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Lets take the hydrogen line frequency of $h_0=1420405751.7667\,\text{Hz}$. This is the frequency we get if the generating hydrogen atom is located far away in space where there is (nearly) no gravity.

When the wave reaches us on earth, it is blue shifted, meaning we will measure a higher frequency.

How does this compare to the frequency we measure from a Hydrogen atom on earth's surface? Does gravitational time dilation lead to a red shift or a blue shift as compared to $h_0$ or will me measure just $h_0$ and why?

Harald
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1 Answers1

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Gravitational time dilation refers to how much slower time moves in gravity compared to far away. If both hydrogen and observer are in gravity of the same strength, such as at the same height on Earth, then their gravitational time dilation is the same. Therefore there is no difference in the time motion between then. Thus the observer would measure the base frequency $h_o$.

The time dilation on the Earth surface is rather small, less than one part in a billion and is equal to the time dilation at the escape velocity of 11.2 km/s. So the gravitational time dilation on Earth is the same as the relativistic time dilation in Special Relativity at the speed of 11.2 km/s.

$$t_o=t_f\sqrt{1-\dfrac{2GM}{Rc^2}}$$

safesphere
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  • Well, "on Earth" was just an example anyway and I am interested in you general answer that $h_0$ will be measured under gravity. – Harald Oct 26 '17 at 14:10
  • @Harald Did I answer your question or what is your specific question that still needs answering? – safesphere Oct 26 '17 at 14:13