The existence of point particles and an infinite universe

[DrDu]

I think it is also interesting to consider the results of axiomatic quantum field theory (AQFT) like, e.g. the Reeh-Schlieder theorem
http://en.wikipedia.org/wiki/Reeh–Schlieder_theorem
which shows that sufficiently localized measurements will lead to the generation of field excitations arbitrarily far from the measurement region. Hence there are limits on the localizability of a particle.

 

[bhobba]

What becomes infinite as you approach the particle?

Classically the field becomes infinite via Coulomb's law.

QM wise as you approach the particle you are probing shorter distances which requires higher and higher energies. What QED tells us is the charge (specifically the coupling constant) actually depends on the energy scale you probe with - and in fact becomes infinite at what is called the Landau pole:
http://en.wikipedia.org/wiki/Landau_pole

However before that energy is reached the electroweak theory takes over and it is thought that gives way to another theory at even higher energy (string theory maybe). The bottom line is there are issues with current physics and quite possibly its pointing to we are not dealing with point particles.

Thanks
Bill