Since the year 1965, computer scientists have been able to forecast the growth of the density of transistors on integrated circuits. This is thanks to the observation that Gordon Moore, co-founder of Intel and lesser-known Fairchild Semiconductor, made on the historical trends of transistor density percentage increase in his 1965 article…

# Time Dilation

You are probably familiar with the fact that time often chooses to work against us. This is something that all commuters are familiar with. All the attempts to rush to work are futile because of the phenomenon known as velocity time dilation.

It doesn’t take much intuition to figure out what causes this type of time dilation, the details of which were for the first time ever written down in Albert Einstein’s’ book ’Special Theory of Relativity’, which was published in 1905. This book argued for the first time ever, that it was not only possible to move through time, in the same way you can move through space, but that it was impossible to do one without doing the other.

Specific experiments have been conducted to observe time dilation. One of the most famous experiments designed specifically to test the theory of relativity was the Hafele-Keating experiment. In this experiment, 4 caesium-beam atomic clocks were flown around the world, once eastwards, and once westward. The measured difference between the displayed time of the clocks that had been around the world, and those that had not supported the idea that time dilation did exist.

Despite the fact that this has been observed to happen, we know that you will always perceive your own time to be passing at normal speed, and that time only appears to speed up or slow down relative to an observer (a moving clock slows down relative to a stationary observer).

Fortunately for the commuter, the speeds at which we need to travel in order for time dilation to be noticeable are, and for a very long time will continue to be unattainable. For a person to notice time dilation with the naked eye, they would need to be travelling at a speed close to the speed of light. The equation:

shows how time dilation increases exponentially (due to the square sign next to v and the square root sign at the bottom of the fraction). As v gets bigger, the bottom half of the fraction tends towards 0, and t’ tends towards infinity. If v=c, then time for you appears to stop to stationary observers. To give a more visual representation, here is a graph displaying this:

As you can see, once you reach speeds around 90% of the speed of light, time dilation rockets upwards and tends towards infinity (which is only reached when you travel at the speed of light). The irony is, for the poor commuter trying to get to work on time, the faster he or she travels, the less time he or she has to get there.

But, fear not, for there is a way around this problem. The solution is gravitational time dilation. This is another phenomenon which is yet again creatively named. You have probably guessed, that this type of time dilation is affected by the strength of the gravitational field that you are in. This is the equation for it (r is the radial coordinate, G is the universal gravitational constant):

This shows that time runs faster outside gravitational fields. It shows that as r tends towards infinity, t (subscript 0) tends towards 0, meaning that a clock an infinite distance away from any gravitational field, would be the fastest clock in the universe.

For many of you, the physics behind time dilation will be of little interest. However, there are some invaluable lessons which we can take away from it:

1. Walking is actually a quicker way to work than travelling by vehicle

2. If you really want to travel by vehicle, travel by spaceship because time passes faster in space (and spaceships are awesome)

# Travelling at the Speed of Light

Light is incredibly annoying. Even if we were to approach the speed of light, or perhaps even reach it, light would still travel at the speed of light relative to us. This is because the speed of light is relative to the observer. This was first realised in the 1900s by Einstein and is today known as Einstein’s Theory of relativity.

Theoretically, however, it should be possible to reach the speed of light relative to another object. A simple way would be to have two objects moving in opposite directions, heading away from each other at half of the speed of light. Using this method, not only could we reach the speed of light, but we could actually exceed the speed of light, because the fastest speed ever reached by any particle, excluding photons, that has been observed by humans was travelling at 99.99999999999999999999951% of c (c is the speed of light). This speed is fast, in fact, if this particle were to travel for 215,000 years alongside a photon, the photon would only gain a 1cm lead.

Whilst this is achievable, remaining stationary relative to a photon (travelling at the speed of light) is not. Theoretically, if force is applied continually to a particle, it can reach any speed. Newton’s laws of motion states that if a force is applied to an object, it will accelerate, decelerate or start moving. This should mean that if enough force were applied, a particle would reach c. This is conveniently not true.

Take a look at this equation:

As v approaches the value of c, the fraction becomes larger, until it becomes 1. At this point, things start to go wrong. 1 – 1 = 0, and the square root of 0 is 0. This means that E = mc2 ÷ 0. I do not know about you, but when I type any number divided by 0 into my calculator, I get ‘math error’. That would conveniently lead us to a dead end, so, for the purpose of avoiding dead ends, let us say that any number divided by 0 is equal to ∞.

This makes sense. 0 can be added to itself an infinite number of times before you reach the number you are dividing by 0. Unfortunately, we have just run into another problem. If v = c, then no matter what the positive value of m is, E = ∞. This means that we need an infinite amount of energy in order to satisfy the equation.

According to the equation, it should be impossible to move at a speed faster than the speed of light, because if v > c, then the fraction is greater than 1. Subtracting a number greater than 1, from 1 gives you a negative number, and negative numbers cannot be square rooted: negative numbers do not have square roots. This means, that even with an infinite amount of energy, we will not be able to exceed the speed of light. This is quite disappointing.

However, suppose we had an infinite amount of energy, and we were to apply this as a force to matter. The matter would accelerate, and eventually, it would match the speed of light. At this point, things start to get weird.

Suppose you are in a car, travelling at exactly the same speed as a photon. If you look behind you, there is darkness. You cannot see a thing because you are travelling at the same speed as the photons behind you, and as such, they will never hit the back of their retina, allowing you to register their presence. However, if you were looking forward, there would be a completely different sight.

Our perception of the colour of a wave of light is dependent on how many waves pass us in a given time frame. If we are travelling towards the photon, a source of EM radiation, then there will be more waves per second, than if we were simply stationary. There would, therefore, be an increase in the frequency of EM waves. This increase in frequency would cause a shift up the EM spectrum. Visible EM radiation would become X-ray radiation, radio waves would become visible, and as a result, the things, which are normally visible to us, would disappear, and we would see the world through radio waves. This is similar to the effect you can observe, as an emergency service vehicle drives past you. As the ambulance passes, the siren seems to change pitch momentarily, at the point it is closest to you, and then pitch returns to normal once it passes you.

Not only would the wavelength of light change relative to you, but so would its intensity. As you drive towards a source of EM radiation at c, photons hit the back of your eyes with higher frequency. This frequency would be so high at c, that, without protection, you would almost certainly be blinded. So, sunglasses are advised.

To the people unfortunate enough to not get a trip in your car, things would also appear strange. Now, imagine that, on the back of your car, you have a giant clock, which observers are able to see trillions of kilometres away. If you were driving away from these observers at a speed just under c, the clock would appear to slow down. The time on the clock would appear to pass slower than it would on an observer's watch. However, you would also perceive the observer in slow motion, if you could see their movement. This is a result of the fact of the increasing time delay between the reflection of a photon, off of the back of your car, and into the observer’s eye. It is known as time dilation. There is even an equation, which can help you to understand:

t’ means time dilation.

If v becomes identical to the value of c, then something even more interesting happens. t’ becomes = to t ÷ 0. This means that t’ becomes infinity. In other words, the clock that is moving away from you at the speed of light appears to freeze, and the time that you read off of the clock no longer changes.

Unfortunately this clock has now become useless, and the passengers inside your car are likely dead, blind or both. Fortunately though, we can now be guided in our future decisions, by the information above, and we have learned a few key lessons:

· We will never be able to travel at, or exceed the speed of light

· If you are offered a ride in a car which travels at c, you should not accept the offer

· If you accept the offer make sure you bring sunglasses

· Prepare to look awesome and see awesome things at the same time