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mysearch
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Hi,
I am interested in trying to better understand the nature of fields in terms of a possibly somewhat contrived example. It seems, from a classical perspective, that an electric or gravitational field is capable of transporting potential energy between two points in space defined by two particles having mass and/or charge. However, I am not sure of my facts and would like to clarify whether the example being illustrated is valid.
First of all, it might be said that all processes in classical physics can be reduced to either kinetic or potential energy. However, unlike kinetic energy that can be assigned to a single particle, potential energy can only be described as existing between two, or more, particles. Therefore, in this respect, a classical field between two particles would seem to align to a generic description of a potential energy field?
Because I don’t want to initially be too specific about whether the field in question is linked to an electric or gravitational field, the example will simply describe an attractive force between the particles. As such, the contrived example consists of two particles isolated in a vacuum at [A] and , separated by a huge distance, such that any propagation at [c] would take a finite time. As a conceptual configuration, it is assumed that both particles are tethered in position, so that any infinitely small force of attraction on each particle can be can be measured independently. Now the particle at [A] is moved to [A’] and back again.
How does the movement of [A] affect this system?
In order to move [A] to [A’] and back, there is the assumption that energy has to be input into this system. However, when the particle is returned to [A], it possesses no additional kinetic energy in its frame of reference, i.e. it is zero, and its potential energy with respect to is not obviously different, if is tethered in its original position. However, if we assume that the change to the field between [A] and is now subject to a finite propagation velocity of [c], then this change may not have yet reached .
But where is the energy input into this system during this period?
In the scope of this example, I am assuming that the input energy must exist as potential energy in transit within the field, i.e. it is in the process of propagating from [A] to at a finite speed of [c]. However, I am not sure that this description is necessarily correct, especially when the electric field is considered in terms of quantized electromagnetic energy, i.e. photons, or as a gravitational field when the issue of the aberration speed of gravity is considered.
Electric Fields:
The following animation seems to suggest that the example cited would cause the implied change in the electric field strength and would propagate out at velocity [c] in vacuum, such that any effect on particle would be subject to a propagation delay and that during this period the energy must reside within the field. Is this a valid assumption?
http://www.its.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html
Of course, at another level, the movement of particle [A] would have involved an acceleration of a charge, which is classical described as the source of EM radiation, but as a photon linked to the quantization of EM energy in quantum mechanics. However, statistically, would it be correct to say the energy distributed by the photon model corresponds to that by EM radiation?
Gravitational Fields
As far as I am aware, gravity is not yet subject to any formal quantization. However, there seems to be an issue associated with the propagation speed of gravity and the issue of measurement aberration. The following link outlines the original arguments suggesting that gravity might propagate at superluminal speed:
http://metaresearch.org/cosmology/speed_of_gravity.asp
However, the following paper by Carlip seems to provide a mathematical argument that this is not the case and gravity is also subject to the relativistic restriction. I do not, as yet, follow all the mathematical arguments or understand whether Carlip is raising any caveats to his conclusion.
http://arxiv.org/pdf/gr-qc/9909087v2.pdf
However, is it now accepted that gravity always propagates at [c] in vacuum and, if so, would the example cited above suggest that electric and gravitational fields both propagate potential energy?
Although, it is not necessarily a question for this forum, the motivation for the example is based on that the perception that quantum theory seems to raise questions about the physical reality of fields that classical theory seems to give tangible physicality, if the concept of energy (and momentum) is an attribute of the field. Thanks
I am interested in trying to better understand the nature of fields in terms of a possibly somewhat contrived example. It seems, from a classical perspective, that an electric or gravitational field is capable of transporting potential energy between two points in space defined by two particles having mass and/or charge. However, I am not sure of my facts and would like to clarify whether the example being illustrated is valid.
First of all, it might be said that all processes in classical physics can be reduced to either kinetic or potential energy. However, unlike kinetic energy that can be assigned to a single particle, potential energy can only be described as existing between two, or more, particles. Therefore, in this respect, a classical field between two particles would seem to align to a generic description of a potential energy field?
Because I don’t want to initially be too specific about whether the field in question is linked to an electric or gravitational field, the example will simply describe an attractive force between the particles. As such, the contrived example consists of two particles isolated in a vacuum at [A] and , separated by a huge distance, such that any propagation at [c] would take a finite time. As a conceptual configuration, it is assumed that both particles are tethered in position, so that any infinitely small force of attraction on each particle can be can be measured independently. Now the particle at [A] is moved to [A’] and back again.
How does the movement of [A] affect this system?
In order to move [A] to [A’] and back, there is the assumption that energy has to be input into this system. However, when the particle is returned to [A], it possesses no additional kinetic energy in its frame of reference, i.e. it is zero, and its potential energy with respect to is not obviously different, if is tethered in its original position. However, if we assume that the change to the field between [A] and is now subject to a finite propagation velocity of [c], then this change may not have yet reached .
But where is the energy input into this system during this period?
In the scope of this example, I am assuming that the input energy must exist as potential energy in transit within the field, i.e. it is in the process of propagating from [A] to at a finite speed of [c]. However, I am not sure that this description is necessarily correct, especially when the electric field is considered in terms of quantized electromagnetic energy, i.e. photons, or as a gravitational field when the issue of the aberration speed of gravity is considered.
Electric Fields:
The following animation seems to suggest that the example cited would cause the implied change in the electric field strength and would propagate out at velocity [c] in vacuum, such that any effect on particle would be subject to a propagation delay and that during this period the energy must reside within the field. Is this a valid assumption?
http://www.its.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html
Of course, at another level, the movement of particle [A] would have involved an acceleration of a charge, which is classical described as the source of EM radiation, but as a photon linked to the quantization of EM energy in quantum mechanics. However, statistically, would it be correct to say the energy distributed by the photon model corresponds to that by EM radiation?
Gravitational Fields
As far as I am aware, gravity is not yet subject to any formal quantization. However, there seems to be an issue associated with the propagation speed of gravity and the issue of measurement aberration. The following link outlines the original arguments suggesting that gravity might propagate at superluminal speed:
http://metaresearch.org/cosmology/speed_of_gravity.asp
However, the following paper by Carlip seems to provide a mathematical argument that this is not the case and gravity is also subject to the relativistic restriction. I do not, as yet, follow all the mathematical arguments or understand whether Carlip is raising any caveats to his conclusion.
http://arxiv.org/pdf/gr-qc/9909087v2.pdf
However, is it now accepted that gravity always propagates at [c] in vacuum and, if so, would the example cited above suggest that electric and gravitational fields both propagate potential energy?
Although, it is not necessarily a question for this forum, the motivation for the example is based on that the perception that quantum theory seems to raise questions about the physical reality of fields that classical theory seems to give tangible physicality, if the concept of energy (and momentum) is an attribute of the field. Thanks
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