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What is the significance of solutions to non-homogeneous wave equations for the scalar and vector potentials that utilize retarded time?
JesseM said:I think the retarded waves are usually discarded as unphysical, but for another perspective see the Wheeler-Feynman absorber theory. The philosopher of science Huw Price argues that there would be no way to distinguish an advanced wave from a retarded wave and that therefore they are just two different descriptions of the same thing (see http://www.jstor.org/pss/687619 and http://www.jstor.org/pss/687664 for debate).
I don't think that's an accurate statement.DaveLush said:Seems to me nobody has a clue how causality really works so to wave away the advanced solutions as non-causal is a mistake.
lbrits said:I don't think that's an accurate statement.
In any case, these are all solutions to the PDE, and the way you build up your wanted solution is by looking at boundary conditions (same is true of any PDE).
But Price didn't say that advanced waves are needed in addition to retarded waves to explain any physical behavior, he just said that an advanced wave is nothing more than a different sort of description of a retarded wave, so retarded waves can be redescribed as advanced waves and vice versa.DaveLush said:To the second statement, yes and what I said is that the boundary condition of charged particle moving in response to an electromagnetic field (more specifically that there will be a force on the particle that causes it to move) requires that the time-advanced solution be non-zero.
To the first statement, you are welcome to your opinion, and perhaps you can refer me to where there is a description of how causality works. This question is a big part of Price's book, "Time's Arrow and Archimedes' Point". I found it quite convincing on this point that the pat explanations for causality are generally based on circular or otherwise fallacious reasoning. Most importantly, this applies to the Second Law of Thermodynamics.
Well I don't want to go down that road here, at least not alone. Read Price if you are interested. For now I just want to say that if you think that by waving away time-advanced solutions to the EM wave equation that causality is explained then you are laboring under a vast misconception.
JesseM said:But Price didn't say that advanced waves are needed in addition to retarded waves to explain any physical behavior, he just said that an advanced wave is nothing more than a different sort of description of a retarded wave, so retarded waves can be redescribed as advanced waves and vice versa.
Well, he said that the time-asymmetric version of the second law involves circular reasoning. You can show that starting from any given low-entropy state, entropy is likely to increase in the future, but the same proof should also show that entropy is likely to have been higher in the past of that state as well.DaveLush said:Yes, I remember Price saying that, and I hope you remember him saying that the standard reasoning behind the Second Law is circular and that Boltzmann realized this.
I don't have any knowledge of QED, but I'm a little skeptical--if this is true, why do most physicists think that they can discard the advanced solutions and still explain electromagnetic behavior?DaveLush said:In any case it fits in perfectly with what you attribute to Price. When a charge moves it radiates and the Green's function for this is retarded, but when the fields reach another charge and the charge moves then from the point of view of the second charge these are time-advanced Green's function solutions.
JesseM said:I don't have any knowledge of QED, but I'm a little skeptical--if this is true, why do most physicists think that they can discard the advanced solutions and still explain electromagnetic behavior?
DaveLush said:When a charge moves it radiates and the Green's function for this is retarded, but when the fields reach another charge and the charge moves then from the point of view of the second charge these are time-advanced Green's function solutions.
Retarded time solutions are a type of solution for non-homogeneous wave equations that take into account the time delay in the propagation of waves. They are used to model wave phenomena in which the effects of the wave are not felt instantaneously, but rather with a time delay.
Retarded time solutions are unique in that they incorporate a time delay factor, while other types of solutions, such as advanced time solutions, do not. This allows for a more accurate representation of wave phenomena in real-world scenarios.
Retarded time solutions can be used to model a wide range of systems, including electromagnetics, acoustics, and fluid dynamics. They have applications in various fields such as engineering, physics, and geology.
Retarded time solutions are typically calculated using integral transforms, such as the Laplace transform or the Fourier transform. These solutions can then be implemented in computer simulations or mathematical models to study the behavior of waves in a non-homogeneous medium.
Retarded time solutions are not suitable for all types of wave phenomena. They are most effective for modeling linear systems and may not accurately represent nonlinear systems. Additionally, they may become more complex and computationally expensive for systems with multiple dimensions or varying boundary conditions.