Thursday Throughput: Tensor Calculus Edition

V.Khram, CC BY-SA 3.0 , via Wikimedia Commons

[ThTh1] So let us consider the intricacies of tensor equations for General Relativity. If you check out equation (1), you’ll find … no, wait … don’t go away! This is cool.

OK, let’s actually talk about General Relativity because there are so many elegant and amazing parts of it. One in particular is relevant to your every day life: time distortion. You see, one of the brilliant insights of Einstein was that objects undergoing acceleration will experience distortions in spacetime. Gravity is an acceleration, so gravity distorts spacetime. Space will compress and time will pass more slowly for something within a gravitational field. If it didn’t, the laws of physics would start to break down.

Usually, when we talk about spacetime distortion, we’re talking about things like black holes. A black hole represents the extreme of gravity and something approaching the event horizon will see time slow down and eventually even stop.

But you don’t need to go to a black hole to see general relativity in action. You only need to pick up your phone. Your phone utilizes the Global Positioning System — a series of satellites in high orbit — to track your position. But the GPS satellites are 20,000 kilometers above the Earth’s surface and are subject to only 5% of the gravitational force we are. What his means is that when we look at at GPS satellite, we can measures its clock moving faster than a clock on the surface of the Earth. 38 microseconds per day, enough to thrown your GPS of by about 10 kilometers.

Well, we just set a new record for how small an effect we can measure. Scientists in Colorado managed to shatter the record for the smallest time dilation measured. They were able to measure the change in the running of an atomic clock if it was raised up a single millimeter. They measured atomic motion to one part in a sextillion, that is a one with 21 zeros.

This isn’t just a cool achievement. This opens up new domains of precision physics, including potential searches for dark matter. We will be able to measure the tiniest physical effects to extreme precision. All because, once again, Einstein was right.

[ThTh2] And speaking of General Relativity, on the largest scales, it can distort spacetime enough to bend light. Here is an illustration of how a cluster of galaxies bends the light of a distant supernova.

This animation demonstrates how light from Supernova Requiem, which exploded ~10 B years ago, was split into multiple images by a massive foreground cluster of galaxies.

ANIMATION: NASA, ESTEC, STScI, Greg T. Bacon (STScI)
via @_AstroErikapic.twitter.com/x0qRHikA3i

— Space Explorer Mike (@MichaelGalanin) October 24, 2021

[ThTh3] The internets lit up yesterday with the revelation that Deborah Birx testified to Congress that Donald Trump was distracted during the pandemic and a more attentive Trump could have saved hundreds of thousands of lives. This is nothing new and I’ve already talked about most of it. I remain skeptical that a more engaged Trump would have saved hundreds of thousands of lives.

The one thing that was a bit different this time was that she was more critical of Scott Atlas, who became one of the Preisident’s closest advisors. Atlas denied, as he has for the last year, that he supports a “herd immunity” approach to COVID-19. But these claims started the second he joined the Administration. A number of people have gone on record, including Fauci, Birx and Redfield. And while Atlas may deny he ever advised Trump to pursue herd immunity, his own public statements saying masks didn’t work, touting the Great Barrington Declaration, opposing testing and pushing to re-open schools and businesses even at the height of the pandemic make that claim dubious. So if he doesn’t support the herd immunity approach, he supports all the elements of it.

[ThTh4] The Hubble Space Telescope has gone into safe mode for the second time in four months. Safe mode is a state a spacecraft goes into when something goes wrong and it doesn’t know how to fix. In the case of a space telescope, it ceases science operations, alerts the ground and tries to keep the spacecraft’s solar panels aligned with the Sun while awaiting instructions. This allows the flight engineers time to process the telemetry, figure out what’s happening and coe up with a solution. You want to take your time. You can’t just go up into space and whack the spacecraft upside the head. You want to be very certain of exactly what went wrong, exactly what the solution is and exactly how to implement it.

I don’t want to sound pedantic or anything, but … spacecraft are complicated. There are many many subsystems and many ways they can go wrong. So you want to make sure you have everything covered (and even then, you can mess up). So I expect it will be a few days, if not weeks, before we hear from the Hubble Team. And hopefully, they can get the grand old lady back in business.

[ThTh5] Using ancient records to dig through 3000 years of aurorae. I can only hope that my work is still useful in 3000 years.

[ThTh6] I support renewable energy. But the combination of renewables with shutting down nuclear power is creating a huge spike in fossil fuel useage.

[ThTh7] The planets are so cool:

Watch the rings — and ring arcs! — of #Neptune zip around the planet in this 129-frame movie captured by #Voyager 2 in 1989. pic.twitter.com/Eh4I4F86Ad

— Ian Regan 💙 (@IanARegan) October 22, 2021

[ThTh8] More relativity? Yes, more. One of the mind-boggling aspects of general relativity is that while nothing can move faster than the speed of light, spacetime itself can expand faster than light. One rough comparison is that a runner on a track might be limited in how fast he can run but the track can expand as fast as it wants. The results of this is that there may be large parts of the universe we will never see because they are moving too fast away from us.