Fundación Canaria Orotava
de Historia de la Ciencia

The Amazing World of Albert Einstein

¿Do you know how to become older than your parents?

Do you know how to live for ever?

Do you realise you could weigh as much as ten jumbo jets - without getting fat?

Do you know how to squash a person flatter than a CD - without them feeling a thing?

No, I’m not talking about some science fiction fantasy world. I am talking about this world - the world you are living in.

These amazing facts about space, time, and mass arise out of the Theory of Relativity. The theory was discovered by one of the most famous scientists of all time: Albert Einstein.

Next year marks the 100th anniversary of his discoveries, so it will be known as Einstein Year. There will be a lot of talk about Relativity next year.

The trouble is, most members of the public will not have a clue what the celebrations are about. Though they might have heard of the Theory of Relativity, they will not know anything about it. They believe that it is all much too hard for ordinary people to understand.

This is a mistake; there is nothing hard about it - as I hope to show you. By the end of this talk, you will be one of the exceptions who know about the amazing World of Albert Einstein. Relativity starts out by considering what happens when one goes fast.

And I mean VERY fast - at speeds approaching that of light: 300,000 kilometres per second.

How can such speeds be achieved? In a machine like this, situated just outside Geneva, Switzerland at the European High Energy Physics Laboratory called CERN.

We take tiny sub-atomic particles and put them in this hollow tube. Then we push on them with strong electric forces to accelerate them.

The tube looks straight, but it is not.

Looked at from this angle, we see it has a slight bend to it. In fact, it is part of a circle. The tube eventually wraps round on itself to form a huge circle, 27 kms in circumference. The machine is so large, it would take four hours just to walk round it.

It is buried in the ground, so you can’t see it from the surface.

But you can get some idea of the size of these particle accelerators from this one here at the Fermi Laboratory just outside Chicago in USA.

The particles are made to go round it many times, getting faster and faster. It’s a bit like an Olympic hammer-thrower whirling the hammer round his head several times, getting up speed, before letting go.

The first thing we discover is that there is a speed limit. Nothing can be made to go faster than the speed of light.

No matter how hard we push on the particles, nor how long we keep pushing, 300,000 kms per second is the limit.


A good way of looking at it is to say that the faster an object travels, the heavier it becomes.

Relativity Theory explains how energy is heavy - it has mass. This is summed up in Einstein’s most famous equation: E = mc2. E is the energy, and m is the mass that goes with that energy. c2 is the speed of light squared and is included to allow us to write mass in units of energy. So, as the particle accelerates, it must get heavier because of the extra energy it now has. It cannot take on the extra energy without also taking on the extra mass that goes with the energy.

And that in turn means it is harder to make it accelerate still more. It is as though you start out pushing a wheel barrow, and end up trying to push a ten-ton truck.

At 9/10ths the speed of light, the particles weigh twice as much as normal.

And as they approach the speed limit, the mass becomes infinite. Here at Stanford in California, where they have a straight accelerator 3 kms long, they accelerate tiny electrons to speeds so close to the speed of light, they emerge at the other end, 40,000 times more massive than when they started out.

If we accelerated you to the same speed as those electrons, you would end up weighing the equivalent of ten jumbo jets.

What do you think happens to the mass of those electrons when they come to rest again?

As they come to a halt, they lose all the energy they had - and that means they lose all the mass that went with that energy. So, the electron’s mass goes back to what it was originally.

Energy and mass go together. If you have energy, you have mass; if you have mass you have energy.

This pen has mass, so what does that mean?

It means that it has energy - even though it is not moving. It has a locked-up form of energy.

How much energy is there in this pen?

Enough to devastate the whole island of Tenerife!

If the energy in here were suddenly released, it would be the equivalent of a nuclear bomb going off.

But don’t worry, it is safely locked up. We can’t get at any of that energy.

But there are certain special circumstances where a small fraction of the locked-up energy of matter can be released. It happens when the central part of an atom - called its nucleus - splits up, or fuses with another atomic nucleus to form other types of nuclei.

This is the source of the energy of nuclear bombs and nuclear power stations: energy in the form of matter is converted into other forms of energy such as heat, light, and other types of radiation.

So, that is the first thing Einstein discovered about what happens when you travel very fast; You cannot ever quite catch up with a light beam - because of this mass increase.

But an even bigger surprise was in store.

Speed affects time.

Time passes more slowly for an astronaut in a high speed spacecraft than it does for the mission controller on the ground.

The clock on the wall of the space craft goes slow, as does the winking of the lights on the control panel.

Everything about the astronaut’s body goes slow: Her rate of breathing; her pulse rate; even the rate at which she ages.

Is she aware of these changes? No.

The point is that if everything in the space craft has slowed down, then her brain processes will also have slowed down - by the same amount, and hence her thinking.

If you look at a slow clock with a slow brain, then it will appear to be normal.

