Re: Is time actually warped by heavenly bodies?

Well-put question, Scott. Many of the predictions of Einstein's theory of relativity do go against "common sense." Almost a century after its development, there are few practicing scientists who can claim to have an intuitive feel for his theory of gravity. (I, for one, could never pretend to have such insight!) Be aware that our "common sense" is developed as we move very slowly through an environment of relatively weak and almost constant gravitational pull. In such a situation, Einstein's theory predicts behavior identical to Newton's old theories. Then again, even Newton's laws went against the "common sense" of his day, which had survived since Aristotle. The first task of science is to test and challenge notions of "common sense."

Now to your question. The general principle of relativity states that all reference frames are equivalent for the description of natural phenomena regardless of their state of motion. (Paraphrasing only slightly from Einstein himself - Relativity: The Special and the General Theory, Chapter 18.)

Let's assume for a moment that you can build a clock which is not affected by gravity - a reasonable enough assumption based on "common sense." Take that clock, and an old, gravity-dependent clock, and move them far away from any large bodies, deep into a clear region of space, inside a small spaceship. Turn on the engine so that you are accelerating at a constant rate. You, the clocks, and all other objects in the ship will feel as though a constant, uniform force is pushing you toward the "back" of the spaceship. I put "back" in quotes, because in your perception that direction would become "down."

An easy way to measure your own acceleration would be to simply drop a ball and measure the time it takes to "fall" to the floor. Now, since both clocks are moving together, they should measure time the same way, so your acceleration calculation will give the same answer regardless of which clock you use. Note that the rate of fall will be independent of the mass of the object, just like in a gravitational field.

Instead of being in a spaceship, let's do the same measurement on a large planet. Qualitatively the system "feels" the same. There still seems to be a force pushing all things "down," in this case toward the center of the planet. Drop the ball and measure the time it takes to hit the ground. The old clock will be slowed down because it is in a gravitational field. We know this because we've measured it, as you described. Your new, gravity-independent clock will be unaffected. Therefore, you will measure two different acceleration rates.

Now you have a gravity vs. acceleration test. You can use your new- fangled clock to determine whether you are in a gravitational field or just accelerating uniformly. In principle, there doesn't seem to be anything wrong with this idea. Einstein, however, started from the assumption that one can't distinguish between gravity and a uniform acceleration by any physical test. He was motivated to do this by a desire to generalize the laws of physics as much as possible, and encouraged by the fact that nobody had been able to measure any difference between gravitational mass - the response of an object to gravity - and inertial mass - the response of an object to acceleration.

One of the predictions that came from this assumption was the behavior of clocks that you described - all clocks, meaning all physical phenomena. Another prediction is the bending of light by gravity, in spite of the fact that light has no mass. (Think about it - if you were in your accelerating spaceship and looked out at a ray of light travelling at a constant velocity, you would see the light appear to bend as you continued to move faster and faster.) A third prediction is a slight variation in the orbit of a planet in a large gravitational field relative to the prediction from Newton's mechanics.

All three of those predictions have been observed. Mercury's orbit precesses 43 arcseconds per century. (That was actually known before Einstein, but had been "explained" by the existence of a hidden, 10th planet.) Light from stars has been observed to bend 1.7 arcseconds as it passes near the sun. (This can only be seen during solar eclipses, when stars are visible at the edge of the sun.) As you pointed out, atomic clocks have also been measured to run faster when taken higher in the earth's field. (The change in time as a function of altitude is one source of error when using the Global Positioning System. The atomic clocks in the satellites don't run at quite the same rate as ground clocks. This can be included in the calculations if needed, but there are lots of other error sources that have to be handled first, and most systems don't bother.)

So, although there is no a priori reason to think that we couldn't build a gravity-independent clock, Einstein's assumption that we can't resulted in a theory that is not only mathematically elegant, but has passed every test we have been able to construct. Based on that, we conclude that it would be impossible to build a clock as you describe. Given that even massless light is ultimately influenced by gravity, it is hard to imagine what material you'd start with to try and build your clock!

Use common sense, but always question it. The ultimate arbitrator of what makes sense is the universe itself.

Jay