Sunday, 29 January 2012

What is Gravity? (1/2)

We know we don't fall off the Earth, but what is it that holds us on there? And how strong is it? If everyone in China jumped at the same time, what would happen?

Firstly, We think we should start by welcoming all our new followers. As you all will have realised, we post regularly, every Sunday, on a range of topics within maths and physics. These span from relativity and the nature of time to the maths of music. We hope you all will continue to visit the blog and read our posts, so now, lets get started:

Everything we see, hear and feel in the universe are due to four fundamental interactions. I have already talked briefly about them in our post: "What are the Subatomic Particles?" and now I am going to talk about one in particular. Gravity is a force that confused people for hundreds of years, and the only force that has not yet been described by quantum physics. In fact, though people had been studying its effects since the Greeks, the first theories of gravity started being formed around the beginning of the 17th century. Galileo Galilei was questionably the first modern physicist, people had been trying to understand the world and the universe but he was the first to do experiments but then describe and test them with mathematical language.

In his first tests of gravity, he rolled balls down slopes and measured the distance they traveled in a certain amount of time. He realised that if he let the balls roll for twice as long, the distance they travel would increase four times. Because this result was consistent no matter the angle of the slope or the weight of the ball, Galileo said that the same must true for a ball free-falling vertically. He worked out that this meant the balls were accelerating uniformly and then thought about two bodies falling in a vacuum, a very new idea. He came up with a theory that was brand new for the time, objects should all fall at the same speed, the only reason they did not was because of the presence of air. If two objects we dropped in a vacuum, or near vacuum, they would fall at exactly the same speed. He was said to have tried experiments, dropping two balls of the same shape but different masses from a tower and got the result he expected, they fell at the same speed, although these are believed to be thought experiments rather than actually being carried out. However 406 years after his birth, the crew of Apollo 15 went one further, dropping a hammer and feather on the moon. The result was as Galileo predicted:
Galileo went on with his experiments and formulated ideas that later became Newton's first law, the law of inertia and, based on his previous discoveries, theorised that in a frictionless environment, accelerated object's trajectory would be a perfect parabola.

The next big development in gravitation theory came only 45 years after Galileo's death in 1645, it is probably one of the most widely know scientific laws ever, and it was all caused, apparently, by someone getting hit on the head by an apple. It is of course Newton's law of universal gravitation, or more simply, Newton's law of gravity. Newton was very interested in the way that objects moved. This lead him to create his laws of motion. He was in competition with another famous physicist, Robert Hooke, and they were both working on a theory on why planets orbit in an elliptical shape. Edmond Halley came to him asking if there was a inverse square law of attraction to the sun, what orbit would a planet have? He realised that he had found the answer to the question. When writing the theory he found out that there we many things he needed to describe that did not yet have a definition, he was to first physicist to describe what we call mass, as mass, and gave the quantity of motion as the product of velocity and mass, what we now call momentum. This was what lead to Newton's law of universal gravitation. In this case, the inverse square law means that the force that one object imposes on another is proportional to the inverse square of the distance between them. The force is also proportional to the distance between the two objects. The equation that emerges is
Which simplifies to
where m1 and m2 are the different masses of the two objects, and r is the distance between them.
 So Newton's theory states that in a system with two masses in it the force of attraction between them is

Where G is the gravitational constant, it is the value that is used to change the two sides of the equations from being proportional to being equal and the reason we use the symbol instead of the actual number is because it is roughly 6.67300×10-11m3kg-1s-2. So why don't we address the idea that, if everyone in China jumped at the same time, it would shift the orbit of the earth. The two steps we have to go through is to see how much force is exerted on the earth, and then by how much the gravitational force pulls back. Firstly, we are going to assume that the average jump distance for someone to jump is 20cm and the average mass of a person is 70kg and we are going to round the population of China down to 1.3 billion. We are also going ignore the effects of air resistance.

