The Biggest Ideas in the Universe: Space, Time, and Motion

by Sean Carroll

Physics is made possible by this predictability. It may not be absolute, but we can somewhat anticipate what’s going to come next in the world if we know what’s going on right now. The most basic kind of predictability is conservation, the fact that some things don’t change at all.

Energy isn’t a kind of substance, like water or dirt. It’s a property that things have, depending on what they are and what kind of situation they’re in.

Mass, on the other hand, is an intrinsic property; roughly speaking, mass is the resistance that an object has to being accelerated.

Classical mechanics says that the world is made of things with definite, measurable values, obeying deterministic equations of motion; it stands in contrast with quantum mechanics. Newtonian mechanics adds specific ideas about absolute space and time. It stands in contrast with “relativistic” mechanics, which is classical but not Newtonian, and in which space and time become unified.

Noether’s theorem states that every smooth, continuous symmetry transformation of a system is associated with the conservation of some quantity.

Noether’s theorem relates these symmetries to conservation laws we already know: Invariance under spatial shifts leads to conservation of momentum, and invariance under temporal shifts leads to conservation of energy.

using “derivatives” to calculate the rate of change of something, and “integrals” to calculate the total amount of change.

Kepler put forward three laws of planetary motion: 1. Planets move on ellipses with the sun at one focus of the ellipse. 2. The orbit of a planet sweeps out equal areas in equal times. Thus, planets move more quickly when they are closer to the sun, more slowly when they are farther away. 3. Larger orbits have a longer orbital period. In particular, the square of the period is proportional to the cube of the long axis of the ellipse. This relates the orbits of different planets to one another.

The Laplacian paradigm holds that all the information we need to determine what will happen to the system, or what did happen to it in the past, is contained in the state of the system at each moment in time.

That’s what a derivative is: the slope of a curve at some point, defined by taking the limit of the slope of a sequence of lines that get closer and closer to the tangent line at that point.

Saint Augustine’s famous formulation, “If no one asks me, I know what time is. If I wish to explain it to he who asks, I do not know.”

the entropy of a closed system, including the universe as a whole, tends to increase over time. Entropy is often roughly defined as the disorderliness or disorganization of a system—a

the second law of thermodynamics—in closed systems, entropy will either increase or stay constant, never spontaneously decrease. (The first law is just energy conservation.)

THE PAST HYPOTHESIS Entropy tends to increase because there are more ways (microstates) to be high-entropy than to be low-entropy.

Our universe is expanding, and about 14 billion years ago, everything we currently see was squeezed into a very hot, very dense, rapidly expanding state. If we extrapolate all the way back, our best current theory (Einstein’s general relativity) predicts a “singularity” of infinite density, labeled “the Big Bang.” The right way to think about that is not that there really was such a singularity but that the theory itself breaks down. Someday we’ll have a better understanding of gravity and the expanding universe, which will hopefully reveal what happened at the moment we call the Big Bang.

our observed universe did start out in a low-entropy state, and entropy has been going up ever since. That’s the ultimate origin of the direction of time. Just as there is an arrow of space nearby because we live close to the Earth, there is an arrow of time because we live close (relatively speaking) to the Big Bang.

the arrow of time isn’t built into the fundamental laws of physics but is an epiphenomenon—a by-product of the fact that the universe started in a condition of low entropy, and that low-entropy states tend to evolve into increasingly higher-entropy ones.

Straight lines in space are the shortest possible distance; straight paths in spacetime are the longest possible time.

You will sometimes hear that time can speed up or slow down according to the theory of relativity. That’s baloney. Or to be more polite about it, it’s a misleading way to describe a real phenomenon. The new feature in relativity is that the total duration experienced by two observers moving in different ways will generally not be equal, even if they begin and end at the same events in spacetime. This isn’t because the rate of time is changing; it’s just because one person moved on a different path, and therefore covered a different amount of spacetime. If one person walks in a straight line between two points, and another walks a crooked path between the same points, the second person travels a different distance, but we don’t say that they experienced a different number of meters per meter.

Classical Quantum Non-Relativistic Newtonian Gravity Quantum Harmonic Oscillator Relativistic Maxwell’s Electromagnetism Quantum Electrodynamics