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November 18 - November 21, 2024
is an acceleration. The little moon accelerates toward the center of Earth.
Newton makes the simple calculation, and the result is . . . 9.8 meters per second per second!
endless spaces way out there, and superhuman silences, and profoundest quiet I picture to myself in thought . . . Figure 2.1 What is the world made of? Figure 2.2 The world of Newton: particles that move in space, as time passes, attracted by forces
the world consists only of a great infinite space where, as time passes, particles move and attract one another by means of forces. We can write precise equations that describe these forces. These equations prove to be immensely effective.
MICHAEL: FIELDS AND LIGHT
The first surprise is that almost all phenomena we see are governed by a single force, other than gravity: the force that today we call “electromagnetism.” It is this force that holds together the matter that forms solid bodies; holds together atoms in molecules, and electrons in atoms.
surprise, crucial to the story I’m telling, is that understanding this force requires an important modification to the world of Newton:
the notion of “field.”
he is led to an intuition that will become the basis of modern physics. He “sees” something new. His intuition is this: we must not think of forces acting directly between distant objects, as Newton presumed. We must instead think that there exists an entity diffused throughout space that is modified by electric and magnetic bodies
and that, in turn, acts upon (pushes and pulls) the bodies. This entity, whose existence Faraday intuits, is today called the “field.”
bundles of very thin lines (infinitely thin), which fill space: an invisible gigantic...
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around us. He calls these lines “lines of force,” because in some way these lines “carry the force”: they transmit the electric and the magnetic forces from one body to anot...
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These are Maxwell’s equations. They describe the behavior of the electric and the magnetic fields, the mathematical version of the “Faraday lines.”*
Maxwell’s equations tell us what light is. Maxwell realizes that his equations predict that Faraday’s lines can tremble and undulate, just like the waves of the sea. He computes the speed at which the undulations of Faraday’s lines move, and the result turns out to be . . . the same as for light! Why? Maxwell understands: because light is nothing other than this rapid trembling of Faraday’s lines! Not only have Faraday and Maxwell figured out how electricity and magnetism work, but with the same stroke, as a collateral effect, they have figured out what light is.
What is color? Put simply, it is the frequency (the speed of oscillation) of the electromagnetic wave light is. If the wave vibrates more rapidly, the light is bluer. If it vibrates a little more slowly, the light is redder.
Light is thus nothing more than a rapid vibration of the spiderweb of Faraday’s lines, which ripple like the surface of a lake as the wind blows.
Maxwell recognizes that the equations foresee that Faraday’s lines can also vibrate at much lower frequencies, that is to say slower than light. Therefore there must be other waves that nobody had ever yet seen, produced by the movement of electrical charges, and that in turn move electrical charges.
Only a few years later, these waves, anticipated theoretically by Maxwell, will be revealed by the German physicist Heinrich Hertz; and just a few years later still, Guglielmo Marconi builds the first radio.
Our entire current technology is founded on the use of a physical thing—electromagnetic waves—that was not discovered empirically: it was predicted by Maxwell,
The world has changed: no longer made up of particles in space, but of particles and fields in space
The deepening of our understanding of the world is based on two theories: general relativity and quantum mechanics.
These two theories—relativity and the quanta—provide the basis on which we are today building a quantum theory of gravity.
3 ALBERT
have already spoken of the first article, in which the young Albert calculates the dimensions of atoms and proves, after twenty-three
centuries, that the ideas of Democritus were correct: matter is granular.
The second article is the one for which Einstein is most famous: the article in which he introduc...
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In fact there are two theories of relativity. The envelope sent by the twenty-five-year-old Einstein contained the exposition of the first of these, the ...
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clarification of the structure of sp...
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The theories of Newton and of Maxwell appear to contradict each other in a subtle way. Maxwell’s equations determine a velocity: the velocity of light. But Newton’s mechanics are not compatible with the existence of a fundamental velocity, because what enters Newton’s equations is acceleration, not velocity.
velocity can only be velocity of something with respect to something else.
That is, there is no meaning to the velocity of an object by itself: the only velocity that exists is the velocity of an object with respect to another object.
But if this is so, then the speed of light determined by Maxwell’s equations is velocity with respect to what?
Einstein has claimed that he was not put on the right track by any experiments, but only by reflecting on the apparent contradiction between Maxwell’s equations and Newton’s mechanics. He asked himself whether there was a way of rendering Newton’s and Galileo’s core discoveries and Maxwell’s theory consistent.
think of all the past, present, and future events (with respect to the moment in which you are reading), and imagine them distributed
Between the past and the future of an event (for example, between the past and the future for you, where you are, and in the precise moment in which you are reading), there exists an “intermediate zone,” an “extended present”; a zone that is neither past nor future. This is the discovery made with special relativity.
very small and depends on where an event takes place relative to you,
the greater the distance of the event from you, the longer the duration of the extended present.
This means we can say that on Mars there are events that in this precise moment have already happened, events that are yet to happen, but also a quarter-of-an-hour of events during which things occur that are neither in our past nor in our future.
This is why it is impossible to hold a smooth conversation
Einstein has understood that “absolute simultaneity” does not exist: there is no collection of events in the universe that exist “now.”
The figure describes that which in physics is called “spacetime”: the set of all past and future events, but also those that are “neither-past-nor-future”; these do not form a single instant: they have a duration.
A first result of this restructuring is that as space and time fuse together in a single concept of spacetime, so the electric field and the magnetic fields fuse together in the same way, merging into a single entity that today we call the “electromagnetic field.”
Before 1905, two general principles appeared certain: conservation of mass, and conservation of energy.
But Einstein realizes that energy and mass are two facets of the same entity, just as the electric and magnetic fields are two facets of the same field, and as space and time are two facets of the one thing, spacetime. This implies that mass, by itself, is not conserved; and energy—as it was conceived at the time—is not independently conserved, either.
only one single law of conservation exists, not two. What is conserved is the sum of mass and energy, not each separately. Processes must exist that transform energy into mass, or mass into energy.
Since the speed of light, c, is a very large number, and c2 an even greater number, the energy obtained transforming one gram of mass is enormous; it is the energy of millions of bombs exploding at the same
“Space” does not exist independently from time.
The theory of general relativity is the most beautiful theory produced by physics, and the first of the pillars of quantum gravity.
THE MOST BEAUTIFUL OF THEORIES
special relativity does not square with what was known about gravity. He
