We’ve all heard of Albert Einstein, the genius with the crazy hair who came up with a mind bending theory that nobody really understands. Most of us just know that it had something to do with the famous equation E=mc2 and was way ahead of its time. However, the fact that Einstein is still a household name, 100 years after his work, speaks volumes. His discoveries are so incredible, and so counterintuitive that his name endures to this day. So what did Albert Einstein actually do? In simplistic terms he explained the fundamental force that shapes the universe and dominates our everyday lives — the force of gravity. This involved an incredible theory that he called “General Relativity” which revealed how the four pillars of science, namely space, time, mass and energy all interact in a surprising way to shape our world. Can everyday people truly understand his theory? Is it within our intellectual reach? To fully understand it would be a stretch, but to appreciate it and get an idea of what it is all about, well that’s easier. You just have to open your mind and follow a few simple everyday analogies.
The first step towards understanding gravity is to realise that we live in 4 dimensions. Yes four — not three. We have the three everyday space dimensions which can be thought of as length, width and height and then we have the fourth dimension of time. Einstein was probably the first human being who was able to truly visualise the world in four dimensions. He understood that time is actually just another form of space — it’s just space for things to happen rather than space for things to exist.
To understand this idea, imagine a dot on a page. The dot has zero dimensions. It doesn’t have a width, length or height. If you then imagine a series of dots drawn very close together then they form a straight line which has one dimension of length. If you then draw a series of straight lines very close together you can form a shape, such as a circle, which has two dimensions of length and width. If you then take several similar circles on different pages and stick them very close together you can form a solid shape, such as a sphere, which has three dimensions of length, width and height. It’s important to note that every time you add another line, or add another shape, the new element is very similar, but not quite identical to its neighbour. If you then take a series of spheres and stick them very close together in the fourth dimension of time, but make each one in a slightly different location in space, you will get a moving sphere which has four dimensions. This represents the world as we know it; balls flying, dogs walking, cars driving, clouds drifting. Thinking about time and space in this way helps us to see that time is simply another form of space.
In fact, Einstein proved that time and space are actually interchangeable with his first theory of relativity. He showed that you could partially trade a journey through time for a journey through space. To understand this imagine driving your car at 100 km/hr in a due north direction. If you turned 45 degrees to your right, your journey in the north direction would slow down and your journey in the east direction would speed up. So north travel and east travel are interchangeable in two dimensions. The same idea applies to three dimensions. If your car were able to take off and start flying up into space at the same speed of 100 km/hr then your journey in the “up” direction would increase and it follows that your journey in the north and east directions would decrease. In a huge intellectual leap, Einstein realised that a journey through the three dimensions of space is interchangeable with a journey through the fourth dimension of time. If you speed up in space then you must slowdown in time because time is simply the fourth dimension of space! In our everyday lives the effect is tiny, but at really high speeds approaching the speed of light the effect is significant. Einstein called this time dilation.
Einstein also realised that space and time are linked in the same way that the two ends of a child’s see-saw are linked. If one end goes up the other end must come down. If time slows down due to a fast journey through space then space must shrink in the direction of travel. It turns out that space shrinks by just the right amount to compensate for the slowing of time so that the journey through space maintains the same speed. Speed after all is simply distance divided by time — we could measure it in kilometres per second. If the seconds slow down then the kilometres must shrink to keep the same kilometres per second! This idea is quite intuitive when you think about observing a car turning a corner on a flat road. If the car is travelling north and turns 45 degrees to the right then it interchanges some of its journey in the north direction with a journey in the east direction and will appear to shrink for an observer looking east. A car that is 5m long will appear to become about 3.5m long after it has turned the corner and will also appear to slow down. However, it will continue to travel its own length in the same amount of time and therefore maintain the same apparent speed. In four dimensions, if some of a journey through time is interchanged with a journey through space, then space appears to shrink in the direction of travel. Einstein called this space dilation.
When Einstein combined time dilation and space dilation, he started to picture the air around us and the nothingness of outer space as a fabric that ties space and time together. He called it “spacetime”. Just like your car travelling at a constant speed, Einstein realised that everything in the universe is travelling through the four dimensions of spacetime at a constant speed. That is to say that their combined speed through both time and space is constant. Yes, everything. That includes you, me and things that are travelling fast such as jet fighters, spaceships and light beams. This is a difficult idea to understand because space is measured in kilometres and time is measured in seconds, so how can we arrive at a total speed through both time and space? If you had 100 US Dollars you could trade some of that currency for Euros at a specific exchange rate. The combined currency is still worth 100 US dollars but the Euros are measured in different units. It turns out that the exchange rate between kilometres and seconds is approximately 300,000 kilometres per second meaning that 300,000 kilometres is worth 1 second. To us mere humans that sounds like a very poor deal if you were buying seconds, but when you think about it on a galactic scale 300,000 km is not that far. The sun for example is nearly 500 times that distance from the earth. But what is so special about the exchange rate of 300,000 km/s. Well that value turns out to be the speed of light and other forms of electromagnetic radiation such as radio waves and microwaves. It’s not that there is anything special about this type of radiation, it’s just that it has absolutely no mass and is therefore compelled to continuously travel through space at that speed. It’s almost as though 300,000 km/s is a sort of cosmic speed limit.
