Ensemble interpretation

[1] The advocates of the ensemble interpretation of quantum mechanics claim that it is minimalist, making the fewest physical assumptions about the meaning of the standard mathematical formalism.

It proposes to take to the fullest extent the statistical interpretation of Max Born, for which he won the Nobel Prize in Physics in 1954.

In one view, the ensemble interpretation may be defined as that advocated by Leslie E. Ballentine, Professor at Simon Fraser University.

It makes the statistical operator primary in reading the wave function, deriving the notion of a pure state from that.

As related in his 1954 Nobel Prize in Physics lecture [5] Born viewed the statistical character of quantum mechanics as an empirical observation with philosophical implications.

[8] Also in the years around 1936, Karl Popper published philosophical studies countering the work of Heisenberg and Bohr.

He held that the quantum state represented statistical assertions which have no predictive power for individual particles.

Although several other notable physicists championed the ensemble concept, including John C. Slater, Edwin C. Kemble, and Dmitry Blokhintsev,[9] Leslie Ballentine's 1970 paper 'The statistical interpretation of quantum mechanics"[10] and his textbook[11] have become the main sources.

[7][9] Ballentine followed up with axiomatic development of propensity theory,[12] analysis of decoherence in the ensemble interpretation[13] and other papers spanning 40 years.

EI: A pure state describes the statistical properties of an ensemble of identically prepared systems.

Popper,[17] Ballentine,[12] Paul Humphreys,[18] and others[19] point to propensity as the correct interpretation of probability in science.

This is agreed, for example, by Born,[21] Dirac,[22] von Neumann,[23] London & Bauer,[24] Messiah,[25] and Feynman & Hibbs.

The system's initial state is defined by the preparative procedure; this is recognized in the ensemble interpretation, as well as in the Copenhagen approach.

The wave function can be multiplied by a complex number of unit magnitude without changing the state as defined by the preparative procedure.

The preparative state, with unspecified phase, leaves room for the several members of the ensemble to interact in respectively several various ways with other systems.

Individual systems with various phases are scattered in various respective directions in the analyzing part of the observing device, in a probabilistic way.

When the system hits the analyzing part of the observing device, that scatters it, it ceases to be adequately described by its own wave function in isolation.

The Born rule describes that derived random process, the observation of a single member of the preparative ensemble.

In the ordinary language of classical or Aristotelian scholarship, the preparative ensemble consists of many specimens of a species.

The quantum mechanical technical term 'system' refers to a single specimen, a particular object that may be prepared or observed.

He is focusing on the phenomenon as a whole, recognizing that the preparative state leaves the phase unfixed, and therefore does not exhaust the properties of the individual system.

Niels Bohr famously insisted that the wave function refers to a single individual quantum system.

The ensemble interpretation is notable for its relative de-emphasis on the duality and theoretical symmetry between bras and kets.

There is no recognition of the notion that a single specimen system could manifest more than one state at a time, as assumed, for example, by Dirac.

The ensemble approach demystifies this situation along the lines advocated by Alfred Landé, accepting Duane's hypothesis.

This gives a clear and utterly non-mysterious physical or direct explanation instead of the debated concept of wave function "collapse".

David Mermin sees the ensemble interpretation as being motivated by an adherence ("not always acknowledged") to classical principles.

The fact that physics cannot make deterministic predictions about individual systems does not excuse us from pursuing the goal of being able to describe them as they currently are.

As an avowedly minimalist approach, the ensemble interpretation does not offer any specific alternative explanation for these phenomena.

Leslie Ballentine promoted the ensemble interpretation in his book Quantum Mechanics, A Modern Development.