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Relational quantum mechanics is an ] which is distinguished by its construal of the state of a quantum system as being the correlation between this system and an observer. The interpretation was first put forward by ] in 1994. Relational quantum mechanics is an ] which is distinguished by its construal of the state of a quantum system as being the correlation between this system and an observer.


== Fundamental propositions == == Overview of the Theory ==

== Derivation & Structure ==
===The Third Man problem=== ===The Third Man problem===
This problem was initially discussed in detail in Everett's thesis, ''The Theory of the Universal Wavefunction''. Consider a system <math>S</math> which may take one of two states, which we shall designate <math>|A \rangle </math> and <math> |B \rangle </math>, ] in the ] <math>H_S</math>. Now, there is an observer <math>O_1</math> who wishes to make a measurement on the system. At time <math>t_1</math>, the system may be characterised as follows: This problem was initially discussed in detail in Everett's thesis, ''The Theory of the Universal Wavefunction''. Consider a system <math>S</math> which may take one of two states, which we shall designate <math>|A \rangle </math> and <math> |B \rangle </math>, ] in the ] <math>H_S</math>. Now, there is an observer <math>O_1</math> who wishes to make a measurement on the system. At time <math>t_1</math>, the system may be characterised as follows:
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This is observer <math>O_1</math>'s description of the measurement event. Now, any measurement is also a physical interaction between two or more systems. Accordingly, we can consider the ] Hilbert space <math>H_S \otimes H_{O_1}</math>, where <math>H_{O_1}</math> is the Hilbert space inhabited by state vectors describing <math>O_1</math>. If the initial state of <math>O_1</math> is <math>|init\rangle</math>. After the measurement, some degrees of freedom in <math>O_1</math> become correlated with the state of <math>S</math>, and this correlation can take one of two values: <math>|O_1A\rangle</math> or <math>|O_1B\rangle</math>, with obvious meanings. If we now consider the description of the measurement event by another observer, <math>O_2</math>, who observes the combined <math>S-O</math> system. So, the following gives the description of the measurement event according to <math>O_2</math> (again assuming that the result of the experiment gives state <math>|A\rangle</math>: This is observer <math>O_1</math>'s description of the measurement event. Now, any measurement is also a physical interaction between two or more systems. Accordingly, we can consider the ] Hilbert space <math>H_S \otimes H_{O_1}</math>, where <math>H_{O_1}</math> is the Hilbert space inhabited by state vectors describing <math>O_1</math>. If the initial state of <math>O_1</math> is <math>|init\rangle</math>. After the measurement, some degrees of freedom in <math>O_1</math> become correlated with the state of <math>S</math>, and this correlation can take one of two values: <math>|O_1A\rangle</math> or <math>|O_1B\rangle</math>, with obvious meanings. If we now consider the description of the measurement event by another observer, <math>O_2</math>, who observes the combined <math>S-O</math> system. So, the following gives the description of the measurement event according to <math>O_2</math> (again assuming that the result of the experiment gives state <math>|A\rangle</math>:


== Structure of questions == === Fundamental Propositions ===

=== Example: EPR ===



== Relationship with other interpretations == == Relationship with other interpretations ==

=== Wave Collapse ===

=== No Wave Collapse ===


== References == == References ==

Revision as of 07:42, 21 July 2006

Relational quantum mechanics is an interpretation of quantum mechanics which is distinguished by its construal of the state of a quantum system as being the correlation between this system and an observer.

Overview of the Theory

Derivation & Structure

The Third Man problem

This problem was initially discussed in detail in Everett's thesis, The Theory of the Universal Wavefunction. Consider a system S {\displaystyle S} which may take one of two states, which we shall designate | A ⟩ {\displaystyle |A\rangle } and | B ⟩ {\displaystyle |B\rangle } , vectors in the Hilbert space H S {\displaystyle H_{S}} . Now, there is an observer O 1 {\displaystyle O_{1}} who wishes to make a measurement on the system. At time t 1 {\displaystyle t_{1}} , the system may be characterised as follows:

| ψ ⟩ = α | A ⟩ + β | B ⟩ {\displaystyle |\psi \rangle =\alpha |A\rangle +\beta |B\rangle }

where | α | 2 {\displaystyle |\alpha |^{2}} and | β | 2 {\displaystyle |\beta |^{2}} are probabilities of finding the system in the respective states, and obviously add up to 1. For our purposes here, we can assume that in a single experiment, the outcome is the eigenstate | A ⟩ {\displaystyle |A\rangle } (but this can be substituted throughout, mutatis mutandis, by | B ⟩ {\displaystyle |B\rangle } ). So, we may represent the sequence of event in this experiment, with observer O 1 {\displaystyle O_{1}} doing the observing, as follows:

t 1 → t 2 {\displaystyle t_{1}\rightarrow t_{2}}

α | A ⟩ + β | B ⟩ → | A ⟩ {\displaystyle \alpha |A\rangle +\beta |B\rangle \rightarrow |A\rangle }

This is observer O 1 {\displaystyle O_{1}} 's description of the measurement event. Now, any measurement is also a physical interaction between two or more systems. Accordingly, we can consider the tensor product Hilbert space H S ⊗ H O 1 {\displaystyle H_{S}\otimes H_{O_{1}}} , where H O 1 {\displaystyle H_{O_{1}}} is the Hilbert space inhabited by state vectors describing O 1 {\displaystyle O_{1}} . If the initial state of O 1 {\displaystyle O_{1}} is | i n i t ⟩ {\displaystyle |init\rangle } . After the measurement, some degrees of freedom in O 1 {\displaystyle O_{1}} become correlated with the state of S {\displaystyle S} , and this correlation can take one of two values: | O 1 A ⟩ {\displaystyle |O_{1}A\rangle } or | O 1 B ⟩ {\displaystyle |O_{1}B\rangle } , with obvious meanings. If we now consider the description of the measurement event by another observer, O 2 {\displaystyle O_{2}} , who observes the combined S − O {\displaystyle S-O} system. So, the following gives the description of the measurement event according to O 2 {\displaystyle O_{2}} (again assuming that the result of the experiment gives state | A ⟩ {\displaystyle |A\rangle } :

Fundamental Propositions

Example: EPR

Relationship with other interpretations

Wave Collapse

No Wave Collapse

References

Get Everett, Rovelli (Int Jour Theor phys), von Neumann.

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