## Energy through a vacuum

A thermos bottle is designed to slow the flow of heat through its walls. You can put warm stuff in there to keep it warm, or cool stuff to keep it cool. Thermos bottles have two walls: an inner and an outer wall. In between the two walls is an insulator. A vacuum is a really good insulator because it has no molecules or atoms of gas in it to conduct heat between the inner and outer walls of the thermos. Of course there will still be heat conduction along the walls. Let's think about a planet. There are no walls, however thin, connecting a planet to anything. The space between the Earth and the Sun is a pretty good vacuum. We know how warm it is in the sunshine, so we know that heat flows from the Sun to the Earth. Yet, separating the Sun from the Earth is 150 million km of vacuum. How can heat be carried through a vacuum?

Light carries heat through a vacuum. Electrons and protons have a property called electric charge. What an electric charge is, fundamentally, no one can tell you, but it interacts through space via a property of the vacuum called the electric field. A positive electric field attracts a negatively charged electron. This is how, in the olden days, a TV tube hurled electrons toward the screen in a picture-tube television until electronic flatscreens came along. It functioned by releasing an electron and then pushing it around through the electric field. The electric field interacts with another property of the vacuum called the magnetic field.

If the strength of the electric field at some location, measured in volts, changes with time, and if the voltage oscillates up and down for example, this will cause a change in the magnetic field, such as a compass would point to. This is how an electromagnet works, converting electrical field energy into magnetic field energy. Going the other direction, if the magnetic field changes, it can produce an electrical field. This is how a generator works.

It turns out that the electric and magnetic fields in a vacuum fit together to form a closed cycle like the ringing of a bell. The up-and-down oscillation in an electric field will cause a complementary oscillation in the magnetic field, which reinforces the electric field in turn. The two fields "ring" together. Such a little bundle of electric and magnetic waves can in principle hurl through the vacuum forever, carrying energy with it.

The ringing of the electromagnetic field in light differs from the ringing of a piano string, in that light can come in any frequency. Frequencies, of oscillators or of light waves, have units of cycles per second (hertz, Hz) and are denoted by the Greek letter v (pronounced "new"). It turns out that different frequencies of light travel at the same speed in a vacuum. Within some nonvacuum medium, such as air, water, or glass, different frequencies of light might vary in their speeds a little bit, which is how a prism separates white light into its component colors. But in a vacuum, all light travels at the same speed. The speed of light in a vacuum, c, is a fundamental constant of nature. The constancy of the speed of light in a vacuum makes it easy to relate the frequency of light to its wavelength, the distance between the crests of a wave. We can figure out what the relationship is between frequency and wavelength by thinking geometrically, imagining the wavy line in Fig. 2.1 to be moving past us at some speed c. If the crests are 1 cm apart and moving at 10 cm/s, then 10 crests would move past us every second. Alternatively, we can make use of units. Pay attention to units, and they will lead you to virtue, or at least to the right answer. Problem: assemble the two things we know, v and c, such that the units combine to be the same as the units of X. Solution:

Don't take my word for it, check and make sure that the units are the same on both sides of the equation.

cm cycle

1 wavelength

1 wavelength

Distance traveled by light in 1 s Frequency = 4 cycles/s

Fig. 2.1 The frequency and wavelength of light are related to each other by the speed of light, which in a vacuum is the same for all different types of light, 3.0 • 1010 cm/s.

Distance traveled by light in 1 s Frequency = 4 cycles/s

Fig. 2.1 The frequency and wavelength of light are related to each other by the speed of light, which in a vacuum is the same for all different types of light, 3.0 • 1010 cm/s.

Scientists who discuss infrared (IR) light often use a third way of describing different colors, called the wave number, which is defined as the number of cycles per centimeter of length. It's simply a matter of convenience; when IR light is described by its wave number, it will have a nice, easy-to-remember number to carry around in our memories. We will use the letter n to designate the wave number. How can we construct the units of n from the building blocks of k, v, and c? All we need is k,

Different frequencies of light all have the same fundamental nature; they are all waves of the same essential physics. Figure 2.2 shows the names assigned to different types of light based on their frequencies. Of course, ifwe know the frequency of light, we know its wavelength and wave numbers also, so we have added "milemarkers" of these units too.

Our eyes are sensitive to light in what we pragmatically call the visible range. Higher frequencies than this are in the ultraviolet, or UV, and x-ray ranges. UV light causes sunburn, and x-rays are even more dangerous. Objects that emit the highest frequency of light are considered radioactive. Extremely short wavelength light is called gamma radiation, and we might encounter it coming from processes that happen in the nuclei of atoms or processes that happen in space such as the explosions of stars, coming to us as cosmic rays. (Other common forms of "radiation" are made of flying electrons [beta radiation] or bundles of two each protons and neutrons, called alpha radiation.) At longer wavelengths than the visible range we find the IR range. Later we will find that objects at about room temperature glow with IR light. Heat lamps at the skating rink warm us by shining invisible IR light on us.

All that energy whizzing around space in the form of coupled electric and magnetic field waves would be of little interest to the energy balance of a planet if they did not give up or carry off energy. There are a number of different mechanisms by which light may interact with matter, but IR light interacts mostly with vibrations of the chemical bonds of a molecule. Light interacts with matter by means of the electric field that they share (Fig. 2.3). Let's imagine matter as constructed with charged oscillators all over its surface; little charged weights sticking out from the surface of the matter on cycle

n cm

Frequency cycles / second or Hz

X-rays

^Ultraviolet ¿Visible!

Infrared

107 H 106

102 -10

Gamma rays

X-rays

^Ultraviolet ¿Visible!

Infrared

Gamma rays

Wavelength nanometers = 10-9 meters

010 011 012

Fig. 2.2 The electromagnetic spectrum.

Charged weight

Spring

Light

Fig. 2.3 A charged oscillator interacting with light.

little springs that stretch and contract. This little oscillator will have a frequency with which it will "ring." Incoming energy in the form of light brings with it an electric field oscillating up and down: voltage goes plus, minus, plus, minus. If the frequency of the cycles of voltage in the light is the same as the frequency of the oscillator light can be absorbed. Its energy is transferred into vibrational energy of the matter.

Important fact to remember: this mechanism of energy transfer is a two-way street. If energy can flow from the light to the oscillator, it can also flow the other way, from the oscillator to light. The vibrational energy of the oscillator is what we have been calling its temperature. Any matter that has a temperature above absolute zero (zero degrees on the Kelvin scale) will have energy in its oscillators that it maybe able to use to create light. The two-way street character of this process is important enough that it is given the name of Kirchhoff's law.

You can think of it as analogous to the vibrations of the oscillator strings of a piano interacting with the pressure field of the atmosphere to generate sound waves. You may have tried the experiment of singing into a piano with the dampers off to hear the strings echo back the note you sang into it. This wave-to-oscillator energy transfer is a two-way street as well.