Frank Close - Collected Quotes

"Anyone who has played with Rubik’s cube knows that twisting the top clockwise and then rotating the right hand side to the back gives a different pattern than if you did the two operations in the reverse order. It is easier to see this with a die. If you rotate a die clockwise and then about the vertical, it will be oriented differently to the case where you had first rotated about the vertical and then clockwise. This is why matrices have proved so useful in keeping track of what happens when things rotate in three  dimensions, as the order matters." (Frank Close, "Antimatter", 2009)

"Dirac’s idea of the bottomless sea full of identical electrons also explains why all electrons and positrons created ‘out of the vacuum’ have identical properties rather than emerging with a random continuum of possibilities. Dirac also proposed that pro tons fill the sea, and today we recognize that their more basic seeds, the ‘quarks’ (which we shall meet in chapter 5), also satisfy the exclusion principle and fill an infinitely deep sea. It is the infinitely deep storehouse of the Dirac sea that provides us with the particles, and antiparticles, that we can materialize." (Frank Close, "Antimatter", 2009)

"In Dirac’s interpretation of the vacuum, if one electron in this sea were missing, it would leave a hole. The absence of a negatively charged electron with energy that is negative relative to sea-level, will appear as a positively charged particle with positive energy, namely with all the attributes of what was later called a positron. This was a strange idea, and quantum mechanics is still strange eighty years later; it was only in its infancy when Dirac made his proposal, which was a piece of radical genius." (Frank Close, "Antimatter", 2009)

"Mechanics is the science of motion. It describes how things move from om one point to another as time passes, the greater the distance moved each second so the greater is the speed. If something moving hits you, the impact will depend not just on how fast it’s travelling but also how massive it is. It is the momentum that matters: the product of mass and velocity. Mechanics also deals with energy, especially the energy due to motion, ‘kinetic energy’." (Frank Close, "Antimatter", 2009)

"Many phenomena require more than just real numbers to describe them mathematically. One such generalization of numbers is known as ‘matrices’. These involve numbers arranged in columns or rows with their own rules for addition and multiplication. Ordi nary numbers correspond to having the same number all down the top left to bottom right diagonal [...]." (Frank Close, "Antimatter", 2009)

"Schrodinger’s equation also explained why the orbital motion of electrons in atoms caused the spectral lines to multiply in magnetic fields. However, it gave no explanation for the electron’s own intrinsic ‘spin’. This known property of the electron had no place in Schrodinger’s theory. A more complete quantum mechanics, one that incorporated spin and applied at relativistic speeds, waited to be discovered." (Frank Close, "Antimatter", 2009)

"The first glimpse of the antiworld came not from experiment, a chance discovery, but from the beautiful patterns that Dirac had seen in his equations. As crotchets, minims, and semiquavers on a stave are mere symbols until interpreted by a maestro and transformed into sublime melody, so can arid equations miraculously reveal harmony in nature." (Frank Close, "Antimatter", 2009)

"The ‘Schrodinger Equation’ explained the behavior of electrons in atoms, and showed that in a hydrogen atom the electron is effectively moving with a speed of about two thousand kilometers a second. This is fast to our senses but is less than one percent of the speed of light. Schrodinger’s theory worked, and even today is widely applied to problems in atomic physics." (Frank Close, "Antimatter", 2009)

"There’s matter, like the electron; antimatter, like the positron; and then there are things that are neither matter nor antimatter. The most familiar example of something that is beyond substance is electromagnetic radiation. All electromagnetic radiation, from gamma rays through X-rays and ultra-violet to visible light, infra red, and radio waves, consists of photons of different energies. Matter and antimatter can cancel one another out, their annihilation leaving non-substance in the form of photons; if the conditions are right this sequence can happen in reverse where photons turn into pieces of matter and antimatter." (Frank Close, "Antimatter", 2009)

"Using matrices, Dirac was able to write an equation relating the total energy of a body to a sum of its energy at rest and its energy in motion, all consistent with Einstein’s theory of relativity. The fact that matrices keep account of what happens when things rotate was a bonus, as the maths was apparently saying that an electron can itself rotate: can spin! Furthermore, the fact that he had been able to solve the mathematics by using the simplest matrices, where a single number was replaced by two columns of pairs, implied a ‘two-ness’ to the spin, precisely what the Zeeman effect had implied. The missing ingredi ent in Schrodinger’s theory had miraculously emerged from the mathematics of matrices, which had been forced on Dirac by the requirements of Einstein’s theory of relativity." (Frank Close, "Antimatter", 2009)