1994: Gravitational Objective Reduction

The essence of this idea is embedded in its title, such that gravity, i.e. the curvature of spacetime, becomes an 'objective' cause for the 'reduction' or collapse of the wave function. It was propose by Roger Penrose, in 1994, and is included because it is possibly reflective of a trend towards interpretations, which appear to be seeking some sort a 'ontological' explanation of the wave function collapse, which doesn't necessarily suspend our belief in the processes at work. Of course, while this may make it plausible, and philosophically more acceptable to some, it does not necessarily make it correct.

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The concept is based on the idea that existence, in the quantum universe, appears to be defined as alternative probabilities that have to be described as a superposition of weighted complex numbers called `probability amplitudes`.

Note, it was the presence of complex numbers, which led Bohr to believe that quantum theory did not describe reality, only a mathematical prediction.

Each alternative path relates to a quantum state, where only the sum total eventually emerges as an observable in classical terms. So, while the system remains at the quantum level, it can evolve in time according to its wave function. Penrose describes this deterministic process as ‘unitary evolution’, denoted by the letter [U].  At some point, which is not well defined or well understood, the quantum universe emerges into the classical universe and the complex-weighted superposition seem to no longer persist. When this happens, the sum of all possibilities seems to converge to just one alternative; Penrose calls this process, the reduction of the state vector, denoted by the letter [R]. In order to describe the [R] process as objective, there needs to be some explanation of the transition between [U] and [R] beyond the nebulous implications of a `wave function collapse` between two states. As you might expect, in the case of Gravitational [OR], Penrose speculates whether gravity could be the influencing factor in the collapse of the wave function. As being described, Gravitational [OR] is when a wave function collapse takes place automatically and is linked to a critical amount of energy and time separating the elements of superposition. Only a system with sufficient mass can govern the reduction of its own state, otherwise the system remains in superposition or else gets entangled with its environment, which in-turn, can then lead to the wave function collapse. Given the level of mathematics associated with this idea, it is fair to say that the following description is only analogous of the processes involved. When applying Heisenberg's Uncertainty Principle to the lifetime [T] of an unstable nucleus, such as Uranium-238, we could also consider whether there is a time uncertainty proportional to its energy uncertainty, i.e.

[1]      1

In the case of Uranium-238, its lifetime is ~109 years, corresponding to an energy uncertainty for each nucleus of about 10-51 joules, which in-turn can be translated to a mass uncertainty via Einstein's equation [E=mc2]. This gives an uncertainty factor of ~10-44 for its total mass. What Penrose draws attention to is that the superposition state may also be unstable due to this inherent uncertainty, where the life of a superposition state is proportional to the gravitation self-energy [Eg]:

[2]      2

This equation suggests that the quantum superposition of 2 possible states should collapse into one, in the timescale [Tg], when in the presence of gravitational self-energy [Eg]. However, there are no stationary solutions for the wave function of a single free particle with positive mass, therefore the wave function would require some form of modification to account for the gravitational effect. Whether this interpretation could ever be empirically tested is unclear.