In the double-slit experiment, when the size of the slits or the overall system becomes very large, classical effects start to dominate and quantum mechanical behavior becomes less significant. The transition from quantum to classical behavior typically occurs when the characteristic scale of the system becomes much larger than the de Broglie wavelength associated with the particles or waves involved.
The Planck mass is the mass scale at which quantum gravitational effects are expected to become important. It is approximately 2.18 × 10^(-8) kilograms. However, the Planck mass is extremely tiny compared to macroscopic objects, and it is not typically relevant for the size of the double-slit experiment.
Instead, the relevant scale for the double-slit experiment is the wavelength of the particles or waves used in the experiment. In quantum mechanics, particles such as electrons or photons can exhibit wave-like behavior, and their associated wavelength is given by the de Broglie wavelength, which is inversely proportional to their momentum. When the size of the slits or the overall system is much larger than the de Broglie wavelength, classical effects become more prominent.
For example, if the slits are large enough or the distance between the slits and the screen is sufficiently large, the interference pattern observed in the double-slit experiment becomes less pronounced, and the particles or waves behave more like classical particles, traveling through one or the other slit and forming a simple distribution pattern on the screen.
In summary, when the size of the double-slit experiment becomes much larger than the relevant quantum mechanical scales, such as the de Broglie wavelength, classical effects start to dominate, and the system behaves in a manner consistent with classical physics. The Planck mass, while important for other aspects of physics, is not directly relevant to the size of the double-slit experiment.