In fact, life in the space craft carries on as normal - as far as the astronaut is concerned. It is only from the point of view of the mission controller, everything happening up there has slowed down.

If you are interested, the amount of the slowing down is given by this formula. t prime is the astronaut’s time, and t is the mission controller’s time. v is the speed of the craft, and c the speed of light.

From this we see that if v is about 9/10ths of c, the expression under the square root sign is 0.25, which means t prime is 0.5 t. So, at 9/10ths the speed of light, time slows down to half of what it is for the mission controller .

And if the craft were to travel right up close to the speed of light, v/c would approach 1, the expression under the square root sign would become zero, and t prime would approach zero - meaning that time on the craft would, in effect, come to a halt. You could live for ever!

Not, of course, that it would feel as though you were living for ever. Why? Because your brain would have stopped.

Mind you, this slowing down of time does offer some interesting possibilities.

Suppose, for example, you yourself had such a high speed space craft. You could invite your parents - and your teachers to go for a cruise in it. You put them on board - but you do not travel with them. You shoot them off at close to the speed of light.

Meanwhile you carry on living your life as normal. The years pass by. You grow up, leave school, get a job, get married, have children, the children grow up.

Then one day, you suddenly remember your parents and teachers. They are still flying around the universe. You bring them back.

They emerge from the craft no older than when they got on it. Meanwhile you have been aging at the normal rate. You find that you now have had more birthdays than they had when they originally got on your craft. So, you are now older than your parents and teachers.

Who gives the orders now!? Now, I hasten to add that no such ultra-high speed craft exists, or is ever likely to exist. They would be far to expensive.

But in those particle accelerators I was talking about, it is possible to accelerate tiny radio-active particles to speeds approaching that of light. These particles decay into other sub-atomic particles after a certain characteristic time called their lifetime.

What is found is that at high speed their lifetime is increased.

In one famous experiment, the lifetime was increased to 30 times what it is normally - 30 times being exactly what this equation of Einstein’s would have predicted for anything travelling at that particular speed.

Another thing worth mentioning is that although we have talked of this slowing down of time being a feature of high speeds, in fact, time slows down at all speeds - even the sorts of speeds we are used to in our daily lives.

As I walk up and down, I am moving relative to you, which means my time is now going more slowly than yours. I am aging less quickly; thinking less quickly, my watch is going slow.

So does that mean that now I am no longer moving, I need to adjust my watch to make up for that lost time, and thus get back in step with your watch?

No - the reason being that at the kind of speed I was moving at the effect is very, very small.

I once worked out that if someone were to drive an express train all his working life, he would age less quickly than his wife who had an office job, by no more then one-millionth of a second. Hardly worth bothering about!

There is one more thing I want to tell you about what happens at high speed. Not only does it affect time, it also affects space.

The faster a craft goes, the shorter it becomes. At 9/10ths the speed of light, the craft shrinks down to half its normal length.

And not only the craft, but everything inside it - including the astronaut. (It is space itself that is squashed up.) At the speed we are talking about, the astronaut is flattened to half her normal width.

Not that she feels a thing. The atoms in her body have shrunk down to half their normal width, so they only need half the normal size body to fit in comfortably.

She cannot even see that things are squashed up. This is because the retina at the back of her eye, containing the picture of what she is looking at, is squashed by the same amount. So, the scene she is looking at still fills up the same fraction of the retina as it would do normally -so to the brain it looks normal.

And right up close to the speed of light, the craft would be squashed thinner than a CD, and the astronaut would still be inside not feeling a thing!

Now all of this sounds very confusing: people not being able to agree about time intervals and distances. But things are not as bad as they sound - not when you see things the way Einstein saw them.

Take a look at this pen.

What do you see from over there? You see a short pen because you are almost directly in line with the direction in which the pen is pointing. It looks foreshortened.

You, on the other hand, see a long pen. This is because you are seeing it broadside on.

Does that worry you - the fact that you disagree about the appearance of the pen - you do not see the same thing?

Of course not. You realise that what you can see is nothing more than a 2-dimensional projection of the pen onto a plane that is at right angles to your line of sight.

The pen itself does not exist in 2-dimensions; it exists in a 3 dimensional space.

If you want to know what the true nature of the pen is, you have to take into account not only the projected length but also its extension along the line of sight in that third dimension.

For you, the pen extends a long way in the third dimension; whereas for you there is hardly any extension at all along your line of sight. The result is that when each of you use your own individual measurements of the projected length at right angles to the line of sight with the projected length along the line of sight, you both arrive at the same identical value for the true length of the pen in 3-dimensional space.

It is because you agree on that 3-dimensional length, you no longer worry about the different appearances of the pen. You recognise them for what they are: mere projections of reality, as seen from different points of view.

Einstein’s genius was that he recognised that there was a similar explanation of the different times and distances we encounter at high speed.

