It was a brilliant intuition, and a correct one. But does it clarify the difference between past and future? It does not. It just shifts the question. The question now becomes: why, in one of the two directions of time—the one we call past—were things more ordered? Why was the great pack of cards of the universe in order in the past? Why, in the past, was entropy lower?
If we observe a phenomenon that begins in a state of lower entropy, it is clear why entropy increases—because in the process of reshuffling, everything becomes disordered. But why do the phenomena that we observe around us in the cosmos begin in a state of lower entropy in the first place?
Here we get to the key point. If the first twenty-six cards in a pack are all red and the next twenty-six are all black, we say that the configuration of the cards is “particular,” that it is “ordered.” This order is lost when the pack is shuffled. The initial ordered configuration is a configuration “of low entropy.” But notice that it is particular if we look at the color of the cards—red or black. It is particular because I am looking at the color. Another configuration will be particular if the first twenty-six cards consist of only hearts and spades. Or if they are all odd numbers, or the twenty-six most creased cards in the pack, or exactly the same twenty-six of three days ago. . . . Or if they share any other characteristic. If we think about it carefully, every configuration is particular, every configuration is singular, if we look at all of its details, since every configuration always has something about it that characterizes it in a unique way. Just as, to its mother, every child is particular and unique.
It follows that the notion of certain configurations being more particular than others (twenty-six red cards followed by twenty-six black, for example) makes sense only if I limit myself to noticing only certain aspects of the cards (in this case, the colors). If I distinguish between all the cards, the configurations are all equivalent: none of them is more or less particular than others.18 The notion of “particularity” is born only at the moment we begin to see the universe in a blurred and approximate way.
Boltzmann has shown that entropy exists because we describe the world in a blurred fashion. He has demonstrated that entropy is precisely the quantity that counts how many are the different configurations that our blurred vision does not distinguish between. Heat, entropy, and the lower entropy of the past are notions that belong to an approximate, statistical description of nature.
The difference between past and future is deeply linked to this blurring. . . . So if I could take into account all the details of the exact, microscopic state of the world, would the characteristic aspects of the flowing of time disappear?
Yes. If I observe the microscopic state of things, then the difference between past and future vanishes. The future of the world, for instance, is determined by its present state—though neither more nor less than is the past.19 We often say that causes precede effects and yet, in the elementary grammar of things, there is no distinction between “cause” and “effect.”* There are regularities, represented by what we call physical laws, that link events of different times, but they are symmetric between future and past. In a microscopic description, there can be no sense in which the past is different from the future.*
This is the disconcerting conclusion that emerges from Boltzmann’s work: the difference between the past and the future refers only to our own blurred vision of the world. It’s a conclusion that leaves us flabbergasted: is it really possible that a perception so vivid, basic, existential—my perception of the passage of time—depends on the fact that I cannot apprehend the world in all of its minute detail? On a kind of distortion that’s produced by myopia? Is it true that, if I could see exactly and take into consideration the actual dance of millions of molecules, then the future would be “just like” the past? Is it possible that I have as much knowledge of the past—or ignorance of it—as I do of the future? Even allowing for the fact that our perceptions of the world are frequently wrong, can the world really be so profoundly different from our perception of it as this?
All this undermines the very basis of our usual way of understanding time. It provokes incredulity, just as much as the discovery of the movement of the Earth did. But just as with the movement of the Earth, the evidence is overwhelming: all the phenomena that characterize the flowing of time are reduced to a “particular” state in the world’s past, the “particularity” of which may be attributed to the blurring of our perspective.
Later on, I will delve into the mystery of this blurring, to see how it is tied to the strange initial improbability of the universe. For now, I will end with the mind-boggling fact that entropy, as Boltzmann fully understood, is nothing other than the number of microscopic states that our blurred vision of the world fails to distinguish.
The equation that states precisely this20 is carved on Boltzmann’s tomb in Vienna, above a marble bust that portrays him as an austere and surly figure, such as I don’t believe he ever was in life. Many young students of physics go to visit his tomb, and linger there to ponder. And sometimes the odd elderly professor of physics as well.
Time has lost another of its crucial components: the intrinsic difference between past and future. Boltzmann understood that there is nothing intrinsic about the flowing of time. That it is only the blurred reflection of a mysterious improbability of the universe at a point in the past.
The source of Rilke’s “eternal current” is nothing other than this.
Appointed a university professor at just twenty-five years old; received at court by the emperor at the apex of his success; severely criticized by the majority of the academic world, which did not understand his ideas; always precariously balanced between enthusiasm and depression: the “dear sweet chubby one,” Ludwig Boltzmann, will end his life by hanging himself.
He does so at Duino, near Trieste, while his wife and daughter are swimming in the Adriatic.
The same Duino where, just a few years later, Rilke will write his Elegy.
3 THE END OF THE PRESENT
It opens
to this gentle breeze
of Spring
the sealed-in cold
of the still season,
and the boats return to the sea . . .
Now we must braid
crowns with which
to adorn our heads. (I, 4)
SPEED ALSO SLOWS DOWN TIME
Ten years before understanding that time is slowed down by mass,21 Einstein had realized that it was slowed down by speed.22 The consequence of this discovery for our basic intuitive perception of time is the most devastating of all.
The fact itself is quite simple. Instead of sending the two friends from the first chapter to the mountains and the plains, respectively, let’s ask one of them to stay still and the other one to walk around. Time passes more slowly for the one who keeps moving.
As before, the two friends experience different durations: the one who moves ages less quickly, his watch marks less time passing; he has less time in which to think; the plant he is carrying takes longer to germinate, and so on. For everything that moves, time passes more slowly.