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September 7 - September 10, 2020
My father, a man of rare intelligence, was an engineer who ran a small business. I got from him the pleasure of trying to understand the world in an intelligent way. My mother, a real Italian mother full of excessive love for her only child, helped me with the “investigations” I did for elementary school, and stimulated my curiosity for discovery and learning.
Science has therefore been a compromise for me: the possibility of not giving up the desire for change and adventure, to maintain my freedom of thinking and to be what I am, without too much into conflict with the world around me; on the contrary, by doing something which the world appreciates. I believe that much intellectual or artistic work is born from this conflict: it is a kind of refuge for potential misfits.
Without this desire for change, civilisation would not have grown and would not have reached the point where it is now; we would still be adoring the pharaohs.
It is the people who lived dreams who in the past have been able to think and construct our world, and only from many new dreams can the future be born.
Today, in reality, we no longer know very well what space is, what time is and what matter is. The problem of reconciling these two visions of the world is the problem of quantum gravity. It is a fundamental problem of greatest importance at
stroke of genius of Maxwell is to have understood that light is nothing else but the fast undulatory movement of those lines.
In fact, people often say that the fields are “invisible”: nothing more false, because we see nothing but the fields!
Space and gravitational field are the same entity: from then on, when one says space one also means gravitational field, and when one says gravitational field one also means space. It is an unexpected and spectacular discovery.
Hence, the world is not made of particles and fields that live in space, but of particles and fields, and this is all. Particles and fields do not live in space: they live on another field, i.e. fields live, so to say, on top of one another. We live on the gravitational field or within the gravitational field, not on a fixed table-space.
The electromagnetic field for example, if observed at a small scale, is made of grains or “quanta” that are called photons.
Thus, quantum mechanics is the discovery that at small scale the world is granular and non deterministic.
If one now combines the basic ideas of general relativity and quantum mechanics, it follows immediately that since space is a field (the gravitational field) space must have a granular structure, as does the electromagnetic field. The quanta of the electromagnetic field are the photons. The quanta of the gravitational field must be “grains of space”, because the gravitational field is the physical space. The dynamics of these grains must be probabilistic. Hence space (i.e. the gravitational field) must be described as “clouds of probability of grains of space”.
The problem of quantum gravity is how to construct a mathematical theory describing these probability clouds of grains of space, and to understand what it means.
The solution determined by a single loop represents a universe consisting only by a thin ringlet of space and nothing else. In other words, space without these “loops of gravity” does not exist, because the loops themselves and their relations constitute space. The existence of these universes made of a single loop was the first concrete indication of the quantum granularity of space.
From Aristotle to Descartes, space has been more often described as a relation and not as an entity. This means that space does not exist if there are no objects. Space is the relation between dynamical objects, like a marriage is a relation between two individuals: there is no marriage without the two individuals. More precisely, space is the relation of adjacency, namely of being in touch, between objects. Newton introduced space as an entity “within
Space is not an entity within which things are located: the space-entity does not exist. What exist is the gravitational field together with the other fields. In loop quantum gravity, the loops are quanta of the gravitational field and it is their relationships which constitute space.
Very often to be aware of your own assumptions is far better than to be guided by methodological prejudices of which you are unaware.
In quantum mechanics many quantities are “quantized”. This means that they can only assume certain discrete values and not just any value. The energy of an ato m, for example, cannot have arbitrary values, but only certain special values that are called energy levels of the atom. To calculate the values that a quantity may have one uses a mathematical technique which is called “calculation of the spectrum of an operator”. Lee and I were interested in a particular physical quantity: the volume.
What is a volume? It is the measure of how much space there is. The volume of a room is the quantity of space there is in the room.
The result of the calculation turned out to be that volume really is not a continuous variable; it is discrete, and hence that space is constituted of quanta of volume, or quanta of space. But this is not all: we also realized that these quanta of volume resided exactly on the intersections of the loops. In other words, the volume is composed of quanta, of finite grains of space, and the intersections of the loops represent precisely these grains of space. They are the grains of space we were looking for from the start.
The intersection points became more important than the lines themselves: we no longer spoke of a collection of loops intersecting at points, but rather of a collection of points interconnected by lines, that is of a network.
When we say that the volume of a room is, for example, 100 cubic metres, in reality we are counting how many grains of space, or rather how many “quanta of the gravitational field” there are in the room. Obviously these quanta are very small. In a room of 100 cubic metres their number is a figure of about one hundred digits. The calculation of the volume spectrum yields exactly the values of the volume that can be observed.
The theory therefore predicts with precision a set of numbers representing the possible results of very precise area and volume measurements.
Stephen discovered that black holes are “hot”, that is, they behave exactly like hot bodies: they emit thermal radiation at a certain temperature.
If a black hole is hot, what are its elementary vibrating “atoms”? Loop theory offers a precise answer to this question. The elementary “atoms” of a black hole which vibrate and are responsible for its temperature, are precisely the individual loops sitting on the surface of the black hole. Using this theory one has been able to understand the result of Hawking in terms of the microscopic “vibrations” of the loops, and to calculate explicitly the temperature predicted by Hawking.
