Kenneth's Picnic

We’ve just been watching the BBC’s enjoyable Horizon programme “Is everything we know about the Universe wrong?“. (more…)

Man walks down the street. Takes him ten minutes every morning.

One day, his watch breaks and starts running fast. It takes twice as long, according to the watch. Completing the same distance took twenty minutes. He buys a new watch.

The following week, some wanker at the council moves his tube station 400 yards further away. According to his new watch, the journey again takes twice as long as usual: twenty minutes. The man blames cheap foreign imports, and buys a new watch.

I have a grid in three dimensions. It’s held together with wires, will balls at the joints. Each wire is 10cm long.

The next day, I measure my grid with a ruler. Each wire is now 20cms long. But none of the balls look any further apart. I buy a new ruler.

I throw away my grid and buy a new one. It’s bigger.

A lot bigger.

My grid has balls one light-year apart. Each ball is held in a rigid cubic system as before. My grid extends to infinity in all six directions: up, down, to the left, to the right, in front, and behind. Infinitely.

I know what you’re thinking: “You must have huge balls”. But I don’t like to brag.

I measure the distance along the wires between the balls, not with a ruler, but with light and a stopwatch. A ball sends out light, and I time exactly one year before the light reaches the next ball. That’s one light-year.

All over the grid, it always takes one year for light to reach the next ball.

The next day, a fine summer’s day in 1665, Newton invents gravity. This does not go unnoticed.

Each one of my balls has a large mass, and so a strong gravitational pull. Each ball attracts every other ball around it, not just the nearest, but all of them. It’s quite a shock to my grid, but my grid still hangs together. I rush out and measure my wires again. To my relief, each wire, measured by pulses of light, is exactly one light-year long.

All is well and good, and my grid holds steady. Of course, it does not collapse in on itself, because it extends infinitely in every direction. As each ball pulls those around it, they are equally pulled away by those more distant. Each ball has an equal pull on its left and its right.

For 250-odd years, my grid hangs together, perfectly happily. Occasionally I step outside to admire my balls (steady), by the light of the moon.

In 1915, some bloke called Einstein completes his General Theory of Relativity. In it, he invents several fundamental principles. Mass-energy equivalence, for example, as shown by the famous equation e=mc^2. Woo.
Something else he does is change gravitational theory. Newton is now proved wrong, for gravity is not a force, it is a distortion of space and time caused by masses.

I have to admit, this funny-looking bloke has me scared. I rush out to check on my beautiful, infinite, gleaming grid and see whether it has been affected. And I find some disturbing results.

Near each of my massive balls (by which I mean, my balls with mass), there are some weird effects happening. Close to the surface of each mass, I find that time is running more slowly.

I dig out my trusty stopwatch and wait for the light. A ball emits light, and the light travels more slowly than usual near the ball. Further from the ball it picks up speed as it moves along the wire away from the ball, but then slows again as it gets near the other ball. In total, my stopwatch shows that two years have passed.

Shit. The bastard’s only gone and ruined my grid. I go back inside to sit down and have a calming cup of tea.

Edwin Hubble catches my attention in 1929. He’s spent ten years looking closely at my grid, and he’s found something more peculiar still. He watches as many balls as he can, from the one ball he’s sat on. He’s been looking at the light beams all over my grid and he’s worked out that my grid is expanding.

I’m incredulous. “Where would it expand to?” I ask, “It’s infinite, FFS.” But the arrogant fool is insistent. Look at the evidence, he says.

The distances, as measured by light, between each ball, are getting further apart. Ipso facto, the grid is getting bigger. I have a quick check, and he’s right. A beam of light now takes 3 years to get from one ball to another.

But if I’m honest, those balls look a bit smaller. They’ve taken some of the mass that was hanging between the balls, and they’ve pulled it in. They’ve squeezed themslves together. Effectively, they’ve become bigger and denser masses, I wasn’t expecting that. With tighter, more compact masses, the light travel time is more affected by the gravity, and so it takes longer to get between the balls.

But my grid is still the same size. Or is it?

Did my watch break, or did someone move the tube station?

You could fall into a black hole, but I’d never see you get there.

Odd, eh?

Reason being, Einstein’s Equivalence Principle – which forms part of his General Theory of Relativity.  This states that an accelerating frame of reference is indistinguishable from a frame under the influence of gravity.

What does that mean?  It means that the force holding you in your seat right now would feel exactly the same as you’d feel if you were sitting in a rocket in space, but accelerating at 1g.

