In quantum entanglement, the properties of two particles become correlated in such a way that the state of one particle cannot be described independently of the state of the other, regardless of the distance between them. However, the specific details of how entanglement works depend on the type of entangled particles and the particular observables being measured.
In the case of entangled photons, their entanglement typically involves their polarization states. The polarization of a photon refers to the orientation of its electric field oscillations. When two photons are entangled in terms of their polarization, the state of one photon is directly linked to the state of the other.
If the wavelength (or frequency) of one entangled photon changes, it does not directly affect the wavelength of the other entangled photon. The wavelength of a photon corresponds to its energy and is related to its frequency through the speed of light. However, entanglement generally does not directly affect the energy or frequency of the particles involved.
What entanglement does affect is the correlation between measurements performed on the entangled particles. If you were to measure the polarization of one photon and find it in a specific state, the entangled nature of the system would guarantee that the other photon's polarization would be correlated in a complementary manner. However, the wavelengths (or frequencies) themselves remain independent.
It's worth noting that entanglement is a complex phenomenon with various manifestations and interpretations, and there are different types of entangled states that can behave differently. So, the specific details of an entangled system can influence the nature of the correlations and measurements that are possible.