# Gravitational Redshift of a laser

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Torog
If we run two identical lasers and put one at sea level and one on top of a high mountain, will they operate at different frequencies?

Staff Emeritus
2022 Award
They might depending on what altitude you're measuring their respective frequencies from. Measuring at an altitude different from the altitude of the respective laser will produce a red/blueshift. Measuring the frequency of the mountain laser from sea level will produce a blueshift, and measuring the frequency of the sea level laser from a higher altitude will produce a redshift.

Mentor
If we run two identical lasers and put one at sea level and one on top of a high mountain, will they operate at different frequencies?
Adding on to what @Drakkith said, if you measure their frequencies with identical local clocks they will read the same.

Torog
What if I use the lasers as clocks - measure the pulses, divide many times and put the data to a readout. Shouldn't the clock (laser) on the mountain be slower?

I do understand that light as it falls into a gravitational field it gains energy and moves to blue and the opposite happens as light has to work its way out of a gravitational field.

Mentor
Shouldn't the clock (laser) on the mountain be slower?
All of the above still applies. It will be slower than normal for any clock above it, faster for any clock below it, and unaltered for a clock right next to it.

Torog
Excuse me if I shift to cosmology. From what I understand the observed red shift of stars should come from three factors - according to the present model - First is a red shift given by the recession velocity (or general expansion of the Universe) second by the red shift caused by light having to make its way out of the gravitational field and third by the light having come from a star, quasar or other with a strong gravitational field where time and chemical processes run slower (redder) due to time being slower in the heavy gravitational field.

Mentor
First is a red shift given by the recession velocity (or general expansion of the Universe) second by the red shift caused by light having to make its way out of the gravitational field and third by the light having come from a star, quasar or other with a strong gravitational field where time and chemical processes run slower (redder) due to time being slower in the heavy gravitational field.
The second and third are the same.

jartsa
Excuse me if I shift to cosmology. From what I understand the observed red shift of stars should come from three factors - according to the present model - First is a red shift given by the recession velocity (or general expansion of the Universe) second by the red shift caused by light having to make its way out of the gravitational field and third by the light having come from a star, quasar or other with a strong gravitational field where time and chemical processes run slower (redder) due to time being slower in the heavy gravitational field.

We can combine redshift and gravitational time dilation like this:

$$totalRedshift = \sqrt {redshift * gravitationalTimeDilation }$$

Or like this:

$$totalRedshift = 0 * redshift + gravitationalTimeDilation$$

Or like this:

$$totalRedshift = redshift + 0 * gravitationalTimeDilation$$

That's a joke or something. But if we calculate the redshift factor and the gravitational time dilation factor, we always get the same number. So the formulas are correct, in a way.

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