Time down Mines and Moons

It seems to be my week for starting posts with Moon pictures, so I might as well start this one by showing you a great picture Infinity took of the Moon on July 7th . . .

Credit: Infinity, one of the forum moderators

. . . a very similar version of which just made APOD today. You can see some of Jupiter's moons if you look closely, but I still think Infinity's is prettier.

Credit: APOD.

For many years I thought the Moon was a sixth of the mass of the Earth - because its gravity is a sixth of the Earth's. Then I learnt (on the forum, of course, from Waveney) that it's much smaller than that: only 0.0123 Earth! I asked why its gravity wasn't much smaller - evidently it's because of the proximity to the centre of mass, and there's some scary formula stating how much gravity increases as you get nearer a planet. If anyone can find it on the forum, they earn several smileys - I have done all kinds of fancy searching to no avail so far.

But it didn't make complete sense to me. What if you're in the very core of a planet, or any body in space? The mass is all around you then - there'd be nothing pulling on you. As Russell Stannard explains beautifully in "Black Holes and Uncle Albert", the natural path of anything is in a straight line through space. But "through" doesn't mean like going through water, chopping it and brushing it aside; it means following the path of space, going along with it. And sometimes space is curved.

Basically, it means the natural path of any object is where gravity takes you. If you're sitting in your chair, you're not in your natural state. Gravity is pulling on you but you can't go where it wants. Even if you find the deepest mine you can, and lie down.

So I asked in a thread which I'm now rather proud of: What does gravity do as you get down a mine? - Or more specifically, because I knew that gravity would tail off as you get closer to the body's centre: What does time do down a mine?

Gravity causes all sorts of strange effects, one of the strangest of which slowing down time. It's not that you can't run so fast under the pressure of strong gravity. It's not something you notice. It's time itself which is slowed down. Your thinking, atoms' movement - the most wonderful proof I heard of this observation was during a lecture at Astrofest 2008, a story of two pulsars orbiting each other, and their beats slowing down when they were closest together. Stannard's earlier book, "The Time and Space of Uncle Albert", deals with the strange effects of special relativity, or "the physics of the very fast": namely, time slowing down at high speeds. Or, rather, at high acceleration or decceleration and changing motion. It's often discussed in terms of the twin paradox, though he doesn't name it or talk about it in particular. The books present it in an original way, designed for children to be able to grasp. (I pretty much did, aged 10-ish!)

The essence of my question was: On the surface of a very heavy planet, time runs slower on the ground (surface) than it would at the top of a skyscraper or in an aeroplane. (In fact, this is true of all planets, and all bodies with gravity; but it's more noticeable when the gravity is very strong.) But what about underneath the surface? What happens nearer the core of the planet?


Edd told me off the thread that time would speed up again down the mine, as there would be less net gravity. This is what I suspected. Hah! Meanwhile, the thread went in other directions.

Alromario asked what things would look like from his 6th floor window, if time was speeded up or slowed down enough for us to notice. Would cars in the street appear to go faster? No - because on the 6th floor, his time is speeded up and the cars' time is slowed down; they would appear to go slower. (If they looked up, they'd think he was scuttling around very fast up there!)

The same happens if you accelerate very fast. In "Black Holes and Uncle Albert", the heroine Gedanken is driving a rocket. She's sitting in the middle of it. At each ends are lights, designed to give out a flash every second. Once she starts accelerating, the photons at the front get to her more frequently than every second - they have less far to go. Since the speed of light from her point of view can't change, this means that their time is affected: their time has speeded up, and the light flashes more than once a second! The opposite, of course, is true at the other end of the rocket. Each flash of light needs more time to catch up with her. Each one has further to go. So their time seems to be slowed down.

Gravity and acceleration can fake each other. Gravity bends space, and light is affected near a heavy planet, as in the cartoon I drew above. It finds it easier to get to the planet than away from it. If we lived on a black hole, I daresay Alromario's skyscraper would look a lot higher: this is why, and this is what causes gravitational lensing:


But as Weezerd points out in the topic, light does get away from the planet if you shine it upwards! And then another interesting effect comes in . . .


Gedanken noticed in her rocket that the light at the front had turned blue, the light at the back red. This is because of the frequency of the light, and it's why we see colours. Blue spiral galaxiess are blue because they're giving off the energetic light of star formation. Their light-waves have a higher frequency than the less energetic red light from elliptical galaxies.

Hang on, we ask. How in the Universe does gravity affect frequency?

Well, it doesn't work like redshift. That's when space is stretching out, pulling bits of the Universe away from each other. Light getting from one star in one galaxy to another star in another galaxy finds that the racing track it's on has expanded. The space it goes through is expanding - like a birthday message on a balloon being blown up. And therefore the wavelength of light gets longer, and the colour of the light turns red.

Graham D writes a long explanation which is worth a read - and I found it particularly interesting that the photon is not really emitted until it is absorbed by something (in the language of the Clangers, "you can't see light until it shines on something"). The gravitational well distorts the space around it. You can think of it as the photon fighting to get away from the planet, but finding it a lot easier to get to it.

If you dropped a light into a black hole, the photons would have a real struggle getting out to you. They would inch their way out, and you'd see the light as it was longer and longer ago, rather than where it is at each progressive "now". It would appear to slow down as it got further in. And the wavelength of light would be stretched out and turn red. Gedanken is confused by this effect in the story, and just for once, she doesn't make the sensible decision . . .

Next question! If you shone a white or yellow light up a mine from the inside of the very heavy planet, what colour would it look? I suspect slightly blue.

You're never too old or young to learn about one of the most beautiful ideas ever thought up, relativity.

In fact, you're never too old or young to learn anything at Galaxy Zoo.