Sunday, 12 February 2012

What is Gravity? (2/2)

A couple of weeks ago, I wrote the first post on gravity. We found out what the fundamental rules that stated what objects in a gravitational field did. But there is a bigger question underlying all of it. What actually is gravity? How does it work?

In the first post, we looked at the first two modern analyses of gravity, by Galileo and Newton. Galileo majorly revolutionised view of gravity at the time that he was alive. Up until then, it was commonly believed that the speed at which something travels at when in free fall, was governed by mass. A three kilogram weight would fall faster than one that weighed only one kilogram. Galileo performed experiments and proved that, in fact, that all objects would fall accelerating uniformly at the same rate. The only reason that a hammer and a feather fall at different speeds is due to air resistance (Video in first post). Then we moved onto Newton, who formulated equations, specifically F=G m1m2r2, that described the force that two objects of mass m1 and m2 at a distance of r from each other exert on one another. Using this equation, and some of Newton's other laws of motion, we worked out what happened if everyone in China jumped at the same time. This was a brief summary, and I recommend you check out the original post before reading this one.

Anyway, Newton's developments into gravity were so revolutionary that they stood for about 200 years until they were added too. This addition came from the mind of one the most brilliant theoretical physicists ever. A man, born in March 1879, called Albert Einstein. He had an ability to look at an everyday situation and to see that there was more to it then there seemed. This lead to his Theory of Relativity, which is split into two parts. Einstein's Special Theory of Relativity looks into the way that our space-time is structured, although at the time that he wrote it, he did not consider there to be unified space-time, but more on that later. Special relativity is where we get the famous formula E=mc2. It also radically changed our understanding of time and what happens to things as their velocity increases. I wrote post on it and a proof that an object moving very quickly will be experiencing slower time than a stationary objects, and you can read that here.
But what we are more interested in this post is Einstein's General Theory of Relativity. It is a theory of gravity, and the most recent and accurate we have so far. What astronomers had noticed at the time was that Mercury's orbit was changing over time. The shape remained the same, but the ellipse itself moved, an effect called apsidal precession. This is shown in this animation:
Newton's theory only went far enough to describe the original elliptical shape, but could not explain this precession. Further more, Einstein was intrigued by the observations of Newton and Galileo. They had both confirmed that two objects with different masses would be pulled on by a different force within a gravitational field. He realised that this was a strange result, any object would accelerate at the same rate towards the source of gravity, but not with the same force and he set out to find out how. 

With Special Relativity, Einstein adapted Newton's laws of motion to work with objects moving at very high velocities near the speed of light. However, these only worked with an object at constant velocity, this is because one of the axioms that the theory is based on only affects objects that are not accelerating. However, when he did a thought experiment two years after publishing his Special Theory of Relativity,  he realised that someone in free fall and someone accelerating due to a force other than gravity would not be able to tell the difference. In other words, gravity is simply an acceleration.  The fact the gravity is equivalent to mass meant that there was also a link between mass and gravity and, through the equation E=mc2, gravity and energy.  If we think about this, it makes sense. Imagine a rocket moving very quickly. One of Einstein's conclusions in Special Relativity says that as an object's speed increases so does its mass. Therefore, this fast moving object has a lot of mass due to it having a lot of energy and therefore, it has a large gravitational pull.

His biggest revelation came after this though. Einstein spent ten years working on this theory and one year after he started a past teacher of his, Hermann Minkowski, came up with a different interpretation of the paper. He concluded that we did not live in three dimensions of space and then a completely separated dimension of time, but instead we lived in four dimensions of Space-time. I go into a little bit more detail about space-time in this post. This interpretation was essential for General Relativity as it enabled on of the most radical changes to gravitational theory since Galileo first analysed it. He did not describe gravity as two objects pulling  on one another. Instead, he said that an object's mass caused it to bend the space-time around it. An object with a large mass would bend it more. When something is being pulled by an object's gravity, it is actually moving along a straight line in this curved space time, but from our perspective, it seems to curve around the centre of gravity. It is easy to imagine this bending and curving if we imagine the phenomenon to occur in two spacial dimensions rather than its usual three and with out the temporal dimension:
Now you can see that an object's path on this plane would be severely distorted. However, from the eye of the person in the object, they would just seem to be pulled towards the object in the centre. It is a bit more difficult to imagine curved space time in its full four dimensions, but the best analogy I came across is imagining putting your finger in a still pool of water. The water ripples and your view of the bottom is distorted. Of course, this still does not really show what curved space-time is really like, but it gives you some idea. So as an object's mass increases, so does the effect it has on its surrounding space-time. One thing that Einstein's theory confirmed was the existence of black holes. Objects of near infinite density that curve space-time so much than nothing can escape. Now Einstein had established a link between space-time and acceleration, he had a theory that worked for all objects, whether at a constant speed or accelerating. In fact, he found that gravity affected time just as speed did. When an object was close to an object with a large mass, time slows down for it. That is describe as gravitational time dilation and is explained in this post. There is a lot more to talk about in the realms of relativity, however, I need to move on!

So as I said, Einstein's theory of gravity in General Relativity has never been disproven. But it poses a problem. The two theories that can describe pretty much everything are the Theory of Relativity, specifically General Relativity, and Quantum Mechanics. Quantum mechanics describes everything at a molecular level, however the one thing it cannot describe is gravity. All the other four fundamental interactions have been modified and work perfectly within quantum mechanics. They each have "force carrying" particles, or bosons, and can be described in this way. However, at sub-atomic scales, gravity, the weakest of all the fundamental interactions, has such a tiny effect, it is negligible. This means that it can not be included in quantum mechanics, and because general relativity describes gravity as a change to the fabric, instead of a field or particle, it can not be integrated with it. This is one of the only things that is stopping us from discovering a "Theory of Everything", a theory that could predict what would happen in any experiment. There are many theories of how to get around this problem, and many theories that could potentially be the theory of everything. However none of these have enough proof to be considered. I would just like to briefly talk about quantum gravity, or trying to develop a theory of gravity that describes it so that it can be integrated into quantum mechanics. One theory is that there is a virtual carrier boson, called the Graviton, that carries the force. This theory comes about because all the other fundamental interactions have been shown to have virtual bosons. The graviton would be massless, as it can affect anything, anywhere instantly. A theory we have discussed before, string theory, predicts the existence of the graviton, however, in almost every other theory it runs into large problems. Quantum gravity is a very grey area and it may be many years until a successful theory integrates gravity and quantum mechanics, though there are some theories out there, look here for a bit more information of quantum gravity. And look here for more information on the standard model particles and the force carrying particles.

We hope you enjoyed this post. Please follow us, @theaftermatter, or email us at We really like hearing your feedback or just talking about the posts or other physics and maths. We hope you enjoyed this post.

Ned Summers.

Check out our last two posts:
What is Harmony? - Following on from our post What is Music?: How can physics and maths describe why some notes work with each other, and some don't?
What is Gravity? (1/2) - What is the history of the force that holds us onto the earth, and what would happen if everyone in China jumped at the same time?

What are we posting about next?
Imaginary Numbers - How can a number not exist? And if it doesn't exist, where and how can we use it in real life?

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