Albert Einstein (1879-1955)

Albert Einstein was born in Germany in 1879, his family moved to Italy when he was 15 and at 16 he chose to go to Switzerland to study. He graduated in 1900 but was unable to get the teaching post he sorely desired as he had failed to impress and had to watch many of his classmates achieve the posts he had tried for. Unable to find work he finally got a break through a friend of his and began working in a patent office, in his spare time he wrote his mathematical physics.

The year 1905 was to be a major turning point for Einstein and indeed for 20th century physics and beyond. Einstein received his doctorate in that year from the university of Zurich for his thesis entitled 'On a New Determination of Molecular Dimensions'. He also published 3 very important theoretical papers that year, which were to have a major impact on the physics of the time and their influence continues to live on today. These papers were on:

• Brownian motion. Using kinetic theory Einstein produced mathematical equations that were able to predict the particle motion and their seemingly random collisions in fluids, this was later proved by experimentation.
• Photoelectric effect. He proposed that light could be considered to be made up of particles. Building on Planck's quantum theory Einstein suggested that the electromagnetic energy in a beam of light was not continuous waves as had previously been believed (despite Newton's efforts), but actually emitted in 'pulses', called Quanta.
  He also proposed that the energy carried by the photon was proportional to the frequency of the radiation of light. Einstein applied Plank's quantum theory to derive E = hu, where E is the energy of the radiation, h is a universal constant (Planck's constant) and u is the frequency of the radiation.
• 'On the Electrodynamics of Moving Bodies'. It was this paper that contained what would become known as 'The Special Theory of Relativity'.

History leading to Special Theory of Relativity

Classical (Newtonian) laws of physics survived unchallenged until the nineteenth century, however once electricity and magnetism were studied in great theoretical depth a new approach to physics was born, this was to have significant impact in our understanding of the universe.

It had been previously believed that electricity and magnetism where unrelated, however once Faraday, Ampere and others derived their laws they effectively unified the two areas into one fundamental force that would become known as electromagnetism.

Following this James Maxwell (1831-1879) was to combine all this work and from his understanding was able to formulate his 4 equations that managed to describe mathematically all the known properties of electromagnetism, as well as producing some important new results.
From his equations Maxwell discovered electromagnetism travelled as an oscillating wave and importantly he realised its speed was always constant whatever the properties of the electric/magnetic field.
Maxwell, however, was not finished there, he went on to calculate the speed of this electromagnetic wave and found that it was travelling at the speed of light.

This work was crucial, it provided the first evidence that the speed of light was a fundamental constant of nature, and this fact would later become very important.
Maxwell's work further demonstrated that magnetism, electricity and optics (light) could all be considered as aspects of an electromagnetic field.

Following Maxwell during the 1880's the Michelson-Morley Experiment tried to explore the idea of an all prevailing aether that acted as a medium for light allowing it travel as waves in the same way that sound travels through the air.
The final conclusions of the experiment was there could be no such aether, so still we had no idea of the underlying properties of light.
They also found that the speed of light seemed to be a constant.
As Maxwell, Michelson and Morley, and others had all shown the speed of light to be constant no matter what the experimental conditions were it was a logical conclusion that light was not like sound which has a speed relative to its medium, nor was it like a bullet with a speed relative to its source.
So what really was the deal with light?

We shall see later that Einstein was to solve this problem.

A consequence of all this work on electromagnetism and optics was that Newton's Laws of Motion were seen to fail as velocity approached the speed of light and the centuries of unchallenged laws of mechanics was at an end.

Einstein's Solution - Special Theory of Relativity

Einstein's final response was of course his Special Theory of Relativity, which supersedes Newton's Three Laws of Motion.
It should be noted that in everyday situations (velocities well below the speed of light, known as sub-relativistic speeds) Newton's Laws provide such a good approximation that they are effectively correct, and indeed, due to the simpler mathematics involved, they are still in common use outside the world of particle physics.
For this reason the Special Theory of Relativity is often thought of as method of describing the motion of matter and light only at high speeds (relativistic speed), but in fact it provides the correct description of the motion of all particles at any speed, and it shows conclusively that Newton's laws are only an approximation that becomes more and more suspect as velocity increases.

