We all surely know the famous anecdote that explains how Galileo Galilei tried to make religious authorities understand that the Earth was moving. Even when the Italian astronomer tried to make his censors reason, they did not hear his proof, arguing that, as the Bible say Joshua ordered the Sun to stop and not the Earth, it is the Sun that moves around, while the Earth stands still. Under torture threats, Galileo was forced to retract and had to spend the last years of his life under home arrest.

A argument that tried to appeal to common sense sustained that the Earth does not move because ``we can not perceive the movement''. It is true that when we take the train to Buenos Aires, we can realise if we are detained or moving: when the train moves forward , it shakes. But what if we travelled by ship? The ship shakes because of the waves and the stronger the sea, the more it shakes; but if we are locked inside the cellar without windows, we would not be able to tell if we are sailing or stuck in the middle of the ocean.

Let's suppose that in our cellar there is a skylight and we see another ship crossing from North to South. Does this tell us anything about our own movement?

There are many options: a) we are anchored and the other ship is moving southwards; b) the other ship is anchored and we are sailing northwards; c) both ships are sailing northwards but we are moving faster and we overtake; d) we both travel southwards and our ship is slower and is being overtaken or e) we are going northwards and the other ship southwards. The only options that are excluded are that both ships are anchored or that they move at identical speed and direction.

Even then, if we peep through to see the sea, we will only be able to see if we are moving respect to the water. If we run out of fuel and the engines stop, the ship will stand still, but finally the stream will take it somewhere. The captain will be interested in knowing if we are getting closer or further from the coast.

It is clear now that before discussing which objects move and which ones do not, it is necessary to say respect to what, that is to say, to establish a reference system.

Let's go back now to our seat on the train. If when passing by Platanos Station, a woman tells his naughty son to ``keep quiet'' it is clear that she wants him to remain sitting.

There is a simple way to relate positions and velocities measured from different reference systems. Let's suppose our seat is exactly twenty-five meters ahead of the freight car. How far are we from Platanos? Obviously, we are twenty-five meters further than the freight car. And how far is the freight car from Platanos? If the train travels at forty kilometers per hour and we passed by Platanos fifteen minutes ago, the freight car will be at ten kilometers from Platanos and we will be twenty-five meters further, at ten thousand and twenty-five meters from Platanos.

Let's suppose now that we get out of our seat and walk to the locomotive. If we walk at five kilometers per hour, as the train travels at forty, we are going to get away from Platanos at forty-five kilometers per hour. If we move backwards and start walking towards the freight-car, we well be also getting further from Platanos, but at thirty-five kilometers per hour.

All this is pretty obvious. It is clear that we have to add our speed to that of the train (or subtract it if we are moving backwards) to know at what speed we move respect to the station. If we want to know at what distance we are from the station, we add the distance that separates the freight car from the station to the distance that separates us from the freight car. These operations are intuitive and are known as Galileo transformations.

About three centuries ago, Isaac Newton invented the laws that describe body movements (later on I will clarify why I say ``invented'' and not ``discovered''). For instance, if I let a coin fall from an altitude of one meter and twenty two centimetres, using Newton's laws I can predict that it will reach the floor in half a second at a speed of about eighteen kilometers per hour. If I repeat the experiment on the train, travelling at forty kilometers per hour, the same will happen and the coin will also fall in front of my shoes. During the half second it takes the coin to fall, the train (and my feet) will have travelled slightly more than eleven meters and eleven centimetres. Then, seen from the station, the coin will have fallen following a curved trajectory ``following the train''. In other words, the coin will fall next to me all the same, independently of the fact that the train is moving or not. In mathematical terms, this fact is expressed by saying that Newton's equations are invariant against Galileo transformations.

When we were in school, they would tell us ``to graphic the following curves'' and we had to draw the graphic representations of each equation. For example the graphic representation of ``y equals x squared'' is a parabola, and that is the reason why this equation is called ``parabola equation''; the equation represented by a straight line is called ``straight line equation'', etc.

There are equations, somewhat more complicated that the ones studied in school, where their solutions are waving curbs. They are known as ``wave equations'' and are used by physicists to describe some nature phenomena and to destroy careless students. For example, if we throw a coin inside a washbowl full of water, circular waves will be formed around the place where it falls. The sound, instead, are rapid variations of the air pressure. The form in which these variations are propagated can be described by an equation of waves, that is why we speak about ``sound waves'' although (contrary to the water surface in the washbowl example) in this case there is nothing that ``waves''.

