Electrons, as elementary particles, are often described as point-like or zero-dimensional entities in standard particle physics. According to the prevailing theories, such as the Standard Model, electrons are considered to have no internal structure or size. In this sense, they do not possess any dimensions in the classical sense of length, width, or height.
However, it is important to note that the concept of dimensionality can be context-dependent and can vary in different theoretical frameworks. In certain theoretical approaches, such as string theory or certain extensions of the Standard Model, particles like electrons are described as tiny one-dimensional strings or branes vibrating in higher-dimensional spacetime. These theories propose that the fundamental building blocks of matter may have extended structures beyond the classical point-like notion.
Regarding the dimension of the smallest particle, it is difficult to provide a definitive answer as our understanding of the fundamental nature of particles is still an active area of research. Currently, the smallest known particles are considered to be point-like entities with no internal structure, such as electrons, quarks, and neutrinos.
However, it is worth noting that the concept of "size" or "dimension" becomes less well-defined at extremely small scales, where quantum effects dominate. At these scales, the uncertainty principle of quantum mechanics implies that the position and momentum of particles cannot be simultaneously precisely determined. This leads to a fundamental fuzziness or indeterminacy in defining the size or dimension of a particle.
In summary, electrons are often treated as point-like particles with zero dimensions in the context of the Standard Model. However, the concept of dimensionality can be more nuanced and can vary depending on the theoretical framework being considered. The nature of the smallest particle and its dimensional characteristics are still active areas of research in theoretical physics.