When Einstein referred to "hidden variables" in the context of action at a distance, he was not looking for new particles or new equations for existing particles. Instead, he was exploring the possibility of explaining certain phenomena in quantum mechanics, specifically the apparent instantaneous influence of one particle on another separated by large distances, without violating the principles of locality and causality.
In the early development of quantum mechanics, there was a debate between Einstein and other physicists, including Niels Bohr, regarding the completeness of the theory. Einstein disagreed with the probabilistic nature of quantum mechanics and its description of certain phenomena as being inherently random. He sought a more deterministic explanation that would account for the apparent non-local correlations between particles.
Einstein, along with collaborators Boris Podolsky and Nathan Rosen, proposed a thought experiment called the EPR paradox (Einstein-Podolsky-Rosen paradox) to highlight what they saw as a potential flaw in the prevailing interpretation of quantum mechanics. They argued that there must be hidden variables—unknown properties or factors—that would account for the correlations observed in quantum entanglement while still preserving locality.
Their aim was to find a local realistic theory, which would mean that the behavior of particles would be determined by hidden variables that exist independently of the act of observation and would be consistent with the principles of locality and causality. In other words, they were searching for a theoretical framework that would explain quantum phenomena in a way that avoided the need for instantaneous action at a distance.
However, subsequent investigations and experiments, particularly the work of physicist John Bell, showed that local realistic theories cannot fully explain the correlations observed in quantum entanglement. Bell's theorem and subsequent experimental tests, such as the Bell inequality violations, supported the probabilistic nature of quantum mechanics and indicated that any theory based on hidden variables must be non-local.
In summary, Einstein's search for hidden variables was an attempt to find a local realistic theory that would provide a deterministic explanation for quantum phenomena, but it did not involve seeking new particles or equations for existing particles. Ultimately, the consensus among physicists is that quantum mechanics accurately describes the behavior of particles, and the non-local nature of quantum entanglement remains a fundamental aspect of the theory.