is there conservation of field-force?

[lemur]

Matter and energy can't be created or destroyed, only transformed into other forms. It seems that matter and energy are interchangeable to some extent, but presumably the total amount of matter-energy in a system is conserved through all transformations of one form to the other.

 

But what about force-fields? Can gravitation, electromagnetic force, and/or the nuclear forces be converted into one another? When matter is converted to energy, for example, some gravitational potential is presumably lost with the lost mass. Is this force-field converted into electromagnetic force in the form of radiation released? If so, is it possible that field-force could exhibit a similar law to the law of conservation of matter/energy? If not, why not?

[Spyman]

According to relativity both mass and energy hold equal value in terms of gravity, as such energy expels gravitational attraction as if it would if converted to matter.

 

"General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1915. It is the current description of gravitation in modern physics. It generalises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations."

http://en.wikipedia.org/wiki/General_theory_of_relativity

[ajb]

But what about force-fields? Can gravitation, electromagnetic force, and/or the nuclear forces be converted into one another?

 

In a way yes, you could build quite complicated Feynman diagrams (S-matrices or amplitudes etc ) with gravitons*, photons, quarks, electrons, Z bosons etc. You would have to ensure that all the necessary conservation laws hold, like energy-momentum, spin, electric charge, colour etc...

 

For instance, the photon has energy-momentum and so can act as a source of gravity. Thus we can expect to have gravitational couplings between photons and gravitons.

 

Things like a mix of electromagnetism and the strong force are also allowed. Quarks carry electric and colour charge.

 

* thinking of quantum general relativity as an effective theory.

[lemur]

In a way yes, you could build quite complicated Feynman diagrams (S-matrices or amplitudes etc ) with gravitons*, photons, quarks, electrons, Z bosons etc. You would have to ensure that all the necessary conservation laws hold, like energy-momentum, spin, electric charge, colour etc...

 

For instance, the photon has energy-momentum and so can act as a source of gravity. Thus we can expect to have gravitational couplings between photons and gravitons.

In my understanding, force-fields are static entities. However, if I think of a gravitational field as radiating gravitons or an electromagnetic field radiating photons, it seems like there should be a long-term dissipation of field-force as that force gets expelled as radiation. Is this a valid thought or am I misunderstanding something fundamental?

[ajb]

In my understanding, force-fields are static entities.

 

They have dynamics in general. The electromagnetic field is governed by Maxwell's equations for example.

 

However, if I think of a gravitational field as radiating gravitons or an electromagnetic field radiating photons, it seems like there should be a long-term dissipation of field-force as that force gets expelled as radiation. Is this a valid thought or am I misunderstanding something fundamental?

 

I don't really follow what you are saying.

 

Think about what happens to the size of the ripples on a pond when you throw a stone in as a function of the distance from the entry point of the stone. They get smaller in order to conserve the total energy contained in the wave. I think you are trying to say something similar with ripples in the electromagnetic or gravitational field?

[lemur]

They have dynamics in general. The electromagnetic field is governed by Maxwell's equations for example.

I'm talking about whether a force-field is a static entity or if it is a constant emission of radiation. An electron, for example, seem to be a point with static properties that can emit photons, which are radiation and therefore non-static. Is this a false distinction?

 

 

Think about what happens to the size of the ripples on a pond when you throw a stone in as a function of the distance from the entry point of the stone. They get smaller in order to conserve the total energy contained in the wave. I think you are trying to say something similar with ripples in the electromagnetic or gravitational field?

Well, I do get confused about whether photons are supposed to be volumeless isolated points of energy or whether they refer to the expanding sphere of energy that emerges from a radiation source. What I was really referring to, though, was whether the electromagnetic force contained in a photon is a transplanted quantity of force from its source of emission? In other words, do force-fields evaporate by radiating themselves away in the form of mobile field-force like photons/gravitons?

 

 

[ajb]

Classically you think of a photon as a little ripple in the electromagnetic field, an electromagnetic wave. Applying quantum theory to these ripples gives you photons.

 

Anyway, so let us suppose we have an isolated electric charge, say an electron. It acts as a source of the electromagnetic field. If we start to accelerate this charge, lets say we make it oscillate in space then this effects the surrounding electromagnetic field. In particular we get electromagnetic radiation originating from the charge. These waves carry energy, so energy needs to be supplied to keep the charge oscillating. However, the electromagnetic field itself does not carry electric charge and so the initial charge remains the same. there is no evaporation of electric charge.

[lemur]

Classically you think of a photon as a little ripple in the electromagnetic field, an electromagnetic wave. Applying quantum theory to these ripples gives you photons.

I guess I still don't get whether to think of photons as the ripples or point-particulate constituents of the ripples

 

Anyway, so let us suppose we have an isolated electric charge, say an electron. It acts as a source of the electromagnetic field. If we start to accelerate this charge, lets say we make it oscillate in space then this effects the surrounding electromagnetic field. In particular we get electromagnetic radiation originating from the charge. These waves carry energy, so energy needs to be supplied to keep the charge oscillating. However, the electromagnetic field itself does not carry electric charge and so the initial charge remains the same. there is no evaporation of electric charge.

so is an electron a point with a static field surrounding it? Generally I think of a magnetic field as exerting force the way a solid object would (technically the solidity of objects is due to EM field-force anyway, no?). However, when such a field becomes the source of photon-emission, you would think that some of the static field would have to be lost as it is radiated away. Otherwise there's not really a conservation of force-field, is there? If a force-field, such as the gravitation surrounding a planet or the electromagnetic field surrounding an electron, is multiplying itself in emissions it radiates, then I think force-fields should be considered a special phenomenon radically distinct from matter-energy, since matter-energy obeys conservation law.

 

Does that make sense or is it possible that force-field may in fact dissipate as they generate radiant emissions?

 

 

[swansont]

Static fields are modeled as particles emitting virtual photons, not real photons. There is no energy dissipation.

[lemur]

Static fields are modeled as particles emitting virtual photons, not real photons. There is no energy dissipation.

First, what are "virtual photons?" Second, am I correct in thinking of a static field as something that can move and has inertia? E.g. is an electron a static field with inertia? It seems that electrons can be viewed as a medium for photon absorption/re-emission but they themselves wouldn't lose field-force by generating photons. Maybe the way to view this is that the photon is a "fold" that builds up in the EM field of the electron and simply transfers into the surrounding EM fields or gravitational field. Maybe the waves also transfer into the nuclear force fields at the center of the atom. Maybe each type of field has a different "consistency" that causes the wave to have a different effect depending on its frequency and intensity. In the sense, force-fields could modulate in "texture" to transfer wave-energy without themselves gaining or losing field-force by doing so. Still, there must be various processes by which such fields decay or are modified, such as when a neutron splits into proton and electron or the reverse, or if a particle fragments into constituent sub-particles, which I assume is possible though I understand very little about quarks, leptons, muons, etc. beyond the names.

 

Still, are these static force-fields themselves always conserved as static fields, e.g. if they transform from one type of force into another somehow? If they never deteriorate in any process of transmutation, there would seem to be conservation of force-field in the same sense as conservation of matter. In fact, force-field conservation would seem to be the logical heir of conservation of matter insofar as matter is a superstructural effect of energetic force-field configurations. However, are all force-fields ultimately massless and move at C except when configured as matter with inertia? If so, that would seem to explain why/how matter can be disassembled into radiation, no?

 

 

[swansont]

http://en.wikipedia.org/wiki/Virtual_particle

 

A static electric field comes from a charged particle at rest. If the particle is moving, you will have both an electric field and a magnetic field.

 

Matter is not a conserved quantity.