Reflections in Cosmology 15: Where Have All the Energy Gone?

The pressure of gas in a cylinder performs work on the piston by pushing it outward, whereby thermal energy is converted into mechanical energy

Imagine a cylinder filled with gas, pressurized by a piston. The kinetic energy (or thermal energy) of the gas particles exerts pressure on the piston, pushing it outward. As the volume in the cylinder increases, the gas particles lose energy and therefore cool down. Thermal energy has been converted into mechanical energy. Simple high school physics.

In a closed system, energy is always conserved. No energy is created nor destroyed. They just turn into more and more useless forms of energy, thereby increasing disorder in the universe. This is the second law of thermodynamics. Entropy always increases in a closed system. So we expect that in the far distant future, the universe will be a cold, lifeless, system filled with disorder. Surprise, surprise:

A popular theme in science in the first half of the 20th century was the eventual heat death of the universe, how all things must fade and die, and how entropy must inexorably rise to its maximum value. We now know that the heat death actually occured long ago and we live in a universe that has very nearly attained maximum entropy. ~ Edward Harrison, Cosmology: The Science of the Universe

So where is this large amount of entropy to be found? We have to look back into the early universe, when the all the photons (radiation particles) first decoupled from the atomic matter to become what we call the cosmic microwave background (CMB) radiation. These photons are where most of the entropy in the universe lie.

As the universe expands, the wavelengths of photons (or radiation) are stretched, causing them to lose energy - but where does all the energy go to?

We live in an expanding universe. As the volume of the universe expands, the density of matter in the universe decreases. At the same time, the density of photons in the universe decreases too. But something else happens. As the universe expands, the wavelengths of the photons are stretched. So in the last 13.7 billion years, the photons of the CMB have been losing lots of energy as they get stretched to longer and longer wavelengths. But where have all the energy gone to? In the case of the cylinder and piston, the loss in energy due to an expanding volume has been converted to work done on the moving piston. But can we say the same for our universe? The cylinder, piston and the gas within form a closed system. But out universe is unbounded. Is this loss in energy somehow linked to the expansion of the universe in some way or another? Is it linked to this mysterious dark energy? No one knows for sure where the energy has gone to, or if it has just vanished. The only answer available at the moment, is that in an expanding universe, energy is NOT conserved. The law of conservation of energy does not apply to cosmology! And this has been the greatest shock I’ve had since I began reading this book.

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