Let's get back on the train and suppose a policeman shoots a suspect. If we want to know what is the velocity of the bullets with respect to the ground, we must to use the Galileo transformations, i.e., the train velocity must be added to the speed of the bullets leaving the pistol. (assuming the policeman shot forward). But what happens if the locomotive blows its horn? Sound always travels at the same speed through the air, independently of the movement of the locomotive. We can also use this property to measure the velocity of the train respect to the air: if the train travels at forty kilometers per hour (assuming there is no wind) from our point of view the air will blow backwards at the same speed. So when the horn blows, for us the sound will travel backwards at forty kilometers per hour faster than the normal and forward at forty kilometers slower, which will permit us to conclude that the train is moving at exactly that speed. Note that the policeman could never reach this conclusion, not even shooting in every possible direction.

James Clerk Maxwell was a physicist who lived in the XIX century and who, working on the mathematical equations that describe electric and magnetic phenomena, arrived to a ``wave equation''. He then predicted, in a theoretic way, the existence of ``electromagnetic waves'' and suggested that light could be an example of these kind of waves. Maxwell died before the radio was invented, but today we know that the light, the heat, the microwaves, radiowaves, TV and radar are all electromagnetic waves.

If we ask a physicist to calculate the intensity of an electromagnetic field at ten kilometers from a radio station in a certain moment, he will have to solve a wave equation. That is the reason we talk about electromagnetic waves, although as in the case of the sound, there is nothing that ``waves''.

Now then: The sound is ``pressure waves'' that are propagated through the air, but light and heat come to us from the Sun and there is no air between the Earth and the Sun. It was assumed then that there had to be a very dim means that would cover space, through which the electromagnetic waves could propagate. This means was called luminiferous ether, that is why in the first broadcasting programs, speakers would talk about the ``ether waves''.

Let's remember the example of the locomotive: As we know at what speed the sound travels in the air, measuring the speed of sound respect to the locomotive, we can calculate the speed of the train. Following the same reasoning, as we know at what speed light travels through the ``luminiferous ether'', if we measure the speed of light respect to the Earth, we will be able to calculate at what velocity the Earth moves through the ether.

Michelson, in one of the most famous experiments of physics, measured the speed of light respect to the Earth in different directions and got always the same result, as if the Earth did not move in the ether.

As the Earth turns around the Sun at a speed of about thirty kilometers per second, if we repeat the experiment six months later, we should expect to find a difference of sixty kilometers per second, as the Earth will have completed half a turn around the Sun and will be moving ``backwards''.

Let's bear in mind that no one has ever measured or detected the ether in any way. It was believed it existed, simply because it was thought that the light needed some material means to propagate. To explain the negative result of Michelson's experiment, some tried to propose that the Earth could ``drag'' some ether while it moves (like the air inside a train coach). Einstein, instead, postulated that the light propagates through the vacuum and its velocity, measured from any reference system is always the same.

Naturally, this is what the results of Michelson's experiments suggested but Einstein's ideas were against ``common sense''.

Let's go back to the train and suppose the locomotive turns on the light. If we measure the speed of its light we will find that it travels roughly at three hundred thousand kilometers per second. If the train travels at forty kilometers per hour, it would be natural to expect that the speed of light measured from the station was forty kilometers faster. But what happens in nature is exactly what Einstein says: The result of measuring the speed of light from a train that is moving or from the station is exactly the same. There is no way to convince light to travel faster.

It is clear then that we must not use Galileo's transformations (add or subtract velocities and distances) to go from one reference system to another. If the speed of light is the same for any system, we have to use Lorentz Transformations (these are equations somewhat more complicated than Galileo's). Now then: Maxwell's equations (electromagnetic wave equations) are invariant to Lorentz's transformations. Speaking plain English this means that the train officer may illuminate in any direction with his flashlight, but the light will behave exactly as it would if the train was detained. And this is what actually happens!

Einstein's ideas (who just accepted the result of Michelson's experience as it was) deeply revolutionised physics. If we recognise that using Lorentz transformations to relate different reference systems is correct, the fact that the speed of light is always the same stops being an uncomfortable phenomenon . But Newton's transformation are not invariant to Lorentz transformations, which means that Newton's theory ``is wrong''.

Now I can justify why I said that Newton invented his laws; If I had said discovered I would have given the false impression that these laws were an already existing property of nature that he made come to light. If it had been that way, it could not be that these laws were wrong. Even if we are told that objects fall to the floor ``because of the gravity law'', the thing is that this used to happen exactly in the same way before Newton was born and continued to fall in the same way after Einstein found out that Newton's laws were ``incorrect''.

