# Is the magnetic field a mathematical abstraction?

• rainstom07
In summary, the magnetic field is there, and it is described by mathematics. It has physical reality, and it can be used to analyze forces.
rainstom07
Is the magnetic field purely a mathematical abstraction or is there actually something there? In other words, if a proton floating in deep space, is there actually something that shoots out in all directions from the proton that will interact with another charge particle?

That is a question of philosophy.
You can measure the magnetic field, so I would say it is there. The proton does not "shoot" with anything, it just has a magnetic field around it, which is as real as the proton itself.

If two protons are floating in space, they'll feel an electrical field between each other and repel, but if you see them zip by you in space at relativistic speeds, they'll behave differently from your point of view by repelling slower than they should, and you'll see a new force.

But it doesn't matter -- the math was invented to describe the behavior, so ultimately it's all mathematical abstraction and you use whatever level of complexity is necessary to solve your problem.

I look at it this way. If the EM field isn't real, then how can an EM wave exist? It may not be physical like a baseball, but I'd say it's as real as anything else.

From wiki:

Defining the field as "numbers in space" shouldn't detract from the idea that it has physical reality. “It occupies space. It contains energy. Its presence eliminates a true vacuum.”[2] The field creates a "condition in space"[3] such that when we put a particle in it, the particle "feels" a force.

If an electrical charge is moved, the effects on another charge do not appear instantaneously. The first charge feels a reaction force, picking up momentum, but the second charge feels nothing until the influence, traveling at the speed of light, reaches it and gives it the momentum. Where is the momentum before the second charge moves? By the law of conservation of momentum it must be somewhere. Physicists have found it of "great utility for the analysis of forces"[3] to think of it as being in the field.

http://en.wikipedia.org/wiki/Field_(physics)

If you consider the relativistic effect of the motion of electrons at snail's pace, in a wire, the resulting forces of attraction and repulsion can be calculated accurately by just looking at the resulting electric forces between two wires. Or you can work it out differently (using the Lorenz - magnetic - force idea).
You can call it magnetism or not, as you please.

rainstom07 said:
Is the magnetic field purely a mathematical abstraction or is there actually something there? In other words, if a proton floating in deep space, is there actually something that shoots out in all directions from the proton that will interact with another charge particle?
Can a mathematical abstraction do all of the things that a magnetic field does?

## 1. What is a mathematical abstraction?

A mathematical abstraction is a simplified representation of a complex concept or phenomenon. It is a way of describing something using mathematical symbols and equations, rather than concrete objects or measurements.

## 2. How is the magnetic field represented mathematically?

The magnetic field is represented mathematically using vector calculus, specifically the vector field concept. This involves using mathematical equations and symbols to describe the direction and strength of the magnetic field at any given point in space.

## 3. Is the magnetic field a physical or conceptual entity?

The magnetic field is both a physical and conceptual entity. It exists in the physical world and affects the motion of charged particles, but it can also be described and understood using abstract mathematical concepts.

## 4. How is the magnetic field measured and observed?

The magnetic field can be measured using a magnetometer, which detects the strength and direction of the field. It can also be observed indirectly by studying the behavior of charged particles, such as electrons, in the presence of a magnetic field.

## 5. Why is the magnetic field considered a mathematical abstraction?

The magnetic field is considered a mathematical abstraction because it is not directly observable or tangible. We can only perceive its effects on other objects or particles, and it can only be fully understood and described using mathematical equations and concepts.

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