Four problematic circumstances are considered, involving models which describe dynamical wavefunction collapse toward energy eigenstates, for which it is shown that wavefunction collapse of macroscopic objects does not work properly. In one case, a common particle position measuring situation, the apparatus evolves to a superposition of macroscopically distinguishable states (does not collapse to one of them as it should) because each such particle/apparatus/environment state has precisely the same energy spectrum. Second, assuming an experiment takes place involving collapse to one of two possible outcomes which is permanently recorded, it is shown in general that this can only happen in the unlikely case that the two apparatus states corresponding to the two outcomes have disjoint energy spectra. Next, the progressive narrowing of the energy spectrum due to the collapse mechanism is considered. This has the effect of broadening the time evolution of objects as the universe evolves. Two examples, one involving a precessing spin, the other involving creation of an excited state followed by its decay, are presented in the form of paradoxes. In both examples, the microscopic behavior predicted by standard quantum theory is significantly altered under energy-driven collapse, but this alteration is not observed by an apparatus when it is included in the quantum description. The resolution involves recognition that the statevector describing the apparatus does not collapse, but evolves to a superposition of macroscopically different states.
Recent quantum reconstruction projects demand pure unitary time evolution which seems to contradict the collapse postulate. Inspired by Zurek's environment assisted invariance idea, a natural unitary realization of wavefunction collapse is proposed using Grothendieck group construction for the tensor product commutative monoid.
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 memori…
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 …
Losing Your Marbles in Wavefunction Collapse Theories
Peter Lewis（[1997]）最近指出，GRW（Ghirardi，Rimini，and Weber [1986]）的波函数坍缩理论只能解决波函数尾部的问题，但代价是预测算术不适用于普通宏观物体。更具体地说，Lewis认为GRW理论必须违反枚举原则：“如果大理石1在盒子里，大理石2在盒子里，依此类推，直到大理石$n$，那么所有的$n$大理石都在盒子里”（[1997]，第321页）。Ghirardi和Bassi（[1999]）回答说，说计数原理被违反是没有意义的，因为根据GRW理论，Lewis用来证明违反的波函数不能持续超过一瞬间（[1999]，p.709）。相反，我们认为，刘易斯的论点幸存下来吉拉迪和巴西的批评毫发无损。然后，我们继续表明，虽然枚举原则可能会失败的GRW理论，理论本身保证，该原则永远不会被经验证伪，留下算术推理的适用性，微观和宏观对象完好无损。
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 …
A relativistic version of the Schr{ö}dinger-Newton equation is analyzed within the recently proposed Grave de Peralta approach [L. Grave de Peralta, {\em Results Phys.} {\bf 18} (2020) 103318], which include relativistic effects by a parametrization of the non-relativistic hamiltonian, so as to impose that the average kinetic energy of the system coincide with its relativistic kinetic energy. The reliability of this method is tested for the particle in a box. By applying this method to the Schr{ö}dinger-Newton equation we shows that the characteristic length of the model [L. Di{ó}si, {\em Phys…
Towards a theory of wavefunction collapse Part 1: How the Diosi-Penrose criterion and Born's rule can be derived from semiclassical gravity, and how the criterion can be relativistically generalised with help of the Einstein-Hilbert action
The speculation that gravity is the key to solving the quantum measurement problem has been alive for decades, without any convincing demonstration of a solution. One necessary factor in the relevant proposals is that the gravitational energy of mutual interaction, which scales quadratically with the mass, facilitates the spontaneous collapse of the wavefunctions in spatially separated superpositions. Relying on a simple physical input from electrodynamics, supported by robust first principle calculations, we show that the speculations connecting gravity and the hypothetical spontaneous collap…
Levitated nano-oscillators are seen as promising platforms for testing fundamental physics and testing quantum mechanics in a new high mass regime. Levitation allows extreme isolation from the environment, reducing the decoherence processes that are crucial for these sensitive experiments. A fundamental property of any oscillator is its line width and mechanical quality factor, Q. Narrow line widths in the microHertz regime and mechanical Q's as high as $10^{12}$ have been predicted for levitated systems, but to date, the poor stability of these oscillators over long periods have prevented dir…
分析了两个思想实验，揭示了宇宙的量子态不包含波函数坍缩的确切证据。第一个思想实验表明，单凭幺正量子演化就可以解释任何量子实验组合的结果。这与量子测量的标准观点相矛盾，后者诉诸于波函数坍缩，但它与特殊状态提议（L.S. Schulman in Phys Lett A 102（9）：396-400，1984; J Stat Phys 42（3）：689-719 1986; Time's arrows and量子测量，Cambridge University Press，Cambridge 1997），存在一些仅通过幺正演化来解释量子实验的稀有状态。第二个思想实验包括连续的测量，并揭示了标准的量子测量方案预测违反守恒定律。它表明，标准的观点量子测量，使一些不必要的假设，导致明显的必要性，调用波函数崩溃。一旦这些假设被删除，一个新的希望出现的测量方案，虽然仍然有开放的问题，是兼容的幺正演化和守恒定律，并提出了手段，以实验区分全幺正性和不连续的崩溃。
In this short communication, I gave a generalization of measurement postulate in quantum mechanics. It is regarding the case with partial measurement, namely, measurement on only part of a wave function. Upon a partial measurement, the wavefunction will either collapse in one of the eigenstate covered by the measured partial wavefunction; or collapses out of the measured part and shifts to the unmeasured part. An explanation in the WISE (Wavefunction Is System Entity) interpretation is given.
We first consider the Einstein-Podolsky-Rosen (EPR) paradox for the system of two particles with spin 1/2 with entangled spins in first-quantized quantum mechanics (QM). If measurement is governed by wavefunction collapse, then gedanken experiments show that a number of fundamental principles including conservation of angular momentum and the Heisenberg uncertainty principle can be violated. We conclude that the collapse of the spin part of the wavefunction cannot happen and therefore an EPR paradox does not arise for this system. QM unitarity alone is sufficient to rule out "spooky" action at…
This paper is an in depth implementation of the proposal that the quantum measurement issue can be resolved by carefully looking at top-down contextual effects within realistic measurement contexts. The specific setup of the measurement apparatus determines the possible events that can take place. The interaction of local heat baths with a quantum system plays a key role in the process. In contrast to the usual attempts to explain quantum measurement by decoherence, we argue that the heat bath follows unitary time evolution only over limited length and time scales and thus leads to localizatio…
