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The Vastest Scales of Cosmic Waves

An exametre (Em) is equal to 1,000 petametres (10¹⁸ metres), representing one of the largest units of length used to describe the longest electromagnetic wavelengths and gravitational waves in the universe. At this scale, wavelengths correspond to frequencies in the zeptohertz (10⁻²¹ Hz) range and lower, which are incredibly slow oscillations occurring over billions of years and spanning distances larger than entire galaxy superclusters.

For example, waves with a frequency of around 1 zeptohertz have wavelengths on the order of 300 exametres. These enormous waves are primarily theoretical and are significant in cosmology and astrophysics for studying the large-scale structure of the universe, primordial fluctuations from the Big Bang, and the behavior of space-time itself.

Using exametres to express wavelength helps scientists conceptualize the almost incomprehensible vastness of the cosmos. These extreme wavelengths provide key insights into the fundamental nature of the universe, including gravitational wave backgrounds and the evolution of cosmic structures on the grandest scales.

A Quantum Limit of the Electron

The electron Compton wavelength is a fundamental constant in quantum physics that represents the limit at which the wave-like nature of an electron becomes significant in high-energy interactions. It is defined by the equation λ = h / (mₑ c), where h is Planck’s constant, mₑ is the mass of the electron, and c is the speed of light. The value of the electron Compton wavelength is approximately 2.426 × 10⁻¹² meters (or 2.426 picometers). This is significantly larger than the Compton wavelengths of heavier particles like the proton or neutron, reflecting the electron's much smaller mass.

The Compton wavelength is important because it sets a quantum limit on how precisely a particle's position can be defined without introducing enough energy to create particle-antiparticle pairs (like an electron and a positron). It plays a key role in quantum electrodynamics (QED), high-energy physics, and particle interactions involving photons and electrons. For instance, Compton scattering, a process where X-rays scatter off electrons, directly involves this wavelength. Understanding the electron’s Compton wavelength helps physicists analyze the structure of matter, radiation–matter interactions, and the behavior of particles at quantum scales.