Unique forms of
continuity in the
space-time tissue

Michele DiEgo

Einstein showed that if you get bored, time passes more slowly and if you have fun, time passes more quickly. I remember this phrase well, I heard it when I was about fifteen years old whilst I was on a trip to Cambridge. It was stated by my tour guide in front of the Corpus Clock, the huge golden clock on which a disturbing grasshopper eats time insatiably. At the time I didn’t know I was going to become a physicist; I didn’t know that this phrase would sound like heresy to me in the future.

22 April 1899, 26 September 1905, 11 April 1913: three moments in time, linked to three works that deal with time. 1905 is year zero, the watershed between the classical conception of time and the modern one. It is also called Albert Einstein’s Annus mirabilis, in which the German physicist radically changes our perception of space, time, mass and energy. 

Man’s progress has created new, curved, dynamic space and time, ready to appear and disappear from it.

Until then, Galileo’s transformations were used to describe the same physical phenomenon from different points of view (which are called different reference systems).
Let’s imagine, for example, that we are in a coach of a moving train. If we are seated, we have the perception of being stationary, if we walk, we feel we are travelling at the same speed as though we were walking on the ground. For us, the train’s movement is not perceived. Exactly in the same way as we do not perceive the movement of the Earth: none of us realize that we are orbiting the Sun, nor that the solar system itself is moving within the Milky Way, moving in the deep universe. But the stationmaster sitting in the train station sees us inside the train in a completely different way: if we are seated, the stationmaster sees us moving at the same speed as the train; if we are walking in the coach, he sees us moving at the train’s plus our own speed. If, for example, we were walking very fast, at the same speed as the train and in the same direction, the stationmaster would see us moving at twice the train’s speed (as in airports, where the so-called “moving walkways” allow us to walk much faster than our legs would allow). If we moved at the same speed as the train, but in the opposite direction of its travel, the stationmaster would see us standing still (like on a treadmill, where you run while standing still).
Nevertheless, despite the different judgements about the movement of the bodies of those in the train and those on the ground, all physics, from whatever chosen reference system, always matches up, always giving unambiguous results: the physics of objects is not influenced by your point of observation. Speed is added up and subtracted in such a way that any onlooker, regardless of their point of observation, will obtain the same results of the world’s phenomena.
Let’s continue with our example: we are seated inside the train, but we decide to stand up and walk for a minute until we reach the dining car. From our point of view, the movement of the train is irrelevant, the speed of our legs is the only variable that determines the time it took to reach our destination. But of course, for the stationmaster who looks at us from the ground, things change: as we walk inside the train, he sees the dining car moving away from us, since the train is also moving. At the same time, however, from his point of view, we too employ the speed of the train to move much faster than we would be able to on ground. Therefore, the net result is that, thanks to the perfect balance of velocity, even in the opinion of the train conductor, it takes us a minute to reach the dining car.
Generally, we can say that the Galilean universe is one in which every spectator, from any reference system, can give an equivalent physical description of the phenomena. Physics describes history unequivocally and unambiguously. Space is conceived as something static, rigid, like an imaginary grid of immobile and immutable steel, within which objects move. And this movement is marked by a single, universal and immutable metronome that is absolute time, imagined as an entity outside of space.

22 April 1899 – pre-Annus mirabilis era, Venice Biennale
Gaetano Previati exhibits his work “The dance of the hours”. The painting represents Earth surrounded by twelve gigantic female figures; gigantic but graceful, in a harmonious flight around the cosmos powerfully illuminated by a distant Sun. As they dance, the women hold a large golden ring on their fingertips. The figures represent the hours in their cyclical dance, the circle represents time, like the mechanism of a clock. And these hours dance on the Earth’s globe without experiencing any influence by it, they surround it, they dominate it. There is joy in their perpetual and inexorable rotation. It is Galileo’s Absolute Time, the insatiable grasshopper who cruelly eats the hours, the metronome that makes everything proceed at the same rhythm.

