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waves and change
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Physics could be fundamentally discrete. Are their any notable theories that have discrete mathematics at its core and have QM, GR and differential equations in general as emergent features?
Here's a discrete part: https://en.wikipedia.org/wiki/Lattice_gauge_theorywaves and change said:Physics could be fundamentally discrete. Are their any notable theories that have discrete mathematics at its core..,
Here's one for that: https://en.wikipedia.org/wiki/Finite_difference_method... and have QM, GR and differential equations...
I didn't know there is one in a continusous set-up.... in general as emergent features?
waves and change said:Thank you !
I knew a professor who saw it the other way around: "Since there is nothing really continuous in the world out there, differentiabilty is an approximation of the discrete things which happen!" O.k. he mainly meant it to motivate the drawings of vector fields, but anyhow, there is some truth in it.waves and change said:Finite difference method is just a discrete method to approximate a diff. Equation.
waves and change said:Physics could be fundamentally discrete. Are their any notable theories that have discrete mathematics at its core and have QM, GR and differential equations in general as emergent features?
phyzguy said:Many people are working along these lines, but it is not simple. If spacetime is discrete, for example, it cannot simply be pixelized like the pixels on your display screen, because this would not be Lorentz invariant and would be observer dependent. An attempt to formulate a discrete model of spacetime, which I personally believe is in the right direction, is to use non-commutative geometry. This draws on the idea of quantum phase space, where the coordinates (x and px, ...) do not commute and the volume of quantum phase space is basically discrete in units of (2 π ħ)^3. An example that helped me to understand these ideas is that of the "fuzzy sphere", where the area of the sphere is discretized into N units (where N can be any integer from 2 on up) in a way that is observer independent. As N goes to infinity, one recovers the usual continuous spherical surface.
Discrete theory of physics, also known as discrete physics or digital physics, is a scientific theory that suggests that the universe is fundamentally made up of discrete, digital units rather than being continuous.
Traditional physics is based on the idea that the universe is continuous, meaning that it is composed of infinitely divisible elements. Discrete theory of physics, on the other hand, proposes that the universe is made up of discrete, indivisible units.
There are several pieces of evidence that support discrete theory of physics, including the quantization of energy levels in atoms, the discrete nature of quantum mechanics, and the discreteness of space and time at the Planck scale.
While there are some theories, such as string theory, that suggest a continuous universe, there is currently no experimental evidence that directly contradicts discrete theory of physics. However, further research and experiments are needed to fully understand the nature of the universe.
Discrete theory of physics challenges our traditional understanding of the universe and raises questions about the nature of reality and the fundamental laws of physics. It has the potential to provide a deeper understanding of the universe and may have practical applications in fields such as quantum computing and cosmology.