Fri. Mar 31st, 2023
Punctual time travel depends on how fast the Earth rotates

Want to set up your time machine to catch an eclipse with a group of curious Mesopotamians in the year 700 BCE? It’s not as easy as you think. You have to adjust to the subtle slowing of the Earth’s rotation over time and know the history of sea level change – and even those bits of knowledge may not be able to get you there in time. That’s the conclusion reached by a team led by Harvard’s Carling Hay when they looked at what the ancient astronomical records tell us about our planet’s timekeeping.

Tidal forces caused by the gravitational pull of the sun and moon act as a brake on the spinning Earth, gradually lengthening the day. It takes a long time for this to yield anything meaningful, but the Earth has been around for a very long time: 400 million years ago, each year contained 400 days. At the current rate, days are getting longer by just a few milliseconds per century, so it would take more than 3.5 million years to add a minute.

This is not the answer to your plea for more time each day to deal with your workload.

But if you were to compare two clocks, one atomic clock ticking with perfect accuracy and another clock exactly in sync with the sun, those milliseconds would add up faster than you might think. If the two clocks show exactly the same time in 500 BCE, they would be 5 hours apart by the current day. So if your time machine works on the kind of time that an atomic clock measures, you may not arrive at the time you intended.

Braking by tidal forces is not the whole story here. Researchers have used astronomers’ careful observations over the centuries of celestial events such as eclipses to work out how our two clocks might have actually drifted apart over the past 3,000 years. By reversing a virtual solar system, we can calculate the time and position in the sky that events should have occurred and use that to examine the Earth’s slowing rotation.

If we simulate the slowdown due to tidal forces alone, we get a bigger difference between the clocks than these historical observations indicate – we’re spinning faster than we should be. Some sort of acceleration of the Earth’s rotation counteracted some of that slowing down. Plus, the change in the length of the day hasn’t been perfectly consistent – there seem to have been some ups and downs along the way.

What could explain these differences? To answer that question, we have to dismiss the well-known example of the angular momentum of a spinning figure skater, which is commonly used to explain spin acceleration. The tighter a skater brings his or her arms to the body, the faster the skater turns. Push the arms out and the rotation slows down. The difference in rotational speed has everything to do with the distribution of mass, and this applies to the Earth as well.

For example, a lower sea level near the equator due to the formation of ice caps at high latitudes may speed up the Earth’s rotation slightly. But those ice sheets also push out the rock underneath, pushing the mantle around a bit and dividing some mass into one different way. Melt the ice away and that stone slowly bounces back. All this shifting of mass has an effect on rotational speed.

So perhaps the small variations in global sea level (before modern climate change) over the past few thousand years can explain the variations in the elongation of the day. That’s the idea the team wanted to test.

The researchers used an accurate reconstruction of global sea level over the past 3,000 years and a complex model that accounts for variations in regional sea level caused by a variety of factors. For an extreme test, all changes in global sea level are attributed to losses (or gains) of glacial ice rather than warming or cooling of the oceans, which shouldn’t change Earth’s mass distribution.

The results of these simulations were used to calculate changes in Earth’s rotational speed, which the team compared to our data from historical eclipse observations.

The simulated effect was obvious but not overwhelming. The influence of sea level could explain some of the most recent swing in the rotational trend around 1200 AD, but it didn’t really come close to explaining the earlier swing around 500 AD and 700 AD. However, those earlier squiggles are based on just a few eclipse sightings, so we’re less sure about the exact timing of things there.

Sea level probably played a role in the story of time over the last millennium, but other factors must have been involved, especially before that. Factors may include shifting exchanges of angular momentum between Earth’s liquid outer core and mantle. Tracking down the cause of a few extra milliseconds added to the length of the day is no easy feat.

We tend to be most interested in studies that provide confident explanations, but results that quantify more subtle relationships — or rule out certain explanations — push science forward just as much. In this case, the crazy fact that we’re working out very precisely how the Earth’s rotational speed changes over time only gets more interesting as it gets more complex.

Earth and planetary science letters2016. DOI: 10.1016/j.epsl.2016.05.020 (About DOIs).

By akfire1

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