Completing Einstein’s homework on special relativity in electromagnetism

Osaka University researchers showed that the predictions of Einstein’s theory of special relativity in electromagnetism could be detected in the contraction of the electric field created by ultrafast electrons. By achieving femtosecond resolution, they were able to visualize the contracted electric field for the first time. This work can be applicable to particle accelerators and high-energy physics.

Illustration of the formation process of the planar electric field contraction that accompanies the propagation of a near-light-speed electron beam (shown as an ellipse in the figure)

Researchers at Osaka University demonstrate the relativistic contraction of an electric field produced by fast-moving charged particles, as predicted by Einstein’s theory, which can help improve radiation and particle physics research

  Osaka, Japan – Albert Einstein, one of the most celebrated modern scientists, proposed the revolutionary theory of special relativity over a century ago. This theory forms the basis of most of what we understand about the Universe, but a part of it has not been experimentally demonstrated until now. Scientists from the Institute of Laser Engineering at Osaka University have used ultrafast electro-optic measurements to visualize for the first time the contraction of the electric field around an electron beam moving at close to the speed of light and demonstrate the generation process.

 In the theory of special relativity, Einstein proposed that in order to properly describe the motion of objects moving past an observer at close to the speed of light, one needs to employ a “Lorentz transformation” 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. While various effects of relativity have been demonstrated many times to a very high degree of experimental precision, there are still aspects that remain unrevealed in experiments. Ironically, these include the contraction of the electric field represented as a phenomenon of special relativity in electromagnetism.

 Now, the research team at Osaka University has 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 electron beam generated by a linear particle accelerator. Using ultrafast electro-optic 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 transformation of electromagnetic potentials. “We visualized the contraction of electric field around an electron beam propagating close to the speed of light,” says Prof. Makoto Nakajima, the project leader. In addition, the team observed the process of electric-field contraction right after the electron beam passed through a metal boundary.

 When developing the theory of relativity, it is said that Einstein used thought experiments to imagine what it would be like to ride on 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 matching closely to Einstein’s predictions of special relativity in electromagnetism, can serve as a platform for measurements of energetic particle beams and other experiments in high-energy physics.


The article, “Ultrafast visualization of an electric field under the Lorentz transformation,” will be published in Nature Physics at DOI:

About Osaka University

Osaka University was founded in 1931 as one of the seven imperial universities of Japan and is now one of Japan's leading comprehensive universities with a broad disciplinary spectrum. This strength is coupled with a singular drive for innovation that extends throughout the scientific process, from fundamental research to the creation of applied technology with positive economic impacts. Its commitment to innovation has been recognized in Japan and around the world, being named Japan's most innovative university in 2015 (Reuters 2015 Top 100) and one of the most innovative institutions in the world in 2017 (Innovative Universities and the Nature Index Innovation 2017). Now, Osaka University is leveraging its role as a Designated National University Corporation selected by the Ministry of Education, Culture, Sports, Science and Technology to contribute to innovation for human welfare, sustainable development of society, and social transformation.



Published: 20 Oct 2022


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Japan Society for the Promotion of Science
NIFS Collaborative Research Program