Dirac also explores the implications of a double slit-interference experiment, the results of which demonstrate that even if you were to have the initial conditions of a particle at the source, there is no way of predicting its precise end location on the screen. This randomness obviously undermines determinism, which requires for the given initial state to uniquely dictate the following states. It would also imply that it would be impossible to determine the trajectory of a single particle having left the source. Quantum Mechanics: problems with the Copenhagen Interpretation and a deterministic alternative The argument posed by Dirac and others that causality breaks down and therefore leads to indeterminism can be countered with the paper Determinism Without Causality 14 , which states that in a more modern context determinism and causality can be declared independent despite much prior confusion (and this can be demonstrated with experimentation and is now commonly accepted). Einstein himself was a life-long sceptic of the Copenhagen interpretation that had effectively become the standard approach to quantum mechanics. The oft-quoted ÂI am convinced God does not play diceÊ 15 , is the foundation for EinsteinÊs convictions and fuelled an attempt to either prove that quantum mechanics is logically inconsistent or an incomplete theory in what became known as the EPR paradox (named after its creators Einstein, Boris Podolsky and Nathan Rosen). The argument is outlined: In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the 14 D'Ariano, Giacomo M., Franco Manessi, and Paolo Perinotti. ÂDeterminism without causalityÊ. arXiv preprint arXiv:1301.7578 (2013). 15 A private letter to Max Born, 4 December 1926, Albert Einstein Archives reel 8, item 180.
total electrons fired would be proportional to this statistical distribution.
In 1927, Heisenberg (yet another senior member of the Copenhagen group) published a paper which contained a number of Âuncertainty relationsÊ ultimately surmised with his statement: ÂOne can never know with perfect accuracy both of those two important factors which determine the movement of one of the smallest particles· its position and its velocity. It is impossible to determine accurately both the position and the direction and speed of a particle at the same instant.Ê 9 This became known as the Heisenberg uncertainty principal. DiracÊs influential book The Principles of Quantum Mechanics expresses how classical concepts can no longer be applied to our approach to quantum mechanics primarily because of the limitations in observing the quantum domain. He states: Âthere is a limit to the fineness of our powers of observation and the smallness of the accompanying disturbance - a limit which is inherent in the nature of things and can never be surpassed by improved technique or increased skill on the part of the observer.Ê 10 This inherent ÂdisturbanceÊ in observation leads Dirac on to claim that Âwe must revise our ideas of causalityÊ 11 . Cushing interprets this as therefore meaning Âthe concept of causality, in the classical deterministic cause and effect sense, must be modifiedÊ 12 . This will be done so in the next section, addressing the complications behind using this breakdown of causality as a basis for DiracÊs call that there is now an element of Âunavoidable indeterminacyÊ 13 . 9 Heisenberg, W., Die Physik der Atomkerne , Taylor & Francis, 1952, p. 30. 10 Dirac, P. A. M. The Principles of Quantum Mechanics . Oxford: Oxford University Press, 1930. pp. 3-4. 11 Dirac, p. 4. 12 Cushing, James T. Philosophical Concepts in Physics, Cambridge: Cambridge University Press, 1998, p. 298. 13 Dirac, p. 4.
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