The dual nature of matter, which encompasses both particle-like and wave-like properties, is a fundamental concept in quantum mechanics. It has been extensively supported by experimental evidence and is considered a cornerstone of modern physics. The wave-particle duality is not limited to matter but also applies to energy in the form of electromagnetic waves.
The behavior of particles and energy at the quantum level is described by wavefunctions and probability distributions, which exhibit wave-like characteristics. This wave-particle duality has been experimentally confirmed through various experiments, such as the double-slit experiment, where particles exhibit interference patterns similar to waves.
While it is true that all forms of matter and energy can exhibit wave-like behavior, it is not accurate to say that they are "nothing but waves" or that their density is directly proportional to their wavelength. Density is a property that relates to the mass or energy content of a given volume, and it does not have a direct correspondence with the wavelength of a wave.
Different forms of matter and energy, such as highly dense solids or radio waves, have distinct characteristics and behaviors. While they can be described in terms of waves, their properties are not solely determined by their wave-like nature. The behavior and properties of matter and energy encompass a range of phenomena, including interactions, particle interactions, and more, which cannot be fully explained by considering them purely as waves.
In summary, the dual nature of matter and energy, combining both wave-like and particle-like properties, is a fundamental aspect of quantum mechanics. While waves play a role in describing their behavior, matter and energy are more complex than just waves, and their properties are determined by a combination of factors beyond wave characteristics alone.