Ask a Physicist: Would a gravitron work in deep space?

In this week's "Ask a Physicist" we tackle the question of whether you could spin yourself nauseous if the universe really were empty, and why so many scifi writers get artificial gravity wrong.

Welcome to the first of our new bimonthly "Ask a Physicist" column. All told, I've received over 150 questions from curious readers on everything from ghosts and the afterlife to atoms and black holes. I decided to bow out of spiritual questions and focus on ones about physics. Today's question comes from Professor Andrew Higgins who asks:

Is there an absolute reference frame for rotation? ... Imagine a space station in deep space (interstellar). Let's say it spins to generate artificial gravity, a la the space station in 2001. What is it spinning relative to? The stars? Which stars? What if they are in a dust cloud and can't see any stars?

I've gotten some grief in the past for turning an overly serious eye to critiquing the science of science fiction, but in your darkest hours, you know you've been guilty of far more egregious nit-picking. Questions like "Why do nearly all aliens look just like us (albeit with forehead makeup)?" or "How do I build a warp drive?" haunt your dreams. They're also harmless enough because after all, we don't really know those things might really work.

There are others, like artificial gravity, that we know how to make work, and nearly every show and movie gets wrong. There's simply no excuse. 2001 got it right, and that was over forty years ago. Babylon 5 got it right, and they were broadcast on TNT, for goodness sake.

You make artificial gravity by spinning your ship. It's as old as Newton's laws. The natural state of motion for a particle is to move in a straight line and at a constant speed. By spinning the ship, and assuming that the radius of the ship is large enough so that your head and feet are moving at roughly the same speed, you'll feel a comfortable artificial gravity where the "out" is "down," and everything behaves like earth normal.

Newton could have designed artificial gravity ships, but he was plagued by a question that wouldn't be answered until the early 20th century. One of the central themes in Newtonian mechanics (and Einstein's special relativity, by the way) is the idea that there's no way that you can tell if you are moving at a constant speed and direction or whether you are standing still. As a result of this, you get some pretty confusing results. But shouldn't that apply to all motion, not just motion in a straight line?

Supposing there was a bucket in deep space with nothing around it, and we fill the bucket with water and start the bucket spinning around the vertical axis. As it spins, the water will rise up the sides of the bucket, and act like a centrifuge, just like Clarke's Discovery One or one of those gravitron rides at the amusement park.

How do the bucket and the water know they're spinning if there's nothing to compare the motion to? As an added bonus, try answering this question without using the word "space."

The philosopher Ernst Mach picked up this question in the 19th century and concluded:

[The] investigator must feel the need of ... knowledge of the immediate connections, say, of the masses of the universe. There will hover before him as an ideal insight into the principles of the whole matter, from which accelerated and inertial motions will result in the same way.

Or, more simply, "Mass there influences inertia here."

The notion is a little more sophisticated than it seems at first. Of course distant mass affects objects here. That's just a little thing called gravity. But that's not what Mach was saying. What he was saying was that if you were to somehow average over all of the stuff in the universe, we could find some sort of absolute rest frame and then Newton's bucket would rotate compared to that.

We probably would have forgotten about Mach in this context (although he would still, of course, be remembered by the shaving system that bears his name), were it not for the fact that Einstein was obsessed with Mach's principle. Does Mach's principle holds up in relativity?

In special relativity – the theory of mechanics in the absence of gravity - no gravity means no distant stars and thus no fixed frame. And yet, even in an (otherwise) empty universe, special relativity says that you would feel artificial gravity in a gravitron. When we do particle physics calculations, for example, we never include gravity, but we always include centripetal force and angular momentum, and everything comes out fine. The problem is that it's not clear whether we've just gotten lucky or whether there's something deeper. We don't really know whether these calculations would work in a truly empty universe.

Fortunately, both for our existence and for answering this puzzle, ours is not an empty universe, and general relativity tells us just how to deal with the masses in the universe. John Wheeler gave a succinct (and widely quoted) summary: "Space tells matter how to move, and matter tells space how to curve." What's more (and as a freebie answer to the three or four folks who asked it) the gravitational waves travel through space at the speed of light. In other words, so long as there are things other than the bucket in the universe, the overall gravitational field has to take account of all of everything self consistently.
In other words:

1. General relativity seems to obey Mach's principle in universes with stuff in them.

2. Our universe has stuff in it.

3. 2001 would work in even the darkest, loneliest corner of the cosmos. Except for the weird psychodelic part. I never quite understood that.

Now that we've got that worked out, there's no excuse for bogus artificial gravity devices in your sci-fi anymore. You can concentrate on more pressing issues like FTL drives or why nearly all aliens speak the same language.

Dave Goldberg is the author, with Jeff Blomquist, of "A User's Guide to the Universe: Surviving the Perils of Black Holes, Time Paradoxes, and Quantum Uncertainty." (Become a fan on facebook!) He is an associate professor of Physics at Drexel University. Feel free to send him your questions about the universe.