During the billions of years travel the moving space occupied by the photon wave packets expands, and its de Broglie wavelength is correspondingly stretched.
Cosmology

Where does the energy of cosmologically red-shifted photons go?

Any astronomer will tell you that the light from distant galaxies is red shifted due to the Hubble expansion of the universe.  Blue photon emitted from a distant galaxy (say, about 10 billion light years away) will be red by the time it arrives at the Earth. The blue – higher energy – photon has lost about half its energy as it travels to us, arriving as a red – lower energy – photon. Where has that energy gone?
It has not transmitted the lost energy to another particle or matter – the space it has traversed is essentially empty. So what is going on?

This is a fascinating question, and the answer throws light on many interesting astronomical and cosmological topics.

First, let’s examine the process in a bit more detail. As the photon crosses the vast expanses of cold, inter-galactic space why does it lose energy? Well, each photon, like all particles, travels as. wave packet, spread out over a (usually) small region of space. During the billions of years travel the moving space occupied by the photon wave packets expands, and its de Broglie wavelength is correspondingly stretched. Longer wavelengths, by de Broglie’s formula, mean lower momentum and less energy. And so the photon arrives on Earth with less energy.

During the billions of years travel the moving space occupied by the photon wave packets expands, and its de Broglie wavelength is correspondingly stretched.
Photon’s wavelength gets stretched when it travels through space because of expansion of universe .

Okay, so that what’s happening, but it still doesn’t tell us where the energy has gone. What has happened is that the photon has been stretched by the expansion of the universe – by the expansion or stretching is of space itself. This stretching of space has lowered the expansion rate of the universe around the photon, which raises the energy of the expansion. This is because the energy of the expansion of the universe is actually negative.

Whoa! Negative energy? What does that mean? One episode of Star Trek says that negative energy is “logically impossible”. (Yes, it is Spock that says this!) But actually negative energy is quite common in physics and chemistry. Binding energies are always negative, for example. You have to put energy into boiling water to make the bonds between the liquid water molecules disappear, to enable the phase change from liquid to vapour. The energy you put in simply cancels out the negative energy molecular bonds. The same in nuclear physics: a single proton has the highest energy, and iron nuclei have the lowest energy (per nucleon) because iron is the most heavily bonded. The creation of negative energy nuclear bonds in stars, as hydrogen is fused to helium, enables the release of positive energy photons and neutrinos.

The energy of the gravitational field – but not electric fields – is also negative and – this is the crucial point – the kinetic energy of the expansion is similarly negative. A faster Hubble expansion has a lower energy density (more negative) than a slower expansion. You can demonstrate this by treating the Friedmann equations as energy balancing equations, which they are. The negative energy of expansion is balanced by the positive energy of matter and dark energy. This is why the total energy of the universe can be, and probably is, zero.

It also explains how inflation was able to simultaneously power the expansion of the universe in the .Big Bang and create matter at the same time. But that’s a story we’ll leave for another day.

Returning to our intergalactic photons, as the traverse space, they are stretched, and transfer some of their energy to the expansion, which slows the expansion down. Again, checking the Friedmann equations tells us that a photon or radiation-filled universe does indeed deaccelerate more quickly than a matter-filled universe.

Another little curious fact: the cosmological red shift also effect particles of matter – their de Broglie wavelengths are also stretched by the Hubble expansion and reduces their momentum, slowing the particles down. The effect is less noticeable for massive particles, since their rest energy is not altered. Photons, with no rest energy, are most effected.

Not understanding the red shift energy business has led many people astray, and you will often hear people saying stuff such as, total energy of the universe is not conserved in general relativity.

Now you know why they are wrong.

Michael Price

Michael Price has completed BSc in physics and a MSc in quantum fields and fundamental forces, Imperial College, London, UK. The MSc included a large component about cosmology and inflation. He lives in UK .

Michael Price
Michael Price has completed BSc in physics and a MSc in quantum fields and fundamental forces, Imperial College, London, UK. The MSc included a large component about cosmology and inflation. He lives in UK .