Completion of Einstein's homework on special relativity in electromagnetism

Completion of Einstein’s homework on special relativity in electromagnetism

Illustration of the formation process of the planar electric field contraction that accompanies the propagation of an electron beam at near the speed of light (represented as an ellipse in the figure). Credit: Masato Ota, Makoto Nakajima

Albert Einstein, one of the most famous modern scientists, proposed the revolutionary theory of special relativity more than a century ago. This theory forms the basis of most of what we know about the universe, but other than that it has not yet been experimentally proven.

Scientists at Osaka University’s Institute of Laser Technology have used ultra-fast electro-optical measurements to visualize for the first time the contraction of the electric field around a beam of electrons traveling at nearly the speed of light and demonstrate the generation process.

In the special theory of relativity, Einstein proposed that in order to properly describe the motion of objects moving past an observer at near the speed of light, one must apply a “Lorentz transform,” which mixes the coordinates of space and time. He was able to explain how these transformations made the equations for electric and magnetic fields internally consistent.

While various effects of relativity have been demonstrated many times with very high experimental accuracy, there are still aspects that remain undiscovered in experiments. Ironically, this involves the contraction of the electric field, presented as a special relativity phenomenon in electromagnetism.

The research team at Osaka University has now demonstrated this effect experimentally for the first time. They accomplished this feat by measuring the profile of the Coulomb field in space and time around a high-energy beam of electrons produced by a linear particle accelerator. Using ultra-fast electro-optical sampling, they were able to record the electric field with extremely high temporal resolution.

It has been reported that the Lorentz transformations of time and space, and those of energy and momentum, have been demonstrated by time dilation experiments and rest mass energy experiments, respectively. Here the team studied a similar relativistic effect called electric field contraction, which corresponds to the Lorentz transform of electromagnetic potentials.

“We have visualized the contraction of the electric field around a beam of electrons propagating at almost the speed of light,” says Prof. Makoto Nakajima, the project manager. In addition, the team observed the process of electric field contraction immediately after the electron beam passed a metal boundary.

In developing the theory of relativity, Einstein is said to have used thought experiments to imagine what it would be like to ride a light wave. “There is something poetic about demonstrating the relativistic effect of electric fields more than 100 years after Einstein’s prediction,” says Prof. Nakajima. “Electric fields were a crucial element in the genesis of the theory of relativity.”

This research, with observations that closely match Einstein’s predictions of special relativity in electromagnetism, can serve as a platform for measurements of high-energy particle beams and other experiments in high-energy physics. The paper was published in natural physics.

Einstein’s theory of relativity passes rigorous tests based on LHAASO observations

More information:
Koichi Kan, Ultrafast Visualization of an Electric Field Under the Lorentz Transform, natural physics (2022). DOI: 10.1038/s41567-022-01767-w.

Provided by Osaka University

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