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A Contrived Example?

  1. Feb 28, 2012 #1


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    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 possess 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?
    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 [Broken]
    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.
    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
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Feb 28, 2012 #2
    One of us is confusing something here. What exactly do you mean by energy input into the system?

    If particle [itex]A[/itex] moves closer to [itex]B[/itex], the energy decreases. To maintain energy conservation a particle (photon for EM) is emitted. Similarly, a classical field would have a wave with that energy that would propagate at [itex]c[/itex]. [itex]A[/itex] would not move back due to potential energy unless it had initially moved away from [itex]B[/itex] which it wouldn't have done without energy being put into the system. So, the only way it moves from [itex]A[/itex] to [itex]A^'[/itex] and back is if energy is put into the system and that energy will be either a wave in the field or a quantum particle depending on how you want to think about it.

    Maybe this answers your question or maybe I am misunderstanding. Either way, I've been looking for that applet with the EM field for a while. Thank you for posting it!
  4. Feb 28, 2012 #3
    Second note, be wary of anything from a site called "metaresearch". I am far from knowledgeable about GR, but I saw no differential geometry on that site and a claim that flies in the face of all of the other research into gravity waves. I can't comment from personal knowledge, but I would look elsewhere.

    I don't know how certain it is, but that is what my professor said.

    I'm not sure if field energy is considered potential energy when it is a propagating wave. Either way, the energy is in the wave no matter what exactly you call it.
  5. Feb 29, 2012 #4


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    DrewD, thank you for the comments. I have posted some responses below.
    I did say it was a contrived example. Particles A and B are initially described as an isolated system where the particles are attracted towards each other, but held in position. However, imagine you could pick up A and simply move it to A’. This requires energy, which is really external to the A/B system described, i.e. this energy is input into this system. So the suggestion is that this causes the ‘potential’ field around A/A’ to change with respect to B, but this change in the field takes a finite time to propagate to B. During this time, A’ is moved back to A, again by some external mechanism. As such, the A/B system is essentially back to its original configuration in that B has not yet been affected by any changes in the field; although the changes are still propagating towards B. Note, this would actually be a two-way way process between A and B.
    If you are interested in the theory, the following links discuss the Larmor formula and some of the wider issues:
    I think your professor is reflecting the current consensus. I believe the Carlip paper in 2000 was generally accepted, although I haven’t be able to work through the maths, as presented. The following links may be of interest, especially the first, which is by Carlip in 2011:
    In part, this was the root of my questions and the purpose of the ‘contrived’ example. For the suggestion is that energy exists within the field, which then takes on some notion of physical existence. From a classical perspective there are really only 2 forms of energy, i.e. kinetic and potential. Examination of mechanical waves, e.g. water, suggests that what is transported is the potential energy minus any loss. Kinetic energy only exists locally within the medium through which the wave is travelling. In terms of electric and gravitational potential in vacuum, the idea of the medium is less obvious, but something seems to define the same propagation velocity, i.e. [c], for both the electric and gravitational field plus the ability to transport energy. However, in the process of trying to understand ‘some’ quantum field theory, the idea of the field having any physical existence appears to become increasingly abstract, so I was reverting to some classical physics just to sort out some basic concepts in my mind. Thanks
  6. Mar 1, 2012 #5


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    mysearch, You've clearly thought a lot about these questions, and generally appear to be on the right track. I have some suggestions to make. The first is to forget for the moment about photons and gravitons and just try to understand these points at the classical level. Secondly the split of energy into kinetic and potential is not entirely appropriate when we are discussing fields. Certainly no one uses these terms in such a context. What you can do instead is talk about energy that is stored in the field as opposed to the particles. Also, trying to draw an analogy with waves in a medium, especially water waves, can be misleading. Finally if you accept general relativity (and it is very well established) there is no doubt at all that gravitational waves exist and propagate at velocity c. This means that influences are retarded just as they are for electromagnetism.

    Turning to your example, what happens when particle A is moved to A' and back again depends to a certain extent on how fast it is done. In the limit of very slow motion, no waves are generated. The energy it takes to move from A' back to A exactly matches and cancels the energy it took to move from A to A'. The change will propagate at c, and at a later time B will be impelled back and forth, reflecting the change. No net energy is transferred. If you are thinking that some energy must have been transmitted to move B, the answer is no, not in the slow motion limit.

    If you do it rapidly a net amount of input energy will be required, and a wave will be generated. This has nothing to do with the presence of B, it is simply because A's field has become time-varying. Energy is stored in the field near A, which then propagates outward at c, not only toward B but in all directions.
  7. Mar 1, 2012 #6


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    Hi Bill, thanks for your insights, I would be appreciative of any help at this stage. See below for explanation.
    In part, this was the intention of this example. As you might be aware from the QM forum, I have been trying to understand QFT for the last couple of months, but have hit a bit of brickwall as far as some of the maths is concerned and the apparent lack of any obvious physical interpretation associated with many of the quantum field descriptions. Hence, I was trying to sort out some of the implications stemming from a classical field description. In particular, I was interested in the fact that the example seems to apply to both EM and gravitational field having a common propagation velocity [c], even though there is no current accepted notion of a quantized gravitational field.
    Again, would appreciate any clarification on offer. However, let me try to quickly outline a few of my assumptions without going too off-topic within this forum. At a fundamental level, I have a problem with the idea/description of particles, because at the quantum level, the idea of matter/substance just doesn’t make sense to me. As such, I was assuming that energy has to be a more fundamental concept, e.g. E=mc^2. However, energy is a scalar quantity, therefore this would seem to require some additional mechanism to move in spacetime, e.g. fields and waves. Again, I am trying to stick within the general remit of classical physics. In this context, there would appear to be just 3 basic forms of energy, i.e. rest mass, kinetic and potential, where rest mass might be describe as some form of potential energy, although this definition is not really of issue at this point. So I was indeed attempting to ‘talk about energy that is stored in the field as opposed to the particles’. I agree, the cross-reference to mechanical (water) wave may be misleading, but I was simply trying to highlight that these waves can be shown to transport potential energy not kinetic energy.
    Yes, I do. I believe the Carlip reference in post #4 supported this position, although I not sure I fully understand all his mathematical arguments at this stage and was simply looking for confirmation that this position was generally accepted. Thanks
    Not totally sure of the point(s) being raised here. At one level there is the issue of an accelerated charge being the source of EM radiation/photons. On another, there is the issue of rate of change of the potential field wrt to the propagation delay to B. Did you have another issue in mind? See below.
    I agree that the net energy of the system is ultimately unchanged, but during the time it takes the changes to the potential field to propagate to B, it would seem that a delta of potential energy exists in the field, which first moves B to B’ and then back again, so that the net change in energy is zero. The only real point of this example was to suggest that the field exists in some tangible form, i.e. it has physicality, and presumably has specific properties that defines the propagation velocity of both the change to the electric and gravitational fields. This is possibly a bit speculative at this point!!!!
    If I am understanding you correctly. I think you are again making reference to an accelerated charge being the source of EM radiation/photons. If so, I also agree.

    Footnote: While it is not the focus of this forum, I guess I was trying to establish some level of physicality to the notion of fields, at least, within classical physics, such that I might reflect further on the physicality of quantum fields, which seems to be such a point of debate in QFT. Thanks
    Last edited: Mar 1, 2012
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