Interpretations of Quantum Theory

 Copenhagen 

This is the most taught interpretation of quantum mechanics, first devised by Bohr and Heisenberg in the 1920s. Despite being the most popular interpretation of the mathematical formalism there is no actual defined set of rules for it that have been definitively laid out. This is an Ontological interpretation of quantum mechanics, defining, as with all other interpretations, the system to be a probabilistic one as opposed to deterministic. This interpretation tells us that the wave function of a quantum system tells us everything we can know about the system prior to measurement and that the system contains no Hidden Variables. This interpretation says that when the system interacts is measured, interacting with a measuring device the wavefunction of the system collapses irreversibly to an eigenstate (a QM state that corresponds to an Eigenvalue (the energy of a quantum state of a system) of the Schrodinger Equation). The result of this measurement can then be described classically.

Many Worlds

The Many-Worlds Interpretation (MWI) of Quantum Mechanics comes a close second for most widely accepted interpretation. Hugh Everett, the person who first proposed the MWI. -honestly, i need to do more work to figure out what the hell is going on with this one, its weird as hell

-this was developed in response to the measurement problem that arises from the Copenhagen interpretation - measurement problem - no mathematical or physical explanation for the dynamics of wavefunction collapse

- suppose that a state of a quantum particle is measured, which can take 2 values (eg spin, which can either be up or down). many worlds interpretation implies that every time a measurement is made, the universe splits into 2 - in one the particle has spin up and in the other the particle is spin down. we cannot transfer information or make any observations about these other 'worlds'

This interpretation can, perhaps be tested, but it requires a lot of dedication. For this, see the Quantum Suicide Thought Experiment

 De Broglie-Bohm Interpretation (Pilot Wave theory) 

De Broglie-Bohm interpretation, otherwise known as as Pilot Wave theory or Bohmian Interpretation is another interpretation of quantum theory, though very specifically not an interpretation of Quantum Mechanics. This looks at the supposed randomness of quantum theory in the same way as one might see a coin flip as random. Provided we know all the forces acting on the coin, we can predict with 100% certainty every time whether we will get heads or tails. This interpretation argues that if we were to know all forces acting on a particle as well as the exact location of the particle at specific times, we can predict with 100% certainty where the particle will end up. These 'quantum forces' acting on a particle are described by a 'Pilot Wave' a wave that effectively guides the particle into its eventual position. This pilot wave is described by Schrodinger's equation, and the pilot wave equation (which in itself is derived from the Schrodinger equation) to provide a complete description of quantum theory. This Pilot Wave, however, does contain hidden variables, which is less than ideal as Von Neuman (1932) attempted to disprove Hidden Variables.

☀von Neumann, J. (1932). Mathematische Grundlagen der Quantenmechanik. Berlin: Springer. Reprints (1968, 1996); Berlin, Heidelberg, New York: Springer

although he disproved the existence of local hidden variables in Quantum Theory, Global Hidden variables were still allowed, which is fortunately the kind that Bohmian Mechanics needs. In its current state, Pilot Wave theory could not be the correct interpretation of quantum theory as it does not account for general relativity in the same way that Quantum Field Theory does, though if it were to be changed to account for relativity it would be a deterministic competitor to the Copenhagen Interpretation.

 Relational Theory 

The relational theory suggests a view on observations inspired by special relativity (how so?). It suggests that if there is an observation made on a system (e.g. electron spin), the observed value of the system (e.g. spin up) is not the actual value of the system, but is instead the value of the system observed by the observer. If another observer comes along and makes an observation on the system and the first observer, there is a possibility that the values are not the same. This causes more than one value observed for the same system. ideally the theory of relational quantum mechanics would be used to develop a theory for quantum gravity(elaborate?why is this significant?).

Gyula Bene (1997) (full reference?)suggested that the observed value of the system is not the absolute value of the system, but instead it is the value of the system observed by a certain observer (with respect to the observer). So if there is a difference in observance, it is fine as it is the observation with respect to an observer, as the system has been affected by the observation of the observer.