## From Ethan Siegel: ” How far does gravity reach?”

Nov 7, 2014
Ethan Siegel

“In my dreams and visions, I seemed to see a line, and on the other side of that line were green fields, and lovely flowers, and beautiful white ladies, who stretched out their arms to me over the line, but I couldn’t reach them no-how. I always fell before I got to the line.” -Harriet Tubman

It’s the end of the week once again, which means we get to take a look at your reader submissions for Ask Ethan, and choose my favorite to share with you. This week’s entry comes from one of my readers who’s been following Starts With A Bang the longest (since my first few months of blogging way back in 2008): Frank Burdge. He asks the following head-scratcher:

If the Universe is not infinite, then what can be said about the range of the gravitational and electromagnetic forces?

This is actually an incredibly profound question, when you think about it. Consider what we know about the gravitational and electromagnetic forces, first off.

Image credit: Regents Physics, via http://aplusphysics.com/wordpress/regents/tag/inverse-square-law/.

It isn’t the magnitude of the forces, or the nature of attraction/repulsion that I want you to consider, but rather the fact that — at long ranges — these are inverse-square forces, meaning that as you double the distance between two such objects, the force between them drops to one-fourth what it was at the previous distance. This is a very special relationship, and not only do gravitation and electromagnetism, so do some other important physical properties, such as the effects of light, sound, and radiation.

Why is this very special? Consider how any of these things — light from a star, for example — spread out as you move farther away from the source.

Image credit: Wikimedia Commons user Borb.

They move radially outward in a sphere, so that a pulse — of light, again, for example — would spread out in an ever expanding spherical shell. Now, why is this special? Because the surface area of a sphere has a very specific formula: A = 4πr^2, where the “r^2” is the important part.

Why? Because if the area expands according to r^2, but the force drops according to an inverse square law (i.e., r^-2), then we can say that phenomenon has an infinite range. This means you can draw a sphere of any size centered around an object — a gravitational source (a mass), an electric source (a charge), a light source (a star), etc. — and the total amount of stuff acting on that sphere, whether it be force or flux, will be the same when you add up all the different parts of the sphere. This is true not only for the whole sphere, but for any given amount of solid angle on the sphere!

Image credit: R Nave of Hyperphysics, via http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html.

So that’s what we mean by gravitation being an “infinite range” force.

But the Universe — at the very least, the part of it observable and accessible to us — is not infinite at all! Quite to the contrary, despite the fact that we can see the starlight coming from hundreds of billions of galaxies, that’s not even such a big number. It’s a beautiful sight, and it boggles the mind to look at. (Seriously, take some time and look at it!) But in no way — despite its grandeur — should you conflate its vastness with infinity.

Image credit: NASA, ESA, R. Windhorst, S. Cohen, M. Mechtley, and M. Rutkowski (Arizona State University, Tempe), R. O’Connell (University of Virginia), P. McCarthy (Carnegie Observatories), N. Hathi (University of California, Riverside), R. Ryan (University of California, Davis), H. Yan (Ohio State University), and A. Koekemoer (Space Telescope Science Institute).

Sure, it seems pretty big, but when you consider that there are billions of times that many grains of sand on Earth’s beaches as there are galaxies in the observable Universe, it doesn’t seem so big. The reason we can’t access more has to do with the fact that the Universe hasn’t been around forever, but rather has only had about 13.8 billion years since the Big Bang for things like light (and gravitation) to reach out towards us.

Image credit: James Schombert of University of Oregon, via http://abyss.uoregon.edu/~js/ast121/lectures/lec06.html.

Or more accurately, to reach spherically outward away from their sources. We do the same thing: the gravitation from every particle in our bodies, on our planet and in our galaxy has been reaching out, “grabbing” at the speed of gravity (which is the speed of light) with a force falling off in magnitude as ~1 / r^2 (but reaching out with an increasing area according to ~r^2) since what we conceive as “our Universe” began.

Image credit: WiseGEEK, via http://www.wisegeek.org/what-happened-after-the-big-bang.htm#.

Now, this — the observable Universe, the part reachable by light, gravity, and other finite-speed phenomenon — is not to be confused with however big (or possibly infinite) the entire Universe, including the unobservable part, actually is.

Images credit: Rob Knop, via http://www.galacticinteractions.org/?p=1623, of the observable Universe at the moment the Universe could first be described by the Big Bang (L), and of the unobservable Universe as well at the same moment (R).

We have good reasons to believe that the entire Universe is far bigger than the observable parts of it are, but our signals are unable to reach it, due to the fact that there’s only been a finite amount of time that we’ve been emitting signals and that the speed at which these signals propagate is also finite.

But this is not a bug with our Universe: it’s a feature!

Image credit: European Gravitational Observatory, Lionel BRET/EUROLIOS.

Imagine the Universe if signals propagated infinitely fast, or if we could feel the gravitation, see the light, or otherwise experience the effects of things from far beyond what ought to be accessible to us.

