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A philosophy problem regarding electromagnetic field

  1. Mar 8, 2009 #1
    What is a field? Say, a velocity field or an electromagnetic field. How we actually define a field?
    I think the most precise definition is mathematical: a set of numbers associated with each point that can describe some physical properties on that point, namely, a function with respect to space and time.
    In this mathematical point of view, a field is nothing more than a relation, or it’s better to say, it defines some kind of relation. For example, for velocity field, it gives the relation between the velocity of the fluid particles and different positions (and time); for electric field, it gives the relation between the force exerted on a test charge and different positions (and time).
    Then the problem is why an electromagnetic field can have energy? It seems to me only entities can have energy, but an electromagnetic field is a kind of relation.
    What I mean is, for example, “a rabbit is in my house” ,”rabbit” and ”my house” is a kind of existence, the spatial relation ”…..in……” is also kind of existence, but definitely not the same kind of existence, ”rabbit” and ”my house” are entities, but “…in…” is not. I want to say by the definition of a field, an electromagnetic field is just like “….in…” how can it have energy?!
    Even if we can admit an electromagnetic field is also a kind of entity, but indeed we never experience any entity that can define a relation all by itself, which an electromagnetic field does!
    What’s more, I heard that in GR, space and time are also kind of entities, for example, gravitational wave, the disturbance of space and time, can have energy. This also confused me in the way that electromagnetic field does. Am I wrong or there really is a duality of a field??
    I am struggling with this problem for days, it really confused me. Any help is appreciated.
  2. jcsd
  3. Mar 8, 2009 #2


    Staff: Mentor

    Why would only "entities" have energy and not "relations"? Energy is not generally a property of an entity, it is generally a property of a relation. For example, the gravitational potential energy is a relation between the earth and some object and not a property of either the earth or the object alone. Or, for example, if two astronauts are passing an asteroid at different speeds then they will disagree about the kinetic energy of the asteroid. They each have a different relation with the asteroid so they each say the asteroid has a different energy.
  4. Mar 8, 2009 #3
    You're first talking about viewing a field as a mathematical definition, which is correct in the classical sense. More general, some field configuration has as an input coordinates of space-time and as an output it can have numbers (scalar fields), vectors (vector fields), tensors, spinors, etc. So far so good.

    But next you turn to question of energy, and you somehow step away from this mathematical treatment.

    The fact is, is that the energy associated with some field is also just a mathematical relation. For instance, the energy can be defined in terms of the derivative of the field, or the value of the field squared (yes, the energy is then also coordinate dependent! So it's actually an energy density).

    The problem lies in viewing the concept of energy on some special, non-mathematical footing - which is wrong. Energy is itself a descriptive quantity, which we can use to describe the fields and their dynamics. What makes energy so special is that, to a large extent, it determines the dynamics of a system.
  5. Mar 8, 2009 #4
    em.......yeah, it make sense, but aren't all physical quantities descriptive quantities?
    So we can associate all physical quantities with anything ,regardless of entity or relation(just a matter of useful or not)?But if so, what's the difference between entities and relations?I always think the world contains no more than entities and relations, it's hard to believe that these two are also one thing
  6. Mar 8, 2009 #5
    Electromagnetic fields are not just any field though, the only reason they can contain energy is due to the last two Maxwell equations which are unique for the electro magnetic fields.
  7. Mar 8, 2009 #6


    Staff: Mentor

    I have never seen any physics definition of either "entities" or "relations". I don't think they are mainstream physics concepts, I think you are introducing an unwarranted distinction.
  8. Mar 8, 2009 #7
    DaleSpam is right. The whole idea in physics is to come up with some quantative way of describing physical phenomena.
  9. Mar 8, 2009 #8
    The distinction between entities and relations is made in the philosophy of science, or in metaphysics they correspond to noumena and phenomena.

    Relations are phenomena, they are things we can actually measure. By observing the relation between the rate of acceleration upon application of a known force to an electron and the corresponding rate of acceleration of a certain aluminum cube in Paris under application of the same force, we say that the ratio of the two is the mass of the electron.

    But normally we don't think of the mass of the electron as a ratio of observations, we imagine a noumenal (unobservable things-in-themselves) object which has mass.

    In relativity, what we actually observe are non-trivial relations between durations and lengths as recorded by observers in various states of motion. That is the phenomena, but we make the jump to noumena when we say that these non-trivial relations apply to space and time themselves, rather than to the recording process of durations and lengths.

