For those standing below, things above are below, while things below are above . . . and this is the case around the entire earth.65
On first reading, the phrase is a muddle, a contradiction in terms. How is it possible that “things above are below, while things below are above”? It makes no sense. It is comparable to the sinister “Fair is foul and foul is fair” in Macbeth. But if we reread it bearing in mind the shape and the physics of the Earth, the phrase becomes clear: its author is saying that for those who live at the Antipodes (in Australia), the direction “upward” is the same as “downward” for those who are in Europe. He is saying, that is, that the direction “above” changes from one place to another on the Earth. He means that what is above with respect to Sydney is below with respect to us. The author of this text, written two thousand years ago, is struggling to adapt his language and his intuition to a new discovery: the fact that the Earth is a sphere, and that “up” and “down” have a meaning that changes between here and there. The terms do not have, as previously thought, a single and universal meaning.
We are in the same situation. We are struggling to adapt our language and our intuition to a new discovery: the fact that “past” and “future” do not have a universal meaning. Instead, they have a meaning that changes between here and there. That’s all there is to it.
In the world, there is change, there is a temporal structure of relations between events that is anything but illusory. It is not a global happening. It is a local and complex one that is not amenable to being described in terms of a single global order.
And what about Einstein’s phrase “the distinction between past, present and future is only a stubbornly persistent illusion”? Does it not seem to say that he thought the opposite?
Even if this were the case, I am not sure that because Einstein has penned some phrase or other we should treat is as the utterance of an oracle. Einstein changed his mind many times on fundamental questions, and it is possible to find numerous erroneous phrases of his that contradict each other.66 But in this instance, things are perhaps much simpler. Or more profound.
Einstein coins this phrase when his friend Michele Besso dies. Michele has been his dearest friend, the companion of his thinking and discussions since his days at the University of Zurich. The letter in which Einstein writes the phrase is not directed at physicists or philosophers. It is addressed to Michele’s family, and in particular to his sister. The sentence that comes before it reads:
Now he [Michele] has departed from this strange world a little ahead of me. That means nothing. . . .
It is not a letter written to pontificate about the structure of the world, it’s a letter written to console a grieving sister. A gentle letter, alluding to the spiritual bond between Michele and Albert. A letter in which Einstein also confronts his own suffering at the loss of his lifelong friend; and in which, evidently, he is thinking about his own approaching death. A deeply emotional letter, in which the illusoriness and the heartrending irrelevance to which he alludes do not refer to time as understood by physicists. They are prompted by the experience of life itself. Fragile, brief, full of illusions. It’s a phrase that speaks of things that lie deeper than the physical nature of time.
Einstein died on April 18, 1955, one month and three days after the death of his friend.
8 DYNAMICS AS RELATION
Sooner or later
the exact measurement of our time
will resume—
and we’ll be on the ship that’s bound
for the bitterest shore. (II, 9)
How does one describe a world in which everything occurs but there is no time variable? In which there is no common time and no privileged direction in which change occurs?
In the simplest way, the same way that we had thought about the world until Newton convinced us all that a variable time was indispensable.
To describe the world, the time variable is not required. What is required are variables that actually describe it: quantities that we can perceive, observe, and eventually measure. The length of a road, the height of a tree, the temperature of a forehead, the weight of a piece of bread, the color of the sky, the number of stars in the celestial vault, the elasticity of a piece of bamboo, the speed of a train, the pressure of a hand on a shoulder, the pain of a loss, the position of the hands on a clock, the height of the sun in the sky . . . These are the terms in which we describe the world. Quantities and properties that we see continuously changing. In these changes there are regularities: a stone falls faster than a feather. Sun and moon circle after each other in the sky, passing by each other once a month. . . . Among these quantities there are some that we see changing regularly with respect to others: the number of days, the phases of the moon, the height of the sun on the horizon, the position of the hands of a clock. It is useful to employ these as points of reference: let’s meet three days after the next full moon, when the sun is at its highest in the sky. I’ll see you tomorrow, when the clock shows 4:35. If we find a sufficient number of variables that remain synchronized enough in relation to each other, it is convenient to use them in order to speak of when.
There is no need in any of this to choose a privileged variable and call it “time.” What we need, if we want to do science, is a theory that tells us how the variables change with respect to each other. That is to say, how one changes when others change. The fundamental theory of the world must be constructed in this way; it does not need a time variable: it needs to tell us only how the things that we see in the world vary with respect to each other. That is to say, what the relations may be between these variables.67
The fundamental equations of quantum gravity are effectively formulated like this: they do not have a time variable, and they describe the world by indicating the possible relations between variable quantities.68
In 1967, an equation accounting for quantum gravity was written for the first time without any time variable. This equation was discovered by two American physicists—Bryce DeWitt and John Wheeler—and today it’s known as the Wheeler–DeWitt equation.69
At first no one could understand the significance of an equation without a time variable, perhaps not even Wheeler and DeWitt themselves. (Wheeler: “Explain time? Not without explaining existence! Explain existence? Not without explaining time! To uncover the deep and hidden connection between time and existence . . . is a task for the future.”70) The issue was discussed at great length; there were conferences, debates; rivers of ink flowed.71 I think that the dust has now settled and things have become much clearer. There is nothing mysterious about the absence of time in the fundamental equation of quantum gravity. It is only the consequence of the fact that, at the fundamental level, no special variable exists.
The theory does not describe how things evolve in time. The theory describes how things change one in respect to the others,72 how things happen in the world in relation to each other. That’s all there is to it.
Bryce and John left us some years ago. I knew them both and had great admiration and respect for them. In my study at the university in Marseille, I have hanging on the wall a letter that John Wheeler wrote to me when he became aware of my first work on quantum gravity. Every so often I reread it with a mixture of pride and nostalgia. I would like to have asked him more, during the handful of meetings that we had together. The last time I went to see him in Princeton, we took a long walk together. He spoke to me with the soft voice of an old man: I could not make out much of what he said but did not dare to ask him too frequently to repeat what he was saying. Now he is no longer with us. I can’t question him anymore, or tell him what I think. I can no longer tell him that it seems to me that his ideas are correct, and that they have guided me throughout a lifetime of research. I can no longer tell him I believe that he was the first to come close to the heart of the mystery of quantum gravity. Because he is no longer here—here and now. This is time for us. Memory and nostalgia. The pain of absence.