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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.
[itex]\def\MACROS{}
\def\hv{\hat v}
\def\hw{\hat w}...
The concept of an electric field seen by an observer is based on the theory of relativity, which states that measurements of physical quantities such as electric fields can vary depending on the observer's frame of reference. This means that the electric field observed by one observer may appear differently to another observer who is moving at a different velocity.
Tensors are mathematical objects that are used to describe the properties of physical systems in a way that is independent of the observer's frame of reference. In the context of calculating the electric field seen by an observer, tensors are used to transform the components of the electric field from one frame of reference to another, taking into account the effects of relativity.
The relativistic calculation of the electric field seen by an observer is significant because it helps us understand the effects of relativity on the behavior of electric fields. This is important in fields such as particle physics and cosmology, where the behavior of particles and fields is affected by their relative velocities.
Yes, the electric field seen by an observer can be measured experimentally. However, the measurements may differ depending on the observer's frame of reference, as predicted by the theory of relativity. This is why it is important to use tensors to accurately calculate and compare the electric field measurements made by different observers.
The concept of an electric field seen by an observer is just one example of how the theory of relativity affects our understanding of physical phenomena. It demonstrates that physical quantities such as electric fields are not absolute, but can vary depending on the observer's frame of reference. This is a fundamental principle of relativity that applies to many other physical quantities and has implications for our understanding of the universe.