The Electric Field Seen by an Observer: A Relativistic Calculation with Tensors

[robphy]

This Insight was inspired by the discussion in “electric field seen by an observer in motion“, which tries to understand the relation between two expressions:

the definition of the electric field as seen by an observer (expressed as an observer-dependent 4-vector, as decomposed from the Maxwell field tensor $E_{a}=F_{ab}v^b$, as found in Wald’s General Relativity [p. 64, Eq (4.2.21)] )
the Lorentz Transformation of the Electric Field, in 3-vector form

I was going to reply to a comment on something I said (here) but then realized that my post was getting too large. So, here it is in the Insight.
\def\MACROS{}<br /> \def\hv{\hat v}<br /> \def\hw{\hat w}...

<br /> <br /> <a href="https://www.physicsforums.com/insights/the-electric-field-seen-by-an-observer-a-relativistic-calculation-with-tensors/" class="link link--internal">Continue reading...</a>

 

[vacuum]

Hello,

Thank you for bringing this discussion to my attention. it is always exciting to see people exploring and trying to understand complex concepts like the electric field in motion.

After reading through the forum post and your response, I wanted to add a few thoughts and clarifications. Firstly, the definition of the electric field as seen by an observer is an important concept in relativity. As you mentioned, it is expressed as an observer-dependent 4-vector, which is derived from the Maxwell field tensor. This definition takes into account the observer's relative motion and shows how the electric field appears to them.

On the other hand, the Lorentz Transformation of the Electric Field is a mathematical tool used to transform the electric field from one reference frame to another. This transformation is necessary because the electric field, like many other physical quantities, is observer-dependent in relativity. This means that different observers will measure different values for the electric field depending on their relative motion.

It is important to note that the Lorentz Transformation of the Electric Field does not change the physical nature of the electric field. It simply shows how the field appears to different observers. This is similar to how the length of an object appears different to different observers in relativity, but the object itself remains the same.

I also wanted to mention that the Lorentz Transformation of the Electric Field is just one aspect of the larger concept of electromagnetic fields in relativity. The full understanding of these fields requires a deeper understanding of the principles of general relativity and how they interact with electromagnetism.

In conclusion, I am glad to see people exploring and discussing these complex concepts. As scientists, it is our job to continue to research and expand our understanding of the world around us. I hope this helps clarify some aspects of the discussion. Keep up the great work!