2

Consider a situation like a magnet which produces a magnetic field, or a point mass which produces a gravitational field. It seems that for practical physical calculation, the physical object's properties are always seen through its fields. Eg See this question.

But is there a clean mathematical description with the objects considering themselves as individual entities and the fields they produce as separate ones? The reason I see this as useful is that sometimes we would want to talk about how the object affects other objects through its fields, and at other times how the objects themselves are affected by other objects' fields.

One could argue, like the above linked question, that electric charges can't be experienced except through the fields they create, but then I'd reply that we very well accept that both the "sun" and the "pull of the sun" on Earth are both real things. So the idea of the particle being identified with the field is not a good cop out.

psmears
  • 333
tryst with freedom
  • 7,940
  • Are you saying that you need a description of a source , fluid and sink? As you can always consider that object as source and fluid as field , is that what you want? – Pradyuman Apr 29 '23 at 04:03
  • No, I am asking for a formalism which fuses source/sink with their effect on fluid as one entity @Pradyuman – tryst with freedom Apr 29 '23 at 04:11
  • 1
    As far as I know, existing theories are able to calculate any scenario involving objects that produce such fields. Can you give an example where this is not the case? In other words, is there a scenario where we cannot compute what happens with our existing theories? – flippiefanus Apr 29 '23 at 04:31
  • I don't understand what your question is. Could you rephrase? – tryst with freedom Apr 29 '23 at 05:24
  • Possible duplicate: What is a field, really? – ACuriousMind Apr 30 '23 at 11:38
  • The mathematical objects you're looking for are scalar fields, vector fields, tensor fields :) – Filip Milovanović Apr 30 '23 at 16:44
  • "[T]he idea of the particle being identified with the field is not a good cop out" – I am not aware of any formalism that actually identifies a particle (such as electron or proton) with the electromagnetic field it produces. "[I]s there a clean mathematical description with the objects considering themselves as individual entities and the fields they produce as separate ones"? – why yes, any field theory, whether classical (e.g. electromagnetism) or quantum (QED) is a "clean mathematical description" which makes a careful distinction between fields and sources of fields. – printf Apr 30 '23 at 22:27

3 Answers3

14

is there a clean mathematical descriptions of the objects considering themself as an entity and the field they produce as a seperate one?

That is the standard classical mathematics. In classical EM the sources, $\rho$ and $\vec J$, are treated as mathematically distinct from the fields, $\vec E$ and $\vec B$. The objects and fields are separate entities represented by separate variables. The equations establish a relationship between them, but do not identify them.

Dale
  • 99,825
10

The way we teach physics is still very much borrowed from the 17th to 19th century when everything was seen from a materialist point of view (probably to a good degree because of the incredible successes of Newtonian mechanics and atomism in chemistry). Some physicists even tried to associate heat with a "Stoff" called phlogiston. Later we insisted that the vacuum has to be made from another "Stoff" called the aether. None of that works. The closer we look at nature, the more it dissolves into fields. Objects don't make fields. Fields make objects.

So when somebody asks "How does a magnet create a magnetic field?", then the short answer is "It doesn't. It's the quantized electromagnetic field that defines the structure of the atoms of the magnet and its external field is merely a remnant of much stronger internal fields.".

Gravity is a very special case on top of that, because it doesn't just bind very large "objects" together, it even defines the geometry of the space between them.

FlatterMann
  • 2,968
  • This IS a better answer, but is snot really mathematical. +1 for attempt. – tryst with freedom Apr 29 '23 at 04:18
  • 1
    @TrystwithFreedom If you want the mathematics of it, then you have to ask a question about quantum field theory and get an answer from somebody else. I know absolutely nothing about QFT... other than that it works. What I would warn people about is to imagine that quanta in QFT are the "material sources" of classical field theory. That's just another "objectification fallacy" IMHO. – FlatterMann Apr 29 '23 at 04:23
  • 5
    If you liked this answer then Id point out that in QFT it is the fields that are fundamental, and particles are but approximately conserved asymptotic excitations on those fields. Trying to make sense of things starting from the particles is a dead end. Only by hoping that the fields make sense, can we make any progress into understanding the physics. There is some natural flow to physics, that going against them in favour of prejudices would lead to endless pain. – naturallyInconsistent Apr 29 '23 at 07:10
2

For an electric, a magnetic and a gravitational field it is true that a test specimen is subject to influence in such a field. A force acts on the specimen and it experiences a translatory (electric potential, gravitational potential) or a rotatory (magnetic field) movement.

How are these fields "generated"? For a permanent magnet, by the alignment of the magnetic dipoles of its subatomic particles (primarily electrons). For an electric field, by the separation of electrons. For a gravitational field by the agglomeration of particles.

An electron in itself unites all three fields. But we would not know this if we could not build up a potential or - for the gravitational potential - if nature did not provide us with one. An electron is attracted by the earth, its dipole aligns itself in a magnetic field and it is moved in a voltage difference.

But is there a clean mathematical description with the objects considering themselves as individual entities and the fields they produce as separate ones?

With the understanding of the above, NO, such separation is not possible and does not make sense. Everything is always both object and subject. The test body is only influenced because it is not just a space-occupying object, but has a field and thus interacts with the common field created from other objects.

HolgerFiedler
  • 10,334