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Every text just describe fields mathematically and as a 'vector field' in which it is said a particle gives rise to a field because each point in space around it becomes associated with with a force vector. But it never explains how does a particle generate a field at the first instance, or what a field really is or how does a field work - how is a particle able to affect another one at a distance?

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  • $\begingroup$ You shouldn't imagine that a field is just a product that depends on some particles. A field exists independently of particles - just like the particles exist. A position and speed describes a particle at a given moment, $x(t),v(t)$. For a field, you need to determine some number at each point of space instead. $\phi(x,y,z,t)$. $\endgroup$ – Luboš Motl Apr 12 '17 at 5:39
  • $\begingroup$ What physically makes up the fields are trillions and trillions of individual photons. $\endgroup$ – Bill Alsept Apr 12 '17 at 5:58
  • $\begingroup$ field is physical quantity, I really like that definition from Wiki. just like mass is physical quantity, so is the field (of some type). And then you have equations that model (predict) how objects and field going to change, just like Newton's law predicts how apple's position going to change when it has mass $m$ $\endgroup$ – aaaaa says reinstate Monica Apr 12 '17 at 6:00
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/13157/2451 and links therein. $\endgroup$ – Qmechanic Apr 12 '17 at 6:08
  • $\begingroup$ Classically, a field is something that occupies space, which can be revealed only by the forces they impart on material bodies placed in that region of space. The effect of such a field can be expressed as numbers at each points in space. $\endgroup$ – UKH Apr 12 '17 at 7:22
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Here is a definition of a field in physics:

In physics, a field is a physical quantity, typically a number or tensor, that has a value for each point in space and time

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As another example, an electric field can be thought of as a "condition in space" emanating from an electric charge and extending throughout the whole of space. When a test electric charge is placed in this electric field, the particle accelerates due to a force. Physicists have found the notion of a field to be of such practical utility for the analysis of forces that they have come to think of a force as due to a field

Note this: that physicists have come to think of a force as due to a field.

That is the crux of the confusion. What can be seen and measured physically is the force. The field in physics is part of a mathematical model, a mathematical representation in space,( scalar , vector or tensor generally,) a mathematical model which is proven to work, i.e. fit existing measurements and predict the value of new measurements in different boundary conditions. In this example predict the force on a test particle.

Since ancient times people tended to think that mathematics represents the underlying reality, and measurements are due to nature obeying the mathematics ( platonic view in a sense).

Physics has progressed now, and it is well understood that physics theoretical models have validity for special boundary conditions:

1)Newtonian mechanics and classical electromagnetism for dimension commensurate with human sizes.

2)Quantum mechanics and quantum electrodynamics for dimensions commensurate to h_bar

3) Special relativity and general relativity for very large speeds and large masses respectively.

These models blend smoothly in areas of overlap, but having them clear in the classification allows to see that there is no unique way of mathematically describing data so that valid predictions can be made. There are just more convenient models. example: one does not use general relativity to calculate the throw of a ball. Newtonian mechanics is quite adequate within the errors of measurement.

In this question of yours

But it never explains how does a particle generate a field at the first instance, or what a field really is or how does a field work - how is a particle able to affect another one at a distance?

The mathematics and the physics are confused.

The particle exists, its effect on other particles can be modeled within classical electricity, if it is a charged ball, using the equations for electric fields and the solutions to the problem will fit the data perfectly. In this, one assumption/axiom is "action at a distance" , and there is no problem for laboratory dimensions . The solutions describe within errors all interactions of macroscopic objects.

If it is an elementary particle, an electron for example, it still can be modeled with the electric field BUT an electron is a quantum mechanical entity, and the quantum electrodynamics (QED) mathematical model has to be used to describe a physical state. In QED there is no action at a distance, all transfers of energy and momentum are limited by the velocity of light, and a complicated formalism exists to predict the behavior of the electrons in specific boundary conditions, at least a semester course. So, no action at a distance at the underlying micro level of quantum mechanics.

As macroscopic theoretical descriptions can be shown to emerge from the microscopic quantum mechanical ones, there is no action at a distance for the classical solutions , but the velocity of light is so huge, the one can ignore it at the macroscopic level.

Similar arguments hold for gravitational fields, which are also dependent on the velocity of light, and this can be seen in the cosmological models of the universe.

In studying physics, one has to keep in mind that the theories describe observations and a successful theory is one that is predictive of new measurements. The concept of a "Field" is a useful variable in the mathematical descriptions for the experimental situation studied, and the appropriate frame has to be chosen to have a simple solution to a given problem.

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  • $\begingroup$ Can all of physics be generalised to be model/ a number of models trying to explain reality as we see it? Newtons laws, energy conservation; it is easy to understand that these are are models that provide a framework with which we can explain phenomena. But let us consider the motion of an accelerating object, the object would have a velocity at a given time. The rate with which velocity changes can be defined, it seems intuitive to say that they exist physically, that it is not merely a model. Or is it a result that we get based on the Newtonian model, that we use to regard the world? $\endgroup$ – SNB Mar 2 '18 at 13:08
  • $\begingroup$ Also what of an electron? Is an electron a model as well; I think the existence of an electron is a result stemming from the model that we develop to consider matters concerning electricty. Is that correct? Also we say that we see because photons hit our eyes, but that's a result of us defining something called photons is it not? If so, all the explainations that we give in physics are not reality itself, but rather the reasons that we ourselves create in the process of trying to develop a theory that manages to explain phenomena. Am I correct? Sorry if this sounds stupid. Much obliged $\endgroup$ – SNB Mar 2 '18 at 13:15
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    $\begingroup$ There are observation and measurements. We measure the length of a field by counting steps. Then there is geometry which can fit the measurements and predict new distances . geometry is the model for mapping the surface of the earth. The measurements are real, and the theorems of geometry are real , and it happens to be a good model for mapping the earth. Electrons are real, they were seen first in cathode ray tubes, and now in detectors hst-archive.web.cern.ch/archiv/HST2005/bubble_chambers/… . We have good models to describe and predict the behavior of electrons. $\endgroup$ – anna v Mar 2 '18 at 14:19
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    $\begingroup$ The importance with physics models is that they should be predictive, if a prediction fails to fit the data, the model is falsified, the data are real and there, to be fitted by a different/better mathematical model. Theories in physics use mathematics to predict real numbers that can be checked against new data. Further than that we go into philosophy and metaphysics $\endgroup$ – anna v Mar 2 '18 at 14:21
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A field is a quantity assigned to each point in space. The quantity can be a scalar (number), a vector, or something more complicated.

A particle doesn't "immediately create" the entire field. It only creates it locally and then the change propagates at a finite speed (typically speed of light $c$).

The spread of the "update" is also local - changes of the field affects only the (infinitesimally close) nearby values of field. This is described by partial differential equations, usually called field equations or wave equations (because of the wave-like behaviour).

Examples of such partial differential equations are Maxwell's equations (for electromagnetism) and Einstein field equations (for gravitation).

So, at least in the classical physics, everything affects everything else only locally.


EDIT: For a nice explanation of this, there is a nice MinutePhysics video.

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  • $\begingroup$ You used the word field eight times but never answered to OP's questions about what it is etc. Try answering the question without using the word. Good luck I've never seen a good answer to this one. $\endgroup$ – Bill Alsept Apr 12 '17 at 5:53
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A field is a mathematical notion (as anna's very good answer explains). What exists is vacuum fluctuations - virtual particles that "connect" real ones to the proper extent. They give rise to the rest.

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