Is the magnetic field a mathematical abstraction?

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Discussion Overview

The discussion revolves around the nature of the magnetic field, questioning whether it is merely a mathematical abstraction or if it has a physical reality. Participants explore this concept through philosophical inquiries, theoretical implications, and practical observations related to electromagnetic fields and forces.

Discussion Character

  • Philosophical inquiry
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants argue that the magnetic field is a real entity, measurable and existing around charged particles like protons.
  • Others suggest that while the magnetic field may not be physical in the same sense as tangible objects, it has a significant physical reality, influencing particles and carrying energy.
  • A participant points out that the mathematical framework developed to describe electromagnetic interactions may imply that the field is ultimately a mathematical abstraction, despite its practical utility.
  • Another viewpoint emphasizes the relativistic effects observed when charged particles move at high speeds, which complicates the understanding of forces and interactions in terms of fields.
  • One participant raises a question about the nature of momentum in the context of electromagnetic fields, suggesting that it is useful to conceptualize momentum as residing in the field until it influences another charge.

Areas of Agreement / Disagreement

Participants express differing views on whether the magnetic field is a mathematical abstraction or a physical reality. There is no consensus, as some emphasize its measurable nature while others focus on its abstract mathematical representation.

Contextual Notes

The discussion includes philosophical considerations and varying interpretations of physical phenomena, highlighting the complexity of defining the magnetic field and its implications in physics.

rainstom07
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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?
 
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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?
 

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