EINSTEIN

Born in Ulm Germany 1879. Did fine and very well in Math and Physics in school, but he chaffed under the rigid discipline in the German High schools. Decided he wanted to go to the ETH in Zurich for university. Failed the entrance exam at first and took a makeup year in a Swiss school. He renounced his German citizenship to avoid military service, and took a year's makeup in Swiss school. Read Philosophy (Kant was a favourite) and discussed philosophy with his landlord. Got his high school matriculation certificate with flying colours (top marks in Math and Physics) and entered ETH for 4 year program. Graduated in 1900. He and another student in his class (Maja) romantically involved, and she had his child in 1902 (no record of what happened to the child), after which they married, which lasted until 1919.

He could not get a teaching job (his degree was also a teacher's certificate), and Marcel Grossmann, a fallow student, got his father (who worked in the Patent office in Bern) to get Einstein a job as patent examiner. He did the job well and quickly and had time to work on his physics interests in the spare time.

In 1905, he published five papers

We will return to the second on later, and will concentrate on the third and fourth paper here.

While Lorentz and Poincare attacked the mystery of how light behaved when seen by a moving observer by trying to understand how matter, and the aether could interact so as to explain the variety of experiments, and theory. Einstein attacked the problem very differently. He took Galileo's relativity seriously and said to himself that the experiments seemed to indicate that Galileo's ideas were right, that it was impossible to carry out any experiment which would show that you are moving. Einstein said to himself, let us assume that there is not way of conducting any experiment, including experiments which included light, which would tell you that you are moving inertially (ie a straight line with constant speed), or were at rest. This would mean that light should have the same speed in all directions, even if you were moving. As a part of this he assumed that the aether did not exist. Maxwell's equations, being equations which referred only to the the electric and magnetic fields, and not at all to any aether, suggested to him that the assumption that these waves had to travel in an aether was entirely unnecessary. Maxwell's theory was a theory in which the electric field and the magnetic field were dynamically related to each other (changing electric field produced a magnetic field,and a changing magnetic field produced an electric field) not to something else.

So, let us assume that one does not need and aether, and one has just electromagnetic waves, including light. He also realised that this meant that he had to abandon Newton's precepts on what both time and space were. Time for Newton was this something which was the same everywhere, independent of anything that occurred in the world. So, let's assume that in any experiments including light, one could never tell if one was travelling or not. This also meant that light had to move with the same speed in all directions for all observers. Let us not for the moment come up with all the questions that show that this is absurd.

Now, Newton said that time was the same everywhere. But how would I test this? Lets say I had a couple of clocks, and I had one here, and another one there. How would I adjust them to make sure they both showed the same time? The first thing I could do is to compare their ticking rate. If every time my clock here hit a second, it would light and then extinguish a little lamp. The lamp would flash, each flash occurring at the second according to my clock. Someone sitting beside the clock over there would also see the flashes and could time them with his clock to see if they occurred one second apart. But there is also the question of making sure that they showed the same time-- ie both at one time showed the same time, say 9AM. Now the problem is that light takes time to travel from here to there, so one would have to take that into account. But we know what the velocity of light is, and so we can compensate for the fact that the light leaving here would arrive there at a later time. Just divide the distance by the velocity of light and subtract that from the time at which light arrived there, and make sure that that time on the distant clock showed was the same as the time here when the light left. So, the clocks now tick at the same rate, and set a uniform standard of when "now" is. Both of these procedures are unexceptional and well attested as sensible. To find the distance, one would use, say, the defined meter stored in Paris and set up under Napoleon. The meter was a distance such that 10,000 of them would exactly fit between the north pole of the earth to the equator of the earth. One could measure the speed of light by putting a mirror at the end of say 100 such meter sticks, and time how long it took the light to travel from here to there and back again. Since light travels in all directions with the same speed, this would allow you to ascertain the speed of light, or would allow you to find out how far away the distant clock is from you, by timing how long it would take light to get from here to there and back.

Ie, you could use light to synchronize two clocks located anywhere, and to make sure that the two clocks. ticked at the same rate anywhere.

So far so good. Now let us assume we have two physicists lab, on on board a boat (or in Einstein's case aboard a train) and both set up their systems in the same way. By Galileo's ideas of relativity there would be no impediment to them doing so. Since there was to be no way of telling whether or not the person on the ground or the person on the train were moving with respect to Newton's idea of fixed space, including by using light, the person on the train can use precisely the same procedure.

But now the person on the ground looks at what is happening on the train. He sees light travelling from the first observer on the train to the second. For him, the light used by the person on the train is travelling with the speed of light c, but the second clock toward which the light is travelling is, if it were in front of the first on the train, is travelling away from the first train clock. Since it is travelling away, it will take the light longer to get from the first clock to the second. Thus the second train clock will compensate for the travel time by subtraction off the distance divided by the velocity of light to figure out when the same time for the second clock as it was when the light left the first train clock. According to the ground observer, he will say there was not a sufficient compensation for the travel time. The travel time was longer than the train physicists calculated.

Of course the train physicists will say the same thing about the ground physicist. They will disagree with the synchronization of their sets of clocks. Who is right? By Galileo's idea of relativity, neither or both are right. Both were right in the way they synchronized their clocks. It is just that their idea of synchronization gave results that disagreed with each other. OK, weird. One might be tempted to just say-- nice idea but it did not work. Newton was right, there is a fixed rest frame of the universe. It is the one in which light travels with the same speed in all directions. But why then can I not measure that? why does the Michelson Morley experiment give a result of 0?