He proposed that instead of having a 3-dimensional space and a separate 1-dimensional time, they should be combined into a single 4-dimensional spacetime.

In that way a distance measured in 3-dimensional space would be merely a 3-dimensional projection of what in truth was 4-dimensional.

Similarly, a time measurement was merely a 1-dimensional projection of that 4-dimensional reality, along the time axis.

We need no longer worry about the astronaut and mission controller having different ideas about the distance from the front to the back of the craft, nor different ideas about time intervals

Like the people looking at the pen, these would differ depending on one’s point of view. In the case of the pen, that meant where they were sitting in the room relative to the pen. In the case of the space craft, what their relative speed was.

The really important thing is that, when they plug their own individual measurements of time and space into the formula for calculating the length in 4 dimensions, they arrive at identically the same result for that 4-dimensional length or interval.

It is the fact that everyone always agrees on measurements in 4 dimensions that makes us believe that reality really is 4-dimensional.

Now, I fully realise just how difficult it is to think in terms of 4-dimensions. It is not something we can readily visualise.

This is the best I can do, but it is a bit of a cheat. Those four fingers, representing the three dimensions of space and one of time ought, strictly speaking to be all mutually at right angles to each other.

That is impossible to demonstrate - and it always hurts to try to do impossible things.

But if you are not too fussy about the angles being wrong, that is a pretty good mental picture to have in mind.

In point of fact, we physicists don’t rely on such mental pictures. We let the mathematics do our thinking for us.

In calculating distances according to ordinary geometry we have a formula involving three terms - each term showing the contribution to the overall distance coming from each of the three spatial projections.

To do calculations in 4-dimensions, we merely have to add on a 4th term to represent the contribution from the projection along the time axis.

OK. What I have been talking about so far comes under the heading of Einstein’s Special Theory of Relativity. It is all to do with the way space and time are affected by relative speed.

This was the discovery he made in 1905 and which gives rise to the celebrations next year - 100 years on.

But Einstein was to go further, and some ten years later he published his General Theory of Relativity.

Let me tell you just a little bit about that. It looks at the way space and time are also affected by gravity.

Suppose we have a space craft in orbit about the earth. Its engines are switched off so it is just coasting in a circular orbit.

We say that the reason it is going in a circle - rather than in a straight line - is because the Earth is exerting a gravitational force on it.

An astronaut steps out of the craft to go for a space walk.

She is now going in an orbit about the Earth, because gravity is pulling on her too.

She is travelling in almost the same identical orbit as the space craft.

This is very odd.

How does gravity know how strongly it ought to pull on the much lighter astronaut in order to get her to follow the same path?

Einstein had a brain wave. He said we were looking at the problem in the wrong way.

Up to then, people thought that the natural path for an object to follow was a straight line - and whenever it deviated from a straight line (like the craft or the space walker in circular orbit) then it must be due to a force.

What Einstein did was to do away with gravitational forces.

He put forward the revolutionary idea that close to a body like the Earth, the natural path was not a straight line.

The natural path was the one followed by the craft and the space walker. It was a curved path because the Earth had curved the space.

The Earth is resting in a kind of dip.

The situation is rather similar to that encountered at a car-racing track where the corners are banked.

In such cases, the natural path is not a straight one. If the driver takes his hands off the steering wheel, the car will coast round the corner quite naturally.

And that is what is happening to the space craft and the space walker - and indeed to the moon - as they coast round the banked race course caused by the Earth’s curvature of space.

Everything passing close to the Earth, or close to any other heavenly body - such as the Sun - is affected by this type of gravitational curvature.

And that includes light.

A light beam coming from a distant star, gets bent by the Sun on its way to us, making it look as though the star has been displaced.

It was the measurement of the apparent shift in the positions of the stars as the Sun passed between us and them that was to provide the experimental proof that Einstein’s curved space idea was a better one than Newton’s law based on gravity forces.

And when gravity becomes exceptionally strong, the curvature of space can become so pronounced that nothing at all, even light, can climb up out of the steep curvature.

This is what we call a black hole.

So gravity affects space. It also affects time.

Did you know, for instance, that time runs faster upstairs than it does downstairs?

So, if you are late doing your homework, you’d be able to work faster at the top of a tall building than at street level. Your mind will work faster and you will be able to write quicker.

Not that I recommend it. For one thing you will age quicker and die sooner.

For another, the effect is so absolutely tiny, you would need highly sophisticated scientific equipment to be able detect any difference at all.

But the effect is there and has been measured.

And out in space, especially close to black holes where gravity is extremely strong, the rate at which time passes depends very much on exactly where you are placed relative to the hole itself.

These are just some of the effects on space and time caused by gravity. As I said, they are all dealt with under Einstein’s General Theory of Relativity.

I hope you are now in a position to realise why we shall all be making such a fuss about Einstein next year.

I also hope that, having heard this talk, you will feel able to explain to your parents and to others a little of what that fuss is all about.