We are going to find out the velocity of a person as they start jumping. This requires a little bit of knowledge of energy, if you do not have this, then you can visit our post on energy. Anyway, when the person jumps they change potential energy to kinetic energy and then back to potential energy. We are just interested in the initial velocity when they jump so we are going to look at the change from kinetic to potential.
Gain in gravitational potential energy = Loss in kinetic energy

So we just found the average velocity of the jump, and we know the distance they jump, so we can work out the time it takes, ds=t so 0.22=t and time=0.1 seconds. From that we can work out that the starting velocity is 4 m/s. Now we can calculate the force that one person jumping exerts on the earth. In this case we are going to have to assume that the amount of time it takes for someone to go from a stand still to moving upwards to be about a twentieth of a second:
Force = Change in momentumTime taken

Where p is momentum
So if all 1.3 billion people in China jump at the same time, the amount of force exerted on the earth will be about 1.82 trillion newtons of force. This may seem like a lot but lets plug that into an equation that will show the acceleration of the earth due to it: 
Force = mass x acceleration
1820000000000=5.9722 x 1024 x a
a =0.0000000000003

m is the mass of the earth
So we can already tell that this change is minimal. The earth would accelerate away from China at a speed of 3 x 10-13 meters per second, equivalent to 4.392 x 10-12 kilometres per hour. This movement is negligible seeing as the earth already moves at 29 kilometres per second in its orbit. However, if we are not done yet. Even if this change was large, what is to say that the force of gravity would not just pull the earth, and the people back to their original position? Well this is were Newton's theory comes in. We are not going imagine the people in China as individual people, but instead a large clump of mass.
m1 is the mass of the earth; m2 is the mass of all the people in China; r is the mean radius of the earth plus the 20 cm the people jump.
As you can see, there is a large force pulling them together, if we plug this force into the equation of force to find the acceleration of Earth we get: 
Force = mass x acceleration
As we can see this acceleration, 1.4981 x 10-7 towards the jumping people is actually larger than that away from them, though in the less than half a second they are in the air, the movement of the Earth would be just as negligible. The force when they land would be just as small. When the people fall they gain momentum.
Where x is distance and u is initial velocity
Apply conservation of momentum
So we can see that the change in velocity is also very small.

In conclusion, if everyone in China jumped at the same time, the Earth would accelerate towards the jumping people at a rate of 1.4981 x 10-7 ms2 and would move in the other direction at 4.31 x 10-16 ms when they land, though both of these numbers are very rough estimates made with a lot of assumptions. Despite that, if all those in China were to jump at the same time change in the Earth's speed/orbit would not be noticeable.

In two weeks, we will post again on gravity. We shall move on from Newton's Law of Universal Gravitation on to Einstein's General Theory of Relativity, and then Quantum Gravity. Less on the effects of gravity, and instead what gravity actually is. We have written posts on Einstein's relativity and how it explains that time is not as constant as we think before, if you would like to read those, click hereThe post is up!

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.


Check out our last two posts:
What is Music? - How can music be described mathematically? Why do different instruments sound different? What actually is sound? (If Stephen Fry liked it then we are sure you will!)
What are the Subatomic Particles? - What are the most basic things that make up everything we see, hear and know?

Sunday, 22 January 2012

What is Music?

We hear music all the time, but has it ever crossed your mind how it works? Why do pianos and guitars sound different, and some notes work together particularly well with others?

This might strike some of you as being somewhat irrelevant to this blog, but the connections with Maths and Physics are very deep-rooted; the very bases of sound and harmony are founded on Mathematics, and possibly the very essence of the Universe is founded upon Music.