So, lets push on and keep taking Galileo's relativity principle seriously. Lets look at lengths. The two people on the ground and on the train both have their meter sticks. Now, they can compare their meter sticks in the direction perpendicular to the direction of travel of the train. (Ie, they both hold their sticks vertically and see if both their ends line up just as the train goes past. Here they must agree. If one of their meter sticks were longer than the other, which would be longer.

However if they tried to test their meter sticks in the direction of travel, one runs into trouble. One of the meter sticks is moving with respect to the other. Thus to compare the sticks, one has to see if the one end lines up when the other ends line up. But they disagree when "the same time" is in that direction. I line up here, but we disagree when that it is at the other end of the meter stick. The person on the ground says that the person on the train thinks the same time is too late because he did not compensate for the light travel time by a sufficient amount.

Lets leave that for now. Since we can agree on the vertical direction whether the two sticks are the same length, because the statement "This end of my stick and that end of your stick are in the same place at an instant of time" makes sense, even if we do not agree on synchronization. And this is either true or not. In the horizontal direction, the two ends always agree at some time. Vertically they need not ever be at the same place at the same time. Only if the meter sticks are the same length will both ends ever be at the same place at some time.

But now, we can ask about light travelling in the vertical direction. Both can "measure" the length of the meter stick by sending out a light ray and measuring how long it took for that pulse, reflected from the other end, to get back. One could define that as 2/30000000 of a second. Each could do that. But now the person on the ground would say that the distance the light had to travel as far as the person on the train was concerned was longer than a meter. Yes, the meter stick was a meter, but after the light left from the bottom, the top of his stick moved sideways so the light had to travel up the hypotenuse of the triangle formed by the meter stick and the distance the train travelled during the light's trip to get there, i.e., the velocity of train times the time of travel. By Pythagoras theorem, the light travelled distance of 1m vertically, and the velocity times the travel time horizontally. So the travel time would be the square root of the 1 meter squared plus the square of the velocity of the train times the time. If we divide that by the speed of light, that will give us the time of travel. If one does the calculation, one finds that the time of travel must be larger than the time to travel one meter by the reciprocal of the square root of 1 minus the velocity of the train divided by the velocity of light squared. But the person on the train would say, nonsense. The time is the time it takes light to travel one meter. Ie, the person on the ground would say that the person on the train had a time which was too small by that factor. Ie, the times for the person on the train are less than those for the person on the ground. But of course the person on the train would argue in exactly the same way. He would say that the clock of the person on on the ground was slow. Who is right? Both. (This is called time dilation). An observer sees another observer travelling past him with some velocity as having a time which runs more slowly. This works in both ways. Both see the other as having a slow time.

One can now come back to lengths. The person on the ground see the person on the train doing a Michelson Morley experiment. As mentioned, the return time when the light goes with and against the motion of the train is slightly longer than up and down as far as the person on the ground is concerned. For the person on the train, both come back at exactly the same time. That they come back at exactly the same time cannot be disputed. Whether or not something collides cannot be a matter of relativity. Thus the person on the ground must see the two beams come back at exactly the same time as well. The only way this is possible is if, for the person on the ground, the length of the meter stick parallel to the motion must be shorter to make up for the longer time it takes because of the addition and subtraction of the velocity of the train. The lengths are shorter by the same factor of square root of 1 minus the velocity of the train over the velocity of light all squared..

Of course even for airplanes, going lets say at 1000km per hour, this factor is only different from 1 by about half a billion billionths (.5/ 10to the power of 18). For the earth itself, travelling at 30km/sec, this factor differs from 1 by about a half of a (100 million)th. Ie, it is still very small.

Note that these effects have been verified. For example a muon, a type of elementary particle which is similar to an electron, but many times more massive, lives for about 2.2 micro seconds when moving slowly. Now light in 2.2 microseconds would travel about .66 km. muons can be created by collisions between cosmic rays from space hitting the upper atmosphere about 30 km above the earth's surface. These should have more than decayed by the time they hit the earth. But they don't. Most of them reach the earth's surface. If, even travelling at the speed of light, then would take about 50 times as long as it would take them to decay, how do they get to earth. It is because for them, time is going more slowly. For them the time between creation and hitting the earth (or rather as far as they are concerned, the earth's surface is hitting them) the time is less than 2.2 microseconds, even though for us, it is abut 60 microseconds. Of course for them the atmosphere is far less than 30km in thickness as well, so the atmosphere takes far less than 30km over the speed of light to whiz past. This is time dilation.

Thus, we have at least three consequences of Einstein's assumption of the Galilean relativity principle.

Note that what Einstein did not do was to try to analyse the behaviour of matter to determine how the Aether would affect the matter. Instead he assumed that the Relativity principle was correct. There is no experiment which can be carried out which can determine the velocity of a system with respect to absolute space. Of course there can be velocities of things with respect to each other, but one cannot carry out any experiment which would show that it is system A that is at rest, say, and system B is moving or vice verso, or even that both are moving. Only the relative velocity of A and B is significant.

copyright W Unruh (2018)