# Discrete spacetime means discrete momentum ?

1. Apr 16, 2008

### 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 lenght 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

2. Apr 16, 2008

### 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.