Completing Einstein’s homework on special relativity in electromagnetism

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

Albert Einstein, one of the most celebrated modern scientists, proposed the revolutionary special theory of relativity more than a century ago. This theory forms the basis of most of what we understand about the universe, but some of it has not been proven experimentally so far.

Scientists at the Institute of Laser Engineering at Osaka University have used ultrafast electro-optical measurements to visualize for the first time the contraction of the electric field around an electron beam moving at nearly the speed of light and demonstrate the generation process.

In special relativity, Einstein proposed that to properly describe the motion of objects moving past an observer at close to the speed of light, one should use a “Lorentz transform” that mixes the coordinates of space and time. He was able to explain how these transformations made the equations for electric and magnetic fields self-consistent.

Although various effects of relativity have been demonstrated many times with a very high degree of experimental precision, there are still aspects that have not been revealed in experiments. Ironically, these include the contraction of the electric field presented as a phenomenon of special relativity in electromagnetism.

Now, the research team at the University of Osaka has experimentally demonstrated this effect for the first time. They achieved this feat by measuring the space-time profile of the Coulomb field around a high-energy electron beam generated 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, as well as those of energy and momentum, were demonstrated by time dilation experiments and rest mass energy experiments, respectively. Here the team looked at a similar relativistic effect called electric field contraction, which corresponds to the Lorentz transform of electromagnetic potentials.

“We visualized the contraction of an electric field around an electron beam propagating close to the speed of light,” said Prof. Makoto Nakajima, the project leader. In addition, the team observed the process of electric field contraction immediately after the electron beam passed through a metallic boundary.

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

This research, with observations closely aligned with Einstein’s predictions of special relativity in electromagnetism, could serve as a platform for energetic particle beam measurements and other experiments in high-energy physics. The newspaper is published in Nature physics


Einstein’s theory of relativity passes rigorous test based on LHAASO observation

More information:
Koichi Kan, Ultrafast visualization of an electric field under the Lorentz transform, Nature physics (2022). DOI: 10.1038/s41567-022-01767-w.

Provided by the University of Osaka

Quote: Completing Einstein’s Homework on Special Relativity in Electromagnetism (2022, Oct. 20) retrieved Oct. 20, 2022 from

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