QUANTUM EFFECTS TO CLASSICAL ONES

 At what size do quantum effects begin to give way to classical ones?

Good question, but it's not a simple one to answer. You see, quantum effects are always there, but they are usually too small to notice at large scales.

Classical effects are just approximations of quantum effects when the system is interacting with the environment. So, there is no sharp boundary between quantum and classical, but rather a gradual transition.

To get an idea of when quantum effects become important, we can use a rule of thumb called the Heisenberg Uncertainty Principle (HUP).

This thing says that the product of the uncertainties in position and momentum of a particle is always greater than or equal to a very small number called Planck's constant divided by two.

This number is so tiny that it's almost zero for everyday objects, like an orange. But for very small objects, like an atom, this number becomes significant and limits how well we can know both the position and momentum of the particle.

This leads to some weird phenomena, like discrete energy levels, tunneling, superposition, entanglement, and so on.

But even for larger objects, quantum effects can sometimes show up, especially when the system is isolated from the environment or cooled down to very low temperatures.

For example, superconductivity and superfluidity are quantum phenomena that happen in macroscopic systems.

Superconductivity is when some materials lose all electrical resistance when they are cooled below a certain temperature.

Superfluidity is when some fluids flow without any friction or viscosity when they are cooled below a certain temperature.

These are examples of quantum coherence, where the particles in the system behave as one big quantum wave.

Verdict:

There is no clear simple answer to your question. It depends on the system you're looking at, how it interacts with the environment, and what kind of measurements you're making.

Quantum effects are always there, but they become more noticeable as the system gets smaller, more isolated, or colder.