Enthusiasm vs. Statistics

Being a theoretician permits one to speculate and make predictions what should be seen in experiments. How reality could, in fact, be. However, this is not always as simple as it looks. Not so much because of how to arrive at a prediction, but when it comes to judge whether a prediction is true.

For example, I am working on interesting new phenomena in connection with the Higgs. Recently, I found some rather interesting results, which lead to some predictions. And now the ATLAS experiment  at the LHC continues to find that the Higgs properties are not exactly what they are expected to be in the standard model. What is actually not completely off from what I would expect because of my own calculations.

Should I now get excited, and cry that I have the explanation? I better not. Why? Why should I not be enthusiastic about these results?

Well, here comes the detective part in particle physics.

First, no calculation we can make today in any theory attempting to describe nature is exact. We always have to make some kind of approximations. For some of them we can make a firm statement how large the error, we are making, is at most. But in many cases, we cannot even reliably estimate the maximum size of the error. Do not get me wrong. It is not that most things are completely uncontrolled. In many cases we just cannot proof how large the error can be at most. But we have experience, experiments, and other kinds of approximations to which we can compare. This gives us a rather good idea of the size of the errors. But still, we cannot be absolutely sure about the true size. We then prefer to be better safe than sorry.

This is one of the reasons why I am not immediately enthusiastic. The approximations are yet too crude to be sure that what ATLAS sees must be unequivocally what my calculations give.

But there is more. It is not only theory which has errors. Experiments have errors as well. The reason is that nature is not strictly consequential. Because of quantum physics we cannot make the firm prediction that if A happens then B has to happen. We can just make a statement how probable B happens if A happens. As a consequence, modern particle physics experiments have, even if the machine itself is perfectly understood and perfectly build, an intrinsic error. Like any error for a probability it becomes smaller when we make more measurements.

Right now, this error for the consistency problems found by ATLAS is large. Not large in the sense of huge, but so large that there is a fair chance that the inconsistencies will go away, and we just see a random glitch of nature.

That sounds a bit odd at first. What should a glitch of nature be? Take a dice. If you throw it often enough, and just note the number of times a number comes up, then for very many throws every number will be there the same number of times. Try it. You will see that this will take a large number of throws before it happens, but it will happen eventually.

However, it may happen that you throw it ten times, and you will never get a one. Would you now conclude that there is no one on the dice? No, you would know that there is a one, just by looking at it. But you may need to throw some more times to get it at last once. But what if you get just told the numbers and never are allowed to look at the dice? Would you know that there is a one? Or could just somebody use a non-standard dice? What you would not expect is that nature just avoids ones, right?

In a particle physics experiment, it is like this. We cannot see the dice. We just get the counts. And like the case without ones, the current results of ATLAS could be a similar glitch. It just came up like this, and we have to go on, and count more.

Fortunately, you can make a statement how improbable it is not to get a one, if you throw the dice often enough. That is a number which quickly becomes small the larger the number of throws is.

Is particle physics, we can do the same thing. For the ATLAS experiment right now, there is a very good chance that things will turn out to be what they should be, and it is jut the good, old Higgs. What do I mean by good? Well, that is something like a one in a hundred chance, or so. That seems to be a far cry. But we physicists made the bitter experience that a one-in-a-hundred chance will turn against you in some cases. We make so many hundred measurements that at least some will turn out against the chances. That led in the past to false claims of discoveries, and nowadays we have become very careful, rather waiting long to reduce it to a one-in-a-million chance then to be premature.

Thus, I currently also think that the glitches seen by ATLAS are more likely not more than just such an effect. And I stay my enthusiasm for other occasions. But if the results of ATLAS should stay even with more data, well, then there may be finally the point reached to be enthusiastic. In spite of the potential problems lurking in my own calculations. Because then there is something new to be explained. And this may still be my own solution.