Special Theory of Relativity is based upon a reinterpretation of the classic principle of relativity (Galilean Relativity). The original interpretation came from Galileo's realisation by observing the motion of objects in a closed room (such as on a boat) there is no way to tell if the room was at rest or was moving at a steady speed in constant direction (note it would be clear if the room was accelerating). This was restated a little later as:

'the laws of physics are the same in a uniformly moving room as they are in a room at rest'

Frame of Reference

We will soon be discussing a physicists tool known as an inertial frame of reference and this is a good point to explain what this entails. A frame of reference can be thought of as a room that has ruler like spatial markings on the walls and a accurate clock.
In other words it is a room which will allow the physicist to find a precise position of any object in the room at a precise time.
An inertial frame of reference is simply a frame of reference where Newton's first law (effectively Galileo's law of inertia) holds true (see TheSpaceSite.com page on Newton's laws for more information on this).

E.g. Take an aeroplane travelling at a constant speed of 400mph with a constant altitude and imagine there are no external factors present, such as turbulence. If you were to throw something across the plane it would behave like the plane was stationary, not moving at 400mph.

So what were Einstein's starting points for the Special Theory of Relativity?

Einstein made two postulates in his formation of his theory, and subsequently both have been proved correct by experimentation.

Postulate 1

Einstein's first postulate was basically a restating of Galilean Relativity. Einstein put it as:

'The laws of Physics are the same in all inertial frames'

What he meant by this was the laws of physics are the same for an observer in a stationary lab as they are for an observer travelling with a non-accelerating relativistic particle, this was an important suggestion as we shall see.

Note: These rules clearly do not mean that the magnitude of the force is the same, but simply effect of the force is the same (e.g. gravity of the Sun is of different magnitude to the gravity of the Moon, but the effect of the force is the same).

Einstein himself liked to explain his ideas with what he termed 'thought experiments' and these often involved trains and such like, so here we shall provide an example in this form.

Take man A who is standing on an open train that is travelling at 40m/s, as he passes point Z he throws a ball towards man B at 30m/s, so how fast is this ball travelling relative to B?

To work out the velocity of the ball in a second reference frame (in this case B's) all you have to do is take the velocity in the first frame (here A's), we know this to be 30m/s, and then add (or subtract, remember velocity also has direction to take into account) the relative velocities between the two frames, here we know this to be 40m/s. So the ball is travelling 30m/s + 40m/s = 70m/s relative to (towards) B, so B should get ready to duck!

Postulate 2

Einstein's new ideas of classical relativity had to encompass the new physics that had been discovered since Galileo's initial theory, clearly this would include Maxwell's equations.
So if we take Maxwell's equations to be correct they must be satisfied in all inertial frames. The practical consequence of this is it is required that the speed of light must always be 300,000 km/s (186,300 miles per second) in any inertial frame, it other words in any inertia frame light is always light. This appears to be a reasonable postulate but what is being suggested here is that light is a fundamental constant of nature, in other words the relative velocities are unimportant.
Let us use another 'thought experiment'.

If A is on his train again and this time we say the train is travelling at 100,000km/s and A shines his flashlight at B, we know that the light is travelling at 300,000km/s so according to Galilean Relativity the light must be travelling at 100,000km/s + 300,000km/s = 400,000km/s towards B.

We have a problem here now though, if it is true that the speed of light is 300,000km/s in A's frame and 400,000km/s in B's frame it directly contradicts Einstein's second postulate that the speed of light must be the same in all frames. We have, however, followed the rules of Galilean Relativity to obtain this figure.
So what is going on?

Well it has been proved experimentally many times that Einstein's postulates are correct. Therefore the only possibilities here are that either:

1. the distance (e.g. 300,000km) differs from one frame to the next
2. the time (e.g. 1 second) differs from one frame to the next

Unfortunately for the sake of sanity both of these possibilities are correct, oh dear...

First thing: don't panic!
Einstein showed that measurements of length and time must change from one observer to another to achieve consistency within the physical world.
While this may seem strange experimental results compare perfectly to the theoretical predictions of differing measurements every time.
The two phenomena are known as length contraction and time dilation, let us look at each in turn:

Length Contraction

Sometimes referred to as either Lorentz contraction or Lorentz/Fitzgerald contraction as both Lorentz and Fitzgerald produced the mathematics describing the phenomena before Einstein had developed special relativity. Einstein was, however, the first to understand exactly what it meant and what the implications of it were.
The principle is fairly straightforward: take an object, in a frame in which it is moving, its length will be shorter than the same object in a frame which it is at rest.
The important point here is that this is not simply an illusion, its physical properties actually change.

Note the change will only occur in the direction the object is travelling, so if it is moving horizontally it will be its horizontal length that will contract, the vertical length will remain the same.

