What happens to the energy if a photon's wavelength increases because of expansion of space?

Question

According to Wikipedia's "red shift" article, the red shift of distant galaxies is a combination of Dopple shift, special relativity, and the stretching of each photon during the time it takes to reach the observer. If the latter is correct, it means that energy is not conserved.

I think the writer is confused about the type of coordinate system be used. Is it an expanding coordinate system, or is the distance between grid lines constant in terms of meters?

I believe the length of a laser pulse will increase over billions of years; a one nanosecond pulse will start 300 millimeters long, and after a few billion yeats, it will be twice as long. But I doubt if the individual photons will be lengthened.

Any brainiacs care to comment?

Answer 1

Energy is conserved, but its value is relative to one's reference frame. The energy of the photon never changed in its travels *in earth's inertial reference frame*. It had, and still has, a higher energy in the frame of the source which emitted it because that source has a high velocity relative to earth.

Answer 2

The expansion of spacetime does "stretch" photon wavelengths.

There is no violation of conservation of energy. Energy is conserved in any Lorentz frame. But the measured amount of energy is frame dependent. For instance, in classical physics, kinetic energy is 1/2 m v^2. A scientist on the shore measures a passing boat to have quite a bit of KE. But the scientist on the boat measures the boat's velocity as 0, and therefore the KE as zero. The potential energy of my laptop depends on whether I measure with the origin on the desk or on the floor. But there's no violation of conservation of energy in any of this.

It's the same with the photons in the universe, except that the relationship between reference frames is more complicated. No single reference frame can contain both the emitter and the receiver. The photon must be received in a reference frame different from that in which it was emitted because of the huge interval of curved spacetime between them. But it's not a violation of energy conservation for an observer in a different frame to measure a different energy.