Once Before Time - Martin Bojowald [153]
8. Initially, the GPS system was developed for military purposes, and it is still overseen by the U.S. Department of Defense. Satellite signals available for civilian applications were, for some time, intentionally disturbed so as to allow position measurements only to within about one hundred meters. Over time, more and more, and very lucrative, applications were invented, and the disturbance mechanism was switched off in May 2007 following a directive from the Clinton administration.
9. Friedrich Nietzsche, On the Genealogy of Morality.
10. Undoubtedly, some readers will, at least occasionally, wish such a fate for this book.
11. An extreme example of a fairly common view is the following statement made by the physicist Frank Tipler on CBS 11 TV (Dallas/Fort Worth) on May 9, 2007: “God is the cosmological singularity. I am not being blasphemous. I’m just following in the ancient tradition in saying that science puts the tenets of religion up to the experimental test, and we find that God exists.”
12. Until Hawking came along, Vladimir Belinsky, Isaak Khalatnikov, and Evgeny Lifshitz thought they could prove the absence of singularities in generic space-time solutions of Einstein’s equations, only to stand corrected by Hawking’s more powerful mathematical methods. Nevertheless, their analysis is still being used to understand space-time close to singularities and represents an important contribution to our knowledge of general relativity.
13. Oscar Wilde, “De Profundis.”
2. QUANTUM THEORY
1. This is a serious problem for the transporter beam process popularized by the series Star Trek, by which an object or a person is completely measured, annihilated, and reconstructed identically at a new place. The very first step, the complete measurement, is already impossible due to the uncertainty principle; the second step, annihilation, seems much easier. According to the inventors of the series, this problem is supposed to be solved by the so-called Heisenberg compensator, which dodges the uncertainty relation. Unfortunately, not much information exists about details: Asked how the Heisenberg compensator works, a technical adviser once replied, “It works very well, thank you.”
2. There are other energies associated with spherical wave functions, but they have larger radii. The one closest to the proton is the stable one, for it cannot be compressed further. Trying to do so would bring us in conflict with the uncertainty relation, limiting the uncertainty achieved for position and velocity at the same time: Compressing the wave function reduces the position uncertainty, for we get to know the size of the wave better. The velocity uncertainty must change accordingly when the radius shrinks, for the electron must remain in a smaller region. The limit to uncertainties then limits the electron’s orbits.
3. The term “Planck length” was coined later by John Wheeler, who recognized its role in quantum gravity.
3. AN INTERLUDE ON THE ROLE OF MATHEMATICS
1. Friedrich Nietzsche, The Gay Science (Stuttgart: Reclam, 2000), 237.
2. In 100 Years of Relativity—Space-Time Structure: Einstein and Beyond, edited by Abhay Ashtekar (Singapore: World Scientific, 2005), 18.
3. There is even a “theory” so mysterious that not even its name is known, except for its first letter. Indeed, this letter is often interpreted as standing for “magic” or “mysterious,” but sometimes also for words such as “membrane,” or even as being a mirror image of the first letter of its originator’s surname, reflected at a horizontal axis.
4. Although the mathematical degree varies, theories in this sense exist not only in physics but also in other areas of science. A well-known example is biological evolution, which, based on principles such as selection and mutation, can explain the richness of the species of life on Earth as well as