Fields as understood in QFT

[geordief]

"Everything is fields",I heard Sean Carroll say in a lecture. 

So I am wondering how they work.

 

How do they interact with each other(is it via their particles/excitations?) and  what is speculated to be their relationship/interactions  with the gravity field?

 

As I have understood it there are as many  fields as there are fundamental particles.

Is there any idea of why there are as many fundamental  particles as there are ?

Edited April 14, 2023 by geordief

[Genady]

23 minutes ago, geordief said:

How do they interact with each other

Their interactions are described by interaction terms in the Lagrangians.

 

25 minutes ago, geordief said:

what is speculated to be their relationship/interactions  with the gravity field?

They operate in the curved spacetime.

 

26 minutes ago, geordief said:

As I have understood it there are as many  fields as there are fundamental particles.

A particle and its anti-particle are excitations of the same field.

 

26 minutes ago, geordief said:

Is there any idea of why there are as many fundamental  particles as there are ?

No.

[geordief]

1 hour ago, Genady said:

They operate in the curved spacetime

Are they responsible for  or have a role in determining 

 the curved spacetime?

 

Is the gravity field entirely distinct from the other fields or  do they  have  any properties and behaviours in common?

1 hour ago, Genady said:

Their interactions are described by interaction terms in the Lagrangians

Would there be as many interactions as there are fields (so as many interactions  as there are fundamental  particles)?

[Genady]

16 minutes ago, geordief said:

Are they responsible for  or have a role in determining 

 the curved spacetime?

In principle, anything that has energy-momentum affects the curvature. Practically, a few million particles will not have a measurable effect.

 

22 minutes ago, geordief said:

Is the gravity field entirely distinct from the other fields or  do they  have  any properties and behaviours in common?

They are all fields, i.e., machines that get spacetime coordinates in and produce a scalar / spinor / vector / tensor out. They all have Lagrangians and obey stationary action principle.

But gravity does not appear in interaction terms of Lagrangians the way other fields do. Thus, it is entirely distinct.

(These are short preliminary answers. Markus will reply with much more depth, I expect.)

 

26 minutes ago, geordief said:

Would there be as many interactions as there are fields (so as many interactions  as there are fundamental  particles)?

No. All charged particles interact with EM (photon) field, but neutral particles don't. Quarks and gluons interact with gluons. All particles interact weakly. All massive particles interact with Higgs (not sure about neutrinos.) Seems, there are more interactions than fields.

 

[MigL]

Keep in mind that QFT stands for Quantum Field Theory, such as Quantum Electrodynamics and Quantum Chromodynamics.
There is no QFT for gravity yet.
For all we know, a quantum gravity theory might not involve geometry at all; it just has to 'reduce' to the equivalent of a geometric field theory at lower energies and larger scales.
( much like GR reduces to Newtonian at even lower energies )

Edited April 14, 2023 by MigL

[iNow]

This is why math is better for understanding these concepts than English, or even any nonmathematical human language more broadly. 

When I hear “field,” I think of mesh or matrix, perhaps even manifolds or membranes in some contexts. It’s a space made of stuff and the nature of the stuff is a different order of explanation. 

But English words are imprecise. So we use numbers and integrals and derivatives and relationships to make our understanding more clear. 

It’s still a map and not a territory whatever we do, even when using higher maths, so always take it with grain of salt and allow only provisional acceptance of anything. 

Edited April 14, 2023 by iNow

[geordief]

2 hours ago, MigL said:

There is no QFT for gravity yet.

Do any of the ongoing theories for a QFT for gravity  explore a unified field including all the existing  fields plus  a gravity field?

[Markus Hanke]

13 hours ago, geordief said:

How do they interact with each other

A quantum field is a mathematical entity that takes a point in spacetime and returns an operator, which can then be used to calculate real-world probabilities. They “interact” in the sense that the probability for some specific event playing out a certain way will, in general, contain contributions by more than one field. 

13 hours ago, geordief said:

and  what is speculated to be their relationship/interactions  with the gravity field?

Quantum fields live in spacetime - so these two are separate entities. Spacetime provides the stage, whereas QFT describes the play that happens on that stage. Ordinary QFT - the kind that is e.g. used to formulate the Standard Model of particle physics - presupposes that the spacetime it lives on must be flat Minkowski spacetime, so it explicitly excludes the presence of gravity. In other words, ordinary QFT doesn’t have anything to say about gravity at all.

Now, it is possible to generalise the mathematical machinery of QFT to curved spacetime backgrounds. The result is something very complicated indeed. But the basic paradigm still holds even here - spacetime (irrespective of its precise geometry) and the quantum fields that live on it are separate entities, so even this generalised version of QFT doesn’t tell you anything about gravity itself, it just lives on a stage that is now no longer flat, which introduces some interesting effects, but no fundamental insights into quantum gravity. QFT in curved spacetime is not a quantisation of General Relativity.

11 hours ago, geordief said:

Is the gravity field entirely distinct from the other fields or  do they  have  any properties and behaviours in common?

