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January 20 - February 6, 2018
Volume is a geometrical quantity which depends on the geometry of space, but the geometry of space – as Einstein understood, and as I recounted in Chapter 3 – is the gravitational field. Volume is therefore a property of the gravitational field, expressing how much gravitational field there is between the walls of the room.
General relativity taught us that space is something dynamic, like the electromagnetic field: an immense, mobile mollusc in which we are immersed, which stretches and bends.
Quantum mechanics teaches us that every field of this sort is made of quanta, that is to say, it has a fine, granular structure.
Space is created by the interaction of individual quanta of gravity.
It must not be claimed that anyone can sense time by itself apart from the movement of things. – Lucretius, De rerum natura
As we abandon the idea of space as an inert container, similarly, we must abandon the idea of time as an inert flow along which reality unfurls.
First, the absence of the variable time from the fundamental equations does not imply that everything is immobile and that change does not happen. On the contrary, it means that change is ubiquitous.
It means that we, in reality, never measure time itself; we always measure the physical variables A, B, C … (oscillations, beats, and many other things) and compare one variable with another, that is to say, we measure the functions A(B), B(C), C(A), and so on.
In other words, the existence of the variable time is a useful assumption, not the result of an observation.
There is no longer space which contains the world, and no longer time during the course of which events occur. There are elementary processes in which the quanta of space and matter continuously interact with each other.
The singularities which render Einstein’s equations absurd when the gravitational field becomes too strong also disappear: they are only the result of neglecting the quantization of the field.
But the word ‘universe’ has assumed another meaning in cosmology: it refers to the spacetime continuum that we see directly around us, filled with galaxies the geometry and history of which we observe.
The objective of scientific research is not just to arrive at predictions: it is to understand how the world functions; to construct and develop an image of the world, a conceptual structure to enable us to think about it. Before being technical, science is visionary.
Our fantasy is too limited to ‘imagine’ how the world may be made, unless we search for inspiration in the traces we have at our disposal.
The surface of a black hole is like the present: it can be crossed only in one direction. From the future, there is no return. For a black hole, the past is the outside; the future is the inside. Seen from outside, a black hole is like a sphere which can be entered
Quantum uncertainty across the horizon of the black hole generates fluctuations of the horizon’s geometry. But fluctuations imply probability, and probability implies thermodynamics, and therefore temperature.
After this time, we can see the black hole explode. In the end, basically, this is what a black hole is: a shortcut to the distant future.
Special relativity may be summarized as the discovery that there exists a maximum velocity for all physical systems.
Quantum mechanics can be summarized as the discovery that there exists a maximum of information for each physical system.
It suggests that what we call infinite often is nothing more than something which we have not yet counted, or understood.
The point at stake here is not the presumption of knowing everything. It is the opposite: an awareness that yesterday’s ignorance may have light shed on it today, and that today’s might be illuminated tomorrow.
The only truly infinite thing is our ignorance.
If this chapter seems particularly opaque, it’s not because your ideas are confused. It’s because the one with the confused ideas is me.
The scientific notion of information, however, was defined with clarity in 1948, by the American mathematician and engineer Claude Shannon, and is something very simple: information is the measure of the number of possible alternatives for something.
scientists measure information in terms of a quantity called S, for ‘Shannon information’. S is defined as the logarithm in base 2 of N: S = log2 N.
The total number of alternatives is then only 2 (white-black or black-white), even if the alternatives are still two on my part and two on yours. Note that, in this situation, something peculiar happens: if you look at your ball, then you know the colour of mine. In this case, we say that the colours of the two balls are correlated, that is to say, linked to one another. We say that my ball ‘has information’ about yours (as well as vice versa).
But what does a telephone line carry? It carries information. It carries the capacity to distinguish between alternatives. For this reason, Shannon defined information.
The world isn’t, then, just a network of colliding atoms: it is also a network of correlations between sets of atoms, a network of real reciprocal information between physical systems.
Why does it cool down? Boltzmann hazarded a splendid hypothesis: because the number of possible states of the molecules in hot tea and cold air is smaller than the number in cool tea and slightly warmer air.
His tomb is incised with his formula S = k log W which expresses (missing) information as the logarithm of the number of alternatives, Shannon’s key idea.
Entropy is ‘missing information’, that is, information with a minus sign. The total amount of entropy can only increase, because information can only diminish.fn50
not just general relativity and quantum mechanics, but also the theory of heat, that is, statistical mechanics and thermodynamics, which we can also describe as information theory.
What does ‘the passage of time’ mean, if time plays no part in the fundamental description of the world?
The origin of time may be similar to that of heat: it comes from averages of many microscopic variables.
The salient characteristic of time is that it moves forwards and not backwards, that is to say, there are irreversible phenomena.
But when the stone reaches the ground and stops, where does its energy go? It heats the ground! At the precise moment when heat is produced, the process is irreversible: the past differs from the future. It is always heat and only heat that distinguishes the past from the future.
But the limitations of our intuitions should not mislead us. Understanding the world better often entails going against intuition.
Time is an effect of our overlooking of the physical microstates of things. Time is information we don’t have. Time is our ignorance.
Perhaps because we must not confuse what we know about a system with the absolute state of the same system.
What we know is something concerning the relation between the system and ourselves. Knowledge is intrinsically relational; it depends just as much on its object as upon its subject.
Classical mechanics misled us into thinking that we could do without taking account of this simple truth, and that we could access, at least in theory, a vision of reality entirely independent of the observer. But the development of phy...
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I believe that in order to understand reality we have to keep in mind that reality is this network of relations, of reciprocal information, which weaves the world. We slice up the reality surrounding us into objects. But reality is not made up of discrete objects. It is a variable flux. Think of an ocean wave. Where does a wave finish? Where does it begin? Think of mountains. Where does a mountain start? Where does it end? How far does it continue beneath the Earth’s surface?
A child begins to live on the day when a person dreams of her for the first time, long before her conception, or when she forms her first self-image, or when she breathes for the first time, or when she recognizes her name, or when we apply any number of other conventions: they are all useful, but arbitrary. They are ways to think, and to orientate ourselves within the complexity of reality.
Democritus gave a strange definition of ‘man’: ‘Man is what we all know.’2 At first sight, this seems rather silly and empty, but it is not so.
The nature of a man is not his internal structure but the network of personal, familial and social interactions within which he exists. It is these which ‘make’ us, these which guard us. As humans, we are that which others know of us, that which we know of ourselves, and that which others know about our knowledge. We are complex nodes in a rich web of reciprocal information.
Awareness of the limits of our knowledge is also awareness of the fact that what we know may turn out to be wrong, or inexact.
To learn something, it is necessary to have the courage to accept that what we think we know, including our most rooted convictions, may be wrong, or at least naïve: shadows on the walls of Plato’s cave.
Science is born from this act of humility: not trusting blindly in our past knowledge and our intuition. Not believing what everyone says. Not having faith in the accumulated knowledge of our fathers and grandfathers. We learn nothing if we think that we already know the essentials, if we assume that they were written in a book or known by the elders of the tribe.
As every researcher working in every laboratory throughout the world knows, doing science means coming up hard against the limits of your ignorance on a daily basis – the innumerable things which you don’t know, and can’t do. This is quite different from claiming to know everything.
Science is not reliable because it provides certainty. It is reliable because it provides us with the best answers we have at present. Science is the most we know so far about the problems confronting us. It is precisely its openness, the fact that it constantly calls current knowledge into question, which guarantees that the answers it offers are the best so far available: if you find better answers, these new answers become science.
