Sandro Donadi presentation

measurement problem

The Schrodinger Equation is Linear and deterinistic. Measurements are Non-linear and stochastic.

It is unclear what qualifies as a Measurement.

To solve the problem, we need an adaptation of Schrodinger Equation that is:

• Non-linear, otherwise we have no collapse
• Stochastic, otherwise there can be faster than light signalling. It is unclear why this is the case. Help me ❓

The collapse model needs to map $\frac{1}{\sqrt{2}}(|+⟩+|-⟩)$ to $\{50\%|+⟩,50\%|-⟩\}$. Using the ??? notation, we want to map

$$\left(\begin{array}{ccc}1& & 1\\ 1& & 1\end{array}\right)\to \left(\begin{array}{ccc}1& & 0\\ 0& & 1\end{array}\right)$$

GRW Theory

General idea:

1. The Schrodinger Equation guides the evolution between Localisations
2. A Localisation spontaneously happens, collapsing the Wave function into a localised version. The Localisation leads to the mass of the Wave function to be focused around a point a.
3. Localisations happen stochastically following a Poisson distribution with rate $\lambda$.

This model is valid for identical particles, it has a preference for Localisation in space, and contains an amplification mechanism that explains the consistency of the macroscopic world

Since this model modifies the Schrodinger Equation, it provides ways to test it:

1. Doing interferometric experiments that searches for loss of Coherence in spatial superposition.
2. Since the wave function collapse is random, we can observe diffusive effects e.g. heating that can be measured without the need for interferometers. This approach can be tested with large masses and without preparing superposition states.

Recently ( see Collapse dynamics are diffusive paper ) it has been proven that any model based of Completely Positive dynamics with collapse in space gives us:

1. No faster than light travel

Which leads to diffusion in momentum space.

Penrose Proposal

Intuition: instead of performing the quantisation of gravity, we hope to add gravity to Quantum Mechanics ( Related Wikipedia Page )