In QFT, gravity isn’t a field, it’s a fixed background on which the quantum field “lives”. This makes gravity fundamentally different from the other interactions.

6 hours ago, geordief said:

Do any of the ongoing theories for a QFT for gravity  explore a unified field including all the existing  fields plus  a gravity field?

It is really simple - almost trivial even - to write down a QFT for a spin-2 particle that couples to the energy-momentum tensor as its source, which would naively be expected to give you a QFT for gravity. This physically just means we are treating gravity the same as we do the other interactions, ie as a process that is mediated by a suitable boson with the right properties that couples to the right source term. Unfortunately, it turns out that the resulting QFT is entirely useless, because once you try and extract any real-world predictions from it, all you find are infinities that cannot be removed. Thus, the paradigm we used so successfully in describing the weak/strong/EM interactions, fails rather spectacularly when we try to apply it to gravity - this is essentially because the other interactions live on spacetime, whereas gravity is given by the dynamics of spacetime. They are fundamentally different things. Plus, there is a multitude of technical reasons why this can’t work.

I think nowadays no one believes any more that it is possible to model quantum gravity simply by applying the old QFT paradigm to GR (if it was that simple, we’d have cracked that nut decades ago). It will require an entirely new paradigm.

[geordief]

5 hours ago, Markus Hanke said:

 

I think nowadays no one believes any more that it is possible to model quantum gravity simply by applying the old QFT paradigm to GR (if it was that simple, we’d have cracked that nut decades ago). It will require an entirely new paradigm.

So we are just trying to make predictions about quantum processes in the presence of extreme gravitational (and other?) conditions.

 

There is no attempt to fuse the two models into one overarching one?

If ,as you say quantum processes are understandable in curved space  and we  say the mathematical singularities are just quirks of the model ,what is the problem?

Will progress just be incremental  and softly softly catchee monkey?

 

 

[Genady]

1 hour ago, geordief said:

There is no attempt to fuse the two models into one overarching one?

The string theory is one of better known such attempts.

 

1 hour ago, geordief said:

If ,as you say quantum processes are understandable in curved space  and we  say the mathematical singularities are just quirks of the model ,what is the problem?

These mathematical singularities make it impossible to analyze physics near the center of BH and at the very early stages on the universe. Anything that gets close to Planck scale.

[Markus Hanke]

1 hour ago, geordief said:

So we are just trying to make predictions about quantum processes in the presence of extreme gravitational (and other?) conditions.

This would be what QFT in curved spacetime does - that’s different from quantum gravity, which is a quantisation of gravity itself.

2 hours ago, geordief said:

There is no attempt to fuse the two models into one overarching one?

Fusing gravity with the Standard Model actually goes beyond mere quantum gravity - this would be an attempt at a ToE, a theory of everything (in contrast to quantum gravity, which only concerns itself with a quantisation of gravity alone). As Genady has said, the most well known attempt at a ToE would be M-Theory, which involves different types of strings and branes. While M-Theory has yielded some interesting and useful results, I don’t think it has been very successful at describing the actual world we live in, so its ultimate scientific value is debatable. 

2 hours ago, geordief said:

If ,as you say quantum processes are understandable in curved space  and we  say the mathematical singularities are just quirks of the model ,what is the problem?

The singularities I mentioned appear if you attempt to quantise gravity itself using the machinery of QFT, ie if we attempt to apply the same mathematical machinery we used so successfully for the other interactions to the case of gravity. The problem is that, unlike is the case for the other interactions, the infinities that appear for gravity cannot be removed from the theory, which makes it impossible to extract any kind of physical prediction from it. You can write down the Lagrangian for this attempted theory, but once you try to actually calculate any sort of real-world situation from it, you get only gibberish. So it’s entirely useless. 

2 hours ago, geordief said:

Will progress just be incremental  and softly softly catchee monkey?

To be honest, no one knows - the problem is that the domain of quantum gravity is way outside of what we can probe with our instruments, so we really don’t have any observational data at all available to provide us with some hints about which direction to take. We are basically groping around in the dark. This is why there are so many very disparate attempts at quantum gravity models. We know only that such a model must reduce to well-known GR in the classical limit, but that’s about it - and that’s not much to go by.

[Mordred]

On 4/14/2023 at 2:33 PM, MigL said:

Keep in mind that QFT stands for Quantum Field Theory, such as Quantum Electrodynamics and Quantum Chromodynamics.
There is no QFT for gravity yet.
For all we know, a quantum gravity theory might not involve geometry at all; it just has to 'reduce' to the equivalent of a geometric field theory at lower energies and larger scales.
( much like GR reduces to Newtonian at even lower energies )

just an fyi one under development though its been around awhile for gravity is quantum geometrodynamics.  It like any quantum gravity theory is still not renormalizable

[MigL]

3 hours ago, Mordred said:

It like any quantum gravity theory is still not renormalizable

Exactly.
The inherent infinities cannot be 'renormalized' away, and make the theory unworkable and incapable of making any valid predictions.

Hope your time away from the forum wasn't all work ...