# Effect of redshift on energy conservation [duplicate]

Light coming from galaxies that are going away from us is redshifted. Since the energy of a photon is purely dependent on its frequency one may conclude that the energy of these photons decreases. The same light coming from the same star in the same galaxy will be seen to a planet in that galaxy as it "actually" is. So dependent on the relative motion the energy will be seen, differently. How does this not conflict with the conservation of energy? Or the "total" energy of the universe depend on the frame?

I was thinking that the light coming to us is located on a larger range since its period is larger. So the light carries the same energy for both observers. Even if its average energy is smaller total energies are same.

However, I could not convince myself and I think I am making wrong interpretations.

## marked as duplicate by Rob Jeffries, Kyle Kanos, John Rennie, Community♦Oct 28 '15 at 11:58

• Even in Newtonian physics energy depends on relative motion. If I am stationary I measure my own kinetic energy to be zero. However if you are moving relative to me at velocity $\mathbf{v}$, in your frame I am moving past you at velocity $-\mathbf{v}$ and therefore you measure my kinetic energy to be $Mv^2/2$. The conservation of energy simply states that in a given inertial frame, energy does not appear from nowhere. Different inertial observers do not have to measure the same energy, however. – Mark Mitchison Oct 27 '15 at 23:01
• You are right, but somehow I did not think about this issue like this before. Probably, I am making the mistake by trying to keep the physical quantities constant even if I change the frame. However, I am still confused about energy conservation. – A. I. Oct 27 '15 at 23:06
• If we assume no acceleration and we ignore spreading and we ignore time dilation, then it's really pretty simple. If the object is moving towards you the same amount of energy is spread out over a smaller distance over the time that it takes the light to reach you. If it's moving away from you, the energy is spread out over a larger distance. The red or blue shift, (we can assume equal number of photons), is essential to the conservation of energy. I obviously simplified the question quite a bit, to just 2 objects, but I think that's the gist of the answer. – userLTK Oct 27 '15 at 23:33
• The total energy of the universe has not been determined observationally, it's therefor not possible to say if energy is actually conserved on the scale of the universe or not. I may well not be. More likely, in my personal opinion, is that total energy is conserved and that we merely don't understand how photons actually interact with the physical vacuum on the scale of the entire universe. – CuriousOne Oct 27 '15 at 23:37

I prefer to look at it based on certain Laws and observations.

1. The First and second Law of Thermodynamics are true Energy is conserved and the universe is moving towards increasing entropy.
2. The Hubble constant is accurate and the universe is expanding at an exponential rate given by $a(t) = e^{Ht}$, where the constant $H$ is the Hubble expansion rate and $t$ is time. As in all FLRW spaces, $a(t)$, the scale factor, describes the expansion of physical spatial distances.

3. Redshift is the displacement of spectral lines toward longer wavelengths (the red end of the spectrum) in radiation from distant galaxies and celestial objects. This is interpreted as a Doppler shift that is proportional to the velocity of recession and thus to distance.

4. Blueshift a shift toward shorter wavelengths of the spectral lines of a celestial object, caused by the motion of the object toward the observer.

You say -

Light coming from galaxies that are going away from us is redshifted. Since the energy of a photon is purely dependent on its frequency one may conclude that the energy of these photons decreases. The same light coming from the same star in the same galaxy will be seen to a planet in that galaxy as it "actually" is. So dependent on the relative motion the energy will be seen, differently. How does this not conflict with the conservation of energy?

Ok let's say that is true we are experiencing a redshift but at the same time let's consider another observer who is moving at the same speed as our recession speed but towards the photon emitter source he is experiencing a blueshift. Each photon will have redshift and a corresponding blueshift depending on the relative frame of refences{one moving towards and one moving away}. The following picture makes it clearer.

"Dopplerfrequenz" by Charly Whisky 18:20, 27 January 2007 (yyy) - Own work. Licensed under CC BY-SA 3.0 via Commons.

An animation illustrating how the Doppler effect causes a car engine or siren to sound higher in pitch when it is approaching than when it is receding. The pink circles represent sound waves.

The energy from each siren waves doesn't change but depending where you are you will here a higher or lower pitch.

Now on a cosmologic scale the with an exponentially expanding universe with local Hubble horizons and trying to decide if the universe is a closed or open system leads to a cluster of different methods to try and verify the Conservation of energy of the universe. But a good way to think about this is to imagine open local systems exchanging matter and energy with each other across the universe and the sum of their energy diferences will be zero thereby conserving energy.