the universe is governed by a set of rational laws that we can discover and understand.

Instead, we may have to use different reflections of the underlying theory in different situations.

When he looked at the planet Jupiter, Galileo found that it was accompanied by several small satellites or moons that orbited around it.

Having discovered almost by accident that elliptical orbits fit the observations well, he could not reconcile them with his idea that the planets were made to orbit the sun by magnetic forces.

As philosopher of science Karl Popper has emphasized, a good theory is characterized by the fact that it makes a number of predictions that could in principle be disproved or falsified by observation.

Unfortunately, however, these two theories are known to be inconsistent with each other—they cannot both be correct.

It can in fact never reach the speed of light, because by then its mass would have become infinite, and by the equivalence of mass and energy, it would have taken an infinite amount of energy to get it there.

Einstein made the revolutionary suggestion that gravity is not a force like other forces, but is a consequence of the fact that space-time is not flat, as had been previously assumed: it is curved, or “warped,” by the distribution of mass and energy in it.

when a body moves, or a force acts, it affects the curvature of space and time—and in turn the structure of space-time affects the way in which bodies move and forces act.

the farther a galaxy is, the faster it is moving away!

there must have been a big bang singularity provided only that general relativity is correct and the universe contains as much matter as we observe.

the singularity theorems really show is that there must have been a time in the very early universe when the universe was so small that one could no longer ignore the small-scale effects of the other great partial theory of the twentieth century, quantum mechanics.

Instead, they had a quantum state, which was a combination of position and velocity.

Each electron, therefore, must be passing through both slits at the same time!

The basic idea of GUTs is as follows: as was mentioned above, the strong nuclear force gets weaker at high energies. On the other hand, the electromagnetic and weak forces, which are not asymptotically free, get stronger at high energies. At some very high energy, called the grand unification energy, these three forces would all have the same strength and so could just be different aspects of a single force.

Thus our very existence could be regarded as a confirmation of grand unified theories, though a qualitative one only; the uncertainties are such that one cannot predict the numbers of quarks that will be left after the annihilation, or even whether it would be quarks or antiquarks that would remain.

In some cases they may explode or manage to throw off enough matter to reduce their mass below the limit and so avoid catastrophic gravitational collapse, but it was difficult to believe that this always happened, no matter how big the star.

For example, observations with the Hubble telescope of the galaxy known as M87 reveal that it contains a disk of gas 130 light-years across rotating about a central object two thousand million times the mass of the sun.

the area of the event horizon might stay the same or increase with time, but it could never decrease

the area of the event horizon was a measure of the entropy of the black hole.

The universe would be completely self-contained and not affected by anything outside itself. It would neither be created nor destroyed. It would just BE.

The uncertainty principle implies that the early universe cannot have been completely uniform because there must have been some uncertainties or fluctuations in the positions and velocities of the particles.

In 1992 the Cosmic Background Explorer satellite (COBE) first detected very slight variations in the intensity of the microwave background with direction.

Thus the heat expelled by the computer’s cooling fan means that when a computer records an item in memory, the total amount of disorder in the universe still goes up.

I realized that I had made a mistake: the no boundary condition implied that disorder would in fact continue to increase during the contraction.

Thus intelligent life could not exist in the contracting phase of the universe.

In other words, quantum theory allows the energy density to be negative in some places, provided that this is made up for by positive energy densities in other places, so that the total energy remains positive.

However, as has been described in earlier chapters, the classical laws were superseded by quantum laws based on the uncertainty principle.

According to this viewpoint, you could not go back in time unless history showed that you had already arrived in the past and, while there, had not killed your great-great-grandfather or committed any other acts that would conflict with your current situation in the present.

This says that the laws of physics conspire to prevent macroscopic bodies from carrying information into the past.

Of course, extra space-time dimensions are a commonplace of science fiction indeed, they provide an ideal way of overcoming the normal restriction of general relativity that one cannot travel faster than light or back in time (see Chapter 10).

Thus the electrons would either escape from the atom altogether or would spiral into the nucleus. In either case, one could not have atoms as we know them.

If one had a particle with an energy above what is called the Planck energy, ten million million million GeV (1 followed by nineteen zeros), its mass would be so concentrated that it would cut itself off from the rest of the universe and form a little black hole.

The unpredictable, random element comes in only when we try to interpret the wave in terms of the positions and velocities of particles.

What is it that breathes fire into the equations and makes a universe for them to describe?

His advocacy of civil disobedience and public encouragement of people to refuse conscription did little to endear him to his colleagues.

But even before the first atomic bomb had been detonated, he was publicly warning of the dangers of nuclear war and proposing international control of nuclear weaponry.

Equations are more important to me, because politics is for the present, but an equation is something for eternity.

Galileo, perhaps more than any other single person, was responsible for the birth of modern science. His renowned conflict with the Catholic Church was central to his philosophy, for Galileo was one of the first to argue that man could hope to understand how the world works, and, moreover, that we could do this by observing the real world.

But the Church was afraid of a scandal that might undermine its fight against Protestantism, and so took repressive measures.

Soon the Pope, realizing that people were seeing the book as a convincing argument in favor of Copernicanism, regretted having allowed its publication.

Newton was incensed and sought his revenge by systematically deleting all references to Flamsteed in later editions of Principia.

Newton, as president, appointed an “impartial” committee to investigate, coincidentally consisting entirely of Newton’s friends!

successfully conducting a major campaign against counterfeiting, even sending several men to their death on the gallows.