Wavefunction Collapse and Conservation Laws

David Z. Albert

Sivapalan Chelvaniththilan

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.

Arnab Acharya, Pratik Jeware, Soumitro Banerjee

Almost a century after the development of quantum mechanics, we still do not have a consensus on the process of collapse of wavefunctions. Some theories require the intervention of a conscious observer while some see it as a stochastic process, and most theories violate energy conservation. In this paper we hypothesise that the collapse of wavefunctions can be caused by interactions with other objects (macroscopic or microscopic) and energy is conserved in that process. To test various hypotheses regarding collapse of wavefunctions, we propose a model system which is the quantum analogue of a classical soft-impact oscillator. We propose some alternative postulates regarding the conditions for and the result of a collapse, and obtain the implication of each on the behavior of observable quantities, which can possibly be experimentally tested.

Carl Frederick

Garrelt Quandt-Wiese

A gravity-induced approach to wavefunction collapse based on semiclassical gravity is enhanced by the hypothesis of a temporally expanding spacetime, which leads to a collapse model that can resolve the conflict between quantum nonlocality and relativity. It is postulated that the spacetime region on which the evolution of the state vector exists is bounded towards the future by a border that is dynamically moving towards the future, and at which the state vector must fulfil a boundary condition. Wavefunction collapse is represented in such a way that the evolution of the state vector changes abruptly at critical spacetime expansions to an evolution resembling a classical trajectory. This can explain the correlations in EPR experiments without coming into conflict with relativity, since the evolution of the state vector before and after the abrupt change is governed solely by local physical laws. This model leads to the same lifetimes of superpositions as the gravity-based approaches of Diosi and Penrose, and is characterised by the facts that energy is conserved at collapse and that the reduction point in time does not vary statistically. Some unique features of the model are that it naturally leads to stochastic behaviour and that it can predict reduction probabilities. It explains why all experiments performed so far behave in agreement with Born's rule, due to a property that they have in common. This gives rise to new experiments for checking Born's rule, which can be realised in the short term.

Dion Fryson