Light has effectively traded all of its seconds for kilometres and therefore does not experience time. It has completely traded its journey through time for a journey through space. If you were able to travel on a beam of light, your clock would not tick. But light is an extreme example. For us mere mortals, who don’t have a significant journey through space, we haven’t traded any of our seconds for kilometres and we experience time passing in the fastest way possible relative to anything that is moving. Going back to our analogy with the car, if north represents a journey through space and east represents a journey through time, then we are the equivalent of the car travelling due east with no northbound component. Now if we were able to board a spaceship and travel through space at say, half the speed of light, our journey through space would speed up and our journey through time would have to slow down because space and time are interchangeable. In the car analogy, it would be like the car travelling north-east. We wouldn’t actually feel time slowing down on the spaceship but when we came back to earth we would find that more time had elapsed. If you travelled fast enough and for long enough this difference would be huge and you would come back to a very futuristic earth. Whilst this is theoretically possible, it requires spaceships that are currently beyond our technology, although anyone that travels on a modern aircraft for a few hours actually loses a few nanoseconds of time. A journey through the four dimensions of spacetime is therefore interchangeable in the same way that we understand a journey through the three dimensions of our everyday life is interchangeable. This stands to reason as time is just another form of space. The four dimensional relationship is more complex than the three dimensional relationship but the idea is the same. This was Einstein’s first major insight.
Einstein’s second major insight was just as mind blowing and was inspired by “the happiest thought of his life”. He imagined what it would be like to stand in a stationary elevator on the earth and then in a stationary elevator floating in outer space with no gravity. If the elevator in outer space started accelerating “upwards” by just the right amount, he realised that it would feel identical to the stationary elevator on earth. In both situations your feet would be firmly planted on the floor and if someone threw a ball to you they would have to aim high and the trajectory would appear to be curved down towards you. Gravity and acceleration are therefore indistinguishable. In fact, when we stand on the surface of the earth we feel an upwards force on our bodies and are therefore accelerating all of the time. If we jumped off a cliff and entered freefall we would think that we are accelerating but we would actually stop feeling any force on our bodies and would therefore stop accelerating. This is very confusing as intuition tells us that we would start accelerating when we jump off a cliff — after all our speed would be increasing. However, this simply proves how differently Einstein thought about the problem. If you ignore wind resistance and the sensation of the ground rushing up towards you, then freefall on earth would feel exactly the same as floating in outer space which clearly involves no acceleration. We therefore stop accelerating when we enter freefall and start accelerating when we stand on the surface of the earth and feel that familiar force pushing upwards. This is very counterintuitive but it is a very important observation that Einstein made.
Therefore, when we stand on the surface of the earth we experience the equivalent of accelerated motion all of the time. As we saw from the spaceship example, motion through space slows down time and shrinks space relative to stationary objects. For constant motion, such as the spaceship, the slowing of time and the shrinking of space is constant. Going back to our car analogy which had constant motion through space, the direction of travel in the north-east direction would be straight. For accelerated motion, such as the space elevator or standing on the surface of the earth, the slowing of time and the shrinking of space is variable. Again, going back to the car analogy for accelerated motion through space, the path of the car in the north-east direction would be variable. The car would be trading more and more of its journey through time for a journey through space as it accelerated and the path of the car would be curved. This is a tricky idea to get your head around because it involves four dimensions and our analogy with the car only involves two dimensions. However, in simple terms it means that as you accelerate, time slows and space shrinks in a way that depends upon your speed which is not constant and therefore produces a curved relationship. This curved slowing of time and shrinking of space created by accelerated motion is the fundamental key to Einstein’s theory of General Relativity which explains how gravity works.
He realised that the presence of a large mass, such as a planet, in the fabric of spacetime, effects the slowing of time and the shrinking of space just like accelerated motion does. Remember that gravity and acceleration are indistinguishable. The mass of the planet effectively warps spacetime around it to slow down time and shrink space in a curved relationship depending upon the distance from the centre of mass. He did not fully understand why the mass of the planet warps spacetime but he intuitively realised that it must have something to do with his famous equation E=mc2.
