spectral beings

When we meet aliens, what will they look like?

Some of the most exotic creatures on earth live farthest from the nurturing warmth of the sun, in deep water abysses. Without sunlight, these creatures create their own light to attract prey, and ward off predators. Spectral beings takes this to its logical conclusion: beings created entirely out of electromagnetic fields.
Maxwell's equations tell us that a moving electric field creates a magnetic field, and a moving magnetic field creates an electric field:

Can these fields self-organize into sustaining entities?