So, the first question that I’ll answer is what actually makes sound? When we hear sound, what we’re actually hearing are the patterns of air particles hitting our eardrum and different speeds and timings. This is caused by an object vibrating, after being struck, plucked, or blown, as seen in the diagram below. For the purposes of this post, I am going to use strings as an example, as they are the easiest to represent diagrammatically.
Credit to for image.
When the string is pulled back at a, it creates an area of low pressure just below a on this diagram, this is called rarefaction. When the string gets to i though, it has compressed all the air particles below it on the diagram, creating an area of high pressure, which is called compression.
So, a diagram of the position of air particles after a sound has been made would look like this:
Credit to for image.

When graphed against time, the pressure due to a sound wave at any point looks like this.

Credit to for image.
The diagram above is where we get the idea of “sound waves,” it is these repeating patterns that make up sound. Different notes are made by varying the time difference between the compression and rarefaction (changing the length of the wave), and the volume varies depending on how great the pressure difference is between compression and rarefaction (changing the height of the wave).

This all seems fairly simple so far, but if this was all there was to it, everything would sound the same! A guitar and a piano can play the same note with the same volume, which would create an identical sound wave. But how come the same note played on different instruments sounds different? Why do people’s voices sound different?

This is all because of a mathematical series known as the “Harmonic Series,” which is as follows:

Essentially, this series is basically the sum of 1 divided by the integers, where the nth term is 1+12+13+⋯+1n. Unlike some series of this form (e.g. 1+12+14+⋯), it doesn’t tend towards any particular value. Whilst 1+12+14+⋯+12n  gets closer and closer to 2 the higher n is, and eventually equals 2 exactly when n = ∞, the Harmonic Series doesn’t converge on any number. When n = ∞, Hn = ∞ (where Hn means the nth Harmonic number, or simply the nth term of the series). This is what is known as a divergent series.
This is all very well, but what does this have to do with music?

Well, when a string vibrates, it doesn’t just move back and forth like the first diagram shows. The string is actually vibrating in an infinite amount of ways, all simultaneously! The diagram below shows how:

This looks familiar doesn’t it? It doesn’t stop at 17 though, theoretically the pattern continues indefinitely.

An important thing to note here is that the string is actually doing all of the vibrations show in the diagram at the same time, and the sound you are hearing is the sum of all these frequencies. When a note is played on the guitar, for the open B string, it is the first frequency (at the top of the diagram) that you notice the most: it is that that makes the note a B. This is called the fundamental frequency of the note, or just f, and this is what is meant when the ‘frequency’ or ‘pitch’ of a note is used in everyday language, even though we now know that there are actually infinite different frequencies.

The frequencies of the 12, 13 and other vibrations are known as harmonics, or overtones, so the fundamental frequency is known as the 1st harmonic, the 12 vibration as the 2nd harmonic and so on. These harmonics have pitches themselves. Here are the first few:

However, most of the upper harmonics are much quieter than the fundamental. This shows that not all the harmonics are played at an equal volume, indeed it varies greatly. An expression for the sound that we hear then, would be this:

x0(1f) + x1(2f) + x2(3f) + ...
Where f is the fundamental frequency, and xn is a variable.
In other words, we hear all of the overtones (at least all the ones within our hearing range), and they're all at different volumes.

Certain instruments or playing techniques emphasise different harmonics (by having different values of xn), which creates the different tones of instruments. Having a larger body to a guitar may emphasise the 7th harmonic for example, which gives the whole guitar a different sound.

The values of xn don't remain constant though. The expression above only describes the xn values at that particular point, when in reality, the values change, and they change at different rates for different harmonics on different instruments. For example, on a guitar, the 2nd harmonic may take a very long time to 'decay,' or get quieter, but on a violin it may be one of the first to decay.

So, it is a combination of the volumes of the various harmonics, and the rate of change in this volume that gives an electric guitar that twang, that gives a saxophone that mellow tone, and gives a bass that warm sound.

Pythagoras was one of the first to look into the mathematical properties of sound, and only really discovered the first harmonic: the octave. He realised that when you halve the length of a string (thereby doubling the frequency), the note becomes exactly one octave higher. However, it was not until the 14th century and Nicole Oresme that the entirety of the Harmonic Series was discovered.

