This is a super important idea, and most weird paradoxes in relativity can be solved by understanding this fact. For instance, you might have thought: "Hey! I don't buy what you said up there in number 2, about me and a friend measuring each other as being squished! Who's actually correct? Even if you could measure something instantaneously, this simultaneous measurement changes in another frame, which leads to the fact that both of you measure a smaller distance. I know it's confusing. But all you need to remember is that sometimes, you might think two things are happening at the same time - and somebody standing right next to you would go: "yes.

Those two things happened at the same time. This person would call you and your friend idiots. That's why you have a friend though, to beat this guy up. If you can catch him. The barn-bus paradox. So let's say a bus that's 30 feet long is driving towards a barn that 20 feet long, with two doors on the barn. Inside the barn are two people who are manning the controls for each door.

The bus is going really fast, and therefore, is experiencing length contraction, and get this, in the reference frame of the people in the barn - the bus looks only 15 feet long! Think about this for a second. This is just a consequence of weirdness number 2 above So, they decide that once the now-squished bus is fully inside the barn, they are going to close the doors at the same time, and then open them quickly, so that for a split second, the bus can fit inside the barn.

Easy enough. But, let's now switch viewpoints, and say we are on the bus. Again, this is an important point. Most of special relativity involves going into different frames, and remember, in the buses frame of reference it is not moving, but the barn is coming towards it So, we're on a 30 foot long bus, and from our perspective, there's a barn moving towards us, and it is all squished, so it looks like it's only 10 feet long!

The bus we're on is 30 feet long! So, to recap: 1. Frame of the barn - Bus is squished, and can fit inside the barn. Frame of the bus - Barn is squished, no freakin' way can the bus fit inside the barn. Who is right? They both are! The bus moves through the barn, and the doors work, and everyone is happy.

In the frame of the barn, they close the doors and open them, and the 30 foot bus does indeed contract to 15 feet and fit inside the 20 foot long barn. The trick comes when we consider the frame of the bus. Now, the bus is moving towards this small squished barn, where two guys are going to try and actually succeed to close the doors. But remember what I said above - simultaneous events depend on the reference frame.

So, for the bus, first one door closes and then opens and then only after the bus passes by the front door, does the other door open and close. Instead of them closing at the same time, one closes before the other, and then instead of them opening at the same time, one opens before the other, and the bus makes it through. You can find some pictures here.

### A Breakthrough Moment

In this second barn's frame of reference, he is going to close the door when the squished bus enters the barn, and then leave it closed. In the bus frame of reference, there is a barn with a wall at the end moving towards it, and this barn is squished to ten feet. What happens? Well, in the reference frame of the barn, the bus comes in, hits the wall, and the door closes behind it. Once the bus stops, it is not length contracted, so it busts out the back door! Well, the trick here comes from the fact that the bus goes into the barn and hits the back wall.

Remember though, that nothing can travel faster than the speed of light - not even the bus crash - so the signal from the front of the bus all of the molecules squishing together as it crashes actually goes back through the bus at some velocity. Meanwhile, since the back of the bus has no idea it has crashed since the signal hasn't gotten there yet , it keeps right on driving in.

Here, the bus will keep driving in and eventually make it all the way into the barn before the door is closed and the signal finally reaches the back of the bus, which stops, and then breaks through the back wall. What you think might happen at the same time doesn't happen that way for someone moving quickly.

General Relativity So, now we will look at Albert Einstein's theory of gravity. Before we get into the nitty gritty - think about what you know about gravity? What have you been taught? You know that gravity is This is a good way of looking at gravity, and certainly, it is the way that most physicists mathematically see gravity. Einstein decided to look at it in a different way. See, Einstein did a lot of thinking about gravity. If you remember, in special relativity, there is no "preferred" reference frame, and so you can't tell, if you're all the way out in the middle of space, if you're moving or stationary.

Well, Einstein got a little worried about this whole deal when he really started to think about it. What if you're in a spaceship and the spaceship is accelerating? Uh-oh, this means that you can tell if you're undergoing an acceleration! Einstein freaked out about this, but finally turned to his friend gravity for the solution. Let's say you woke up tomorrow and you were in an empty locked room.

As you walked around, I guarantee that since you're totally in love with physics, you'll probably think: "hrm, this room has gravity in it! You could even do some physics experiments in your room and never tell that you were in a spaceship or on Earth. Einstein had previously shown that the speed of light is always the same for everyone, and that space and time are experienced differently by different people.

Time is just another coordinate — if space comes in three dimensions; length, breadth and depth, then time is the fourth dimension. If attraction between the Sun and the Earth was what caused gravity, then a shift in the position of the Sun would cause an instantaneous shift in the orbit of the Earth.

General relativity married special relativity with gravity. General relativity has been incredibly successful at providing a new way to understand the universe, and research into spacetime has yielded unprecedented insights into how our universe operates. What takes over at these extremes is quantum theory, a set of rules for how matter behaves at the smallest scales.

