Symmetric nature of universe

Initially when studies related to light were made Huygens, Maxwell, and Young claimed that light is a wave considering the diffraction ,interference, polarization experiments but when new phenomenon were discovered like photoelectric effect, Compton effect , wave nature of light could not explain it.

Max Planck , Einstein and Newton thought about the particle nature of light calling it has discrete energy packets known as photons or corpuscles. particle nature of light succesfully explained the phenomenon which wave nature could not explain . light behaving wave like and particle like in different times was called duality and led to think about symmetry in universe.

If light can behave like particle can matter behave like waves?

The dual nature of light made people to think about dual nature of matter as well. For instance consider an electron of mass 'm' moving with some velocity 'v' having momentum 'mv'. This electron has kinetic energy as well as the energy due to its mass. This mass energy is actually due to its very own mass.

If the equations for Einstein's and plank's equation are equated stating that the energy in its particle state is equal to the energy in its wave state. Then we get the famous De Broglie's equation -

From this We can get the the wavelength associated with the electron calling it matter waves.

Therefore symmetry is everywhere irrespective of massive or massless entities.