Thursday, 13 March 2014

Houdini Hannam's Grand Gravity Illusion!

Behold! At the end of the illusion I am now going to perform, any reader of this article of sufficient intellectual prowess to read the words, will completely understand the conceptual underpinnings of Einstein's general theory of relativity and gravitational waves.

How amazing is this feat? General relativity is one of the most famously incomprehensible theories in human history. A few years after Einstein published the theory in 1915, it was said that only three people in the world understood it. Now they are all dead. That's how hard this will be. But I will perform this incredible illusion right before your very screens.

We start with questions so deep that it is madness to believe we can answer them. What is gravity? Well, it's this effect that reputedly makes apples drop on Newton's head [1], and makes the Earth go around the sun. Yes, but what is it? What is pulling the apple towards the ground? Zombies reaching out of the soft orchard soil? A fine explanation, but that cannot be what also pulls the Earth in orbit around the sun. Are there little strings that we can't see? As we learnt in the last post from our grouchy friend Feynman, an explanation involving strings will only tie us in knots. We would like to know what is actually there, what is really doing this incredible job.

Now that we've set ourselves up for disappointment with such an impossible question, we're open to any crazy idea. Newton said there was just a "force". That hardly helps, and he wouldn't have been any more convincing than George Lucas, if he didn't also provide a handy formula to calculate it with. Lots of people were unconvinced. "Really? There's just this force, that magically crosses the wastes of space, in no time at all, and pulls the Earth around the sun? Are you kidding me?" But his little formula worked. No matter what the problem -- lots of planets, with moons and asteroids, all on crazy complicated orbits around the sun and each other -- it was possible to calculate exactly what they did with Newton's little formula. So in the end you just had to shrug your shoulders and pretend that everything had been explained after all.

Then along comes Einstein. He has his favourite idea, which is that nothing can travel faster than the speed of light. He's realised that this one idea is going to keep him in business for life. He looks at Newton's formula and he says, "Aha! This `force', whatever it is, mustn't travel faster than the speed of light. But where in Newton's formula does it say that? Huh? Where? There must be something missing."

So he goes back to the same impossible questions as before, and decides to roll in a few more. What is time? What is space? Now we're getting deep. A mystic can wallow in these deep questions  for years, achieving nothing besides making a fortune peddling their babblings to other mystics. A scientist tries to be more concrete, and asks about things they can measure. We know how much space we have by measuring distances. We know how much time we have by measuring some duration of it. Have we explained anything? No -- but at least we've got some numbers!

Einstein's brilliant idea was to say that distances and times change depending on the objects that are around. If you buy yourself a quarter acre of space, and then fill it with some good heavy objects, the space itself will stretch, and you'll have more than a quarter of an acre. Plus, all of your cosmic bric-a-brac will slow down time as well, at least when you get close to pieces of it. It's quite a bargain.

Now, you might conclude from all this merely that Einstein had a dangerous drug habit. But no -- it turns out to be true. Clocks on Earth really do tick slower than clocks in space, and this is crucial to how GPS works. You can thank Einstein every time your phone helps you find a restaurant (but blame google when it doesn't) [2].

Ok, very good, space and time have limbered up. What about gravity? No problem. If objects were to stretch and curve and warp space and time in just the right way, then that would surely affect the way anything moves through space, and maybe that could be used to reproduce the effect of gravity.

If that sounds far-fetched, imagine rolling a ball across a trampoline. It goes straight across. Now get someone to stand in the middle of the trampoline, and roll the ball past them. The ball curves towards them. If you send it at just the right speed, it will circle right round them. By changing the shape of the trampoline mat, you can mimic gravity! You can even imagine that the ball doesn't even notice that the mat is stretched, and thinks it is travelling in a perfectly straight line.

If you don't quite get this last point, you can perform the following experiment at home. Get yourself a really big trampoline, and paint a large circle around the centre of the mat. Make it a dashed circle, like the lines on a road. Now put a light person in the centre of the circle, like a baby, except that the baby needs to be asleep, otherwise it will crawl away and mimic the nightmarish gravitational effect of the sun sticking the Earth in its mouth and possibly choking. Then attach wheels to your smartphone; phone cases with wheels are available from all good online retailers. Switch on the little video camera, and then roll the phone along the trampoline at just the right speed that it orbits around the sleeping baby. Now watch the video. The result will be a blurry mess, and you'll be utterly discouraged, but now you'll know what experimental science is like every day.

So now we have a picture of how Einstein thought gravity works. Would Feynman approve? I'm afraid not. "What the hell kind of explanation is that, you goddamn phoney! The reason the ball goes around the baby is the same as the reason a trampoline works in the first place -- gravity. So you've used gravity to explain gravity. That's the worst cheat I've ever heard!"

Ok, can I say that it's an even simpler effect? If I draw a straight line on a flat sheet of paper, it goes from one side to the other. But if I wrap the paper into a tube, then the line meets up with itself, just like a planet going in orbit.

"No you can't! Are you crazy? Anything that follows the line on the paper will travel the same circle, no matter how fast it moves, or how heavy it is. But things that orbit the sun would instead fly off into space if they went faster, or fall into the sun if they went slower or were heavier. So you haven't explained a thing! It's a fake!"

He's right. It's just an illusion. Einstein's theory says that space and time really are distorted by massive objects, and uses this effect to describe gravity. But there is no corresponding effect in everyday life; that's why the real theory is so difficult to understand.

Don't be discouraged. It's not just innocent bystanders who are told this guff. Generations of physicists have been trained on it as well, and among the shambling crowds of relativists who currently roam the Earth, most of them labour every day with these illusory pictures at the back of their minds. Many would be surprised to have got the finger from Feynman. That's Ok, because in the end it's Einstein's equations that they use for their calculations, and they work: they predict all of the same effects as Newton's formula, plus a few effects that Newton's formula didn't, which are entirely real and measurable. And all of these effects now travel at the speed of light, just as Einstein wanted. If some cosmic prankster plops a planet into space, its effects on space and time ripple out from it at the speed of light. Those ripples are called gravitational waves. If the same prankster took away the sun right now, the Earth would continue to orbit around nothing for a full eight minutes, until the new shape of space and time washed out across the solar system, and only then would the Earth fly away, feeling very alone, and especially cold.

Maybe you've concluded that this wasn't all so bad after all, and can't understand why Einstein's theory is famous for being so difficult. The difficult bit is getting all those distances and times straight. (Or curved, as it were.) You need coordinates, like the coordinates on a map. Now those coordinates can stretch and warp and twist. In fact, for Einstein's formulas to work, it's important that we can do just about any damn thing we like with the coordinates. But in the end we still also have to be able to work out actual distances and navigate the map. That's the part that gets hairy.

In the next post we'll see how this fooled Einstein himself. So tune in next time, folks: see Einstein get himself tangled in the net of his own coordinates, and then watch him escape!


Notes.
1. It's nice to think that Newton was just sitting in an orchard contemplating a life as an economist, before suddenly an apple fell on his head and he discovered gravity and his life changed forever. That's unlikely to be true. Although he did later work on monetary policy.

2. I've argued with scientists who believe that the best way to communicate Einstein's achievements to the general public is to point them to GPS. How depressing! "Why is Einstein one of the greatest minds in human history? Because he wrote an app."
 

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