and grammar. See grammar
granularity of, 85–86
and the gravitational field, 74–79, 90, 124, 195,
197, 198–99. See also gravitational field
and heat. See heat
internal consciousness of, 183–86
loss of direction, 19–36, 194, 195
loss of independence, 57–79
loss of the present, 37–56, 107–8, 194
loss of unity, 9–17
as measurement of change, and Aristotle’s space, 63–79, 97
and memory. See memory/memories
modification of structure of, 9–13
multilayered aspect of, 3, 198
multiple meanings of, 17n
mystery of, 1–5, 199–202
and network of relations, 89–91. See also relationality
when nothing changes, 63–64, 72
Planck time, 83
proper time, 16, 40, 216n8
quantum superpositions of times, 87–88. See also quantum mechanics
quantum time. See quantum time
and relativity. See relativity
sources of, 193–203
spacetime. See spacetime
standardized, 61–62
as suffering, 190–91
temporal structure of universe without the present, 46–56, 106–7, 109
thermal, 134–38, 139–40, 142, 196, 222n87
traces of the past, 166–67, 181, 183, 187, 196–97. See also memory/memories
“true” time and Newton’s space, 65–79
Tomita–Takesaki theorem, 225n85
universal man, 154–55
Wheeler, John, 119–21, 122, 124
Wheeler–DeWitt equation, 119, 224n72
ABOUT THE AUTHOR
Carlo Rovelli, an Italian theoretical physicist, is the head of the quantum gravity group at the Centre de Physique Théorique of Aix-Marseille Université. He is one of the founders of the loop quantum gravity theory and author of the international bestseller Seven Brief Lessons on Physics, Reality Is Not What It Seems, and The Order of Time. Rovelli lives in Marseille, France.
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* Grammatical note: The word “time” has several meanings linked to each other but distinct from one another: 1. “Time” is the general phenomenon of the succession of events (“The inaudible and noiseless foot of time”); 2. “Time” indicates an interval in this succession (“To morrow, and to morrow, and to morrow, /Creeps in this petty pace from day to day, /To the last syllable of recorded time”); or 3. its duration (“O gentlemen, the time of life is short”); 4. “Time” can also indicate a particular moment (“Time will come and take my love away”; often the current one (“The time is out of joint”); 6. “Time” indicates the variable that measures duration (“Acceleration is the derivative of speed with respect to time”). In this book, I employ each of these meanings freely, just as in common usage. In case of any confusion, please refer back to this note.
* Strictly speaking, the arrow of time can also manifest itself in phenomena that are not linked directly to heat but share crucial aspects with it—for instance, in the use of retarded potentials in electrodynamics. What follows applies also for these phenomena—in particular, the conclusions. I prefer here not to overload the discussion by breaking it down into all its different subcases.
* There are a few more details given on this point in chapter 11.
* The point is not that what happens to a cold teaspoon in a cup of hot tea depends on whether I have a blurred vision of it or not. What happens to the spoon and to its molecules as well, obviously, does not depend on how I view it. It just happens, regardless. The point is that the description in terms of heat, temperature, and the passage of heat from tea to spoon is a blurred vision of what happens, and that it is only in this blurred vision that a startling difference between past and future appears.
* “In motion” in relation to what? How can we determine which of the two objects moves, if motion is only relative? This is an issue that confuses many. The correct answer (rarely given) is this: in motion relative to the only reference in which the point in space where the two clocks separate is the same point in space where they get back together. There is only a single straight line between two events in spacetime, from A to B: it’s the one along which time is maximum, and the speed relative to this line is the one that slows time. If the clocks separate and are not brought together again, there is no point asking which one is fast and which one is slow. If they come together, they can be compared, and the speed of each one becomes a well-defined notion.
* The “closed temporal lines,” where the future returns us to the past, are the ones that frighten those who imagine that a son could go on to kill his mother before his own birth. But there is no logical contradiction entailed by the existence of closed temporal lines or journeys to the past; we are the ones who complicate things with our confused fantasies about the supposed freedom of the future.
* I have been criticized for telling the history of science as if it were just the result of the ideas of a few brilliant minds rather than the painstaking work of generations. It’s a fair enough criticism, and I apologize to the generations who have done and are doing the necessary work. My only excuse is that I am not attempting a detailed historical analysis or scientific methodology. I am only synthesizing a few crucial steps. Slow, technical, cultural, and artistic advances made by innumerable workshops of painters and artisans were necessary before the Sistine Chapel was possible. But in the end, it was Michelangelo who painted it.
* The route by which Einstein arrived at this conclusion was a long one: it didn’t end with the writing of the equations of the field in 1915 but continued in his tortuous efforts to understand its physical significance, causing him in the process to change his ideas repeatedly. He was confused in particular regarding the existence of solutions without matter, and by whether gravitational waves were real or not. He achieves definitive clarity only in his last writings and, in particular, in the fifth appendix, “Relativity and the Problem of Space,” which was added to the fifth edition of Relativity: The Special and General Theory (Methuen: London, 1954). This appendix can be read at http://www.relativitybook.com/resources/Einstein_space.html. For copyright reasons, this appendix is not included in most editions of the book. A more in-depth discussion can be found in chapter 2 of my Quantum Gravity (Cambridge, UK: Cambridge University Press, 2004).
* The technical term for interaction used in this context, “measure,” is misleading because it seems to imply that in order to create reality, we need an experimental physicist in a white coat.
* I’m making use here of the relational interpretation of quantum mechanics, which is the one I myself find least implausible. The observations that follow, in particular the loss of a classic spacetime satisfying Einstein’s equations, remain valid in every other interpretation that I know of.