In the quantum world, the positions of particles are described in terms of probabilities rather than in certainties. Quantum theory has been supremely successful in describing atoms and subatomic particles when gravity can be neglected. However, one of the biggest questions in modern physics is how to unite general relativity and quantum theory, into a theory of quantum gravity.

Experiments that probe the very large and very small together are hard to imagine, but some of the best laboratories for exploring the relationship, at least theoretically, are black holes. This is one of areas where Professor Stephen Hawking has made his name.

## Relativity: A Short Guide

Black holes are regions of incredibly dense matter that bend spacetime so drastically that it rips. In this broken centre, called a singularity by physicists, matter is crushed to an infinite density, and quantum theory takes over its behaviour. It was , two years after his special theory of relativity had rewritten textbook notions about time and motion. But in real life, objects and people move in all sorts of nonuniform ways. Let the air out of a balloon, for instance. Einstein wanted to extend relativity to all forms of accelerated motions. Then his happy thought in the patent office raised hope.

A person falling freely accelerates toward the ground because of gravity but feels no force until impact. Therefore, Einstein realized, gravity and acceleration are two sides of a coin. The upward thrust of an accelerating rocket ship pins the occupants to the floor just as the gravitational pull of the Earth keeps your feet on the ground. At first progress was slow. In special relativity, measures of space or time differ for different observers. But Minkowski showed that space and time combined — spacetime — yielded a mathematical description of events that all observers could agree on.

One of the first predictions of general relativity to be tested involved the bending of light. Because a massive body, such as a star, warps spacetime around it, a light beam passing nearby should be deflected from a straight-line path. From Earth, light from a distant star passing near the sun would be bent in such a way as to alter the apparent position of the distant star.

In , astronomers photographed stars near the sun during a solar eclipse. General relativity requires twice as much bending because the light ray is bent while passing through space already curved to begin with.

Establishing such coordinates requires a frame of reference, or origin point. Different observers will choose different origins. By , Einstein realized that his goal would require abandoning Euclidean geometry. Real space, he realized, could not conform to the idealized lines and angles of the textbooks.

Gravity distorted the coordinates, just as a grid of straight lines on a rubber sheet would curve if you placed a heavy cannonball on it. But Einstein did not possess the mathematical skills to cope with non-Euclidean geometry.

Fortunately, his college friend Marcel Grossmann, an accomplished mathematician, was eager to help. It had one drawback, though — it worked for some coordinate systems, but not all possible systems. That made his original goal impossible. But Einstein seemed satisfied that he had done the best that nature would permit.

It turned out that there actually was something more beautiful. But to find it, Einstein had to move to Berlin. Born in Ulm, Germany, in , he moved when an infant to Munich and then as a teenager to Milan, Italy, having dropped out of high school. He went back to school in Switzerland, eventually graduating from college in Zurich. During his years at the patent office, Einstein produced an explosive output of papers poking holes in traditional physics, including reports on his special theory of relativity and Nobel Prize—winning work on quantum physics. Eventually those papers led to sufficient recognition in the physics world to get a faculty appointment in Prague.

But at the first chance he returned to Zurich, where Grossmann now taught math. There Einstein and Grossmann developed the Entwurf theory. And then Berlin, the pinnacle of German and world physics, called. With help from his friend Marcel Grossmann, Einstein adopted further advances by the mathematicians Gregorio Ricci-Curbastro, Tullio Levi-Civita and Elwin Christoffel to describe spacetime geometry in terms of mathematical expressions called tensors.

### What Is General Relativity?

Tensors are similar but can encompass more than just two components. Einstein used tensors to develop his equation describing the gravitational field, known as the Einstein field equation. On the left side of the equation is a tensor describing the geometry of spacetime — the gravitational field. On the right is the tensor describing the matter and energy density — the source of the gravitational field. The equation shows that spacetime geometry equals mass-energy density when adjusted with the proper units and numerical constants.

Actually, the equation stands for a set of multiple equations owing to the complexity of tensors. So experts usually speak of the Einstein field equations, plural.

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## Einstein's Pathway to General Relativity

When he applied this equation to the entire universe, Einstein found that the universe would be unstable, easily disturbed into a state in which spacetime would be either expanding or collapsing. So he added a term that came to be called the cosmological constant, symbolized by the Greek letter lambda. It represents a constant amount of energy density throughout space that would supposedly keep the universe stable and changeless.

Later, evidence that the universe was indeed expanding led Einstein to renounce lambda. Growing apart from Mileva, he pursued a relationship with his cousin Elsa. And Mileva did not relish the idea of life in Berlin. During the following year his freedom nourished a fertile few months in which he saw a new path to success. In mid he saw that there was a way to make relativity truly general. Rather than imposing energy-momentum conservation on the equations, he worked on devising equations that would impose the conservation law on the universe.