How does quantum mechanics differ from classical mechanics?

In a nutshell, the distinction between a ramp and a staircase represents the fundamental distinction between quantum and classical physics.

A good example of classical mechanics is projectile motion, or the colors of the rainbow, where frequencies continuously progress from red through violet. Events, in other words, proceed incrementally up a ramp. In classical mechanics, events (in general) are continuous, that is, they move in smooth, orderly, and predictable patterns.

The word "quantum leaps" refers to the fact that events in quantum mechanics, in particular, are unpredictable and involve "jumps" that appear to be random transitions between states. Additionally, a quantum leap is an all-or-nothing proposition, similar to jumping from one building's roof onto another—you either make it or break it! Events in the quantum world, in other words, jump from one stair to the next and are seemingly discontinuous.

For example, electrons in an atom transition between energy levels by quantum leaps from one level to the next; this can be observed in emission spectra where different colors correspond to the energy level transitions made by electrons, and dark areas denote the region through which electrons quantum (and hence non-continuous) leaps between energy levels occur.

The so-called "ultraviolet catastrophe" and many other aspects of quantum mechanics differ greatly from those of classical mechanics, but they are too technical to go into here.

As a last point, let me mention that the quantum idea of the "complementary nature of light"—which holds that light is both a particle, which has mass, and a wave, which has none—demonstrates how strange quantum physics can be in comparison to classical physics.

Quantum mechanics differs from classical mechanics in several key aspects:

1. Scale: Quantum mechanics applies to the microscopic world of atoms and subatomic particles, while classical mechanics describes the macroscopic world of everyday objects.

2. Probability: Quantum mechanics introduces the concept of probability into physical systems, where the behavior of particles is described by wave functions that represent probabilities of finding a particle in a particular state.

3. Uncertainty Principle: Quantum mechanics incorporates Heisenberg's uncertainty principle, which states that it is impossible to simultaneously measure certain pairs of properties, such as position and momentum, with arbitrary precision.

4. Superposition: Quantum mechanics allows for the phenomenon of superposition, where particles can exist in multiple states simultaneously until measured, in contrast to classical mechanics where particles have definite states at all times.

5. Entanglement: Quantum mechanics includes the phenomenon of entanglement, where the states of particles become correlated in such a way that the state of one particle instantaneously influences the state of another particle, regardless of the distance between them.

6. Wave-particle duality: Quantum mechanics describes particles as having both wave-like and particle-like properties, whereas classical mechanics treats particles strictly as particles with definite positions and momenta.

7. Quantization: Quantum mechanics introduces the concept of quantization, where physical quantities such as energy, angular momentum, and charge are restricted to discrete, quantized values rather than continuous values as in classical mechanics.

Quantum mechanics differs from classical mechanics in several key aspects:

1. Nature of particles: Quantum mechanics describes particles as having both particle-like and wave-like properties, while classical mechanics treats particles strictly as point-like objects.

2. Determinism: Classical mechanics operates under the principle of determinism, where the future state of a system can be precisely predicted given its initial conditions, whereas quantum mechanics introduces inherent uncertainty, expressed through principles like the Heisenberg Uncertainty Principle.

3. Measurement: In quantum mechanics, measurement outcomes are probabilistic, whereas in classical mechanics, measurements are deterministic and precise.

4. Superposition: Quantum mechanics allows for the existence of superposition, where particles can exist in multiple states simultaneously, while classical mechanics does not account for such phenomena.

5. Entanglement: Quantum mechanics introduces the concept of entanglement, where the states of two or more particles become correlated in such a way that the state of one particle cannot be described independently of the others. Classical mechanics does not account for entanglement.

6. Quantization: Quantum mechanics quantizes certain physical quantities, such as energy levels in atoms or the angular momentum of particles, whereas classical mechanics treats these quantities as continuous.

Overall, quantum mechanics represents a departure from the deterministic and classical worldview, introducing probabilistic and wave-like behavior at the microscopic scale.