Yesterday, I went to our physics department’s weekly colloquium. The speaker was James Overduin from The Gravity Probe B project at Standford. (His introducer kept on calling it the Gravity Probe B “effort” not project. No idea why? I guess this is what you do when a project lasts for more than two generations.) In the picture is the Probe following orbits around the Earth.
Anyway, he gave a highly non-technical introduction about ideas of gravity, as if none of the audience had wrote theses on General Relativity (GR). Then he gave a quick and dirty overview of what Gravity Probe B is about. They mainly wanted to test a consequence of Einstein theory of GR, and they will do this by watching the spin of a ball in orbit around the Earth. They did many amazing things to have their experimental errors very small so they can see the tiny effects of GR on this ball. I will just give an example that caught my attention. He said they have made the most perfect spheres to date; if their ball was the size of the Earth, the tallest mountain or deepest valley in it would be only 8 meters high or deep. They had to do all kind of amazing things like this.
In his introduction, he talked about a principle called Mach’s Principle. Each GR expert has her own definitions of what the principle is, and as usual Mach himself never stated it. Einstein was the first name it and use his own version of it. Later, he deemed it useless and said that one should never talk about Mach’s Principle. But still, people like it. My one sentence version: Only the stuff objects are made of and their relative motion affect their motion. One cool question that couldn’t be answered for a long time is this: We know the earth is squished on the poles because of its spin around its own axis, so it doesn’t look perfectly spherical. Would it still be squished if you fix the Earth and make the rest of the universe? It is a pretty tough experiment to set up :) Big debate before Mach, but in relativity it turns out the answer is Yes! it would be squished. Somebody actually did the calculation and I believe others actually tried to do the experiment, but on a smaller scale; they tried to spin something the size of a room around itself and sees if things inside gets squished. But turns out the calculation says the squishing in such a small setup will be about the size of an atom. They couldn’t measure that at the time.
Writing this, I found myself explaining more about Mach’s Principle and where it came from. Knock yourself out.
This is my own understanding of Mach’s Principle in a glance: First, it is an assertion that only matter influences matter. Mach wrote much about how absolute space can have no influence on real things, rejecting one of the basic ideas in Newtonian Mechanics. (Absolute space just means that when something moves its motion is not only relative to other objects, but its motion is absolute in reference to absolute space.) Newton had a nice experiment to “prove” the existence of this absolute space “stuff”, as awkward as that seems. Get a bucket, fill it up with water, and hang it from the ceiling, then spin the bucket around its axis. If the spinning is fast enough, water will rise up the walls of the bucket and make the surface of water concave, due to the so-called centrifugal force acting on rotating objects. Here is the reasoning. First, bucket spinning and water at rest, water is flat. Second, bucket and water spinning together, water becomes concave. Third, bucket stops but water continues spin, still water is concave. The only conclusion is the water being concave has nothing to do the bucket’s motion or even the water’s motion relative to bucket, but it must be caused by the water’s own “absolute” motion. Newton’s calls its the water’s motion with respect to absolute space. It is an ugly but inevitable conclusion. Mach didn’t like this and he postulated that this effect is only due to the relative motion of the bucket and water to the distant stars (now clusters of galaxies). But it wasn’t till special relativity came that people were able to dismiss the notion of absolute space and time and talk about the dynamic spacetime. The resolution in a form like this: the water climbing the walls of the bucket always follow the most natural path there is, and relative acceleration “curves” the path of water to make it rise up the bucket’s walls. Punchline: Unlike Newton’s “relative”, “relative” here means relative to all the rest of the universe not just the bucket.
In the above photo, these paths are drawn out for the probe, and guess what, they are very close to Kepler’s and Newton’s old orbits.