Remarkably, one finds that the equations of loop quantum gravity do not break down at this point, as do the Einstein equations. Therefore, the equations are capable of describing the Big Bang itself.
To understand how, recall that when light propagates in a crystal, the different wavelengths, namely the different colours, travel at slightly different speed. The microstructure of space might affect the propagation of light in the same manner.
If so, we should receive the different components (with different colour) of the light of distant stars with small time delays with respect to one another. This may be tested and precise observations are under way. The problem is that this effect is difficult to compute within the theory, and therefore it is not completely clear what the theory really predicts.
In most equations of classical physics time occurs. It is the variable indicated by the letter “t”.
More precisely, we measure variables, for instance the position A of an object, the amplitude B of an oscillating pendulum, the temperature C of a body, etc. and the equations tell us how these variables A, B and C change in time. That is, equations determine the functions A(t), B(t), C(t) and so forth, that describe the change of these variables through time “t”.
Thus one could measure the time by simply counting the oscillations of a pendulum.
What we have to do to avoid using “t” is simply to restrict ourselves to list the variables A, B, C... that we effectively observe, and establish relations between these variables. We have to write equations for the functions A(B), B(C), C(A)... that we do observe; and not for the functions A(t), B(t), C(t), that we do not observe. In the example, we will not have the pulse and the pendulum that both evolve in time, but only equations that tell us how the one and the other may evolve with respect to one another. Not “how many beats per second and how many oscillations per second”; but only
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At the fundamental level there is no time. This impression of “time flow” that we all have is only an approximation that is only valuable for our macroscopic scales, and derives only from the fact that we observe the world only in a very coarse way. The elementary structure of physical reality is timeless.
A novel image of the world is taking shape: a world without space and without time. The space where the world “inhabits” and the time “along which” things evolve might soon disappear from our fundamental description of the physical world, in the same manner in which notions such as “the centre of the universe” have disappeared in the past.
One of these problems is the following: if time does not exist at the fundamental level, what about the time we do perceive as the time that flows; what could that be?
We rarely have complete control over all the variables of a problem. When we do, we can verify that the system is governed by dynamical equations in which, at the fundamental level, as we have seen, time does not appear. However, most of the time we measure only a tiny fraction of the innumerable variables that characterize the system. For example, if we study a piece of metal at a certain temperature, we can measure its temperature, its length, its position, the speed at which the piece of iron is moving, but not the microscopic movements of each of its little atoms which, as we know, are
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For example, if we study a piece of metal at a certain temperature, we can measure its temperature, its length, its position, the speed at which the piece of iron is moving, but not the microscopic movements of each of its little atoms which, as we know, are responsible for the temperature. In these cases we not only use the equations of dynamics to describe the physics of the object, but also those of statistical mechanics and thermodynamics.
That is to say that time is an effect of our ignorance of the details of the world. If we had complete knowledge of all the details of the world, we would not have the sensation of the flow of time.
For a European, though, to stay in the United States is also difficult. The values are different, human relations are different. Too many aspects of American culture are intolerable for a European: the urban violence, the racial tensions, the death penalty, the absence of medical assistance for all and of social security, the abandonment of the weakest and the poor to their fate, the arrogance of money and power. The very idea of “social justice” is understood in almost exactly opposite manners, the two sides of the Atlantic. In the US, social justice means that anybody who has the capacities
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The positive interpretation is that the catastrophe of the last World War has left a bit of wisdom into the European soul, and the awareness that collaboration is better than confrontation.
In spite of an apparent resemblance between strings and loops, the difference is substantial: strings are little cords that move around within space, unlike loops which are themselves space.
String theory has emerged from the community of the high-energy physicists that studied the elementary particles. This community that has obtained spectacular scientific successes during the twentieth century, and is therefore proud of its own peculiar methods, in particular quantum field theory.
Loop theory, on the other hand, has grown more from the community of the relativists, the specialists of general relativity. This is a community, clearly, far more aware of the specific physical meaning of general relativity, and less impressed, on the other hand, by the techniques of quantum field theory. For a relativist, therefore, quantum gravity is more about incorporating quantum field theory into the conceptual revolution of general relativity, than in taming general relativity into conventional quantum field theory.
One part of physics is concerned with applying these equations to understand this or that phenomenon. Another part, however, is concerned with seeking these fundamental equations: this is called fundamental physics.
Fundamental science is always motivated almost uniquely by curiosity. By the “desire to know”. Without fundamental science the whole of science would not exist. Without
What fascinates me most in science is the possibility of continually re-discussing ourselves and our very way of thinking.
Science is not credible because it is absolutely true. But because on a large number of problems, it is the best answer we have found so far. It is precisely the fact that scientific knowledge changes, which makes scientific knowledge so strong. Science is based on doubt, and this is the opposite of most of non-scientific thinking.
The worst enemies of knowledge are those who are certain that they already know the truth.
Science is the result of the opposite attitude. Questioning encrusted assumptions, be ready to see the world with new eyes. Knowing that what we know might be incorrect. Be open to change.
Science is born when certainties, myths and old values are questioned and discussed, and one looks at the world with new eyes, like a child which is still open to everything.
