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General Relativity

General Relativity – even the name sounds scary! It is essentially a theory of gravity that was discovered in 1915 by Albert Einstein. It details the observed gravitational effect between masses that results from their warping of space-time. Still confused? Let’s look at this revolutionary theory a little closer.

Classical Relativity The first thing to get your head around is the idea that an object can never be completely stationary. We may believe we are standing still at a given point, but if you think about it the earth is constantly moving around the sun, and both the sun and our galaxy are also constantly rotating. And so, none of us are ever truly standing still. We are all constantly moving in a slightly different ways to any other object.

Therefore ‘Absolute Rest’ and ‘Absolute motion’ does not exist. When we say ‘Absolute’ we mean that this motion is observed to be the same by anyone person who sees it. This cannot exist as we are all constantly moving in slightly different ways and so will observe any motion slightly differently to another person This is where the concept of classical relativity comes from. It states that we all observe motion relative to our own state of motion.

A good way to visualise this is to think about a fly in a car. The car is moving at +60 mph, and the fly is flying through the car at +2 mph. To anyone inside the car the fly is moving at +2 mph, however to anyone standing by the road the fly is moving at +62 mph. This is because the fly’s motion is observed relative to our own, and so will depend on the speed at which the observer is moving.

Special Relativity The second thing we need to accept is that the speed of light is the same for all observers. Now this one is quite tricky! Let’s imagine we have this set up. We have two matching pairs of mirrors with a light beam reflecting between each. One pair is at ‘rest’ and the other pair is moving close to the speed of light, relative to the first pair.

You can see that in the second scenario, the beam of light has to travel a much greater distance in order to keep reflecting between the mirrors as they travel. Now let’s put an observer into each situation. This is where things get fun!

As we previously identified, the speed of light is the same to every observer, no matter their relative motion, therefore the light beam must hit the bottom mirror at the same instant in both scenarios. But how can that be possible, when Bea’s light beam is travelling a greater distance?

Using speed = distance/time, Bea’s light beam should be moving faster.

The only possible explanation for this is that for Bea, time slows down. This allows her light beam to travel a greater distance at the same speed, in the same amount of time. This idea of time slowing down is called Time Dilation. Therefore, we must think of time, not as a fixed unit, but as relative. Remember that in these scenarios we are dealing with incredible speeds, and we would never experience Time Dilation on a practical level.

Length Contraction However, Bea’s time does not dilate enough to compensate for the speed of light being the same for both girls. Instead, two things are happening at once- Time dilation and Length Contraction. When an object is moving at a speed close to the speed of light, not only does time slow down but the objects themselves contract. This means that Bea and her set of mirrors are actually smaller than Alice and her set. Therefore, the distance the light beam has to travel is smaller than we thought. Time dilation and length contraction therefore work together to ensure the speed of light is the same for both Bea and Alice.

Still with me? Let’s talk about Time Travel.

If time slows down for objects travelling close to the speed of light, and it stops all together for objects travelling at the speed of light, it therefore follows that time must go backwards for objects travelling at more than the speed of light! So could time travel be possible?

Let’s introduce a property of an object called Inertia. Inertia is the resistance of any moving object to a change in its direction. For example, how hard it is to stop a moving tennis ball, or to blow a kite in another direction. Inertia increases with mass, as for example it is harder to change the velocity of a bowling ball than the velocity of a ping pong ball.

In addition, inertia also increases with an increase in velocity. For example, more energy is required to change the velocity of a car moving at 60 mph than the same car moving at 30 mph. This means that as an object increases towards the speed of light, its inertia increases. And, as its inertia increases, its mass increases. This is called relativistic mass.

This is where the equation E = mc2 comes from. On a basic level this equation states that Energy and Mass are interchangeable quantities. They differ by a constant, which is the speed of light squared. However, it also shows that as an object nears the speed of light, and its mass becomes nearly infinite due to its increase in inertia the energy required to accelerate it is also nearly infinite. This puts a cap on how fast objects can travel in the universe and shows that the speed of light is the fastest an object can travel in a vacuum.

Therefore, it would take an infinite amount of energy for an object to even reach the speed of light, and this is why we cannot travel back in time- we simply cannot achieve a great enough speed.

Now finally, The General Theory of Relativity. After Albert Einstein published his Theory of Special Relativity (aka explaining Time Dilation and Length Contraction) in 1905, he realised that this theory only applies to circumstances when objects are moving at constant speeds and in straight lines through the universe, but not for accelerating bodies or those moving with a curved path.

Then, while at work in his patent office, Einstein conducted maybe the most important thought experiment of all time. Watching a window-washer, Einstein thought about what would happen if the window-washer fell off his ladder (bit gruesome). Negating air resistance, the washer would accelerate due to gravity towards the ground, and the washer would feel weightless. Einstein realised that this is essentially the same motion as accelerating through the vacuum of space, and that gravity is equivalent to acceleration.

Einstein then pictured a rocket moving with an acceleration of 9.8 m/s2 through space, the same as the acceleration due to gravity on Earth. If a man weighed himself on the rocket, he would have the same weight as on earth. If he didn’t know he was on a rocket, there would in theory be no way of him telling if he was on earth or in space. Or would there?

Einstein then asked himself if he would have been able to tell the difference.

(bending effect exaggerated in diagram)

He imagined what would happen if he took a flashlight or a laser beam and pointed it at one side of the room from the other while the spaceship was accelerating upwards. He realised that if he measured the height of the light beam on the opposite wall, it would be slightly lower than the height of projection, because in the time it took for the light beam to reach the other side of the room, the speed of the rocket had increased.

Einstein realised that this bending effect should apply for a light beam on earth, due to the principle of equivalence, that acceleration = gravity. However, the ground on earth is not accelerating upwards like this spaceship, so the bending effect must be solely caused by gravity, not by acceleration. This means that light must bend in the presence of a gravitational field. And, as light always takes the shortest path between two points, this means that the shortest path is not a straight line, but a curved one. Einstein then theorised that gravity must cause a curvature of space-time in order that the shortest path between two objects is a curve.

Therefore, in the presence of mass and energy, space-time warps. Einstein concluded that Gravity was the result of an interaction between space-time and massive objects. This is why planets orbit the sun – not because of a mysterious force like Newton theorised, but because the sun’s mass is literally warping space-time around itself. The planets, which are accelerating, will then follow the shortest path through space-time. However, due to this warping, instead of this being a straight line, the shortest path is an elliptical orbit around the sun.

The mathematics behind this was incredibly complicated, but this theory became the status quo when it proved the unusual orbit of mercury. It also explained why the position of the stars appeared to change during a solar eclipse in comparison to their position at night - due to the curvature of space-time caused by the suns mass, that isn’t present at night, the light from the stars will bend in a different way and so they will appear to be in different positions to our eyes This theory forms the basis of our understanding of the universe in modern physics and gave Einstein the honour of being one of the most famous and celebrated modern scientists ever.

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