Tuesday, August 21, 2012

The speed of light - and its consquences

So far, I did not say anything about gravity. This will remain so. However, I will have to say something about special relativity. Somehow, special relativity is often associated with gravity. This is actual not the case. Einstein's theory of special relativity does not make any reference to gravity. Only the theory of general relativity, of which special relativity is just a small subset, does so.

If special relativity is not about gravity, what is it about? Well, it is about the fact that our universe is a bit more weird than one expects.

What do you expect of a law of nature? One property is likely that it is always valid. This simple requirement has quite profound consequences. Assume for a second that you and your experiment are alone in the universe. This means ta you have no point of reference. If now the experiment moves, you could not say whether it is moving, or you. Still, you would expect that it gives the same results, irrespective of whether it or you are moving. We made experiments to test this idea, and it was confirmed beautifully. This fact that experiments are independent of relative motion, is one of the basic observations leading to special relativity.

The next ingredient is much more harder to believe. Take a light beam. What speed does it have? Well, the speed of light, of course. Now, if you move the thing creating the light at a fixed speed, how fast should the light move? Naively, one would expect that the light would now move faster. Unfortunately, our universe does not tick that way: The light still moves with the same speed. Actually, the light is actually made up out of massless photons, which travel at the speed of light. And this observation is the same for anything which is massless: All massless particles move at the speed of light. And the speed of light is always the same, no matter how fast the light source moves.

This is nothing we can really explain. It is an experimental fact. Our universe is like this. But this observation is the second basic fact underlying special relativity.

If we cannot explain why this second fact comes about, can we at least describe it? We can, and that is what leads to special relativity.

Now, how do we describe this? Well, this is a bit more involved. Take the universe. Then at each instance you have three directions in space. Distances you measure do not depend on the direction in space. You can also measure time elapsing. Works out also nicely. But now, try to measure a space-time distance. You do this by measuring a distance in the space direction. Then you take the elapsed time, and calculate what distance a light ray would have moved during this time. By this, you can talk about a distance in time direction.

The speed of an object is given (if the speed does not change) by the ratio of distance over time required to move over this distance. If you now want that the speed of light is independent of whether the light source moves or not, something peculiar is found: To get this, a distance in space-time direction is obtained by subtracting the distance in the time direction and in the space direction, when you do your Phytagorean geometry. That is completely different than what you have in the three time directions, but the only way to get the light speed to agree with experiment. The geometry of space-time is hence quite different from the one we know just from space.

As a theoretician, I say that the way we measure the distances is not like the ordinary one in three space directions (a so-called Euclidean measure), but we have rather a Lorentz measure. This is in honor to the first one who has described it. Again, we cannot yet explain why this is the case, it just is an experimental fact.

You may wonder why you never noticed this in real lifer. The answer is that when the light source moves very slowly compared to the light ray, the effect is negligible. This becomes only relevant, if you move at a considerable fraction of the speed of light. But then all the nice effects result of which you may have heard in Science Fiction movies or novels: Things like the twin paradox, time dilatation, length contraction, and so on. All of these result from these two basic observations. And are described by the theory of special relativity.

This all sound pretty weird, and it is. It is nothing we have a real handle on with our everyday experience. Just like the quantum effects. The universe is just this way.

As you see, gravity enters here nowhere. And also no quantum stuff. If you add gravity, you get to the theory of general relativity. If you add quantum stuff, you end up with quantum field theory. The standard model is of the latter kind. And this combination leads to very interesting effects, which I will discuss in more detail next time.

Thursday, August 2, 2012

Two worlds: Theory and experiment

You will probably have heard that we have found the Higgs boson - or something similar to it. We are not quite sure yet. You may also have heard that we found it in an experiment, and that this was a triumph for theory, which predicted it long ago. This seems to be a wonderful combination, theory and experiment. But, as always, nothing is just as simple as it seems.

Let us undertake the journey and accompany a theoretical idea from its inception until its experimental test, to see what is going on.

Having an idea of how physics beyond the standard model could look like is essentially simple. Though, of course, many ideas have already found by some of the people thinking about it since the early 1970ies. The interesting question after having an idea is, how to check, whether it is actually describing nature, or is just an interesting mathematical toy.