Time Dilation

In much the same way time will pass at different rates for two people travelling at different speeds relative to each other. The best demonstration of this principle is the famous twins paradox.

The first twin launches from Earth on a 20 year mission on which they travel at a velocity of 0.9c (c represents the speed of light, so this means travelling at 90% of the speed of light). Given it is known that at this speed time slows by about 50%, upon returning at the end of the mission 20 years have passed on Earth but the astronaut will only have aged 10 years!

To restate the reason for this: in the astronaut's frame of reference the time relative to Earth's frame has slowed by 50% due to the effects of time dilation, so only 10 years have passed for the astronaut. This does not mean the astronaut is living longer, their time has only slowed relative to other people's frames, within their own frame time passes normally, so they will still only live their normal lifespan. Indeed they would not even realise time had dilated until they returned home and saw people much older.

Although this seems bizarre there are many experiments that prove time dilation, e.g. in the use of sub atomic high speed particle accelerators which deal with relativistic speeds and also the use of the supremely accurate atomic clocks. If an atomic clock is taken onboard a plane after the flight the clock on the plane will read a different time than a clock on the ground due to the effect of time dilation.
This is an example of the maxim 'moving clocks run slow', which points out that, speaking relatively, travelling from one location to another will slow down time.

More Length Contraction & Time Dilation

So if these points are such established scientific facts why do we not notice these occurrences in everyday life?
The answer is simple, these phenomena do occur in everyday life but they are simply too small for us to detect, in fact they only become noticeable as we approach the speed of light.

The change in the length or the time due to these effects can be described mathematically as gamma.

In everyday life velocities, v, are never anywhere near the speed of light, c. So v²/c² will be an extremely small number and therefore can be described as insignificant. So we are left with 1/sqroute1 (which of course equals 1), hence gamma essentially equals 1.
As length contraction and time dilation effects are calculated by multiplying and dividing by gamma, the values remain essentially unchanged (e.g. 10 x 1 = 10!).

The following table demonstrates the effect of length contraction of a 1 metre stick travelling at various speeds:

Speed travelled	Value of gamma	New Length of 1 m stick
at 100km/s (approx 224,000mph)	1.000000056	0.999999944m
at 0.1c (30,000km/s)	1.005	0.995m or a 5mm reduction.
at 0.9c (270,000km/s)	2.29	0.44m

So it is clear that at low velocities the effects are too small to be detected, as the velocity increases the effects become more pronounced and if we continue to increase the velocity until we approach the speed of light the effects become very notable.
It is, then, fair to say that the only time in the real world that we really encounter these phenomena is in particle physics where tiny particles, such as electrons, are accelerated to speeds that are approaching the speed of light. Of course in this branch of physics these effects are extremely important and must be taken into account.

E=mc²

Note this can also be denoted as E=mc^2, this is because some browsers cannot see the squared notation.

Later in 1905 Einstein was to derive the most famous equation of 20th century physics from his Special Theory of Relativity, which was of course E = mc².

So what does this have to do with relativity, well the equations that work with length contraction and time dilation demonstrate other consequences, one of these being as velocity increases then mass increases. Einstein felt that this was important due to his belief in the law of conservation of momentum.

As an example, take a spaceship, the rockets can produce kinetic energy to accelerate the spaceship. The relativity equations show that the faster the ship travels the greater the resistance to acceleration becomes, or in other words the greater the increase in inertial mass (we will examine this concept of inertial mass in more detail later under general relativity, for now just accept that it is resistance to acceleration).
Once again this increase in inertial mass with increasing velocity happens in every day situations, but is not detectable until we are approaching the speed of light.
So as we approach c the kinetic energy being produced by the engines continues to be applied, but the rate of increase of velocity is slowing as some of this energy is being converted into inertial mass, which in turn increases the resistance to acceleration. Once we are close to c any increase in velocity results in a very large increase in mass.

From a scientific point of view, this example shows that mass and energy are equivalent, or interchangeable, and in more modern times we have seen a practical demonstration of this in the release of atomic energy, which effectively proves E = mc² and as it is derived from Special Theory of Relativity and nothing else, this effectively proves special relativity to be correct.

When Einstein first published this theory it was felt that it seemed to go against two accepted fundamental laws of physics:

Law of Conservation of Mass

E.g. after burning something the mass after the burning will be the same as that before the burning took place, i.e. if u add up the masses of the smoke particles, ashes etc the mass will remain the same as the original mass

Law of Conservation of Energy

The theory that no energy in the universe is ever created or destroyed, energy is simply converted from one form to another

Einstein though showed that as mass and energy are essentially the same thing converting one form to the other clearly violates neither law.

