Does Light Lose Energy As It Travels The Universe?

As a wave of light travels through the universe, does it lose energy? For example, what is the wavelength of 450 nm (blue) light after traveling a trillion (1,000,000,000,000) km in the universe? Thank you very much.
The anisotropies of the Cosmic microwave background (CMB) as observed by Planck. The CMB is a snapshot of the oldest light in our Universe, imprinted on the sky when the Universe was just 380,000 years old. Image credit: ESA/Planck Collaboration, CC BY SA IGO

The anisotropies of the Cosmic microwave background (CMB) as observed by Planck. The CMB is a snapshot of the oldest light in our Universe, imprinted on the sky when the Universe was just 380,000 years old. Image credit: ESA/Planck Collaboration, CC BY SA IGO

Originally posted at Forbes!

It does! This loss of energy is usually officially termed a cosmological redshift, and it’s an interesting combination of the way that light moves through space, and the nature of our Universe’s expansion.

Light behaves both as a particle and as a wave. Depending on the situation, it can be easier to talk about photons the light particle, or light waves- for travelling the vast distances of space, either works. However, light’s energy is very tightly tied to one of its more wave-like properties - its wavelength. Wavelength measures the distances between peaks, and can be used to measure the distances between ocean waves, or it can be used to very precisely measure the color of light reaching your eyes or a camera. The shorter the wavelength of light, the bluer the color. The bluer the light, the more energy it has, and things like gamma rays and X-rays have more energy still than anything our eyes can detect.

This new false-colored image from NASA's Hubble, Chandra and Spitzer space telescopes shows a giant jet of particles that has been shot out from the vicinity of a type of supermassive black hole called a quasar. Different wavelengths of light are reflected in the different colors. Image credit: NASA/JPL-Caltech/Yale Univ.

This new false-colored image from NASA's Hubble, Chandra and Spitzer space telescopes shows a giant jet of particles that has been shot out from the vicinity of a type of supermassive black hole called a quasar. Different wavelengths of light are reflected in the different colors. Image credit: NASA/JPL-Caltech/Yale Univ.

So let’s imagine that we have a space three feet long, and a flexible spring, almost three feet long. To reach from one edge of our space to the other, we’ll have to stretch the spring a little, but the distance between the coils won’t be very large. If we started to extend the spring, and suddenly found that our space had doubled in size, we’d have to stretch the spring much further, and the distance between coils would be much greater.

This is fundamentally what happens to light, as it travels through an expanding universe. The universe as a whole is expanding, meaning that the space between many galaxies is increasing. As light travels away from a galaxy, the Universe is continually expanding, meaning that the distance the light needs to travel is continually increasing as well. As space stretches out underneath a beam of light, its wavelength increases, and its energy decreases. Measuring this loss of energy is one of the main ways that distance is now measured in the Universe. This metric works well because we have a good sense (from other measurements) of how fast the Universe has been expanding, and what the energy loss should be for light which began its journey at an earlier time.

This artist's concept puts solar system distances in perspective. The scale bar is in astronomical units, with each set distance beyond 1 AU representing 10 times the previous distance. Image credit: NASA/JPL-Caltech

This artist's concept puts solar system distances in perspective. The scale bar is in astronomical units, with each set distance beyond 1 AU representing 10 times the previous distance. Image credit: NASA/JPL-Caltech

However, a trillion kilometers, on an astronomical standard, is still relatively small. A trillion kilometers is roughly a tenth of a light year (about five weeks of light travel time). This distance is sufficiently small that a more useful unit is the astronomical unit (au) which measures the distance between the Earth and the Sun. A trillion kilometers is about 10,000 au. On the scale of our solar system, this would stretch from the Sun to not quite out into the Oort cloud. This distance would put you way past Pluto, which orbits our sun at around 40 au from the Sun, and well past any hypothetical Planet 9, which is supposed to hang out around 200 au from the Sun.

As distant as these measures are, this measures only our very closest cosmic neighborhood, and in this regime, space is not expanding. Everything within our Galaxy is bound gravitationally to each other much more tightly than the expansion of the Universe can pull apart. The expansion is not so rapid that it is able to shear the Galaxy apart. Light’s loss of energy really only comes into play at much larger scales, far beyond the nearest galaxies.

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If a light source is moving away from us, does the light arrive moving slower?

If an object is moving away from us at half the speed of light and shining a light back at us, is the light that hits us going half the speed of light relative to us?
A source of light waves moving to the right, relative to observers, with velocity 0.7c. The frequency is higher for observers on the right, and lower for observers on the left. Image credit; wikimedia user TxAlien, CC A-SA 3.0

A source of light waves moving to the right, relative to observers, with velocity 0.7c. The frequency is higher for observers on the right, and lower for observers on the left. Image credit; wikimedia user TxAlien, CC A-SA 3.0

It is not!

One of the fundamental principles of relativity is that the speed of light in a vacuum is always a constant. It doesn’t matter where you’re standing or how fast you’re moving, you should always observe light in space to move at the same speed.

That’s not to say that light is unaffected by the motion of whatever is giving off the light! To understand what’s going on here, it’s easier to think of light as a wave than it is to think of it as a series of particles.

We’re all familiar with the change in tone of an ambulance’s siren as it passes us. It seems higher pitched as it moves towards us, and then as it passes us and moves away from us, the siren drops in tone. The speed of the sound wave going through the air hasn’t changed, but because the source is moving, we perceive a change in pitch. This is the Doppler effect.

Imagine touching the surface of a pool of water so that you create one ripple in the surface. It will move smoothly away from where you touched it in all directions. If you keep tapping the same place in the water, you’ll get a series of concentric rings. But if instead of tapping the same place, you move your finger over a little bit, your second ring is offset from the first one. The inner ripple of water will be closer to the outer ripple on one side, and further from the other side. Depending on how fast you move your hand between your first and second taps, this effect can be more or less obvious - the faster you move your hand, the more crushed together the ripples will be on one side, and the further apart they get on the other. 

The same thing can happen to light waves. While light is always moving away from its source at the same speed, if your source is moving at a significant fraction of the speed of light relative to whoever’s watching, the wavelength (or color) of the light will change dramatically.

Let’s use your example: 50% of the speed of light. If that object is shining a pure blue light, as blue as the human eye can detect (about 400 nm), if it’s moving away from us at half the speed of light, the light I would observe would be shifted to longer wavelengths to such a degree that it would be an extremely deep red (690 nm).

The color spectrum rendered into the sRGB color space using a gray background to preserve the actual colors. The numbers are wavelength, in nanometers. Image credit: wikimedia user Spigget, CC A-SA 3.0

The color spectrum rendered into the sRGB color space using a gray background to preserve the actual colors. The numbers are wavelength, in nanometers. Image credit: wikimedia user Spigget, CC A-SA 3.0

This is the fundamental idea behind using a redshift as a measure of distance.  The further away an object is, the faster it's moving away from us, and the redder its light has become. So if we can measure that shift, we can figure out how far away it must be.

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