# Where does the energy loss from redshifted photons go?

• josephpalazzo
In summary: That is, the frequency of the photon is shifted as a result of the change in gravitational potential energy. This energy is lost to the absorber as heat.
josephpalazzo
When a photon passes from a high gravity field to a low gravity field, it is redshifted. Therefore it has less energy. Where does that energy loss go to?

The local energy of the photon does not stay constant, however, the energy at infinity does and is furthermore constant. (Energy-at-infinity is a term used in MTW's Gravitation).

If a photon falls into a black hole, it is not the energy of the photon that gets added to the black hole, but the energy at infinity. So when you think of conserved energy in GR, don't think of the local energy as being conserved, but rather the "energy at infinity".

This is a very rough overview, the concept of energy in GR is quite subtle and is different from the concept in other areas of physics. There is no *general* notion of conserved energy in GR, but for important cases such as photons falling into Schwarzschild black holes, there are useful concepts of energy.

For more on energy in GR that is not too technical, try the sci.physics.faq:
http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

http://en.wikipedia.org/w/index.php?title=Mass_in_general_relativity&oldid=186756158

might also be useful

josephpalazzo said:
When a photon passes from a high gravity field to a low gravity field, it is redshifted. Therefore it has less energy. Where does that energy loss go to?
The frequency of light does not change as if moves through a gravitational field. What changes is the frequency as measured by local observers. I.e. an observer at a particular position in at a high gravitational potential will measure a frequency which is higher that an observer at a lower position will. However any particular observer will measure a constant frequency. The energy of a photon moving through a gravitational field is conserved if the field is static. Lev B. Okun published an article on this topic. It copy is located at http://arxiv.org/PS_cache/hep-ph/pdf/0010/0010120v2.pdf

Best wishes

Pete

pmb_phy said:
The frequency of light does not change as if moves through a gravitational field. What changes is the frequency as measured by local observers. I.e. an observer at a particular position in at a high gravitational potential will measure a frequency which is higher that an observer at a lower position will. However any particular observer will measure a constant frequency. The energy of a photon moving through a gravitational field is conserved if the field is static. Lev B. Okun published an article on this topic. It copy is located at http://arxiv.org/PS_cache/hep-ph/pdf/0010/0010120v2.pdf

Best wishes

Pete

My interpretation of that paper is as follows.

Measurements of a photon made by a distant observer (at infinity):

Coordinate frequency $$w = w_o$$ ,

Coordinate wavelength $$\lambda = {\lambda_o \over g^2}$$ ,

Coordinate momentum $$p = p_o g^2$$ ,

Coordinate speed $$c = {c_o \over g^2}$$ and

Coordinate energy $$E = homework = {hc \over \lambda}= pc = E_o$$

Where $$g = {1 \over \sqrt{\left( 1-{GM \over R c^2}\right)}}$$ and $$w_o , p_o , c_o , \lambda_o , E_o$$ are measurements of the photon at infinity made by the observer at infinity.

Measurements of a photon made by a stationary local observer:

$$w = {w_o g}$$ ,

$$\lambda = {\lambda_o \over g}$$ ,

$$p = {p_o g}$$ ,

$$c = c_o$$ and

$$E = homework = pc_o = {hc_o \over \lambda} = {E_o g}$$

On the other hand, the rest energy of a particle with non zero rest mass, increases higher up in the gravity well. Conversely, this implies (from the formula given) that the rest mass of a brick lowered towards a black hole goes to zero at the event horizon. The paper seems to suggest that the rest mass represents the gravitational potential energy of the particle.

Last edited:
josephpalazzo said:
When a photon passes from a high gravity field to a low gravity field, it is redshifted. Therefore it has less energy. Where does that energy loss go to?
The observed redshift of the photon has nothing to do with the photon but is due to the relative blueshift of the absorber compared to the emitter.

Last edited:

## 1. Where does the energy go when we turn off a light?

When we turn off a light, the energy does not simply disappear. It is converted into another form, such as heat, sound, or chemical energy. The light bulb's filament, which is made of a material that resists the flow of electricity, heats up and releases energy in the form of heat and light. This is why the light bulb feels warm after being turned off.

## 2. Where does the energy go when we use a battery?

The energy in a battery is stored in the form of chemical energy. When we use a battery, the chemical reactions inside the battery convert this energy into electrical energy, which can then power devices such as phones or flashlights. As the battery is used, the chemical energy is gradually depleted until the battery is no longer able to produce electricity.

## 3. Where does the energy go when we drive a car?

The energy in a car's fuel is converted into mechanical energy to power the engine. When gasoline is ignited in the engine, it releases energy in the form of heat, which expands and pushes the pistons. The pistons then transfer this energy to the wheels, causing the car to move. However, not all of the energy from the fuel is converted into mechanical energy - some is lost as heat and sound.

## 4. Where does the energy go when we use a computer?

When we use a computer, the energy from the power source is converted into electrical energy, which is then used to power the computer's components such as the CPU and memory. The energy is also converted into light energy to display images on the screen. However, not all of the energy is converted into useful work - some is lost as heat and sound, which is why computers can get warm when in use.

## 5. Where does the energy go when we exercise?

When we exercise, our bodies convert food into chemical energy, which is then used to power our muscles. This energy allows us to move and perform physical tasks. However, during exercise, not all of the energy is converted into useful work - some is lost as heat and sound, which is why we feel warm and may sweat during physical activity.

• Special and General Relativity
Replies
7
Views
1K
• Special and General Relativity
Replies
13
Views
918
• Special and General Relativity
Replies
1
Views
385
• Special and General Relativity
Replies
1
Views
349
• Special and General Relativity
Replies
3
Views
335
• Special and General Relativity
Replies
12
Views
750
• Special and General Relativity
Replies
5
Views
1K
• Special and General Relativity
Replies
73
Views
5K
• Special and General Relativity
Replies
10
Views
1K
• Special and General Relativity
Replies
17
Views
1K