In this paper I present a thought experiment that gives different results depending on whether or not the wavefunction collapses. Since the wavefunction does not obey the Schrodinger equation during the collapse, conservation laws are violated. This is the reason why the results are different. Quantities that are conserved if the wavefunction does not collapse might change if it does. I also show that using the Born Rule to derive probabilities of states before a measurement given the state after it (rather than the other way round as it is usually used) leads to the conclusion that the memories that an observer has about making measurements of quantum systems have a significant probability of being false memories.
In this paper I present a thought experiment that gives different results depending on whether or not the wavefunction collapses. Since the wavefunction does not obey the Schrodinger equation during the collapse, conservation laws are violated. This is the reason why the results are different. Quantities that are conserved if the wavefunction does not collapse might change if it does. I also show that using the Born Rule to derive probabilities of states before a measurement given the state after it (rather than the other way round as it is usually used) leads to the conclusion that the memories that an observer has about making measurements of quantum systems have a significant probability of being false memories.
In this treatise I introduce the time dependent Generalized Born's Rule for the probabilities of quantum events, including conditional and consecutive probabilities, as the unique fundamental time evolution equation of quantum theory. Then these probabilities, computed from states and events, are to be compared with relative frequencies of observations. Schrodinger's equation still is valid in one model of the axioms of quantum theory, which I call the Schrodinger model. However, the role of Schrodinger's equation is auxiliary, since it serves to help compute the continuous temporal evolution of the probabilities given by the Generalized Born's Rule. In other models, such as the Heisenberg model, the auxiliary equations are quite different, but the Generalized Born's Rule is the same formula (covariance) and gives the same results (invariance). Also some aspects of the Schrodinger model are not found in the isomorphic Heisenberg model, and they therefore do not have any physical significance. One example of this is the infamous collapse of the quantum state. Other quantum phenomena, such as entanglement, are easy to analyze in terms of the Generalized Born's Rule without any reference to the unnecessary concept of collapse. Finally, this leads to the possibility of quantum theory with other sorts of auxiliary equations instead of Schrodinger's equation, and examples of this are given. Throughout this treatise the leit motif is the central importance of quantum probability and most especially of the simplifying role of the time dependent Generalized Born's Rule in quantum theory.
The Born Rule is central to quantum mechanics, yet it remains a postulate: a probabilistic rule grafted onto the deterministic evolution of the Schrödinger equation. This work derives the Born Rule as an emergent statistical law grounded in thermodynamic principles. We propose that quantum probability reflects the survival likelihood of a branch under decoherence, determined by its informational reversibility, structural fragility, and exposure to entropy.In this formulation, reversibility quantifies the mutual information retained during measurement, entropy reflects environmental disruption, and buffering represents the system’s capacity to absorb it. In low-entropy, high-buffering conditions typical of laboratory systems, the survival probability of a branch closely approximates the squared amplitude of its wavefunction — recovering the Born Rule as a limiting case.This approach reframes quantum amplitude as a measure of structural persistence and interprets wavefunction collapse as a form of thermodynamic selection. The result unifies concepts from measurement theory, thermodynamics, and information theory into a coherent physical framework, while also predicting conditions under which deviations from the Born Rule could arise — offering new directions for theoretical and experimental inquiry.
Because quantum measurements have probabilistic outcomes they can seem to violate conservation laws in individual experiments. Despite these appearances, strict conservation of momentum, orbital angular momentum, and energy can be shown to be consistent with the assumption that the entangling interactions that constitute measurements induce a real collapse of the wave function. The essential idea is that measured systems always have some pre-existing entanglement relations with (usually larger) systems, and that apparent changes in conserved quantities in the measured system are correlated with compensating changes in these larger systems. Since wave function collapse is mediated by entanglement relations a full accounting of the relevant quantities requires a computation over all interacting, entangled systems. The demonstrations by Gemmer and Mahler[1], and by Durt[2,3], that entanglement is a generic result of interaction are central to the argument. A stochastic collapse equation based on interaction potentials is described and shown to guarantee conservation of the relevant quantities at all stages of evolution.
In quantum mechanics, conservation laws are usually understood only statistically and only in the context of unitary evolution: during such evolution, if an observable commutes with the Hamiltonian, its expectation value and Born-rule probability distribution remain unchanged. Individual measurement outcomes, however, disrupt even this weak form of statistical conservation. Recently, though, it has been argued that a stronger, non-statistical form of conservation, valid at the level of individual measurement outcomes, can be recovered. The proposal relies on the claim that any superposition of eigenstates of a conserved quantity must ultimately be prepared relative to another physical system, which serves as the relevant reference frame and remains correlated with the system being prepared. On this enlarged description, the change observed in the measured system is claimed to be exactly compensated by an opposite change in the preparer, thereby restoring conservation at the level of individual measurement outcomes. We analyze this proposal and argue that it faces significant conceptual difficulties. We show that the proposed mechanism is not adequately justified and, moreover, does not establish conservation in individual measurement outcomes as claimed.
Because quantum measurements have probabilistic outcomes they can seem to violate conservation laws in individual experiments. Despite these appearances, strict conservation of momentum, orbital angular momentum, and energy can be shown to be consistent with the assumption that the entangling interactions that constitute measurements induce a real collapse of the wave function. The essential idea is that measured systems always have some pre-existing entanglement relations with (usually larger) systems, and that apparent changes in conserved quantities in the measured system are correlated with compensating changes in these larger systems. Since wave function collapse is mediated by entanglement relations a full accounting of the relevant quantities requires a computation over all interacting, entangled systems. The demonstrations by Gemmer and Mahler[1], and by Durt[2,3], that entanglement is a generic result of interaction are central to the argument. A stochastic collapse equation based on interaction potentials is described and shown to guarantee conservation of the relevant quantities at all stages of evolution.
Attempts to derive the Born rule, either in the Many Worlds or Copenhagen interpretation, are unsatisfactory for systems with only a finite number of degrees of freedom. In the case of Many Worlds this is a serious problem, since its goal is to account for apparent collapse phenomena, including the Born rule for probabilities, assuming only unitary evolution of the wavefunction. For finite number of degrees of freedom, observers on the vast majority of branches would not deduce the Born rule. However, discreteness of the quantum state space, even if extremely tiny, may restore the validity of the usual arguments.