Question: What was a problem for classical physics?
About the article "Physics", section "Modern physics".

Candidate passages:
  Classical central-force problem  Kepler problem, a special case (inverse-square central force)  Two-body problem, which may be reduced to a central-force problem  
Three-body problem has two distinguishable meanings in physics and classical mechanics:  In its traditional sense, the three-body problem is the problem of taking an initial set of data that specifies the positions, masses and velocities of three bodies for some particular point in time and then determining the motions of the three bodies, in accordance with the laws of classical mechanics (Newton's laws of motion and of universal gravitation).
In an extended modern sense, a three-body problem is a class of problems in classical or quantum mechanics that model the motion of three particles.
Historically, the first specific three-body problem to receive extended study was the one involving the Moon, the Earth and the Sun. 
The semi-classical limit.
What is the semiclassical limit?The classical limit or correspondence limit is the ability of a physical theory to approximate or "recover" classical mechanics when considered over special values of its parameters.
The classical limit is used with physical theories that predict non-classical behavior.
In physics, the correspondence principle states that the behavior of systems described by the theory of quantum mechanics (or by the old quantum theory) reproduces classical physics in the limit of large quantum numbers.
In other words, it says that for large orbits and for large energies, quantum calculations must agree with classical calculations.
The principle was formulated by Niels Bohr in 1920, though he had previously made use of it as early as 1913 in developing his model of the atom.
There are two basic requirements in establishing the semi-classical limit of any quantum theory:i) reproduction of the Poisson brackets (of the diffeomorphism constraints in the case of general relativity).
This is extremely important because, as noted above, the Poisson bracket algebra formed between the (smeared) constraints themselves completely determines the classical theory.
This is analogous to establishing Ehrenfest's theorem;ii) the specification of a complete set of classical observables whose corresponding operators when acted on by appropriate semi-classical states reproduce the same classical variables with small quantum corrections (a subtle point is that states that are semi-classical for one class of observables may not be semi-classical for a different class of observables).
This may be easily done, for example, in ordinary quantum mechanics for a particle but in general relativity this becomes a highly non-trivial problem as we will see below. 
Modern physics began in the early 20th century with the work of Max Planck in quantum theory and Albert Einstein's theory of relativity.
Both of these theories came about due to inaccuracies in classical mechanics in certain situations.
Classical mechanics predicted a varying speed of light, which could not be resolved with the constant speed predicted by Maxwell's equations of electromagnetism; this discrepancy was corrected by Einstein's theory of special relativity, which replaced classical mechanics for fast-moving bodies and allowed for a constant speed of light.
Black body radiation provided another problem for classical physics, which was corrected when Planck proposed that light comes in individual packets known as photons; this, along with the photoelectric effect and a complete theory predicting discrete energy levels of electron orbitals, led to the theory of quantum mechanics taking over from classical physics at very small scales.
Quantum mechanics would come to be pioneered by Werner Heisenberg, Erwin Schrödinger and Paul Dirac.
From this early work, and work in related fields, the Standard Model of particle physics was derived.
Following the discovery of a particle with properties consistent with the Higgs boson at CERN in 2012, all fundamental particles predicted by the standard model, and no others, appear to exist; however physics beyond the Standard Model, with theories such as supersymmetry, is an active area of research.
Beginning with a brief consideration of classical physics, which concentrates on the major conflicts in physics, Greene establishes a historical context for string theory as a necessary means of integrating the probabilistic world of the standard model of particle physics and the deterministic Newtonian physics of the macroscopic world.
Greene discusses the essential problem facing modern physics: unification of Albert Einstein's theory of General Relativity and Quantum Mechanics.
Greene suggests that string theory is the solution to these two conflicting approaches.
Greene frequently uses analogies and thought experiments to provide a means for the layman to come to terms with the theory which has the potential to create a unified theory of physics.