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Since distances have to be multiples of the quantum of length, how can there be irrational distances? Please provide a non-technical explanation if possible, or correct me if my assumption is wrong.
I don't know of any theories that talk about distance, but I can mention a similar situation for area in LQG:Since distances have to be multiples of the quantum of length
Quantised geometry is a mathematical framework that describes the properties and behavior of physical space at a very small scale, such as at the level of subatomic particles. It combines concepts from quantum mechanics and geometry to understand the fundamental structure of the universe.
Irrational distances in quantised geometry refer to the measurement of distances that cannot be expressed as a simple fraction or ratio. These distances are considered to be "incommensurable" and do not have a finite or repeating decimal representation. They are important in understanding the discrete and non-continuous nature of quantised geometry.
Irrational distances play a crucial role in quantised geometry as they challenge our traditional understanding of space as a continuous and infinitely divisible entity. Instead, they suggest that space is made up of discrete units that are not infinitely divisible, and that the distances between these units may not always be rational or measurable in traditional ways.
Irrational distances have significant implications in physics, particularly in the study of quantum mechanics and the behavior of subatomic particles. They suggest that at a fundamental level, our understanding of space and distance may need to be revised, which could impact our understanding of physical laws and the behavior of matter at a very small scale.
Irrational distances in quantised geometry are studied using mathematical models and simulations that incorporate principles from quantum mechanics and geometry. These models help us to better understand the behavior of space and distance at a very small scale, and how irrational distances may impact our understanding of the universe.