Recently, String Theory and related theories have stated that the entirety of the universe, all the sub-atomic particles that make up our world are themselves made up of vibrating strings. Michio Kaku explains this in this video:

If String Theory is correct, then harmony is emanating all throughout our universe: the sub-atomic particles are the notes, the atoms and molecules are the melodies, and our entire universe combines into one glorious piece.

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.


Check out our last two posts:
What are the Subatomic Particles? - What are the most basic things that make up everything we see, hear and know?
What is Time? - It is one of the most debated phenomenon of the universe so, what is time? Is time travel possible? Does time even exist?

Monday, 16 January 2012

What Are The Subatomic Particles?

So in school you learn atoms are the smallest particles, but then you find out that this can be broken down into protons, neutrons and electrons. However even those can be broken down further, but to what?

We live in an age where development in particle physics is powering along. Facilities like the Large Hadron Collider in CERN, Switzerland, are, as I write, colliding Protons together and analyzing the particles that are produced. So what are the looking for? Well firstly lets get a sense of scale. In the full stop at the end of this sentence, there are 7.5 trillion atoms. 99.9999999999999% of atoms are just empty space, so the particles we are going to be looking at can be 10-20 meters small, so small in fact that we cannot even imagine being able to see them individually in a microscope for years. So now that we know that lets move onto the particles:
Source AAAS
This list may not mean very much to you at the moment, except if you have read our post on Neutrinos. However, by the end of this post, I hope you will know what every one of these particles are. So let me start by explaining the main properties that they can have.

When reading about these particles, you will come across the words spin and charge, so what do they mean? Well lets start with charge, also called electrical charge. Charge is a property that changes the way that the object will interact with other charged objects. They produce a force. There are two types of charge, positive and negative. When two particles with the same charge meet, they repel each other, when two particles with different charges, on the other hand, meet, they will attract each other. Charge can be measured in Coulombs but when looking at particles the coulomb is too large a unit and therefore we will use the unit e. A Proton has a positive charge of one e. Electricity is the movement of charged particles, specifically Electrons.

The other property is spin. Spin is a measure of angular momentum in a particle. However it is not angular momentum in the way that we think of it. The angular momentum we usually see is in the form of an object's rotation at a certain rate. At an atomic level it doesn't work in this way. When you run a current through a loop or wire, or take a charged object and spin it around, a magnetic field is formed, like you find around a bar magnet. Using the object's speed, charge and magnetic field you can work out the speed it is spinning at. The magnetic field of an electron, though, is much too larger than it should be, if it was spinning. When calculating the speed it must spin at it has to be larger than the speed of light, which is not possible. However, the fields are there and therefore it must have the angular momentum, this is what we call spin. More information on spin here and here. Now onto the particles:

There are two major sets of particles, Fermions and Bosons. Firstly I would like to talk about Fermions. Fermions are the main building blocks of matter. All atoms consist of them and there are only 12 (as well as antimatter), split into two categories, quarks and leptons. Every lepton has half integer spin, no matter which category they are in. So what is a quark? Quarks are the building blocks of Hadrons, a particle like a Proton or Neutron. There are 6 'flavors' of them, the up, charm and top quarks, or up-type quarks, and the down, strange and bottom quarks, or down-type quarks. Although it can be said that there are 12 quarks, as each of the previously mentioned ones have their own antiparticle. These quarks stick together due to the strong force to form the particles, or hadrons.  Hadrons can only be formed by triplets of quarks, baryons, or a quark and anti-quark, mesons. Only the up and down quarks are stable. Protons are made from two up quarks and a down quark, whilst neutrons are two down quarks and an up quark. So how does a Proton have a charge but a neutron does not? Well the quarks have weird charges, all of the down type quarks have a charge of -12e and up type quarks have a charge of +23e. Another strange ability of  quarks are that, in certain conditions, they can change flavors. So, sometimes, a Neutron emit a W boson and become a proton, electron and electron anti-neutrino. Read more about quarks here.

