What Are Quantum Fields and How Do They Relate to Particles?

[sayetsu]

TL;DR Summary

Hey, all, I have a sudden interest in particles. I've heard two things that I'm going to remember incorrectly:
1. They're probabilities until observed.
2. They're fields, or fields bumping into each other, or something.
Can anyone elaborate?

The summary, erm, sums it up. I just can't wrap my head around "probability." ...Does space even exist? And the field thing I'm really half-remembering. I read somewhere particles are vibrations in fields, or fields bumping into each other, or something. What's a field?

 

[Drakkith]

It depends on the context of the question. In Quantum Field Theory, particles are excitations of an underlying field and can interact with other excitations. So an electron is an excitation of the electron field, a photon is an excitation of the electromagnetic field, etc.

...Does space even exist?

Of course.

What's a field?

Originally, a field was a mathematical object that just stores numbers. These were/are used for various purposes, like recording the temperature of 1 square mile sections in a larger area. Just like what you see when you check the weather and there are various temperatures for different cities in a region. That's a field.

For physics, this mathematical tool was used to describe the strength of interactions of magnets and electrical charges. Imagine using graph paper (the paper with lines arranged in a big grid) and writing down numbers in each of the blocks.

Over time, this idea became abstracted and we started to refer to "an electric field" as its own 'thing', independent of how we were describing it. This trend has continued and fields have become accepted as the most fundamental 'objects' there are.

 

[PeterDonis]

Trying to make sense of things you "hear" is usually not the best way to try to understand science. Our best current theory of "particles" comes from quantum field theory, but QFT is a fairly advanced topic and most people find they need to have a decent background in other physics topics first.

That said, the basic theory of particles from QFT is fairly simple schematically:

(1) The fundamental entities of QFT are quantum fields. In the Standard Model of particle physics, which covers all known particles and interactions other than gravitation, every "particle" (electron, quark, etc.) actually is a name for a quantum field with particular properties (mass, charge, spin, etc.). All ordinary matter is made of these fields, and all known interactions except gravitation involve these fields.

(2) What we call "particles" in experiments (things that make bright spots on detector screens, tracks in cloud chambers, etc.) are particular states of the quantum fields that are reasonably localized and move in ways that are reasonably close to the way we would expect a classical particle (i.e., a particle in Newtonian physics or special relativity) to move.

(3) Because we are talking about quantum field theory, i.e., quantum mechanics, in general we cannot predict exactly what a given particle will do; we can only predict probabilities for various possible outcomes. Once a particular outcome is observed, though, that outcome is fixed and doesn't change (as with any observation in QM). In situations where we don't observe a particle, we have to be careful making assertions about its properties (again, as with anything in QM).

 

[sayetsu]

So do fields occupy space? Are they space? What is space? Or matter? Do these questions mean anything? Sorry, miy mmind is blowing.

 

[PeterDonis]

do fields occupy space?

In QFT, fields are entities that exist in a fixed background spacetime (spacetime, not "space", because we are dealing with a relativistic theory).

Are they space?

No. See above.

What is space?

Spacetime (see above) is a four-dimensional geometry that, in a relativistic theory, provides the framework in which events happen.

Or matter?

"Matter" is just a shorthand way of referring to anything that is made of the Standard Model quantum fields.

 

[sayetsu]

Trying to make sense of things you "hear" is usually not the best way to try to understand science. Our best current theory of "particles" comes from quantum field theory, but QFT is a fairly advanced topic and most people find they need to have a decent background in other physics topics first.

That said, the basic theory of particles from QFT is fairly simple schematically:

(1) The fundamental entities of QFT are quantum fields. In the Standard Model of particle physics, which covers all known particles and interactions other than gravitation, every "particle" (electron, quark, etc.) actually is a name for a quantum field with particular properties (mass, charge, spin, etc.). All ordinary matter is made of these fields, and all known interactions except gravitation involve these fields.

(2) What we call "particles" in experiments (things that make bright spots on detector screens, tracks in cloud chambers, etc.) are particular states of the quantum fields that are reasonably localized and move in ways that are reasonably close to the way we would expect a classical particle (i.e., a particle in Newtonian physics or special relativity) to move.

(3) Because we are talking about quantum field theory, i.e., quantum mechanics, in general we cannot predict exactly what a given particle will do; we can only predict probabilities for various possible outcomes. Once a particular outcome is observed, though, that outcome is fixed and doesn't change (as with any observation in QM). In situations where we don't observe a particle, we have to be careful making assertions about its properties (again, as with anything in QM).

I am totally lost. :( My mental picture is of a bunch of flat planes (the fields) with little bumps, and I know that's wrong. I'm not sure what to picture.

 

[PeterDonis]

My mental picture is of a bunch of flat planes (the fields)

"Field" in physics has a very different meaning from "field" in common language (as in "the open field next to our house").

