Fermilab

Dear Fermilab:

I have a question, but first, thank you for the terrific new web site. You did a fantastic job.

Question:

Where does present theory say the energy of a red shifted photon goes?

The idea that universal expansion is responsible for the red shift of intergalactic light would seem correct if light were a continuous wave. However, since a photon is a quantum of energy, and since the entire photon is presumably captured, the photon should still have the same amount of energy when the packet is fully captured even if it was stretched by universal expansion, unless of course the photon is loosing energy in transit, which it must do to not conflict with Planck's equation. And if a photon looses energy in transit, there is no need to claim universal expansion.

There is a fundamental conflict here and I would very much like to know how it is presently resolved. The only logical answer I see is the photon must loose energy traveling great distances in space. (I realize they don't think a photon can loose energy to a vacuum, but they also don't think a vacuum is empty.)

This is not as general of question as you might like, but I cannot find the answer anywhere.

Thank you for considering answering my question, David Rees

Your question about the redshift of a single photon is a great one. It really gets to the heart of the meaning of redshift and the expansion of the universe. The solution to the dilemma, however, lies in a careful consideration of the viewpoint of the observer who is measuring the energy of the photon.

As you know, the basic idea of redshift is that when a source of light recedes from us, the crests and troughs of the wave (actually the peaks in the electric and magnetic fields that make up light) get delayed by the motion of the source. We see a longer wavelength than was emitted by the source. In the case of light in the visible portion of the electromagnetic spectrum, we see light shifted to the longer-wavelength or redder portion of the spectrum. Thus, the spectrum of stars and galaxies is "redshifted" when the source of light is moving away from us. Faraway sources are moving away from us because of the expansion of the universe. Your question is about what this means for the energy carried by the light, because the energy and the frequency of light are related. E=h*f, where f is the frequency of the light.

First, let's put aside the idea of the photon losing energy in transit, as an explanation for redshift. A photon doesn't lose energy unless it collides with a particle. Photons can scatter off interstellar electrons, for example. (Perhaps you were thinking about particles, like electrons, losing energy "in transit" in a vacuum. That can happen if they change direction. Electrons radiate and lose energy if they travel on a curved path around a magnetic field line.) Photons carry energy, but they don't lose energy just because they travel.

The key to understanding the dilemma of a red-shifted photon is that not all observers will measure the same energy of the photon. Let's say an observer is traveling with the star or galaxy and sees a photon in the yellow portion of the spectrum. An observer who is moving with respect to the star (it doesn't matter if it's the star or the observer moving away) sees the same photon in the red part of the spectrum. That's OK--it doesn't violate the principle of conservation of energy--because they make their measurements in different reference frames. Similarly if you roll a marble while you are riding on a train, you will find that the marble has a certain velocity and kinetic energy as seen from your seat in the train, but an observer in the train station, who (somehow) sees the marble as it goes whipping by on the train, measures a different velocity and hence a different kinetic energy. The energy of a photon comes from its frequency, and that is different for different observers.

[It can be confusing to think about the conservation of energy and measurements made from different reference frames. Keep in mind that energy is conserved within each reference frame, or (to put it another way) for two observers who are moving at the same speed with respect to the thing they observe. Consider an observer on earth and an observer who is close to the galaxy of interest, but moving away from the galaxy at the same speed that the observer on earth is moving away from the galaxy. These two observers are in the same reference frame, even if they are separated by millions of miles. They measure the same energy carried by a photon from the galaxy. But the value they come up with for the energy is different from that obtained by an observer in the same frame as the galaxy, or any other reference frame.]

The argument I've given you does not depend on special relativity, but you can find a good discussion of the importance of the observer's reference frame in the book "Space and Time in Special Relativity" by N. David Mermin of Cornell University. I think you would enjoy it.

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