This one is absolutely, 100% true. A flashlight (or any other source of light) that travels toward the Earth (or any other gravity well) will increase in frequency. This is known as gravitational blueshift (or gravitational redshift when light travels away from a source of gravity).
The part that’s somewhat deceptive is that the change is so small that it cannot be detected with the human eye, so in actuality the light will appear the same color, even though it is actually “bluer”.
Gravitational blueshift is due to general relativity and can be explained in one of (at least) three ways…
1. Time runs slower in a gravitational field; the more gravity, the slower it runs. And the closer you are to the Earth, the higher the gravity. So the frequency will be more because: frequency = 1 / time
2. Anything that falls into a gravity well gains speed, or momentum. This is an increase in energy. Since light is already traveling at the speed limit it can’t go any faster when it “falls” in, so the only way it can gain energy is to increase its frequency.
3. Because of the equivalence principle, gravity is acceleration and the source of the light has lower gravity because it is further away, and so it is accelerating slower at that point than it is when it is closer to Earth with higher gravity, so the frequency shifts due to the Doppler effect.
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