He had previously proven the equivalence of mass and energy through his famous equation E=mc2. This simply means that Energy (E) is equal to mass (m) multiplied by the speed of light (c ) squared. Therefore, a small amount of mass is the equivalent to a large amount of energy, an idea that is borne out in nuclear power. When we split a uranium atom, we lose a tiny bit of mass which is converted into a large amount of heat energy. But the idea relates to our everyday lives in a far more common way than that. When you get into your car and drive down the freeway at 100 km/hr your car gains kinetic energy which actually adds to its mass because mass and energy are equivalent. The difference is tiny because the speed of the car is only a tiny fraction of the speed of light; but if it were able to keep accelerating towards the speed of light its mass would become enormous. E=mc2 is therefore happening all around us everyday; we just don’t notice it. What has all this got to do with gravity? The earth, being a medium sized planet, is effectively a huge ball of energy in the form of mass. It is almost as though this energy displaces spacetime around it and makes it “bunch up” around the planet to create the warping effect.
This bending or warping of spacetime can be imagined like a bowling ball being placed in the middle of a trampoline. The mass of the bowling ball will bend and warp the fabric of the trampoline just as a large mass, such as a planet, will bend and warp the four dimensional fabric of spacetime. The fabric of the trampoline would be curved near the bowling ball in the same way that the spacetime relationship is curved by the apparent accelerated motion of gravity. The effect of this is that time slows down and distances shrink very slightly close to a large mass, such as a planet, in the same way that time slows down and distances shrink on an accelerated spaceship. The bigger the mass of the planet the bigger the effect. In fact this is what makes a black hole. If the mass is very large, then time grinds to a complete standstill at what is called the “event horizon” and even light cannot escape — hence the name “black hole”. For a more modest sized planet such as earth, time slows down slightly more as you get closer to the planet compared to outer space. This creates a very small time gradient around the planet where objects nearer the planet’s centre of mass travel through time very slightly slower than objects further away. To put it another way, it means that your feet are travelling through time very slightly slower than your head.
How does this time gradient create the effect of gravity? Good question. Imagine driving your car at 100 km/hr parallel to a solid brick wall. If the wheels closest to the wall are turning very slightly slower than the wheels furthest from the wall then the car’s path will curve towards the wall and, at some point, there will be an impact and the car will probably continue and grind along the wall. To an observer it will appear as though the car is attracted to the wall just like our feet are attracted to the ground. If the car started some distance away, say 5m, from the wall then the impact would be quite large and the car may get crunched and come to a sad demise. However, if the car started closer to the wall, say 1m, then the impact would be smaller and it should be able to continue. This is how gravity works. Our feet, or anything closer to the centre of the earth, are travelling through time very slightly slower than our heads, or anything further from the centre of the earth. This causes our journey through time to be curved down towards the surface of the earth just like the car’s path is curved towards the wall. If we jumped off a 5m cliff, we would hit the ground with a splat and probably come to a sad demise. If we jumped off a 1m box we would bend our knees and recover.
This time gradient is all around us and is very uniform but is actually extremely small. In fact, the difference in the rate that time passes between our feet and our head is only approximately 1 second every 150 million years which is absolutely miniscule! This tiny time gradient has been scientifically proven in a number of ways including placing extremely accurate, synchronised clocks at low and high altitudes on mountains and observing the tiny differences in the rate that they experience time. Therefore, when we picture the earth, we should not really imagine a bowling ball on the trampoline, we should imagine a feather weight air filled beach ball that makes a tiny dent on the fabric of the trampoline. In galactic terms the earth is a very small mass that only makes a tiny dent in the fabric of spacetime. However, the thing that really makes gravity significant for us is the speed that we are travelling through time, which is the equivalent of the speed of light. If your car was travelling parallel to the brick wall at the speed of light, instead of at 100 km/hr, then it would take only a miniscule difference in the speed of the right hand wheels compared to the left hand wheels for the cars path to curve significantly towards the wall. This makes intuitive sense if you imagine how easily a fast moving vehicle can veer off a road compared to a slow moving vehicle. Our feet are therefore travelling through time only very, very slightly slower than our heads — it just that we are careering through time so fast that the pull of gravity feels significant.
Remember what is happening next time you sink into a comfortable chair. Try to picture the world in four dimensions just like Einstein did. Imagine yourself travelling through time at the speed of light, your feet travelling slightly slower through time than your head and your journey therefore curved very gently down towards the ground. Feel the gentle “pull” of the earth and marvel at the strangeness of it. Marvel at how one man, Albert Einstein, the genius with the crazy hair, managed to explain it all without ever doing a scientific experiment in his life. He arrived at his incredible insights by doing what he called “thought experiments”; simply imagining what would happen in certain situations and then applying a good dose of algebra to develop his insights. When other scientists set out to test his theories with actual experiments, he was never in any doubt about the outcome. To him, the theory was so simple and so beautiful that it simply had to be right.