The general meaning of "field" in physics is an assignment of some mathematical object, chosen from some set of such objects, to every point in some set of points. In QFT, the set of points is spacetime and the set of mathematical objects is a set of quantum operators (or sets of operators), which, for the basic purpose of a discussion like this, can just be thought of as a set of numbers. So when we say, for example, that the "electron" in the Standard Model is a quantum field (some sources will explicitly call it the "electron field"), we mean that at every point in spacetime there is a set of numbers that describes events involving electrons at that point.

I'm not sure what to picture.

There is no good way to picture a quantum field in general, certainly not with intuitions that have not been trained by years of study of QFT.

However, in certain special cases there are ways of picturing aspects of QFT that can be helpful. You might try Feynman's popular book QED: The Strange Theory of Light and Matter. This is a layman's description of quantum electrodynamics, which was the first quantum theory to be fully developed, and is basically the "piece" of the Standard Model that you get if you pretend that there is nothing else in the universe but electrons and photons (which are the QFT "particles" associated with light and the electromagnetic field). In the book Feynman discusses Feynman diagrams, which are probably the closest physics has come to "picturing" aspects of quantum fields. He also gives some other helpful pictures and visualizations.

 

[Drakkith]

I am totally lost. :( My mental picture is of a bunch of flat planes (the fields) with little bumps, and I know that's wrong. I'm not sure what to picture.

Indeed. We are dealing with 3 spatial dimensions, so a 2d viewpoint is just a single 'slice' of this larger space.

Perhaps think about fields as existing like water does in a swimming pool. They fill space. Particles would be sort of like pressure waves that interact with other objects. But note that we'd be dealing with many different fields all occupying the same space, and this analogy is extremely limited, so don't try to take it too far.

 

[sayetsu]

Perhaps think about fields as existing like water does in a swimming pool. They fill space. Particles would be sort of like pressure waves that interact with other objects.

Other objects also being particles?

@Everyone: so particles arenumbers or act like numbers in these fields? How can a number fill space?

 

[Drakkith]

Other objects also being particles?

That's right.

@Everyone: so particles arenumbers or act like numbers in these fields? How can a number fill space?

Neither. The numbers are in the mathematical field. We 'borrowed' the word field and used it for something different. In physics, specifically QFT, a field is a fundamental object that extends throughout space.

 

[sayetsu]

So if particles are all points in a field, and fields fill all of spacetime, particles are space?

Also, if each point in space has numbers describing, say, electrons at that point, but electrons aren't infinitely small, does that mean there aren't infinitely many points in space (assuming a finite universe)?

 

[Drakkith]

So if particles are all points in a field, and fields fill all of spacetime, particles are space?

No. Particles aren't 'points' in a field. They are excitations of the field. And just because something fills space, doesn't mean that it is space. Water fills the space in a pool, but water isn't space.

Also, if each point in space has numbers describing, say, electrons at that point, but electrons aren't infinitely small, does that mean there aren't infinitely many points in space (assuming a finite universe)?

The number of electrons within a region of space can be zero, so there's no problem even if electrons have a non-zero size (they do and they don't. It's complicated and for another thread).

 

[sayetsu]

Okay, I have some inlking now. Thanks!

 

[PeterDonis]

each point in space has numbers describing, say, electrons at that point

Each point in spacetime has numbers describing events involving electrons (and the other Standard Model fields) at that point. Events at a point can involve objects that cover more than just that point.

 

[sayetsu]

Sorry, one more line of questioning: what are the fields made of? Matter? Energy? I've heard E=mc^2, but I've never gotten what it meant for energy to equal matter (x c^2).

 

[Vanadium 50]

Sorry, one more line of questioning: what are the fields made of?

Why do they have to be "made of" anything?

 

[A. Neumaier]

So do fields occupy space? Are they space? What is space? Or matter? Do these questions mean anything? Sorry, miy mmind is blowing.

Fields assign properties to the points in space. For example, there is a temperature field that tells you where it is hot and cold. Space is where you live and walk. Solid matter is where the fields tell you that you can't move through, liquid matter is where the fields tell you that you can swim, and gaseous matter is where the fields tell you that you can walk through.

 

[PeterDonis]

what are the fields made of? Matter? Energy?

You have it backwards. What we call "matter" and "energy" are made of fields--specifically the quantum fields of the Standard Model.

I've heard E=mc^2, but I've never gotten what it meant for energy to equal matter (x c^2).

The equation $E = mc^2$ isn't telling you that energy "equals" matter. It's just a unit conversion: it's telling you that you can measure the same thing in either "energy" units or "mass" units. The "energy" units are just $c^2$ times the "mass" units. It's no different than deciding whether to measure lengths in inches or miles.

 

[sayetsu]

Hooph. Okay, thanks, all!

 

[PeroK]

Sorry, one more line of questioning: what are the fields made of? Matter? Energy? I've heard E=mc^2, but I've never gotten what it meant for energy to equal matter (x c^2).

Try searching YouTube for the "Science Asylum" video on Quantum Fields.

His videos on many topics are as good as your going to get as a pop science introduction.

He has ones on "what is mass" and "What is energy" as well.