On Monday, August 26, 2019 at 11:52:38 AM UTC-5, Alan Grayson wrote: > > Is the existence of the quantum foam, with virtual particles incessantly > coming into existence and being annihilated, generally accepted? If I > recall correctly, Bruce was extremely doubtful, claiming it's based on > reifying, or making concrete, terms in an approximation method which are > alleged to be off-shell particles. AG > > This discussion has a couple of confusions. Quantum foam refers to the hypothesis that spacetime is roiling with undulations in its metric description on a small scale due to the uncertainty principle. Virtual particles are descriptions of fields that are not on-shell due to the uncertainty principle and these occur in a fixed spacetime background.
Virtual particles have two meanings. First they define a zero point energy in a vacuum. For standard QFT these can be removed by a procedure called normal ordering. A usual method in QFT is to assign zero commutators between field amplitudes separated by spatial distances. This is called the Wightman condition, and it imposes a form of locality on QFT. Because of this we can simply assign a lowering operator b and b raising operator b^† on different regions, ignore the commutator [b, b^†] = 1, take a limit the two are at the same place and then justify shoving operators b^† to the left and b to the right. This is really a bit tricky, for we are removing an infinite ZPE by taking a type of calculus limit and people into axiomatic QFT spent a lot of time worrying about this. It also clips some wing feathers off from quantum nonlocality, because we are doing this in a classical spacetime. The other meaning for virtual particles is in Feynman diagrams for internal diagram lines, lines with endpoint vertices internal and not at the end of the diagram, and these are evaluated as sums over momenta and are not on-shell. In effect a bare charge or mass for a quantum particle couples to the vacuum in a way that renormalizes the charge and mass of the bare charge/mass of the particle. These virtual particles in a sense "exist" below the uncertainty bound ΔpΔx ≥ ħ and are then not directly observable. Two electrons with momenta p1 and p2 may have a virtual photon between them so the electrons have final mometa p1 + p and p2 - p. where this virtual photon acts as a conveyor of momenta. However, this is evaluated for the virtual photon with a summation of possible momenta. Quantum foam refers to a similar situation for spacetime. A particles with some mass m that is quantized may have amplitudes for being at x and y, and this does mean there is a quantum superposition of the metric for gravity at x and y. Without the mass spacetime for reasons similar to the ZPE vacuum will also have an uncertainty description. This is with a standard quantization perspective of spacetime, which outside of maybe very weak gravity or low momenta cut-off has some serious problems. Also the above conditions on QFT are not very applicable, for in effect the field is spacetime itself and how can one really assign that field to some point in spacetime? String theory has a background metric, which allows one to perturbatively work around this some. String theory description of quantum gravity is more successful that loop quantum gravity, but it has some difficulties of its own. In addition the spacetime foam in loo[p quantum gravity predicts that different wavelengths of light will be perturbed differently, shorter wavelength more so, and this means there is some dispersion of photons. However measurement of the arrival times for photons at different wavelengths from very distant burstars has found no such dispersion. The LQG mavens have made some work arounds on this, but the idea of quantum foam has its troubles. LC -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/33652a25-4a7e-4713-a2bd-fe16284aef7e%40googlegroups.com.
