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An objective-collapse theory treats wave-function collapse as a physical process localized in spacetime, rather than only as an observer's update of information.

Assume an objective-collapse theory in which collapses occur at localized spacetime events. At an event $x$, define the local quantum state under objective collapse by taking the reduced density operator on spacelike hypersurfaces that approach the past light cone of $x$. A quantum state readout device at $x$ prints a complete classical description of this local density operator, in a fixed basis and here with infinite precision, without disturbing it.

For a localized pure state whose relevant preparation lies in the past light cone, the output is its rank-one projector $|\psi ⟩⟨\psi |$. For an improper mixed state produced by entanglement with an uncollapsed exterior system, it is the reduced density matrix. For a proper mixed state, once the selecting preparation or collapse event is in the past light cone, it is the actually selected component; before that causal information arrives, it is the corresponding local mixture.

A spacelike-separated collapse is excluded from the hypersurface limit and cannot change the output. Its effect appears only on and inside its future light cone. The definition therefore prevents superluminal signalling while allowing light-speed changes in the readout.

Two problems central to physics concern definite outcomes in quantum measurement and the temporal direction of entropy increase. They expose different gaps between a dynamical description and the phenomena explained; neither can be resolved merely by saying that physics predicts observations successfully.

For the measurement problem, combine a two-state system with an apparatus initially in a ready state. If an ideal unitary operator correlates basis states with distinct pointer states, its linearity givesThe same dynamics that gives reliable correlations therefore gives an entangled final state, rather than a rule choosing one pointer value. The problem is not that the state has failed to predict possible outcomes, but how definite outcomes and their probabilities are related to that state.

Quantum decoherence explains why interaction with an environment suppresses interference in the apparatus's reduced density matrix: its off-diagonal term is multiplied by the inner product of the corresponding environmental states. Near-orthogonal records make this term very small. Tracing out the environment, however, does not by itself select one term in the global superposition. An objective-collapse theory changes the dynamics, while a many-worlds interpretation changes what is required of an outcome. Distinguishable modifications can be tested; interpretations reproducing the same predictions raise additional explanatory and conceptual questions. Decoherence solves a substantial dynamical part of the problem without automatically settling every interpretation.

The second issue is the thermodynamic arrow of time. In a classical model, time reversal in classical mechanics can pair an entropy-increasing trajectory with a reversed entropy-decreasing one. Liouville theorem in Hamiltonian mechanics preserves phase-space volume, so reversible Hamiltonian dynamics does not imply a universal monotonic increase of fine-grained entropy. The Second law of thermodynamics therefore needs a statistical and boundary-condition account, not a deduction from reversibility alone.

Boltzmann entropy assigns larger entropy to a macrostate occupying more compatible phase-space volume. Starting from a suitable low-entropy condition, overwhelmingly more accessible microstates can evolve toward larger macrostates. But an unrestricted typicality argument applied at an arbitrary low-entropy instant generally points toward increasing entropy in both temporal directions. The past hypothesis supplies an asymmetric low-entropy boundary condition in the past; one must still justify the probability measure and the macroscopic description used.

These are genuine partial resolutions rather than interchangeable cures. Decoherence concerns the accessibility of interference and records; a past boundary condition concerns temporal asymmetry in a statistical explanation. A satisfactory account must say which extra assumptions it introduces and which observable consequences follow. Neither problem licenses dismissing successful physics, but both show why a predictive formalism and a complete interpretation of its success are different achievements.