    In other words, we prefer to think of the relativity as belonging to spacetime itself, and since this reproduces the observations we are allowed to do so. In general, physics discusses things-in-themselves and leaves it to philosophy to clarify that such things can never be known to us.
  10. Mar 8, 2009 #9
    Yeah, so I think it's sort of philosophical, I can't really give an exact definition of "entity"or"relation", but they should be different, aren't they?And I think a field is a relation, it makes some sense ,right?So it seems strange to me we can describe these two by the same set of physical quantities, say ,energy, momentum etc.
    In other cases, for example, two charges in electrostatics, I would rather say "the whole system have a potential energy" than "the electric field has energy", but we know EM waves, in absence of any charge, have energy,we can even use it to heat food. It forces me to think twice about the concept of "field energy"
    What's your opinion? Do you think "rabbit" "house" and "......in......" are the same kind of existence?Or maybe this comparison is not very appropriate?
  11. Mar 8, 2009 #10
    to Klockan:Yeah, indeed if there are no that two equations, only electrostatics or magneto statics case will exist, then the concept of "field energy" is not useful
  12. Mar 8, 2009 #11

    Ben Niehoff

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    Science Advisor
    Gold Member

    I'm fairly sure that energy usually is a property of relations, not objects. For example, an object on Earth has potential energy due to its distance from the ground. And an object has kinetic energy due to its motion with respect to some reference frame.
  13. Mar 8, 2009 #12
    to confinement: good point! but even though entity can be never know to us, we can say it's a kind of thing different from relation, am i right?
  14. Mar 8, 2009 #13
    emm, it makes sense
  15. Mar 8, 2009 #14


    Staff: Mentor

    Without an exact physics definition I cannot tell if they are different. Frankly, they seem to be fairly "sloppy" concepts so I wouldn't base any rigorous conclusions on them. Stick with well-defined terms. Poorly defined terms inevitably lead to confusion as I think you are seeing.

    The problem here is not the physics of energy and fields. The problem is the use of poorly-defined terms like "entity" and "relation" and trying to make concrete conclusions based on them. If I had to make a classification I would say that energy is usually a property of a relation as I described in post 2, with the caviat that "relation" is poorly-defined so you can't make a well-defined conclusion based on that.
  16. Mar 8, 2009 #15
    Yes, in order to know that entities can not themselves be known, we must know that entities are distinct from that which can be known, viz relations.

    Here is the wikipedia article which describes entities as distinct from relations:

  17. Mar 10, 2009 #16
    There is no known sub-electromagnetic field so it's impossible to accurately describe an electromagnetic field. I don't even think anyone has come up with a good analogy. Saying that there's a sea of charges that are separated (like a dielectric) doesn't really help since that still depends on an em field. It has to be described by something else. However, an em wave is associated with the transfer of energy and is independent of the charges that created it; eg. there are no wires connecting the Sun to the Earth yet the Sun's em waves still warm the Earth.

    There are many fundamental unknowns in em theory. For example, why does an em wave make a charge accelerate? I imagine that a thorough examination and explanation of that would lead to all sorts of new discoveries and answers.
  18. Mar 10, 2009 #17
    Consider two objects: You, and a campfire. You may be toasting marshmellows or just enjoying the evening and your friends. You feel warmth on your face. Electromagnetic radiation, otherwise known as infrared radiation is hitting your face. So the electromagnetic field hitting your face has energy (roughly 1 joule per coulomb of light photons).

    If you have a bettery and apply the battery terminals onto two parallel metal plates, you create an entity (or property) we call an electric field. If you put a proton between the two plates it will move (accelerate) toward the negative plate. If you put holes in the two plates, the proton will still move toward the negative plate (and if you are lucky, it will exit through the hole). Now if you put a ring of magnets with sufficient strength to bend the proton in a circle back to the hole in the positive plate it will re enter the field. (But it will have lost enegy due to the external fields outside the plates). If you put an ac voltage on the plates such that the transit time of the proton around the magnet ring is an integer number of ac cycles, the proton willl accelerate again, and again, and again. If the two plates become a metal box with 6 sides, and holes in each end, you can still generate electric fields inside that are not due to dc charges from a bettery, but due to the induction of an oscillating electromagnetic field. If the box is the correct length, the electric field inside will be resonant, meaning that it takes very little electric power to maintain them.
  19. Mar 11, 2009 #18
    Do you think rabbits and houses are composed of other than entities.

    This is very fuzzy physics. It's a good thing there are rabbits.
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