Pretty obvious, pretty boring so far.  However, we also know that Moving Clocks Run Slowly.  If you’re moving through space, you move through less time than someone outside of your frame of reference.

And that gets interesting.  One of the consequences is that a photon (a “ray” of light) does not pass through time at all.  It moves so fast that it never ages.

If you wave your arm, then your hand is fractionally younger than your elbow.  And yet they’re still attached.

Equally astonishing is that a clock on a high tower will run faster than a clock at the bottom of a tower.  I would have thought this is because it is simply moving faster (since it’s on a further radius from the earth).  But actually, it’s because the bottom of the clock is under the influence of gravity, and due to the Equivalence Principle, that clock is accelerating.

Ok, so this is exciting.  Because that means us earth-dwellers are moving through time faster than those in space. (Spacemen actually age less quickly, but this is because they orbit at 17,000mph). (If our clocks are running slowly, then we’re passing through time faster – think about it over a beer).

So if gravity is cumulative enough to hold the galaxy together, then what on earth is the time curve like for the disc?  The galaxy must spin in a very funny way, if the centre of the galaxy is passing through time at a faster rate than the outside.  Actually, galactic discs really do have very odd spin ratios, attributed to dark matter.  How fast is time passing out in Extra-Galactic Space?  Does it pass at all?

Or, let’s face it, at the time of the Big Bang?  Everything was much closer together back then, gravity must’ve been a massive force, and though other short-range forces would dominate, they wouldn’t have gravity’s influence over time.  Perhaps that question isn’t relevant, because everything was uniformly dense.  But you can imagine this might drive “inflation”, where the early universe did some things in strange amounts of time.

Now, back to the Black Holes.

A Black Hole is sufficiently dense that nothing (except imaginary particles like gravitons) can escape.  Not even light.  Something that dense does really weird things to time.

According to my physics books here, if you fell into a black hole, you wouldn’t notice anything particular peculiar.  Except for the whole crushing-to-death thing.

To me watching, it would take an infinite amount of time for you to fall in.

So actually, you would watch the Universe end around you, probably in a very Douglas Adams style.

Now that’s a funny concept.

And here’s the question:  assuming this is so, how did Black Holes ever grow?  Presumably all the holes we can see are primordial, because it would have taken longer than our mere 13.7 billion years to see anything fall in?

Physics: gotta love it.

I’ve finally finished the project.
When looking into the most recent papers, it seems there’s a general consistency in the data between values of H0. I was really expecting a lot of variation in this, but this seems to have settled down over the past few years, and there’s general agreement on a value of around 71 or 72.

Yet this only works with the data from Gravitational Lensing if we model the mass of the galaxy in line with the observed light of the galaxy. This sounds ok, but is in direct conflict with dark matter theories – where we believe 90% of a galaxy’s mass must lie outside the visible disc, in a large near-spherical halo. If they take dark matter into account, the GL figures are all ~10% too low – and there’s too much agreement between other methods (WMAP, Chandra, HST Key Project) to allow that.

So really, GL is offering information on dark matter rather than on the Hubble Constant, which is quite a surprise. Hopefully the report has made that clear.

I’ve had a week off work to finish up, and it’s been a long time since I’ve been able to work on the project, so it’s been a busy week! I’ve had to catch up on stuff I already knew, and I know the report isn’t as polished as I would have liked. But it should hit all the targets.

75%.  Awesome   I was a lot happier with this years TMA03 than the previous years, even though I rewrote quite a lot at the last minute to focus on being a literary review, rather than an overview of the subject.

Review of feedback from TMA03:

Abstract – good, but I need to explain more to non-astronomy people.  This should be fine, but of course it’s hard to do that when all you’re reading is hardcore science papers

Contents – good.

Introduction – good, but omitted discussion of the objectives of the paper.

Literature review – good.  “In the final ECA report be sure to keep the ‘critical’ aspects of your analysis (‘critical’ in the sense of comparing/contrasting different results and theories, discussing any contested ideas or controversial issues, evaluating different perspectives/proposals etc.) to the fore.”

All in all, a good result from TMA03.  I need to do more research to find more contentious issues, so I can focus the review section a bit more.  That should be easy to do – previously I was ignoring these to try to get a better picture of the established consensus.

Obviously, I’m focused on the gravitational lensing aspects of this, so this is where more research comes in.