What is currently known about fields other than gravitation?

[mister i]

TL;DR

A field is spatial&time region in which each point has a physical quantity associated with it (vector or scalar). We know from GR that in the case of the gravitational field it is due (only?) to a curvature of space. But what about the other fields? What gives the value information to this space point?

As far as I know a field is spatial&time region in which each point has a physical quantity associated with it (vector or scalar). We know from GR that in the case of the gravitational field it is due (only?) to a curvature of space. But what about the other fields? What gives the value information to this space point? (Is it also just a characteristic of space&time or is there something else that we don't know exactly?). For example, in the magnetic field: we know what causes it, its properties and its effect on the particles, but what exactly "is there" in this space? Or is it just another property (geometric/topological?) of space&time itself? In short: what exactly is a field made of?

 

[PeroK]

As far as I know a field is spatial&time region in which each point has a physical quantity associated with it (vector or scalar). We know from GR that in the case of the gravitational field it is due (only?) to a curvature of space.

In the Newtonian theory, gravity is a field at each point in space - and that field may evolve over time. In GR, gravity is the curvature (geometry) of spacetime itself. And, at each point in spacetime there is the stres-energy tensor. This can be seen as the source of spacetime curvature.

https://en.wikipedia.org/wiki/Stress–energy_tensor

But what about the other fields? What gives the value information to this space point? (Is it also just a characteristic of space&time or is there something else that we don't know exactly?).

The source of the electromagnetic field are the charges and currents, as described by Maxwell's equations:

https://en.wikipedia.org/wiki/Maxwell's_equations

For example, in the magnetic field: we know what causes it, its properties and its effect on the particles, but what exactly "is there" in this space? Or is it just another property (geometric/topological?) of space&time itself? In short: what exactly is a field made of?

Field theory is a mathematical model. To what extent you can ascribe a direct reality to the fields and to what extent they remain (only) a mathematical model is more a question of philosophy than physics.

 

[Dale]

what exactly is a field made of?

And in the models that @PeroK mentions, the fields are fundamental. They are not made of anything. They are what other things are made of.

 

[haushofer]

TL;DR Summary: A field is spatial&time region in which each point has a physical quantity associated with it (vector or scalar). We know from GR that in the case of the gravitational field it is due (only?) to a curvature of space. But what about the other fields? What gives the value information to this space point?

As far as I know a field is spatial&time region in which each point has a physical quantity associated with it (vector or scalar). We know from GR that in the case of the gravitational field it is due (only?) to a curvature of space. But what about the other fields? What gives the value information to this space point? (Is it also just a characteristic of space&time or is there something else that we don't know exactly?). For example, in the magnetic field: we know what causes it, its properties and its effect on the particles, but what exactly "is there" in this space? Or is it just another property (geometric/topological?) of space&time itself? In short: what exactly is a field made of?

What kind of answer would satisfy you?

I mean, if I say that fields consist of Schlumpfs, giving a precise mathematical and ontological definition, the next question is: what exactly is a Schlumpf made of?

So: what kind of explanatory power would you want to see?

 

[pervect]

This may or may not be helpful, but most of our physical theories (including electromagnetism and GR) can be described as "Lagrangian field theories". For these sorts of theories, it is sufficient to associate a scalar (more precisely a scalar density) with every point. As I recall most if not all of the various "fields" can be computed from the Lagrangian as a kind of derivative of the Lagrangian - how fast it changes when you change position.

There is a bit of discussion in wiki, https://en.wikipedia.org/wiki/Lagrangian_(field_theory), but I wouldn't expect anyone to actually learn Lagrangian field theory by reading the wiki, as it is a graduate level topic. For instance, it's described in the very last chapter of Goldstein's graduate level textbook, "Classical Mechanics" (and that text doesn't specifically cover General relativity). By "learning" Lagrangian field theory, I mean understanding the theory at a level where one can use it to make actual physical predictions.

Lagrangian theories exist for discreete systems, and applying them yields differential equations. I would definitely recommend learning about Lagrangian theory for discreete systems before even attempting to learn about it for continuous systems / Lagrangian field theories. Some useful keywords for possible reading about the Lagrangian for discreete systems - "the "principle of least action".

Discreete systems are solvable by solving differential equations. Continuous systems require solving partial differential equations.

Science has little to say about what the Lagrangian actually is - that's more of a philosophical question. Philosophis of science vary, but it's widely thought (sorry, I don't have a specific reference for this) that science is about making testable predictions and comparing these predictions to experiments. Questions about things that cannot be answered by the result of some experiment (such as why questions) are outside the scope of the scientific method, strictly speaking. As a practical matter, usually some philsophical interpretation of scientific theories is needed to be able to use them effectively, however.

 

[Ibix]

what exactly is a Schlumpf made of?

Schlumpfons, obviously.

(Sorry - I know you're making a serious point.)

 

[Vanadium 50]

Unless it is a fermionic field. Then they would be Schlumpfnos.

 

[Baluncore]

Schlumpf is the active ingredient in turtle wax, and it goes all the way down.

The experiments by Faraday, with electric and magnetic field lines, were formulated by Maxwell in the 1860s.

Maxwell's equations were reformatted as vectors by Heaviside in 1884. Experiments by Hertz, in the 1890s, tested and demonstrated the validity of Maxwell's equations.

Those electric and magnetic vector fields were connected by Einstein in 1905, in what is now Special Relativity. Later, Einstein's General Relativity connected gravity with the curvature of space.

 

[mister i]

What kind of answer would satisfy you?

I mean, if I say that fields consist of Schlumpfs, giving a precise mathematical and ontological definition, the next question is: what exactly is a Schlumpf made of?

So: what kind of explanatory power would you want to see?

I'm not English (I speak Catalan), but I suppose schlumpf has no translation or meaning and is an ironic response. I would have really liked this answer. For me, all the answers are useful to see what physicists currently think about the matter. But the question was to rule out that there was some theory that I didn't know about this theme similar to the (unproven) string theory saying that electrons and quarks are made of vibrating strings (vibrating schlumpfs). I would like to see the response of physicists in the year 3024.

 

[Dale]

I would like to see the response of physicists in the year 3024.

Me too. But I think that I would actually be excited just to know that there will be physicists in the year 3024!

 

[SebasHerbert]

When I was at school about eight years ago, I asked a similar question, but the teacher did not give me a specific answer to this question and also brushed it off as not knowing what these fields were made of. I hope that now there will be some deeper research.
If this does not happen in my lifetime, I would like to become a ghost in a few centuries and see what progress there would be in this issue and in science in general, maybe even travel between planets)))

 

[pines-demon]

What kind of answer would satisfy you?

I mean, if I say that fields consist of Schlumpfs, giving a precise mathematical and ontological definition, the next question is: what exactly is a Schlumpf made of?

So: what kind of explanatory power would you want to see?

You can see Schlumpfs as rubber bands. But rubber bands are made of Schlumps, the very things that we are trying to explain, so in Feynman's terms "I will be cheating very badly".