Some three hundred years ago, Newton elaborated a theory that predicts the movements of all planets and satellites with amazing precision, and the movement of planet Mercury with a very slight error. Very precise astronomical observations are necessary to detect that minimal difference (that is why I wrote ``incorrect'' between quotation marks) but Einstein's relativity theory is equally exact for the movements of all planets, and it also works for Mercury. That is the reason why it is better.

Another aspect in which Einstein's theory is against common sense is time dilation. As we have seen, when we used Galileo's transformations to connect measurements taken from different reference systems, we had to add or subtract distances and velocities. But with Lorentz's transformations it is not so easy, as time also intervenes. The time on the moving train passes by more slowly than on the station.

Naturally the time dilation is so slight that it is not perceptible on a train ride. But let's imagine that the speed of light, instead of being three hundred thousand kilometers per second (more than one thousand million kilometers per hour) was only of fifty kilometers per hour: In that case, if we take the train in La Plata Station at two PM and get off after a half an hour ride (at forty kilometers per hour) we will find that everyone says it is ten to three. If we immediately take the train back, it will take us another half an hour to arrive, but in La Plata it will be already twenty to four. This does not mean that the clocks are ahead or retarded, we, on the train, will not notice anything unusual, we will only have completed a thirty minute ride to go and another thirty minute ride to return . Those who were waiting for us in La Plata will not have notice anything either, but will tell us that our trip lasted fifty minutes to go and fifty to return . In the real world, as the light travels at more than one thousand million kilometers per hour, and not at fifty, even if we travelled by train continuously for fifty years, we would only save one millionth of a second.

All these phenomena look like theoretic curiosities, as we do not perceive them in everyday life. There are no trains, planes, rockets or any kind of vehicle able to get close to the speed of light. But there are in fact extremely precise clocks: The atomic clocks. In an experiment conducted in 1971 four of these clocks were embarked in commercial planes and it was proved that time really elapses as the theory of relativity explains. The magazine Scientific American said that this was the cheapest proof of this theory, as it cost eight thousand dollars, from which seven thousand and seven hundred were spent in plane tickets.

Despite how fantastic the phenomenon of time dilation may be, the theory of relativity has resulted rather uncomfortable for science fiction writers, as it prohibits to travel faster than light. This causes problems impossible to solve for stories of travels beyond the solar system.

What happens in the real world when we try to travel faster than the speed of light? Again, there is no way to accelerate a body to such velocity, but there do exist some extremely powerful particle accelerators (called syncrotrons) that can accelerate the particles that constitute matter.

Let's suppose again the speed of light was only fifty kilometers per hour and that we have a ``tennistron'' that could accelerate tennis balls. We turn it on and after one hour our balls travel at forty kilometers per hour. We wait for another hour and they now go at forty-five. We leave the device working for a whole week and they travel at forty-eight. The balls continuously increase their speed: it will become more and more difficult to get to forty-nine, forty-nine and a half, etc., but they will never make it to fifty. However, if we stand on the way of a ball that has been accelerated for just an hour we will only receive a soft ball hit while if we try to stop one that has been accelerated for one day, it will hit us as if it was made of solid rock. And if we are brave enough to stay on the way of a ball that has been accelerated for many weeks, it will be like being hit by a locomotive, although the three balls will be travelling nearly at the same speed. The balls do not travel faster but they hit harder and harder. The same happens with the real particles: The particles gain more and more impulse but they can never reach the speed of light.

In many science fiction stories the recourse is to say that, in the future, a mistake is discovered in Einstein's theories and that it is possible to overpass the speed of light.

As we have seen Einstein found that Newton's theory was ``wrong'' and this did not mean things would start falling upwards. Moreover, if we say Newton's theory is ``incorrect'' it gives the impression that Einstein's is the ``correct'' one.

Maybe tomorrow or in a few years, a hypothetical physicist, say Mr Jacob Newtenstein, may discover that Einstein's theory is really ``wrong''. But even if this happens, things will not start falling onto the roof or to move faster than light.

Einstein simply elaborated a description of nature that is more accurate than Newton's, and it is possible that someone finds a better one. But nature will not change its behaviour to satisfy any physicist's theory: It is the scientist who will have to burn his brains to make his theory describe nature better than all the previous ones.

Translation by Gerardo A. Ostrov - gerarost@yahoo.com