26-3 During inflation, all the mass and energy in the universe burst forth from the vacuum of space

If the ideas of inflation are correct, it was a brief but stupendous expansion of the universe soon after the beginning of time. Physicists now realize that inflation helps explain where all the matter and radiation in the universe came from. To see how a violent expansion of space could create particles, we must first understand what quantum mechanics tells us about space.

Quantum Mechanics and the Heisenberg Uncertainty Principle

Quantum mechanics is the branch of physics that explains the behavior of nature on the atomic scale and smaller. For example, quantum mechanics tells us how to calculate the structure of atoms and the interactions between atomic nuclei. Elementary particle physics is the branch of quantum mechanics that deals with individual subatomic particles and their interactions, including the strong, weak, and electromagnetic forces that we discussed in Section 26-2.

The microscopic world of quantum mechanics is significantly different from the ordinary world around us. In the ordinary world we have no trouble knowing where things are. You know where your house is; you know where your car is; you know where this book is. In the subatomic world of electrons and nuclei, however, you can no longer speak with this same confidence. A certain amount of fuzziness, or uncertainty, enters into the description of reality at the incredibly small dimensions of the quantum world.

To appreciate the reasons for this uncertainty, imagine trying to measure the position of a single electron. To find out where it is located, you must observe it. And to observe it, you must shine a light on it. However, the electron is so tiny and has such a small mass that the photons in your beam of light possess enough energy to give the electron a mighty kick. As soon as a photon strikes the electron, the electron recoils in some unpredictable direction. Consequently, no matter how carefully you try to measure the precise location of an electron, you necessarily introduce some uncertainty into the speed of that electron.

These ideas are at the heart of the Heisenberg uncertainty principle, first formulated in 1927 by the German physicist Werner Heisenberg, one of the founders of quantum mechanics. This principle states that there is a reciprocal uncertainty between position and momentum (momentum is equal to the mass of a particle multiplied by its velocity). The more precisely you try to measure the position of a particle, the more unsure you become of how the particle is moving. Conversely, the more accurately you determine the momentum of a particle, the less sure you are of its location. These restrictions are not a result of errors in making measurements; they are fundamental limitations inherent to all natural phenomena.

There is an analogous uncertainty involving energy and time. You cannot know the energy of a system with infinite precision at every moment in time. Over short time intervals, there can be great uncertainty about the amounts of energy in a subatomic system. Specifically, let ΔE be the smallest possible uncertainty in energy measured over a short interval of time Δt. (Astronomers and physicists often use the capital Greek letter delta, Δ, as a prefix to denote a small quantity or a small change in a quantity.)

Heisenberg uncertainty principle for energy and time

• ΔE = uncertainty in energy
• Δt = time interval over which energy is measured
• h = Planck’s constant = 6.625 × 10⁻³⁴ J s

This equation says that the shorter the time interval Δt, the greater the energy uncertainty ΔE must be in order to ensure that the product of ΔE and Δt is equal to h/2π.

We might look upon the Heisenberg uncertainty principle as merely an unfortunate limitation on our ability to know everything with infinite precision. But, in fact, this principle provides startling insights into the nature of the universe.

Spontaneously Created Matter and Antimatter

We have seen that one of the important conclusions of Einstein’s special theory of relativity is the equivalence of mass and energy: E = mc² (see Section 16-1). There is nothing uncertain about the speed of light (c), which is an absolute constant. Therefore, any uncertainty in the energy of a physical system can be attributed to an uncertainty Δm in the mass. Thus,

Combining this expression with the previous equation, we obtain

Heisenberg uncertainty principle for mass and time

• Δm = uncertainty in mass
• Δt = time interval over which mass is measured
• h = Planck’s constant = 6.625 × 10^{−34 J} s
• c = speed of light = 3.00 × 10⁸ m/s

This result is astonishing. It means that over a very brief interval Δt of time, we cannot be sure how much matter there is in a particular location, even in “empty space.” During this brief moment, matter can spontaneously appear and then disappear. The greater the amount of matter (Δm) that appears spontaneously, the shorter the time interval (Δt) during which it can exist before disappearing into nothingness. This bizarre state of affairs is a natural consequence of quantum mechanics.

No particle can appear spontaneously by itself, however. For each particle created, so is a second, almost identical antiparticle particles are made of matter, and antiparticles are made of antimatter. In other words, equal amounts of matter and antimatter come into existence and then disappear. (These are the virtual particle pairs discussed in Section 25-7, and in more depth below.)

Despite its exotic name, there is actually nothing terribly mysterious about antimatter. A particle and an antiparticle are identical in almost every respect; their main distinction is that they carry opposite electric charges. For example, an ordinary electron (e⁻) carries a negative charge; the corresponding antiparticle has the same mass but a positive charge, which is why it is called a positron (e⁺, and also called an antielectron). Protons (with positive charge) also have an antimatter partner called an antiproton (with negative charge). Particles that have no electric charge can also have corresponding antiparticles. An example is the neutrino (ν); we met its antiparticle, the antineutrino ( ), in Section 26-2. The antineutrino is also electrically neutral, but differs from the neutrino in having opposite values of other, more subtle physical properties.

