"Suppose... motion of an electron in the absence of a field of force, is to be investigated... by testing the validity of [no force implies zero acceleration]...\frac{d^2q}{dt^2} = 0, \quad ...18(3)...q ...the position of the particle at time t. The... procedure is to measure the position and momentum of the electron at... time t = t_0... to obtain two "initial conditions" which can be inserted in the solution of 18(3)... then calculate the position and momentum at some later time... and see if the calculation agrees with... observation... Suppose we observe... with light of wavelength \lambda. ...[D]iffraction of the wave sets the limit to the accuracy of a position measurement...\vartriangle q \sim \frac{\lambda}{2sin\theta}, \quad ...18(4)where \vartriangle q is the probable error in... q, and \theta is the semi-angle of the cone of rays accepted by the microscope... [and] \sim means "at least of the order of magnitude of". The experiment of Compton... shows that the interaction... involves an exchange of momentum. We may assume that the momenta... were exactly known before their interaction, but... [those] after the interaction depends on the accuracy [of the] momentum exchanged during the interaction. [T]he photon enters the microscope, and... we know its direction... within an angle 2\theta. Any attempt [to reduce] the effective aperture... increases \vartriangle q. Thus... the momentum of the photon in the plane [in which q is measured] perpendicular to the axis of the microscope... is uncertain by an amount\vartriangle p \sim \frac{2h\nu}{c}sin\theta \quad. ...18(5)The momentum of the particle after the interaction is uncertain by \vartriangle p. Combining... we have\vartriangle p \vartriangle q \sim \frac{\lambda}{2sin\theta} \frac{2h\nu}{c} sin\theta,i.e.,\vartriangle p \vartriangle q \sim h \quad. ...18(6)"
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Original Language: English
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Sources
R. W. Ditchburn, Light (1953) pp. 584-585.
https://en.wikiquote.org/wiki/Uncertainty_principle
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Uncertainty principle
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