and time. The model proposes that microscopically the\nstructure of space-time is analogous to a crystal which consists of lattice\npoints or `tickmarks\u0027 (for measurements) connected by identical `elastic\nsprings\u0027. When at rest the `springs\u0027 are at their natural states. When set in\nmotion and used to measure objects at rest, however, the lattice effectively\nvibrates in a manner described by Einstein\u0027s theory of the heat capacity of\nsolids, with consequent widening of the `tickmarks\u0027 because the\nroot-mean-square separation now increases. I associate a vibration temperature\n$T$ with the speed of motion $v$ via the fundamental postulate of this theory,\nviz. the relation $\\frac{v^2}{c^2} = e^{-\\frac{\\epsilon}{kT}}$ where $\\epsilon$\nis a quantum of energy of the lattice harmonic oscillator. A moving observer\nwho measures distances with such a vibrating lattice obtains results which are\nprecisely those given by the Lorentz transformation. Apart from its obvious\nbeauty, this approach provides many new prospects in understanding space and\ntime. For example, a consequence of the model is that space-time, like mass,\ncan in principle be converted to energy.",
"arxiv_id": "physics/0004007",
"authors": [
"Lieu",
"Richard"
],
"categories": [
"physics.acc-ph",
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"title": "A microscopic derivation of Special Relativity: simple harmonic oscillations of a moving space-time lattice",
"url": "https://arxiv.org/abs/physics/0004007"
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