350-Year-Old Mechanical Theorem Reveals New Properties of Light; How Does the Helmholtz Equation Describe the Behavior of Waves?

In 1672, a debate started, which has continued for several centuries. It focuses on the fundamental question about the nature of light and involves prominent physicists at the time. Isaac Newton described that light behaves like particles in his corpuscular theory, while Christiaan Huygens argued that light behaves like waves in his wave theory. Since then, scientists have been baffled over whether light is best viewed as a wave or particle.

Particle or Wave?

Newton's corpuscular theory suggests that light comes from a source continuously emitting tiny elastic particles called corpuscles. This theory can explain the three properties of light: reflection, refraction, and rectilinear propagation. It also describes that light color depends on the size of the corpuscles. However, the corpuscular theory cannot explain other phenomena such as diffraction, interference, and polarization.

Meanwhile, Huygens' wave theory explains that each point in a light source sends waves in all directions in a hypothetical medium known as ether. It assumes that light waves are mechanical and transverse. It can successfully describe phenomena such as reflection, refraction, interference, and diffraction.

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Connecting the Two Theories

Physicists from Stevens Institute of Technology have discovered the connection between the two perspectives. Using a 350-year-old mechanical theorem typically used in describing the movement of large, physical objects, they tried to explain the most complex behaviors of light waves.

Led by assistant professor Xiaofeng Qian, the team proved for the first time that a light wave's degree of non-quantum entanglement has a direct and complementary relationship with its degree of polarization. As one rises and the other falls, it enables the level of entanglement to be derived directly from the level of polarization. This means that the properties of light that are hard to measure can be deduced from light intensity, which is a lot easier to measure.

Qian clarifies that their work does not reconcile the two theories regarding the nature of light. Instead, they tried to prove that there are profound connections between the particle and wave concepts at the quantum level and in classical light waves and point-mass systems.

The mechanical theorem used by the research team was originally developed by Huygens in 1673. In his book on pendulums, Huygens explained how the energy needed to rotate an object depends on its mass and the axis around which it turns. The well-established theorem explains the mechanisms of physical systems such as clocks and prosthetic limbs, but the researchers showed that it can also be applied to light.

The theorem describes the relationship between masses and their rotational momentum. In applying this to light with no mass to measure, Qian's team interpreted the light intensity as the equivalent mass of a physical object. These measurements are then mapped onto a coordinate system which can be interpreted using the mechanical theorem.

Once the light wave was visualized as part of a mechanical system, the connection between the properties of waves became more evident. This includes the fact that entanglement and polarization establish a clear relationship. This discovery could have significant implications as it allows subtle properties of light or quantum systems to be deduced from simpler light intensity measurements.