Discrete spacetime means discrete momentum ?

[mhill]

discrete spacetime means discrete momentum ??

the question is using De Broglie's Wavelength $$\lambda = h|p|^{-1}$$

then in case space is discrete would mean that there is a minimum possible wavelength in nature , for example $$\lambda = k l_{p}$$ for Planck's length this would mean that the maximum allowed momentum modulus would be $$h(k l_{p})^{-1}$$ for 'k' a constant , then since momentum is finite and spacetime is also finite there wouldn't be any IR or UV divergences but does this make sense

 

[genneth]

Yes. Lattice models are often used in calculations for high energy physics or in condensed matter when considering lattices. However, note that discrete spacetime may not be that simple --- if we take GR seriously and treat the spacetime as part of the system, it will be in a quantum superposition of states, and it may not be necessarily the case that physical properties are still as manifestly discretised.

 

[denian]

?

I would say that the concept of discrete spacetime does not necessarily imply discrete momentum. While it is true that a discrete spacetime would lead to a minimum possible wavelength, this does not necessarily mean that momentum must also be discrete. Momentum can still vary continuously within the constraints of a discrete spacetime.

Furthermore, the idea of a minimum possible wavelength in nature is still a topic of debate in physics. While some theories, such as string theory, suggest a minimum length scale, it has not been experimentally confirmed. Therefore, it would be premature to say that discrete spacetime automatically leads to discrete momentum.

Additionally, the statement that there wouldn't be any IR or UV divergences in a discrete spacetime is not necessarily true. Divergences can still arise in calculations involving discrete quantities, and it would depend on the specific theory being used.

In summary, while there may be some connections between discrete spacetime and discrete momentum, it is not a direct implication and more research and experimentation would be needed to fully understand these concepts.