## Doppler Shift, Expansion, and Cooling

A few seconds after the gamma rays began to collide, there were hardly enough of them left to make new particles. There is another reason why particle production stopped. The expansion and the cooling weakened all the photons, even those that had not collided and therefore had not fractured.

If we draw a picture of a wave on a wide rubber band and then stretch it we will see the distance increase between the wave crests. In other words, the stretching increases the wavelength. But the energy of a photon is inversely proportional to the wavelength, so stretching reduces the energy. A stretched-out wave moves at the speed of light just as any other electromagnetic wave does, but it brings in less energy per unit time than a compact wave. The temperature in a region is proportional to the amount of energy in that region. Reducing the energy lowers the temperature.

This process has another description. Christian Johann Doppler (Austrian physicist, 1803–1853) discovered that stars moving away from an observer appear reddened, and stars moving toward an observer appear bluer than usual. This effect is called the Doppler shift.

People who have heard a car driven by with its horn blowing are familiar with the Doppler shift. The car’s horn plays a musical note, that is, it has a certain pitch. As the car approaches the horn’s pitch is higher than usual. It drops smoothly to a lower-than-usual pitch when the car passes and recedes into the distance. We should not confuse pitch with loudness. It is true that a car’s horn sounds louder as it approaches and softer as it recedes. Loudness and musical pitch in this case go up and down together. But the Doppler Effect is about musical pitch or frequency, not about loudness.

One hears the note the designer intended when the car is stationary. Now let’s consider the sound waves when the car is blowing its horn and approaching the listener. At a certain moment the horn emits the crest of a sound wave. By the time it emits the following wave crest the car is closer. The crests arrive at the listener’s ear closer together than usual. They have a shorter wave length and therefore a higher frequency. They sound like a musical note of higher pitch. After the car passes the listener, its horn emits each successive wave crest at a greater distance from the observer. This stretches the wavelength and decreases the frequency. The pitch drops to a lower note than the one the horn plays when the car is stationary.

The same thing happens when a star is moving away from an observer. At a certain moment it emits the crest of a wave of light. By the time it emits another wave crest, the star is farther away, since it is moving all the time. The distance between wave crests is greater than it would be if the star were stationary with respect to the observer. Red light has the longest visible wavelengths and visible photons of the lowest energy. Therefore we say that the light is redder and cooler. If the star happens to be moving toward the observer, the wave crests are closer together. The light is bluer and warmer.

The amount of change in wavelength, divided by the wavelength, is called the Doppler shift. The Doppler shift is positive if the star is moving away from the observer. In the same situation the distance between the star and the observer is expanding, the light is redder, and the light is cooler. All of these are different ways of describing the same thing.

If we draw a picture of a wave on a wide rubber band and then stretch it we will see the distance increase between the wave crests. In other words, the stretching increases the wavelength. But the energy of a photon is inversely proportional to the wavelength, so stretching reduces the energy. A stretched-out wave moves at the speed of light just as any other electromagnetic wave does, but it brings in less energy per unit time than a compact wave. The temperature in a region is proportional to the amount of energy in that region. Reducing the energy lowers the temperature.

This process has another description. Christian Johann Doppler (Austrian physicist, 1803–1853) discovered that stars moving away from an observer appear reddened, and stars moving toward an observer appear bluer than usual. This effect is called the Doppler shift.

People who have heard a car driven by with its horn blowing are familiar with the Doppler shift. The car’s horn plays a musical note, that is, it has a certain pitch. As the car approaches the horn’s pitch is higher than usual. It drops smoothly to a lower-than-usual pitch when the car passes and recedes into the distance. We should not confuse pitch with loudness. It is true that a car’s horn sounds louder as it approaches and softer as it recedes. Loudness and musical pitch in this case go up and down together. But the Doppler Effect is about musical pitch or frequency, not about loudness.

One hears the note the designer intended when the car is stationary. Now let’s consider the sound waves when the car is blowing its horn and approaching the listener. At a certain moment the horn emits the crest of a sound wave. By the time it emits the following wave crest the car is closer. The crests arrive at the listener’s ear closer together than usual. They have a shorter wave length and therefore a higher frequency. They sound like a musical note of higher pitch. After the car passes the listener, its horn emits each successive wave crest at a greater distance from the observer. This stretches the wavelength and decreases the frequency. The pitch drops to a lower note than the one the horn plays when the car is stationary.

The same thing happens when a star is moving away from an observer. At a certain moment it emits the crest of a wave of light. By the time it emits another wave crest, the star is farther away, since it is moving all the time. The distance between wave crests is greater than it would be if the star were stationary with respect to the observer. Red light has the longest visible wavelengths and visible photons of the lowest energy. Therefore we say that the light is redder and cooler. If the star happens to be moving toward the observer, the wave crests are closer together. The light is bluer and warmer.

The amount of change in wavelength, divided by the wavelength, is called the Doppler shift. The Doppler shift is positive if the star is moving away from the observer. In the same situation the distance between the star and the observer is expanding, the light is redder, and the light is cooler. All of these are different ways of describing the same thing.