It is interesting to point out that we have said as you approach c gamma becomes very significant with the net result being mass, length and time change significantly, but locally the person travelling at such speed (e.g. an astronaut) would not notice these changes, they would only be witnessed by outside observers.
To the astronaut it would appear that everything else in the universe has changed. We can now start to get a feel for why this theory is known as relativity.

Implications of E = mc ²

This part of special relativity has crucial implications for space exploration, according to the Special Theory of Relativity it is impossible for any wave or particle to travel faster then the speed of light. The equations clearly show that as velocity increases mass increases and upon reaching the speed of light an object's mass will be infinite. As an infinite amount of energy would be required to move an infinite mass, attaining light speed for any object with mass would be impossible, therefore clearly ruling out faster than light travel.

The other major problem with ideas of travelling faster than light are issues of causality that can produce major contradictions, overall it really does appear that the speed of light probably represents an unbreakable barrier.

So if it is impossible to travel at the speed of light and we know that light is made of particles how do they travel at such speeds?
Well photons, as the particles are known, are a very interesting phenomena, they have 0 rest mass, so by equations it has been proved that they actually have to travel at c!
Now let us assume that a particular photon has travelled from our nearest star, the journey would take 4.2yrs in our frame of reference but as time dilation is 100% at c in the photon's frame of reference it would not exist until it reaches us, which would occur instantly.

It is interesting to note that it seems a few tiny particles are actually able to travel faster than the speed of light, and there is a known phenomena called quantum tunnelling that allows tiny particles to travel faster than light, however the implications of this is unclear, whether it has any practical significance at this point is unknown, and at out current level of technology will probably remain unknown for some time to come.

The implications for interstellar travel from all this is therefore clear, the nearest star to us is Alpha Centauri which is 4.2 light years away and as it is physically impossible for our spaceships to travel faster than light it would take several years to get there even if we could get somewhere near c. Of course if we could get up to such speed then the travellers would gain the advantages of length contraction and time dilation which would reduce the journey relative to them, so they would not have to spend several years in the spaceship, but there is a problem here.
As we have seen by the twins paradox everyone back home would have grown older and technology would have advanced four and half years without them. There is also the less cited problem of communications would still take 4.2 years each way.
It must also be remembered that these problems are only for the nearest star, the case could be worse by a factors of 100's, 1000's or more for more distant stars, making this option not particularly attractive.
There is also the major problem that we do not possess the technology to get a craft anywhere near light speed!

A point to bear in mind is there are possible ways around this limiting factor of the speed of light. For example while special theory of relativity prevents an object with mass travelling faster than light there is no suggestion from the equations that there is such a speed limit on spacetime (see next paragraph) itself. There may also be ways to explore space without having to travel such great distances, by bending or folding spacetime or by jumping to higher dimensions resulting in the spaceship's velocity being far less crucial.
These ideas will be explored later under the section of this website entitled the future of space exploration, although the ideas of warping spacetime will be explored under General Theory of Relativity where the idea originates from.

For completeness in should be stated that contained within this theory was a statement that space and time were not separate but were actually one entity, known as spacetime, which has 4 dimensions, the usual 3 spatial dimensions and a fourth temporal dimension. This idea is central to the General Theory of Relativity and we shall wait until that section to explore this idea in detail.

Final Thoughts on the Special Theory of Relativity

The important limiting factor for the theory of special relativity is that it only applies if the system is not accelerating. Thus as long as the particle, body etc is either at rest, or travelling at a constant speed in a constant direction the theory works fine.

What are the implications of this?

Well from Newton's second law if a body is accelerating a force must be acting upon it thus implying that the Special Theory of Relativity only works where there are no forces acting, so, for example, it will not work in a gravitational field (this was the point that led Einstein to create general relativity).

Just as with all the great theories that have changed our view of the universe, the Special Theory of Relativity did not have all its components worked out by one man. As Newton was the first man to fully understand the theories of Galileo and Kepler, and was able to bring them together as a complete theory, Einstein brought together classical thinking (such as Galileo) together with the modern work such as Maxwell's work on electrodynamics and Lorentz mathematics of length contraction to bring a completely new understanding of the universe.

Continue onto the General Theory of Relativity
Go back to the Contents Page

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