We’d find ourselves — and likely many other parts of our Universe — catastrophically pulled in a random direction, seemingly without cause. We’d have the entire night sky lit up by sources that ought never to have reached our eyes.

Image credit: James Schombert of University of Oregon, via http://abyss.uoregon.edu/~js/ast123/lectures/lec15.html.

And we, ourselves, would be exerting far more force that we’ve had any physical right to do. In short, the laws of physics would break down, as General Relativity could no longer describe where we live, there would be a catastrophe of too much energy density in our Universe, and — as a consequence of that gravitational binding energy — the Universe itself would inevitably recollapse in short order.

Image credit: Shashi M. Kanbur of SUNY Oswego, via http://oswego.edu/~kanbur/.

To quote Egon from Ghostbusters, “It would be bad.”

So what we have, instead, is gravitation, electromagnetism, and all the other “infinite range” forces reaching the distances they could have reached after traveling at the speed of light in a 13.8 billion year old Universe that’s expanded according to our own unique history, or about 46 billion light years. This is — since the speed of gravity and the speed of light are identical — also equal to the size of our observable Universe in all directions!

Image credit: Wikimedia Commons user Azcolvin429.

And that’s how far the range of the gravitational and electromagnetic forces extend! Thanks for a tough but informative question, Frank, and if you want to see your question featured on Ask Ethan, send in your questions and suggestions here. The next column could be all about whatever you choose!

Starts With A Bang! is a blog/video blog about cosmology, physics, astronomy, and anything else I find interesting enough to write about. I am a firm believer that the highest good in life is learning, and the greatest evil is willful ignorance. The goal of everything on this site is to help inform you about our world, how we came to be here, and to understand how it all works. As I write these pages for you, I hope to not only explain to you what we know, think, and believe, but how we know it, and why we draw the conclusions we do. It is my hope that you find this interesting, informative, and accessible.

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## From Science@NASA: “NASA Announces Results of Epic Space-Time Experiment” 2011

[This is from 2011, but it just hit NASA’s Twitter feed]

May 4, 2011
Dr. Tony Phillips

[Albert Einstein] was right again. There is a space-time vortex around Earth, and its shape precisely matches the predictions of Einstein’s theory of gravity.

Dr. Albert Einstein, Nobel Laureate

Researchers confirmed these points at a press conference today at NASA headquarters where they announced the long-awaited results of Gravity Probe B (GP-B).

Gravity Probe B (GP-B)

“The space-time around Earth appears to be distorted just as general relativity predicts,” says Stanford University physicist Francis Everitt, principal investigator of the Gravity Probe B mission.

An artist’s concept of GP-B measuring the curved spacetime around Earth.

“This is an epic result,” adds Clifford Will of Washington University in St. Louis. An expert in Einstein’s theories, Will chairs an independent panel of the National Research Council set up by NASA in 1998 to monitor and review the results of Gravity Probe B. “One day,” he predicts, “this will be written up in textbooks as one of the classic experiments in the history of physics.”

Time and space, according to Einstein’s theories of relativity, are woven together, forming a four-dimensional fabric called “space-time.” The mass of Earth dimples this fabric, much like a heavy person sitting in the middle of a trampoline. Gravity, says Einstein, is simply the motion of objects following the curvaceous lines of the dimple.

If Earth were stationary, that would be the end of the story. But Earth is not stationary. Our planet spins, and the spin should twist the dimple, slightly, pulling it around into a 4-dimensional swirl. This is what GP-B went to space in 2004 to check.

The idea behind the experiment is simple:

Put a spinning gyroscope into orbit around the Earth, with the spin axis pointed toward some distant star as a fixed reference point. Free from external forces, the gyroscope’s axis should continue pointing at the star–forever. But if space is twisted, the direction of the gyroscope’s axis should drift over time. By noting this change in direction relative to the star, the twists of space-time could be measured.

In practice, the experiment is tremendously difficult.

One of the super-spherical gyroscopes of Gravity Probe B.

The four gyroscopes in GP-B are the most perfect spheres ever made by humans. These ping pong-sized balls of fused quartz and silicon are 1.5 inches across and never vary from a perfect sphere by more than 40 atomic layers. If the gyroscopes weren’t so spherical, their spin axes would wobble even without the effects of relativity.

According to calculations, the twisted space-time around Earth should cause the axes of the gyros to drift merely 0.041 arcseconds over a year. An arcsecond is 1/3600th of a degree. To measure this angle reasonably well, GP-B needed a fantastic precision of 0.0005 arcseconds. It’s like measuring the thickness of a sheet of paper held edge-on 100 miles away.

“GP-B researchers had to invent whole new technologies to make this possible,” notes Will.

