Lorentz contrast/EM wave question.

In summary, the Lorenz contrast is a term that appears in an equation relating scalar and vector potentials. It's important because it decouples the potentials, and the Lorenz condition is used to achieve uniqueness.
  • #1
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In my EM course I've encountered what is called the "Lorentz contrast". If I derive the wave equation using the scalar and vector potential, I end up with a non-homogenous wave equation with the term:

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(left hand side), or more precisely, the divergence of said term.

What does it mean and why is making it equal to zero important/useful/possible?
 
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  • #2
You mean Lorentz condition, right? It's both important and useful to make this term disappear because what you're left with is easy to interpret: A and φ both satisfy the ordinary wave equation, which describes something that can propagate at the speed of light.
 
  • #3
So making it disappear is necessary because a change in potential also needs to "propagate" at the speed of light, along with E and B?
 
  • #4
It's not necessary, it's a convenient solution to an overriding problem. The real problem is that the scalar and vector potentials are non-unique. We can apply an arbitrary transformation to them and still result in the same electric and magnetic fields. The reason why the Lorenz condition is used is that it decouples the scalar and vector potentials. The new decoupled potential equations are wave equations. However, we can still achieve uniqueness by using a different gauge. The Couloumb gauge only restricts that the divergence of the vector potential be zero. The difference with the Coulomb gauge is that the scalar potential is now the instantaneous Coulombic potential. On the other hand, the Lorenz gauge requires that the potentials be retarded potentials since they satisfy a wave equation.

And it's Lorenz, not Lorentz. People mix that one up A LOT. In fact, looking at Jackson's text shows that the section title uses "Lorenz" but the section title at the page header is "Lorentz." *SIGH*
I also see that Wikipedia mixes the two even on the same page.

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5672647&tag=1
 
  • #5
Why this nice gauge condition should be attributed to the Danish physicst Ludvig Lorenz and not the Dutch physicicsts Hendrik Antoon Lorentz you can read in

Jackson, J.D., and Okun, L.B.: Historical roots of gauge invariance, Rev. Mod. Phys. 73, 663 (2001)
 
  • #6

FAQ: Lorentz contrast/EM wave question.

What is Lorentz contrast?

Lorentz contrast, also known as Lorentz factor, is a term used in special relativity to describe the ratio of the time interval between two events measured in one inertial frame of reference to the time interval measured in another frame of reference that is moving at a constant velocity relative to the first frame. It is represented by the symbol γ and can be calculated using the formula γ = 1/√(1-v²/c²), where v is the relative velocity between the frames and c is the speed of light.

How is Lorentz contrast related to electromagnetic waves?

Lorentz contrast is related to electromagnetic (EM) waves through the theory of special relativity. According to this theory, EM waves, which are a form of energy, travel at the speed of light. As Lorentz contrast takes into account the effects of relative velocity on time and space, it also affects the propagation of EM waves. This means that the frequency and wavelength of an EM wave can appear different to an observer in a different frame of reference due to the Lorentz factor.

Why is Lorentz contrast important in understanding the behavior of EM waves?

Lorentz contrast is important in understanding the behavior of EM waves because it allows scientists to account for the effects of relative motion on the propagation of these waves. This is crucial in fields such as astrophysics and cosmology, where objects are often moving at very high speeds. Without taking into account the Lorentz factor, there would be discrepancies in the observations and calculations of EM waves, leading to incorrect interpretations and conclusions.

How does Lorentz contrast impact the concept of time dilation?

Time dilation is a phenomenon predicted by the theory of special relativity, where time passes slower for objects that are moving at high velocities relative to an observer. This effect is directly related to the Lorentz contrast, as the time interval measured in one frame of reference will appear different to an observer in another frame due to the relative velocity between them. The greater the relative velocity, the larger the Lorentz contrast and the more pronounced the time dilation effect.

Are there any practical applications of Lorentz contrast?

Yes, there are many practical applications of Lorentz contrast, especially in modern technologies such as GPS systems, particle accelerators, and satellite communications. These technologies rely on precise measurements and calculations of time and space, which are affected by the Lorentz factor. Understanding Lorentz contrast also allows scientists to make accurate predictions and calculations in fields such as astrophysics, where the effects of relative motion on EM waves are crucial in studying the universe.

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