He was an inspiration to many of us in IT.
He will be missed.
A site devoted mostly to everything related to Information Technology under the sun - among other things.
He was an inspiration to many of us in IT.
He will be missed.
From BBC
From Grauniad of the UK
This is a good book on various techniques and approaches to innovation & problem-solving. Its chapters are brief surveys of different techniques and approaches to innovation and problem solving, such as TRIZ, with references to more in-depth resources. (Each chapter, in my opinion, could be expanded into a book in itself.)
This book could be useful to inventors, business analysts, requirements analysts, system builders, product owners and others in creative fields.
Abstract: A fictional system is introduced as a pedagogical device to unify several elementary topics in quantum mechanics within a single worked example. Using standard textbook formulas, we examine de Broglie wavelength, tunneling, Doppler shift, Compton scattering, and momentum transfer in a consistent, order-of-magnitude framework. No claims are made regarding the physical existence of the system considered.
This article presents a pedagogical exercise rather than a physical model of a real system. “Ghosts” are treated throughout as a fictional construct, introduced solely to unify several elementary topics in quantum mechanics—including the de Broglie wavelength, tunneling, Doppler shift, Compton scattering, and momentum transfer—within a single worked example. Standard textbook formulas are applied in an internally consistent manner to emphasize order-of-magnitude reasoning and conceptual coherence, without implying any physical reality for the system described.
Within this fictional framework, ghosts are assumed to penetrate closed doors and interior walls with thicknesses of order \(0.1~\mathrm{m}\), while remaining confined by substantially thicker exterior walls. For instructional purposes, this behavior is modeled using quantum-mechanical tunneling,[1] requiring an associated de Broglie wavelength of comparable scale. We further assume that a typical ghost, in the absence of illumination, can attain a velocity of approximately \(v = 3000~\mathrm{m\,s^{-1}}\).
Using the de Broglie relation,[2]
$$\lambda = \frac{h}{mv}$$
the mass is
$$m = \frac{h}{\lambda v}$$
Substituting
$$h = 6.626\times10^{-34}~\mathrm{J\,s},\quad \lambda = 0.1~\mathrm{m},\quad v = 3000~\mathrm{m\,s^{-1}}$$
yields
$$m \approx 2.21\times10^{-36}~\mathrm{kg}$$
This mass is approximately \(10^9\) times smaller than the electron mass,[3] illustrating why macroscopic tunneling lengths arise in this constructed example.
The kinetic energy is
$$K = \frac{1}{2}mv^2 \approx 9.95\times10^{-30}~\mathrm{J}$$
For a rectangular potential barrier of thickness \(d\), the tunneling probability is approximated by[1]
$$T \approx e^{-2\kappa d}, \quad \kappa = \sqrt{\frac{2m(U-E)}{\hbar^2}}$$
Solving for the barrier height \(U\) gives
$$U = E + \frac{\hbar^2}{2md^2}\left[\ln\left(\frac{1}{T}\right)\right]^2$$
For pedagogical simplicity, we consider the high-transmission limit \(T \approx 1\), yielding \(U \approx E\).
For incident light of wavelength \(\lambda_0 = 600~\mathrm{nm}\), the relativistic Doppler shift gives
$$\lambda' \approx 599.994~\mathrm{nm}$$
For backscattering (\(\theta = \pi\)), the Compton shift is
$$\Delta\lambda = \frac{2h}{mc} \approx 2000~\mathrm{nm}$$
placing the scattered radiation in the infrared.
The momentum change associated with photon scattering is
$$\Delta p \approx 1.36\times10^{-27}~\mathrm{kg\,m\,s^{-1}}$$
which, when applied relativistically, leads to a final velocity approaching \(0.9c\).[5]
The exaggerated numerical results obtained here are a direct consequence of the intentionally extreme parameter choices used to illustrate quantum-mechanical principles. The example is intended to provoke discussion, reinforce scaling arguments, and encourage careful examination of assumptions when applying familiar formulas beyond their usual domains.
The problems presented here are adapted from a homework assignment by the late Professor Karl T. Hect of the University of Michigan in Ann Arbor. The solutions are provided by the author. ChatGPT produced the same results. ChatGPT created the HTML version of this work.
The author has no conflicts to disclose.
From Grauniad of the UK