The size of the group of atoms necessary for the fringes to become undetectable in an interference experiment depends on several factors, including the specific setup and conditions of the experiment. In general, as the number of particles or atoms increases, the interference fringes become less pronounced or disappear altogether. This phenomenon is known as decoherence, where interactions with the surrounding environment cause the quantum coherence of the system to degrade.
The exact number of atoms required for fringes to become undetectable can vary depending on factors such as the temperature, isolation from external disturbances, and the coherence properties of the atoms involved. In some experiments, the interference fringes can be observed with thousands or even millions of atoms, while in other cases, coherence may be preserved with larger ensembles of atoms.
Regarding entanglement, it does not require both objects to have the exact same shape or occupy the same spot for a split second. Entanglement is a property that emerges between quantum systems, regardless of their shapes or positions. The key aspect of entanglement is the correlation of their quantum states, such that the measurement of one system instantaneously affects the state of the other, regardless of the spatial separation between them.
Entangled particles do not need to occupy the same location or exist in the same shape simultaneously. They can be widely separated in space, and their shapes can be different. The crucial factor is that their quantum states are entangled, meaning the state of one particle cannot be described independently of the other. The entanglement arises due to the fundamental principles of quantum mechanics, such as superposition and measurement correlations.
It's important to note that while the specific spatial configuration and shape of particles are not essential for entanglement, they can influence how entanglement is detected or utilized in practical applications. Different experimental setups and systems can be used to generate and detect entanglement depending on the specific requirements of a given scenario.