There are six Leptons too. Three electron-type Leptons, the electron, muon and tau, and three neutrinos, the electron, muon and tau Neutrinos. The only difference between electrons, muons and taus are their size, the electron being the smallest and the tau being the largest. These electron-type particles are what gives almost every substance in our universe it's physical properties. All chemical reactions are due to the electrons in each of the substance's atoms and how they are arranged. Most of the importance of these electron-type particles is because they have a charge of one -e, the opposite of a proton. In fact, an electrical current is just the flow of electrons around a loop of wire; a lightning bolt a lot of electrons traveling from the clouds to earth and a static shock just electrons traveling to or from your finger. I may do a post on electricity soon. Neutrinos I have already done a post about so I will let you look there for more information, but essentially they are very similar to the Electron-type particles, but without charge, and they can pass through matter. However there have been test showing that Neutrinos can go faster than the speed of light, something that shouldn't be possible due to Einstein's theory of relativity. I talk about this in the previously mentioned post about Neutrinos.

and if you are more interested in quarks and leptons, here is another video:

The other set of particles are called Bosons. These Bosons are what are known as force carriers. You see, in the universe their are four fundamental forces in physics, these being the electromagnetic force, the weak force, the strong force and the gravitational force, the Higgs boson does not relate to any of these, but more on that later. Electromagnetism is the previously mentioned force that acts between charged particle. Leading to effects such as friction, electrical current and even rainbows. It is a very strong force. Photons are the carriers of the electromagnetic forces. You may recognize it as the particle of light, this is because light is just how we see electromagnetic radiation, or just how we see photons.  They don't have a mass and can travel infinite distances, this is why we can see stars that are light years away. This is also the reason why light can travel to infinite distance and we can see stars that are far away.
The strong force is the force that holds quarks together to form Hadrons, as up-type quarks should repel other up-type quarks and down-type quarks should repel other down-type quarks due to their similar charges. However the strong force carrying particles, Gluons, act as a glue, hence the name, and stick the quarks together. They have no mass and no charge, but act with charge-like properties in order to stick the quarks together.
The weak force causes the decay of particles. This is through the emitting and absorption of the weak force carrying particles, the Z and W bosons. Referring to the example I used about quarks changing flavor, Neutrons can become Protons but only if one of their down quarks becomes an up quark through emitting a W boson. This W boson then becomes a Anti-electron neutrino and an Electron.  The Z and W Bosons are the only Bosons that have mass (other than the Higgs) and that means that the the range of the weak force is very small.
The final force is gravity. I have talked about gravity and its effects on time before, but never gravity itself. Gravity was described by Einstein's theory of relativity, and he discovered that it was twisted spacetime. However there is no way to describe it in the standard model. A theoretical particle called the Graviton was theorized in the 1930s and tries to describe gravity in terms of quantum mechanics, however they would be very difficult to spot Gravitons. Wikipedia gives a good example, saying that "A detector with the mass of Jupiter and 100% efficiency, placed in close orbit around a neutron star, would only be expected to observe one graviton every 10 years, even under the most favorable conditions." This shows just how rare they are. Gravity is very weak, the electromagnetic forces that repel two jugs of 1 gallon of water put 1 meter from each other are stronger than the gravitational force of a planet the same mass as ours would way on our planet. However the repelling and attracting forces cancel out in the case of the water jugs so they do not move. If you move beyond the standard model, there are more theories as to how gravity could fit into quantum theory but that isn't relevant at the moment.