They developed a “drag free” satellite that could brush against the outer layers of Earth’s atmosphere without disturbing the gyros. They figured out how to keep Earth’s magnetic field from penetrating the spacecraft. And they created a device to measure the spin of a gyro–without touching the gyro. More information about these technologies may be found in the Science@NASA story “A Pocket of Near-Perfection.”

Pulling off the experiment was an exceptional challenge. But after a year of data-taking and nearly five years of analysis, the GP-B scientists appear to have done it.

“We measured a geodetic precession of 6.600 plus or minus 0.017 arcseconds and a frame dragging effect of 0.039 plus or minus 0.007 arcseconds,” says Everitt.

For readers who are not experts in relativity: Geodetic precession is the amount of wobble caused by the static mass of the Earth (the dimple in spacetime) and the frame dragging effect is the amount of wobble caused by the spin of the Earth (the twist in spacetime). Both values are in precise accord with Einstein’s predictions.

“In the opinion of the committee that I chair, this effort was truly heroic. We were just blown away,” says Will.

An artist’s concept of twisted spacetime around a black hole. Credit: Joe Bergeron of Sky & Telescope magazine.

The results of Gravity Probe B give physicists renewed confidence that the strange predictions of Einstein’s theory are indeed correct, and that these predictions may be applied elsewhere. The type of spacetime vortex that exists around Earth is duplicated and magnified elsewhere in the cosmos–around massive neutron stars, black holes, and active galactic nuclei.

“If you tried to spin a gyroscope in the severely twisted space-time around a black hole,” says Will, “it wouldn’t just gently precess by a fraction of a degree. It would wobble crazily and possibly even flip over.”

In binary black hole systems–that is, where one black hole orbits another black hole–the black holes themselves are spinning and thus behave like gyroscopes. Imagine a system of orbiting, spinning, wobbling, flipping black holes! That’s the sort of thing general relativity predicts and which GP-B tells us can really be true.

The scientific legacy of GP-B isn’t limited to general relativity. The project also touched the lives of hundreds of young scientists:

“Because it was based at a university many students were able to work on the project,” says Everitt. “More than 86 PhD theses at Stanford plus 14 more at other Universities were granted to students working on GP-B. Several hundred undergraduates and 55 high-school students also participated, including astronaut Sally Ride and eventual Nobel Laureate Eric Cornell.”

NASA funding for Gravity Probe B began in the fall of 1963. That means Everitt and some colleagues have been planning, promoting, building, operating, and analyzing data from the experiment for more than 47 years—truly, an epic effort.

What’s next?

Everitt recalls some advice given to him by his thesis advisor and Nobel Laureate Patrick M.S. Blackett: “If you can’t think of what physics to do next, invent some new technology, and it will lead to new physics.”

“Well,” says Everitt, “we invented 13 new technologies for Gravity Probe B. Who knows where they will take us?”

This epic might just be getting started, after all….

NASA leads the nation on a great journey of discovery, seeking new knowledge and understanding of our planet Earth, our Sun and solar system, and the universe out to its farthest reaches and back to its earliest moments of existence. NASA’s Science Mission Directorate (SMD) and the nation’s science community use space observatories to conduct scientific studies of the Earth from space to visit and return samples from other bodies in the solar system, and to peer out into our Galaxy and beyond. NASA’s science program seeks answers to profound questions that touch us all:

This is NASA’s science vision: using the vantage point of space to achieve with the science community and our partners a deep scientific understanding of our planet, other planets and solar system bodies, the interplanetary environment, the Sun and its effects on the solar system, and the universe beyond. In so doing, we lay the intellectual foundation for the robotic and human expeditions of the future while meeting today’s needs for scientific information to address national concerns, such as climate change and space weather. At every step we share the journey of scientific exploration with the public and partner with others to substantially improve science, technology, engineering and mathematics (STEM) education nationwide.

## From Symmetry: “Matter, antimatter, we all fall down—right?”

April 30, 2013
Ashley WennersHerron

Scientists perform the first direct investigation into how antimatter interacts with gravity.

What goes up must come down, the saying goes. But things might work a little differently with antimatter.
A CERN-based experiment has taken the first step in investigating exactly how antimatter interacts with gravity.

Photo: CERN

Atimatter particles should mimic those of matter particles. If it turns out that there is a difference, it will be a sign of dramatically new physics.
So far, no one has been able to test directly how antimatter interacts with gravity—but the ALPHA experiment has begun to try.

The ALPHA experiment’s main purpose is to trap and study antihydrogen atoms, the antimatter partners of hydrogen atoms. The antihydrogen atoms are held in place inside a tube by magnetic forces. Physicists on ALPHA have trapped more than 500 antiatoms since 2010. They keep them in their trap for up to about 16 minutes. When they turn off their magnets, the antiatoms fall out of the trap. A highly sensitive detector tracks the antiatoms and records where they first come in contact with matter and annihilate.”

Symmetry is a joint Fermilab/SLAC publication.

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