A spontaneously created particle-antiparticle pair lasts for only an incredibly brief time. For example, consider an electron and a positron, each with a mass of 9.11 × 10⁻³¹ kg. If we rewrite the Heisenberg uncertainty principle for mass and time to solve for Δt and then substitute the combined mass of 2 × 9.11 × 10⁻³¹ kg, we find that a spontaneously created electron-positron pair can last for a time

In other words, an electron and a positron can spontaneously appear and then disappear without violating any laws of physics—but they can remain in existence for no longer than 6.43 × 10⁻²² second. In fact, the laws of quantum physics require that electrons and positrons constantly pop in and out of existence. The same behavior applies to all massive particles, but the more massive the particle, the shorter the time interval it can exist. Next, we look at this process in more detail.

Virtual Pairs

Spontaneous creation can and does happen absolutely anywhere and at any time, not just under the unusual conditions of the early universe. (It is happening right now in the space between this book and your eyes.) Quantum mechanics tells us that if a process is not strictly forbidden, then it must occur. Pairs of every conceivable particle and antiparticle are constantly being created and destroyed at every location across the universe. However, we have no way of observing these pairs directly without violating the uncertainty principle. For this reason, they are called virtual pairs. They do not “really” exist in the same sense as ordinary particles; they “virtually” exist. The particles that are exchanged in the four fundamental forces (see Section 26-2) are also virtual particles.

Although virtual pairs of particles and antiparticles cannot be observed directly, their effects have nonetheless been detected. Imagine, for example, an electron in orbit about the nucleus of an atom, such as a hydrogen atom. Ideally, the electron should follow its orbit in a smooth, unhampered fashion. However, because of the constant brief appearance and disappearance of pairs of particles and antiparticles, minuscule electric fields exist for extremely short intervals of time. These tiny, fleeting electric fields cause the electron to jiggle slightly in its orbit. This jiggling produces slight changes in the energies of different electron orbits in the hydrogen atom, which manifest themselves as a minuscule shift in the wavelengths of the hydrogen spectral lines. (We discussed the connection between the energies of electron orbits in hydrogen and the hydrogen spectrum in Section 5-8.)

This shift was first detected in 1947 and today is known as the Lamb shift. The Lamb shift and more recent experiments provide powerful evidence that every point in space, all across the universe, is seething with virtual pairs of particles and antiparticles. In this sense, “empty space” is actually not empty at all. Figure 26-12 sketches the constant appearance and disappearance of virtual particles and antiparticles.

Figure 26-13: Pair Production and Annihilation (a) Pairs of virtual particles can be converted into real particles by high-energy gamma-ray photons. In this illustration, an electron (shown in green) and a positron (in red) are produced. This process can take place only if the combined energy of the two photons is no less than Mc², where M is the total mass of the electron and positron. (b) Conversely, a particle and an antiparticle can annihilate each other and be transformed into energy in the form of gamma rays.

Figure 26-12: Virtual Pairs Pairs of particles and antiparticles can appear and then disappear anywhere in space provided that each pair exists only for a very short time interval, as dictated by the uncertainty principle. In this sketch, electrons are shown in green and positrons are shown in red.

Pair production is routinely observed in high-energy particle accelerators. Indeed, it is one of the ways in which physicists manufacture exotic species of particles and antiparticles. The only requirement is that nature’s balance sheet be satisfied. To create a particle and an antiparticle having a total mass M, the incoming gamma-ray photons must possess an amount of energy E that is greater than or equal to Mc². If the photons carry too little energy (less than Mc²), pair production will not occur. Likewise, the more energetic the photons, the more massive the particles and antiparticles that can be manufactured.

Figure 26-14: Inflation The universe expanded by such a tremendous factor during the inflationary epoch that the members of virtual particle-antiparticle pairs could no longer find each other. As a result, these virtual particles and antiparticles became real particles and antiparticles.

Not all pairs of particles and antiparticles are virtual. In a phenomenon called pair production, pairs of highly energetic gamma rays (photons) can convert their energy into pairs of particles and antiparticles (Figure 26-13a). Quite simply, the gamma-ray photons disappear upon colliding into each other and convert their energy into a particle and an antiparticle. As real particles, they are directly observable and do not have to annihilate. While Figure 26-13a shows this process of pair production, Figure 26-13b shows the inverse process of annihilation, in which a particle and antiparticle collide with each other and are converted into high-energy gamma rays.

Around 1980, physicists began applying these ideas to their thinking about the creation of the universe. During the inflationary epoch, space was expanding with explosive vigor. As we have seen, however, all space is seething with virtual pairs of particles and antiparticles. Normally, a particle and an antiparticle have no trouble getting back together in a time interval (Δt) short enough to be in compliance with the uncertainty principle. During inflation, however, the universe expanded so fast that particles were rapidly separated from their corresponding antiparticles. Deprived of the opportunity to recombine and annihilate, these virtual particles became real particles in the real world. In this way, the universe was flooded with particles and antiparticles created by the violent expansion of space (Figure 26-14). For a “report card” on cosmology theories, including inflation, see the article at the end of this chapter.