QotW: Does relativity make moon rocks older?
Ranjit wrote in to ask, "As gravity and time have an inverse relationship, at some time in the future, will astronauts bring back moon rocks that are older than the Earth?"
James Tytko spoke to Proffessor Ruth Gregory from King's College London who helped makes sense of relativity in a relatively straightforward way...
Ruth - What you are probably referring to, Ranjit, is the fact that gravitational fields affect the local passage of time, with time slowing down in a strong gravitational field, such as near a black hole.
James - For this theory, we have Albert Einstein to thank, who abolished the Newtonian idea that we inhabit a 3 dimensional universe in which time passes uniformly throughout.
Ruth - The effect we are discussing is known as gravitational redshift, an amazing example of how taking simple physical knowledge can lead to a deep result. We all know it takes work to climb a flight of stairs, and that is no different for a quantum of light, called a photon.
James - Light comes in little packets, photons. If a photon loses energy (such as when it experiences stronger gravity), it increases its wavelength, and since the red end of the spectrum of visual light is the longest, we call this phenomenon redshifting.
Ruth - What was remarkable about Einstein’s intuition is that he realised this frequency of light was like the ticking of a clock. Think of a wave, from crest to crest is the wavelength, and the frequency is the number of crests passing per second. Each crest is like the tick of a clock, and a second for an observer deeper in a gravitational well would be longer than a second for someone outside this gravitational potential.
James - This effect has been verified experimentally, but the effect is tiny for objects in our solar system, such as the Earth and Moon.
Ruth - It requires the supreme precision of atomic clocks to see. For example, the difference in a clock at the Earth’s surface and one at the Moon is roughly a second in a human lifetime. Even over 5 billion years the difference is just a handful of years. So, to answer your question, no, it is not going to be a detectable effect for astronauts collecting rocks from the Moon for quite some time! Great question though!
James - So Ranjit, as I understand it, Gravitational time dilation can equivalently be interpreted as gravitational redshift, during which, photons losing energy in higher gravitational potential experience an increase in their wavelength, and thus a slowing down of the passage of time. The effect is so tiny in the context of the earth and the moon that, sadly, you would not expect astronauts to ever be bringing back moon rocks which look visibly any older than they would be if they had been residing here.