Transverse and longitudinal waves are classified according to the direction of propagation of wave motion and direction of oscillations of particles of the medium. But in the case of non-mechanical waves there is no medium, so there are no particles of a medium to oscillate. In this case how does one classify longitudinal and transverse waves?
[Physics] Classification of non-mechanical waves
waves
Related Solutions
Gravitational waves are transverse waves but they are not dipole transverse waves like most electromagnetic waves, they are quadrupole waves. They simultaneously squeeze and stretch matter in two perpendicular directions. Gravitational waves definitely propagate in a given direction but the effect that they have on matter is completely perpendicular to the direction of motion. Below is a picture of what the metric of a passing wave does to space (the wave traveling is perpendicular to the screen). If you imagine a free particle sitting at each grid intersection point, the particle would move sinusoidally right along with the grid:
This diagram is from this paper
When a wave travels through a rope, the rope goes up and down, the position of all the 'rope-particles' changes, they oscillate and this makes up the wave.
With light, it is indeed the electromagnetic field oscillating, but you shouldn't think of the arrows that represent that field in your first picture of light as 'extending into the rest of the space'. They are not spatial, they just represent the magnitude and direction of the electric/magnetic field at that point.
Best Answer
Usually you consider a test particle and describe the wave based on how that test particle would move within the wave. For instance EM waves you imagine a charged particle within the field and the direction that charged particle moves in would determine the classification, Transverse or longitudinal for instance.