So those are the four fundamental forces, and the four force carrying Bosons. But what about the most famous boson that has caused such a  fuss in the news at the moment? I am, of course talking about the Higgs boson. It is the last predicted particle in the standard model that had not yet been prove to exist. Before we start talking about the Higgs, first we have to talk about virtual particles. These particles are mainly bosons that flash in and out of existence by temporally borrowing energy from other particles. When these particles flash into existence they form a sort of field, the gluons that stick quarks to each other in hadrons are virtual particles. So these Higgs bosons form the Higgs field, the way particles interact with this field governs their mass. A top quark, the most massive particle, interacts a lot with the Higgs field, whilst photons, which have no mass, pass straight through it without interacting. When I say massive, I do not mean they are larger in size, in fact all these particles don't really have a size, instead massive means it has a large mass. So, how do we find all these virtual particles? They cannot be detected when they are virtual particles because they are in existence for a tiny amount of time, instead you have to make them real particles. The way to do this is to give them huge amounts of energy, this is what the large hadron collider is trying to do. It has already detected gluons and has been searching for the Higgs for a while now. The other problem with finding the Higgs is that even as a normal particle it decays very quickly. So instead they have to look for what the Higgs decays into, two lighter particles (more information in a video bellow). However they have been finding the more and more likely masses the Higgs will have, so they are looking within that mass range, and expect to find, or discover it doesn't exist, later this year.

More information of what the Higgs actually is:

More information on finding Higgs Bosons:

and a good diagram here, about all the particles and their interaction.

I really hope you enjoyed this post. There is a lot more to learn about everything I said in here, and I tried to include as many useful sources as I could so that, if you like, you can read and watch some more. 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.

Check out our last two posts: 
What is Time? - It is one of the most debated phenomenon of the universe so, what is time? Is time travel possible? Does time even exist?
The Irregularity of Time [2/2] -  Why is time moving slower for us on earth than for someone is space? Part of a series (the others are linked within this one) looking a relativity and how time is not as constant as we like to think.

Saturday, 7 January 2012

What is Time?

Hello! This is Theo here for another post, on the nature of time. Does time exist? Why does it go one way? What about time travel?
Time is possibly one of the most baffling aspects of our universe. In the everyday world, it seems to be constant, stable, and relentless, yet as we have found out in the Irregularity of Time posts (1, 2, 3) on relativity, this is not always the case. In this post, I will talk about the question that has challenged scientists and philosophers from Plato to Hawking: what is time?

Firstly, there is an argument as to whether time exists at all. This might sound absurd, but the two titanic theories of modern physics, General Relativity and Quantum Mechanics, treat time in very different ways. In order to unify these theories, they must treat time identically. Bryce DeWitt and John Wheeler came up with the form of an equation that could describe the whole if the universe which works with both theories, and tine was not included in this equation. Essentially, this implies that time does not exist in their description of the universe, but all of history was instead contained within it.
This sounds quite complicated, but it may help to think of the universe as a roll of film for an old projector. When watching the movie, it feels like time is passing, but if you take out the roll of film and stretch it out, you just see a series of frames. In other words, one does not need time to describe the film. So, whilst it feels like time is passing in the universe, DeWitt and Wheeler argue that like the film, it can be described without it. It seems that this is saying that the passage of time is an illusion, in the same way that that time passing in a film is actually the roll moving through the projector.

Time is, however, considered to be a dimension by almost all physicists, although this is slightly misleading. It is much easier to think of the dimension as duration, when we move forward in time we are only moving in one direction in this dimension. Mentioned in a previous post on Neutrinos, Rob Bryaton has done a great video on the fourth dimension:

It seems strange then, that we can only travel in one direction in time, but can move freely in other dimensions. However, Stephen Hawking has an answer. He identifies three main 'arrows' of time. The first one is the psychological arrow, i.e. we remember the past, but not the future. The second is the cosmological arrow, in which time is defined as passing in the direction in which the universe is expanding (If there is a 'Big Crunch,' where the universe begins to contract then this will become more complicated). The final arrow is given to us by the Second Law of Thermodynamics. This states that entropy, or chaos, will always increase in a closed system. This is easily observable in everyday life. Imagine watching a film backwards. Many things would still look reasonable, such as a ball bouncing. One of the main clues that the film is playing backwards would be people and cars running backwards, although it would be physically possible, just psychologically unlikely, so this is of limited interest from a physicist's perspective. However, if you saw a vase falling off a window ledge and breaking backwards, it would look impossible. The disorderly pieces would suddenly pick themselves up and arrange themselves into an orderly pattern, which the Second Law of Thermodynamics says cannot happen.
To a certain extent though, the cosmological arrow is quite weak, that is to say it becomes irrelevant if the universe begins to contract. Originally, Hawking thought that time would begin to run backwards at this point: that vases would reassemble, and the universe would simply be playing back everything since the Big Bang in reverse, but since then he has adjusted his theory to state that the Thermodynamic arrow would remain the same (humans most likely will have died out before this happens, so the Psychological arrow is of reduced importance). That leaves the Thermodynamic arrow as being the only main constant arrow of time. Incidentally, there are other arrows, but most are derived from the Thermodynamic arrow. It is this, then, that is our most solid definition of time: the constant increase of entropy.
Entropy  can be thought of disorder. Brian Cox described it very well in a TV show he did recently, if you imagine a small pile of sand next to a sand castle containing the same amount of sand grains. There are a huge amount of ways to rearrange the sand in the pile of sand so that it would stay the same, you can pick up some and pour it back on top and the structure would stay the same, this is because it is so disorganized. This means the pile of sand has High Entropy. On the other hand, almost anything you do to the sand castle would change its structure and therefore it has Low Entropy. The Universe is slowly moving towards a high entropy state and this happens over time.
So to round that up, Stephen Hawking's arrows of time are:

But what about time travel? A staple of science-fiction for many years, it is a common misconception that the current laws of physics treat it as impossible. However, this is not the case. Due to Special Relativity, time travel happens every time we move (admittedly on a very small scale). However, the closer you get to the speed of light, the more significant this becomes.
Special Relativity states that time passes slower for an object the faster it is travelling. In everyday terms this discrepancy is negligible, but if we consider long missions on extremely fast spaceships there is quite a large effect. For example, if a spaceship from Earth spent five years (as measured by a clock on board) travelling at 80% of the speed of light, 8 years would have passed on Earth when they returned. This effect increases exponentially as one approaches the speed of light, so that if one reached the exact speed of light, their time would stop completely.
This means that it is technically possible to travel to any point in time in the future simply by travelling very fast. However, to reach 99% of the speed of light in a 10 tonne spaceship would take more than a billion tonnes of petrol! The only energy source that has the potential to propel this spaceship would be antimatter. Even using that, 3 tonnes of antimatter would be needed, and considering that humans have not produced more than 1/1000000 of a gram in total, this is a tall order, and even if it could be done, there would need to be extremely strong dust shields to avoid stray particles ripping through the ship and radioactively decaying. If we could do that, humans could travel to the future. Simples!
Travelling back is harder still. Even if such a time machine was built, and you took a trip to the future tomorrow, it would be impossible to travel backwards further than the moment in which the machine first operated, so unfortunately, we can't go back to Wembley in 1966 and watch England win the world cup! In some ways, that's probably a relief considering all the potential paradoxes. But even to return to the present would be hard work: one would have to harness anti-gravity to spin at least 10 neutron stars in a circle to open a wormhole through which the ship could travel. Brian Clegg's upcoming book "Build Your own Time Machine" promises to explain this further.

This post has been a bit of a whistle-stop tour through the mysteries of time, but I hope you have enjoyed it! Time is a subject that has much left to discover, and I'm sure that before long some of the remaining questions will have been definitively answered.

Check out our last two posts: 
The Irregularity of Time [2/2] -  Why is time moving slower for us on earth than for someone is space? Part of a series (the others are linked within this one) looking a relativity and how time is not as constant as we like to think.
What is Energy? - The word energy is used so loosely these days, so what does it actually mean?