dorsal/arxiv
View SchemaRelativity as the quantum mechanics of space-time measurements
| Authors | Richard Lieu |
|---|---|
| Categories | |
| ArXiv ID | physics/0005034 |
| URL | https://arxiv.org/abs/physics/0005034 |
Abstract
Can a simple microscopic model of space and time demonstrate Special Relativity as the macroscopic (aggregate) behavior of an ensemble ? The question will be investigated in three parts. First, it is shown that the Lorentz transformation formally stems from the First Relativity Postulate (FRP) {\it alone} if space-time quantization is a fundamental law of physics which must be included as part of the Postulate. An important corollary, however, is that when measuring devices which carry the basic units of lengths and time (e.g. a clock ticking every time quantum) are `moving' uniformly, they appear to be measuring with larger units. Secondly, such an apparent increase in the sizes of the quanta can be attributed to extra fluctuations associated with motion, which are precisely described in terms of a thermally agitated harmonic oscillator by using a temperature parameter. This provides a stringent constraint on the microscopic properties of flat space-time: it is an array of quantized oscillators. Thirdly, since the foregoing development would suggest that the space-time array of an accelerated frame cannot be in thermal equilibrium, (i.e. it will have a distribution of temperatures), the approach is applied to the case of acceleration by the field of {\it any} point object, which corresponds to a temperature `spike' in the array. It is shown that the outward transport of energy by phonon conduction implies an inverse-square law of force at low speeds, and the full Schwarzschild metric at high speeds. A prediction of the new theory is that when two inertial observers move too fast relative to each other, or when fields are too strong, anharmonic corrections will modify effects like time dilation, and will lead to asymmetries which implies that the FRP may not be sustainable in this extreme limit.
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"abstract": "Can a simple microscopic model of space and time demonstrate Special\nRelativity as the macroscopic (aggregate) behavior of an ensemble ? The\nquestion will be investigated in three parts. First, it is shown that the\nLorentz transformation formally stems from the First Relativity Postulate (FRP)\n{\\it alone} if space-time quantization is a fundamental law of physics which\nmust be included as part of the Postulate. An important corollary, however, is\nthat when measuring devices which carry the basic units of lengths and time\n(e.g. a clock ticking every time quantum) are `moving\u0027 uniformly, they appear\nto be measuring with larger units. Secondly, such an apparent increase in the\nsizes of the quanta can be attributed to extra fluctuations associated with\nmotion, which are precisely described in terms of a thermally agitated harmonic\noscillator by using a temperature parameter. This provides a stringent\nconstraint on the microscopic properties of flat space-time: it is an array of\nquantized oscillators. Thirdly, since the foregoing development would suggest\nthat the space-time array of an accelerated frame cannot be in thermal\nequilibrium, (i.e. it will have a distribution of temperatures), the approach\nis applied to the case of acceleration by the field of {\\it any} point object,\nwhich corresponds to a temperature `spike\u0027 in the array. It is shown that the\noutward transport of energy by phonon conduction implies an inverse-square law\nof force at low speeds, and the full Schwarzschild metric at high speeds. A\nprediction of the new theory is that when two inertial observers move too fast\nrelative to each other, or when fields are too strong, anharmonic corrections\nwill modify effects like time dilation, and will lead to asymmetries which\nimplies that the FRP may not be sustainable in this extreme limit.",
"arxiv_id": "physics/0005034",
"authors": [
"Richard Lieu"
],
"categories": [
"physics.gen-ph"
],
"title": "Relativity as the quantum mechanics of space-time measurements",
"url": "https://arxiv.org/abs/physics/0005034"
},
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