# Derivation of gravitational redshift: Mass of a photon?

• SgrA*
In summary, the conversation was about deriving an expression for gravitational redshift in a physics textbook. The expression involves taking a photon as a mass and expending its electromagnetic/quantum energy against a gravitational potential. The mass of the photon is represented by the equation m = (hν)/c² and a photon with a frequency of 10^21 Hz would have a mass approximately 8 times that of an electron. There was discussion about the appropriateness of this approach, with the understanding that the accepted derivation for gravitational redshift involves general relativity. The participant also mentioned that using the energy E instead of the mass m would result in the correct approach.
SgrA*
This is not exactly a homework question.

In a physics textbook, they derive an expression for gravitational redshift of a photon emitted by a star at a large distance from the source by taking photon as a mass traveling up, against a gravitational potential and hence expending its electromagnetic/quantum energy. The mass of the photon is taken to be:
$m = \frac{h\nu}{c^{2}}.$​

According to that equation, the mass of an X-ray photon of $10^{21} Hz$ would be about 8 times mass of an electron.

Is this treatment appropriate?

PS: I'm aware that the "accepted" derivation for gravitational redshift involves general relativity, but the expression derived in this text is a special case of that expression.

If you replace m by the energy E, you get a correct approach, so where is the point of using a relativistic mass...
Anyway, it gives correct results.

A photon with that frequency (I would call it gamma instead of X-ray, but that does not matter) has more energy than an electron at rest, indeed.

## 1. How does the mass of a photon affect gravitational redshift?

The mass of a photon does not play a role in gravitational redshift. Gravitational redshift is caused by the bending of space-time around massive objects, which affects the path of the photon, not its mass.

## 2. What is the equation for calculating gravitational redshift?

The equation for calculating gravitational redshift is Δλ/λ = GM/rc², where Δλ is the change in wavelength, λ is the original wavelength, G is the gravitational constant, M is the mass of the object, r is the distance from the object, and c is the speed of light.

## 3. How is the mass of a photon related to its energy?

The mass of a photon is directly proportional to its energy, according to the equation E=mc². However, this only applies to massive particles, as photons are massless particles and do not have a rest mass.

## 4. Can gravitational redshift be observed in everyday life?

Yes, gravitational redshift can be observed in everyday life. For example, the global positioning system (GPS) takes into account gravitational redshift when calculating the precise location of objects on Earth.

## 5. Is the gravitational redshift effect the same for all types of light?

Yes, the gravitational redshift effect is the same for all types of light. This is because all electromagnetic radiation, including visible light, behaves as a photon and is affected by the bending of space-time caused by massive objects.

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