Yes, there is a well-established theory and evidence for the exchange of information between two entangled particles. This phenomenon is known as quantum entanglement and is a fundamental concept in quantum mechanics.
Quantum entanglement refers to a state where two or more particles become correlated in such a way that the state of one particle is instantaneously linked to the state of the other, regardless of the distance between them. This correlation is maintained even if the particles are separated by vast distances.
The theory of quantum mechanics, which has been extensively tested and confirmed through numerous experiments, describes entanglement as a non-local phenomenon. This means that the entangled particles are connected in a way that cannot be explained by classical physics, where information cannot travel faster than the speed of light.
Entanglement has been experimentally verified in various ways, including tests of Bell's inequality and the violation of locality. These experiments have shown that the correlations between entangled particles cannot be explained by any local hidden variable theories, where the particles would possess pre-determined properties that are revealed upon measurement.
Instead, the measurements of one entangled particle are found to be correlated with the measurements of the other, indicating that information or properties are being exchanged between the particles. However, it is important to note that this exchange of information cannot be used to transmit classical information faster than the speed of light, as it is not possible to control or manipulate the specific outcome of measurements on the entangled particles.
In summary, quantum entanglement provides strong evidence for the exchange of information between entangled particles, but the nature of this information exchange is fundamentally different from classical communication and does not violate the principles of relativity.