To do this, two things are necessary. The first is to check whether the idea is compatible with what we know so far about nature. The second is to use the idea to predict something which is different from the standard model. That is necessary, so that we can distinguish both, and decide how nature can be described. To do both we have to to somehow compare to an experiment.

Unfortunately, experiments cannot directly work with the mathematical stuff a theoretician writes down. Modern particle experiments work in the following way: You send something into a box and then detect what comes out of the box. In case of the suspected Higgs, we send in protons. The box is an empty space where these protons hit each other. Because the encounter is violent enough, everything comes apart, and out of the box come a lot of other (known) particles. These are then detected. Actually, we can pretty well by now not only say that there is a particle, but also what particle it is, and where it is headed with which speed. The set of detected particles is what we call an event. We then do many collisions and collect many events. The reason for this is that quantum physics forbids us to know precisely what is going on, but only what happens on the average. And to get an average, we have to average over many events.

At any rate, we end up with such information. That is what modern experiments do.

Now, the theoretician has to somehow convert his idea to something which can be compared to this experimental outcome.

In most cases, things roughly proceed as follows:

What we actually collide are not protons, but the quarks and gluons inside the proton. Thus, the theoretician first computes how quarks and gluons become converted into a new particle. Unfortunately, the experiment can only talk about the protons going into the box. So we have to first compute how we find quarks inside the proton. This is actually very complicated, and so far only partially solved. Nonetheless, we can do it sufficiently well for our purpose, though it is a challenging calculation.

The next problem is that the new particles lives usually only for a very short time. Too short to escape the box. It will decay into other particles before it can leave the box. In fact, it will often decay into particles, which in turn still do not live long enough to escape the box, but also decay first. So you have to calculate the whole chain of decays, until you reach particles, which are so stable that they will escape the box, and can be detected in the detector.

Once you have this, you have what we call a cross section. This is a number, which tells you how often two colliding protons will end up being a certain set of particles, which come from the decay chain of the new particle. Usually, you also know how often these particles go with which speed into which direction.

Unfortunately, we cannot yet compare to experiment, for two reasons.

The first is that the detector is not perfect. For example, the detector has to have a hole where the protons enter. Also, we cannot suspend the detector in thin air, and the holding devices produce blind spots. In addition, we are actually not able to measure all the speeds and directions perfectly. And it can happen that we mistake one particle for a particle of a different species. All of this is part of the so-called detector efficiency. An experimentalist can determine this with a great amount of work for a given detector. As a theoretician, we have to combine our prediction with this detector efficiency, to make a reliable prediction. Just think what would happen if our idea produces a signal which would escape preferentially along the way the protons came in. If we would not take the detector efficiency into account, we would just see nothing, and would decide our idea is wrong. But knowing the detector efficiency, we can figure out what is going on.

The second problem is what we call background. This background has two origins.

One is that the remainder quarks and gluons of the protons usually do not go away nicely, but will produce many other particles in other collisions. At LHC we even have that usually more than two protons collide. This produces a lot of debris in the detector. To find the new particle then means to separate all the debris from the particles into which the new particle has decayed.

The second problem is that other processes may mimic the searched for particle to some extent. For example, by having similar decay products. Then we have to distinguish both cases.

Because of the detector efficiency, we are not able to resole both types of background perfectly. And neither can we resolve the signal perfectly. We just get a big pileup, and have to find the signal in it. To do this, theoreticians have to calculate all this background. By comparing than what one gets from background alone and from background plus the desired signal, we have reached our goal: We know, how our searched for new particle appears in the detector. And how the experiment will look like, if we were incorrect, and just the known bunch of things is there.

All of this is quite laborious, and a lot of groundwork. And all too often it comes out that for a given detector efficiency we will not be able to get the signal out of the background. Or that the number of times we have to try is so large that we cannot afford it - we would just have to get too many events to get a reasonable reliable average.

But well, this is life. Your options are then either to wait for a better experiment (which will usually take a couple of decades to build), or to go back to the drawing board. And find a new signal, which the present experiment can find. And then it may still happen that they find nothing, and this means you idea was incorrect from the very beginning. And then you can go back to step one. In case of the Higgs, it appears likely that it turned out be correct. But there the process was so complicated that it took 48 years to have good enough experiments and reliably enough theory. Physics beyond the standard model may require even more, if we are unlucky. If we are lucky, we may have something in a few months.