[Lukman]

Worth reading for this sentence (p.5): "The core obstacle to an integration of gravity in the context of quantum field theory is the occurrence of untreatable infinities in calculations of particle interactions due to the possibility of point particles coming arbitrarily close to each other." First time I've heard the problem of integrating gravity with QFT explained that way.

[c517402]

"untreatable infinities in calculations of particle interactions due to the possibility of point particles coming arbitrarily close to each other." This is actually very misleading. As mentioned in other comments, QED has "infinities in calculations of particle interactions due to the possibility of point particles coming arbitrarily close to each other," but these are treated via renormalization. QED (Quantum ElectroDynamics) is the QFT (Quantum Field Theory) based on Maxwells equations of Electromagnetism. Maxwells equations are linear partial differential equations and when converted to a quantized form, via QFT, the infinities can be dealt with by Renormalization. Einstein's General Relativity equations are non-linear partial differential equations and when converted to a quantized form, via QFT, the infinities cannot be dealt with by Renormalization. The quote makes it sound like classical point particles "coming arbitrarily close" is the problem with quantizing gravity(General Relativity), but the same problem exists in QED and yet QED yields a viable theory through Renormalization. The real difference is that Maxwell's equations are linear and Einstein's equations are non-linear. OTOH, the non-linearities in Einstein's equations do not become important until the particles are very close.

So, IMHO the quote is correct but misleading.

[westoncb]

I remember hearing about this issue—or perhaps a related one in another formulation/area of quantum theory—where the 'infinities' had to be treated by something called renormalization[0].

Every time I hear about these problematic 'infinities,' I can't help but think of a novice programmer looking at the console output of their failing program, "it gave me all these weird symbols and says something about an 'exception'".

Maybe what's confusing to me is that 'getting infinities' in this way is somehow normal and not indicative of a bug, maybe? Otherwise, how can they be brought up in this way without the conclusion being, "seems like we got it wrong, time to try something else."

[0] https://en.wikipedia.org/wiki/Renormalization

[chunky1994]

The problem is that the gravitational infinities one gets in QFT are non-reonormalizable. Renormalizable theories must follow a very strict criteria (and even then they are rather difficult to grasp if you don't really put a lot of thought into it).

[westoncb]

I assumed that was the case, but it doesn't alter the impression I get about the situation. That still sounds to me like, "we can only apply this fix when instances of the problem follow certain strict criteria".

[c517402]

IIRC Feynman was also concerned about the infinities as well, but ultimately pragmatic. The infinities bother me as well. But, on reflection classical point particles produce forces that approach infinity as they become close, so the quantatization reflecting this seems reasonable. Please see my other comments.

[rayuela]

Thanks for pointing this out. I may have overlooked this article otherwise. As a non-physicist I can't say I've ever come close to understanding the problem of integrating gravity with QFT and this statement alone really helped.

[amelius]

If point particles come really close, doesn't the problem become easier, because you can lump the particles and treat them as one?

[goldfeld]

Under what model?

[amelius]

In an n-body model, where interactions are additive and become smaller depending on distance.

See e.g. [1].

[1] https://en.wikipedia.org/wiki/Fast_multipole_method

[c517402]

If you follow your Wikipedia link and then follow the link for Green's function two times, you come to the article that points out that Green's function methods only work on linear differential equations. The multipole method you refer to is based on the Green's function and only works for linear differential equations. Einstein's equations are non-linear. Trying to quantize a non-linear theory leads to problems that no one has yet resolved. You should also note that non-linear differntial equations do not support superposition; that is, the solutions cannot be added to yield another valid solution. They are not additive. So, the method you suggest fails because it does not meet the criteria you refer to.

[Govindae]

Gravitational interactions become stronger with decreasing distance.

Take the Newtonian gravity model, if force is proportional to 1/distance^2, as distance approaches zero, the force approaches infinity.

You can simplify all points in a region as being one point for points that are far away, but that doesn't help with the infinite force problem with close points.

[alnitak]

Metropolis?