26 September 1905, Annalen der Physik (Germany)
Albert Einstein’s Annus mirabilis, year zero of time. The German physicist published the work “On the electrodynamics of bodies in motion”, which went down in history as “Theory of special relativity”. The first postulate of the theory completely breaks with the physics known until that time: the speed of light is the same in every reference system. So, what does it mean? Returning to our train, if we are sitting inside the moving train and turn on a laser beam, we see it traveling at three hundred thousand kilometers per second. What about the stationmaster sitting at the train station? He also sees the beam moving at three hundred thousand kilometers per second. Unlike our walking speed, there is no sum between the laser beam’s speed and that of the moving train. Therefore, if for us, sitting on board the train, the light took a certain amount of time to reach the dining car, it must have taken the stationmaster longer time because while the light was moving, the train was also moving forward. Two different observers have established that the time needed for the same event to happen (the arrival of the laser beam to the restaurant car) is not univocal, it depends on where the phenomenon was looked at. And which one is right? Both: relativistic physics loses its absoluteness.
One may be led to think that this is an effect due to the immateriality of light that makes it completely different from any other moving object. Nothing could be more wrong. The truth is that in no case, for any body, material or immaterial, Galileo’s laws of summation of velocities are correct. Simply the closer the velocities at stake are to those of light, the more obvious the error appears. For low speeds, like a walking man or a moving train, it is impossible to notice the relativistic effect and certainly Galileo could not notice it with the instruments of his time. But if a man could walk at speeds similar to those of light, the effect would be the same as the laser beam.
The example cited may seem bizarre without consequences, a paradox that can be ignored, but it is actually only one of the infinite twists and turns of events that Einstein’s relativity entails. Twists that affect any object in motion at any speed but whose effects begin to become not insignificant only at very high speeds.
The universe conceived by Einstein is a universe in which the concept of simultaneity of events is lost: two events can happen simultaneously in one reference system and out of phase in another. Time itself slows down for moving bodies: the faster a body moves, the more its time slows down. Lengths are no longer absolute: a body shortens the higher its speed. It does not shorten because of a compression effect but because its geometric space shrinks. The mass of a body becomes a function of its speed: the faster a body moves, the more its mass increases, making its acceleration more and more difficult. Any body endowed with mass, if accelerated at the speed of light, will have infinite mass (in fact every particle that moves at the speed of light is not endowed with mass). In a state of stillness, every body possesses enormous energy, derived from the mere fact of possessing mass (E=mc2).
One could continue with apparent paradoxical examples for hours. Let’s imagine two photons (the particles that make up light) chasing each other. An external observer would first notice that the two particles move at the same speed and then, that the furthest photon would never be able to reach the one ahead. What if we moved the observation to the two photons, imagining that we could ride them? If we sat on the furthest photon, our photon would be stationary compared to us, and the photon in front of us would move at three hundred thousand kilometers per second: it would be out of our reach in an instant by gradually increasing the distance between us. What if we put ourselves on the photon further ahead? We would be stationary on the photon, and we would see the other photon coming towards us at the speed of light. Then in three different reference systems we would see: the two photons endlessly chasing each other at the same distance; the photon ahead leaving the other behind at a remarkable speed, increasing in every instant the advantage it has over it; the photon left behind reaching ever so faster the one ahead. Three totally opposite visions, born from three different perspectives, all three equally valid.
Moreover, for physics, motion is always relative: if we are sitting inside a moving train, we can describe the situation as if the train were standstill and the rest of the world is moving against it. For Einstein, this means that if we see a moving body (and therefore for it time runs slower, the lengths are shortened, the mass increases), the body sees us moving with the same speed in the opposite direction and therefore, for him, it is us who have slower time, shortened lengths and increased mass.
It is difficult for us to conceive all these seemingly senseless phenomena. We’re not designed to intuit them. Our daily life is made up of bodies that move at speeds slow enough to allow us to ignore all relative phenomena and to allow us to live with a mindset shaped on an approximation, that of Galileo. Yet it is we that live in error, even though this error is infinitely small compared to for the speeds to which we are accustomed. Einstein’s universe, on the other hand, transcends our common thinking, but it is enormously closer to the truth of nature than Galileo’s one. Einstein’s universe is a universe in which space and time are fused together to create a dynamic space-time tissue, perpetually subject to stretching and contracting. Time is a local variable, not absolute as it was before. Every observer has his own space and time, there is no longer any absolute metronome, there is no longer any dance of the hours.

11 April 1912 – post-Annus mirabilis era, Milan
Umberto Boccioni publishes the “Technical manifesto of futurist sculpture”. Inside it one reads phrases such as: “There can be no renewal in an art if its essence is not renewed, that is, the vision and conception of the line and the masses that form the arabesque”. And again: “We must start from the central nucleus of the object we want to create, to discover new laws, that is the new forms that invisibly but mathematically link it to the apparent plastic infinity and to the inner plastic infinity”.
Boccioni looks for an innovation tout court, a paradigm shift that disintegrates the past. And this innovation takes place according to futuristic canons of dynamics, speed and vibration. His revolution is similar to that applied by Einstein in a different field. I cannot say that Boccioni knew Einstein’s theories well enough to be directly influenced by them, but evidently the artist felt an instinctive – albeit unconscious – affinity between Einstein’s space-time tissue and the futurist world in which he wanted to project his art.
In fact, the sculpture’s “Unique forms of continuity in space” is a formidable representation of the new space-time. The sculpture (also represented on the back of Italy’s 20-euro cents) shows a man in movement, or rather: the movement of a man. The movement is the real protagonist of the work, the man is only his original source relegated to the background. The movement deforms space, it describes surfaces and volumes that arise from the movement itself and fold into it. Man’s progress creates a new, curved, dynamic space and time, ready to appear and disappear in it. The exact opposite of Previati’s “The Dance of the hours”: in the post-1905 era, Boccioni realizes that even in art there is no longer a rigid, unmodified space, with a common time, outside the world; it is the individual who generates his own space-time universe. Moreover, the individual is divided into muscles, limbs, in an infinite continuity of points. Thus it is the movement, being non-uniform, that creates new time frames and new spaces in each point. The individual is crossed by infinite space- time microcosms that are born and implode in movement: an infinitely complex war in which we are constantly immersed. Einstein managed to describe the war in mathematical terms, Boccioni managed to sculpt it.