Theories without a stress tensor refer to physical theories that do not explicitly include the concept of stress tensor, which is a mathematical representation of the distribution of forces within a system. These theories may still consider the effects of forces, but they do not use the stress tensor as a fundamental concept.
There are several reasons why a theory may not include a stress tensor. One possible reason is that the system being studied does not have a well-defined stress tensor, such as in the case of non-continuum systems. Another reason could be that the theory is attempting to describe a phenomenon at a scale where the concept of stress tensor is not applicable.
Theories without a stress tensor account for forces through alternative mathematical representations, such as energy density or momentum density. These theories may also use different mathematical frameworks, such as Lagrangian or Hamiltonian mechanics, to describe the dynamics of a system without explicitly using the stress tensor.
Not necessarily. The accuracy of a theory without a stress tensor depends on how well it can describe and predict the behavior of a system. In some cases, a theory without a stress tensor may provide a more accurate description of a system compared to one that relies on the stress tensor. However, in other cases, the stress tensor may be a crucial concept for accurately describing the behavior of a system.
Yes, theories without a stress tensor can be used in various fields of science, such as physics, chemistry, and engineering. The applicability of these theories depends on the specific system being studied and the level of accuracy required. In some fields, such as fluid mechanics, theories without a stress tensor may be more commonly used due to the non-continuum nature of the systems being studied.