String theorists consider particles to be individual oscillating one-dimensional strings rather than individual oscillations or groups of oscillations in a multidimensional elastic membrane due to several reasons:
Consistency with quantum mechanics: Strings naturally incorporate the principles of quantum mechanics. In quantum mechanics, particles are described by wavefunctions, which encode their probability distributions. One-dimensional strings can naturally vibrate in different modes, each corresponding to different quantum states, allowing for the description of particle-like behavior. This provides a consistent framework for combining quantum mechanics with general relativity.
Unification of forces: String theory aims to unify all fundamental forces, including gravity. By considering particles as strings, which interact through their vibrations, it becomes possible to describe the gravitational force in a quantum mechanical framework. This unification is not straightforward when considering particles as oscillations on a higher-dimensional elastic membrane.
Geometric simplicity: The concept of strings simplifies the geometry of the theory. Instead of considering higher-dimensional structures like membranes, strings introduce the idea of one-dimensional objects moving through a fixed background spacetime. This simplification makes it easier to mathematically describe the theory and explore its consequences.
Emergent dimensions: String theory suggests that the extra dimensions beyond our familiar three spatial dimensions may be "compactified" or curled up at extremely small scales. The vibrations of strings in these compact dimensions can give rise to the observed particle spectrum. In this context, strings naturally provide a framework for incorporating the presence of additional dimensions.
Experimental implications: String theory predicts the existence of new particles called string excitations or "stringy" states. These states have properties that distinguish them from ordinary particles, such as having a characteristic mass spectrum with a particular pattern. These predictions provide a potential avenue for experimental tests of string theory, even though they currently lie beyond the reach of our current particle accelerators.
Overall, the idea of particles as individual oscillating strings provides a rich framework that unifies quantum mechanics and gravity, incorporates additional dimensions, and offers potential experimental implications. While other theories, such as the membrane paradigm (M-theory), have also been explored, the concept of strings has gained prominence due to its mathematical and conceptual elegance and its ability to address fundamental questions in physics.