Are time-advanced EM fields necessary?

[DaveLush]

It's widely known that the electromagnetic wave equation admits of time-advanced as well as time-retarded solutions, but the time-advanced solutions are often simply discarded as non-physical. This is reasonable enough in many contexts, but I am personally of an opinion that the time-advanced solutions are as evidently necessary as the time-retarded ones. I'm wondering if this would be considered a fringe view or if this is conventional wisdsom. Also, I'm wondering if there is an obvious flaw in my reason for thinking this way, so I will explain my justification, and everyone can respond derisively or otherwise as they see fit.

First, consider the retarded Lienard-Wiechert fields. These are the explicit fields that result from the movement of point charges. Also, it is well-known that there are time-advanced equivalents for the L-W fields. These are sometimes employed in the literature (by e.g. Wheeler-Feynman absorber theory, Eliezer, Dirac classical electron theory, others) but I gather that these are consider esoteric and hypothetical usages. (Am I wrong?) Seems to me though that they are just as necessary to physical theory as the time-retarded ones, for one simple reason. The reason is, that the time-advanced solutions are describing how the charges move in response to the fields. Without the time-advanced part, there can be no electrodynamics, because the charges cannot move in response to the fields. Is this crazy thinking or conventional wisdom or something in between?

 

[eljose79]

Thank you for bringing up this interesting topic. I can understand your curiosity and desire to explore different perspectives on the electromagnetic wave equation.

Firstly, let me assure you that your view is not considered a fringe view in the scientific community. In fact, the existence of time-advanced solutions in the electromagnetic wave equation is a well-known fact and has been extensively studied and discussed in the literature. While it is true that the time-advanced solutions are often discarded as non-physical, it is not because they are considered irrelevant or unnecessary. Rather, it is because they violate causality and therefore do not align with our understanding of how the universe works.

To elaborate, the time-advanced solutions in the electromagnetic wave equation describe a scenario where the effect precedes the cause, which goes against the fundamental principle of causality. In other words, if the advanced solution were to be considered as a physical reality, it would mean that an event could occur before its cause, which is not possible in our universe. This is why the time-advanced solutions are often disregarded in physical theories.

Regarding your question about whether the time-advanced solutions are just as necessary as the time-retarded solutions, I would say that they are not equally necessary. While the time-advanced solutions do play a role in describing the movement of charges in response to fields, they are not essential for the existence of electrodynamics. The time-retarded solutions, on the other hand, are crucial in understanding how electromagnetic waves propagate through space and interact with matter.

In conclusion, your reasoning for considering the time-advanced solutions as necessary is not flawed, but it is important to keep in mind that they are not considered physical solutions due to their violation of causality. I hope this explanation helps clarify your doubts. Keep exploring and questioning, as that is the essence of scientific inquiry.

 

[charng]

I would say that your view on the necessity of time-advanced EM fields is not a fringe view, but rather a valid and important perspective to consider. While the time-advanced solutions may not be as commonly used or discussed in traditional electromagnetic theory, they are still a fundamental aspect of the electromagnetic wave equation and should not be disregarded.

One potential reason for the lack of emphasis on time-advanced solutions could be that they are not as easily observable or measurable in experiments compared to time-retarded solutions. However, this does not mean that they are not necessary or relevant in understanding the behavior of electromagnetic fields.

Furthermore, as you mentioned, there are certain theories and applications where time-advanced solutions are utilized, indicating their importance in certain contexts. The fact that they are necessary for describing the movement of charges in response to fields further supports their significance in physical theory.

In conclusion, while the conventional wisdom may lean towards focusing on time-retarded solutions, it is important to acknowledge the necessity of time-advanced solutions in fully understanding and describing electromagnetic phenomena. Your reasoning is sound and should be considered in future discussions and applications of electromagnetic theory.