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Lynch101
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- TL;DR Summary
- Trying to understand the issue of continuity vs discreteness.
I've come across the question of continuity vs discreteness in different articles, discussions, etc. but I'm not sure that I am 100% clear on what the precise question is.
My basic interpretation of it is a question of whether the Universe is made up of lots of separate entities which all interact with each other, or if it is just one single continuous thing. To us the analogy of a jigsaw puzzle, it would be like questioning whether the Universe is more like the completed jigsaw puzzle, with all the different pieces fitted together to give the complete picture, or if it is more like the picture on the box that the puzzle comes in, a single, continuous entity not made up of lots of different parts.
The idea of the Universe as being made up of lots of discrete parts would seem to follow naturally from the subatomic picture of the world, where the world is made up of atoms or subatomic particles all interacting with each other.
Is it more precise to say that the question relates to spacetime i.e. the question is, more precisely, is spactime continuous or discrete? To my mind this would, essentially, be the same question as asking whether the Universe is continuous or discrete. Is there a nuance that I am perhaps missing out on there? Could the jigsaw puzzle analogy still be applied in this instance?
I've also heard that the question of discreteness applies more to energy quanta and need not, necessarily, imply a lack of and underlying continuity. This idea is better articulated in this article: Nova - Are space and time discrete or continuous?
My basic interpretation of it is a question of whether the Universe is made up of lots of separate entities which all interact with each other, or if it is just one single continuous thing. To us the analogy of a jigsaw puzzle, it would be like questioning whether the Universe is more like the completed jigsaw puzzle, with all the different pieces fitted together to give the complete picture, or if it is more like the picture on the box that the puzzle comes in, a single, continuous entity not made up of lots of different parts.
The idea of the Universe as being made up of lots of discrete parts would seem to follow naturally from the subatomic picture of the world, where the world is made up of atoms or subatomic particles all interacting with each other.
Is it more precise to say that the question relates to spacetime i.e. the question is, more precisely, is spactime continuous or discrete? To my mind this would, essentially, be the same question as asking whether the Universe is continuous or discrete. Is there a nuance that I am perhaps missing out on there? Could the jigsaw puzzle analogy still be applied in this instance?
I've also heard that the question of discreteness applies more to energy quanta and need not, necessarily, imply a lack of and underlying continuity. This idea is better articulated in this article: Nova - Are space and time discrete or continuous?
I would take this to, effectively, be an argument in favour of a continuous spacetime/Universe. Would that be an accurate interpretation?While almost all approaches to quantum gravity bring in a minimal length one way or the other, not all approaches do so by means of “discretization”—that is, by “chunking” space and time. In some theories of quantum gravity, the minimal length emerges from a “resolution limit,” without the need of discreteness. Think of studying samples with a microscope, for example. Magnify too much, and you encounter a resolution-limit beyond which images remain blurry. And if you zoom into a digital photo, you eventually see single pixels: further zooming will not reveal any more detail. In both cases there is a limit to resolution, but only in the latter case is it due to discretization.
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