What exactly is a "field" - can you provide an elegant conceptual definition?

Thanks, but I am NOT interested in the run of the mill regurgitated stuff. 鈥?***I am looking for an elegant conceptual definition.*** 鈥?Like, for instance, the conceptual definition of gravity as the curvature of spacetime in the vicinity of a massive object, as set forth by General Relativity. Can you give an analogous conceptual definition of the field itself? Again, I am NOT interested in the traditional manifestations and definitions of the field such as lines of force, or its mathematical definition, or even more enigmatic expos茅鈥檚 like: field is the region of space characterized by a physical property, such as gravitational or electromagnetic force or fluid pressure, having a determinable value at every point in the region, etc.|||Try this one.





Depending on the field, it is a potential caused by the


particle carrier of the field. For an electromagnetic field


it can be thought of as if photons were the ground (or


landscape). How energetic these photons are and how


they travel cause the reactions we see in charged particles


moving through the field. Of course, the photons are virtual!


The virtual photons and the e+e- production (and other particle


antiparticle pair production if applicable) create the


hills, valleys, type of ground, etc. which affects how a river


(charged particles) will travel over it.





This is why field theory is based mathematically on the


second quantization of many photons. See for example,





"Gauge Field Theories" by Guidry


(which was my graduate field theory text)|||Unfortunately, those characterizations that you dislike are the correct ones. A field - plain and simple field - is nothing but a mathematical conceptualization; it describes the force that would act on an item of a particular property placed anywhere within space. It's always in units of newtons per property. Electric fields, for example, are newtons per coulomb (force per charge).





Gravity is rather special, in that we've been able to explain the values that a gravitational field takes as being the result of spacetime curvature. Other types of fields aren't necessarily the same way.





And, of course, that's only the classical treatment of fields. Quantum physics quantizes them, and treats them mathematically as particles, instead.





There are some theories that tried to treat other fields the same way as gravity, and some of them actually work; the problem is that you need extra spacial dimensions in order to make them work. Since no one has been able to verify the existence of extra physical dimensions, those sorts of theories have been somewhat ignored by science at large. There are still some physicists who work on them, though.





The actual, physical nature of many of the force fields in nature is the subject of some debate.|||A field is an array of numbers, with values associated with each point in space. There are many kinds of fields. Scalar fields have only a single value associated with each point in space (example: temperature) vector fields have multiple values. See http://en.wikipedia.org/wiki/Field_%28ph鈥?/a>





Fields are also defined in mathematics as arrays of values not necessarily associated with physical quantities.|||You want poetry not physics. A field is a non-existent mathematical concoction used to discribe a force acting over a distance between bodies and its strength per unit area.|||Well, you just described exactly what a field is. It is an area in space affected by some force. For example, a planet's gravitational field is the area in space affected by the force of its gravity. We have to resort to such descriptions because fields aren't really "stuff" like matter is. It's hard to talk about.|||You can think of a field as like a football field or a basketball court. Mathematically when you do certain operations in a field the result should still be found inside this Field. so think of it this way, when your playing a basketball game and your down 1 point with 5 seconds to go, you have possession of the ball and your team is the Atlanta hawks. there is no way that you can insert michael jordan or kobe bryant into the game to solve your problem because they are not part of the "Field". They were not part of the problem from the beginning so they cant be part of the solution. hope this kind of explanation is what your looking for.|||A field is the region in which one object has an effect on another, this is not enigmatic to me at all.


How about:


The electric field is the curvature of charge-time in the vicinity of a charged object.


The gravitational example seems no more or less clear to me! The point is that your question may be wrong, you are assuming ("What is") that a field is a thing. It is not, it is just a useful concept, kindof like numbers.