Category Archives: Simplicity

The Art of Thinking Clearly, (not yet) Applied to Particle Physics

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Rolf Dobelli’s collection of cognitive biases, fallacies and wrong decision strategies has become a bestseller because people are becoming more and more aware of the irrational elements of the human mind. The textbook example, of course, is economics, where nobody anticipated the 2008 crash. “Never has a group of experts failed so spectacularly,” Dobelli comments, but it is obvious that our deficiencies in rational decision making can produce bizarre situations elsewhere – particle physics is a field that comes to mind when reading Dobelli’s book.

An obvious concern is social proof or groupthink (Dobelli’s error No. 4). The particle physics community, consisting of more than 10,000 physicists, devotes its entire activity to a model of reality that may well be plain wrong (scientists prefer to call it “incomplete”) – but not a single individual dares to spell out the catastrophic consequences – that eight decades of research might be completely useless for a profound understanding of the laws of nature.

An important contributor at work here is the sunk cost fallacy (No. 5). The excessive funding for particle physics must continue – despite no visible advance either in fundamental questions or in technological applications. Questioning the need for a new particle accelerator would mean admitting that the investments of the past, tens of billions of dollars, would have been spent in vain. It is inconceivable not only for the experts working in the field, but also for those responsible for the funding (even if they happen to coincide frequently).

And when watching the CERN seminar in which the Higgs discovery was celebrated, the following description in the calamity of conformity (No. 25) fits perfectly: “Members of a close-knit group cultivate team spirit… if others are of the same opinion, any dissenting view must be wrong. Nobody wants to be the naysayer who destroys ream unity. Finally, each person is happy to be part of the group. Expressing reservations could mean exclusion from it.” Imagine a dissenting physicist in the seminar asking for more explanations of a certain data analysis… unthinkable.

But even when looking at more technical aspects, the experimenter’s ears should be burning when hearing about the rara sunt cara illusion (No. 27): the rarer the occurrence of today’s elementary particles, the more interesting they are considered – for no good methodological reason.

The deep reason why the standard model of particle physics has not been replaced yet is Dobelli’s illusion No. 11: “Why prefer a wrong map to no map at all. Well, we just have this standard model of particle physics”, which is what you hear everywhere. Many other fallacies could be mentioned:

- How bonuses destroy motivation (No. 56, the abundant funding…)

- Chauffeur knowledge (No. 16), which you hear from the dozens of science polularizers that allegedly `explain’ the Higgs boson…

- Make engineers stand underneath their constructions at their bridge opening ceremonies (No. 18, no way to implement such a policy in particle physics).

- Clear thoughts become clear statements, whereas ambiguous ideas transform into vacant ramblings… (No. 57 – think about it the next time somebody explains what the LHC might discover next).

- Effort justification (No. 60): Think about it when listening to particle physicists who tell you about their 20-year hunt for the Higgs boson.

Finally, there is one point where Dobelli explicitly mentions science, the feature-positive-effect (No. 95): “The falsification of a hypothesis is a lot harder to get published, and as far as I know, there has never been a Nobel Prize awarded for this.” Correct! That’s exactly what Gary Taubes noted in his book Nobel Dreams (about the W and Z boson search) … but this is another story!

In short, Dobelli’s book could well be useful for scientists, but alas, the last place its message is likely to sink in is a big science laboratory such as CERN.

Why did Nature Invent Spin?

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I think this issue receives too little attention. Usually, it is said that spin is a consequence of the Dirac equation and thus, something that follows necessarily from relativity and quantum mechanics. Let us have a brief look at the argument. Schrödinger’s non-relativistic equation is .

The momentum operator p = m v is and thus, the term on the left-hand side of Schrödinger’s equation is derived simply from the kinetic energy  ½ mv2. It is interesting that none of the successful predictions of Schrödinger’s equation for the hydrogen atom make specific reference to the nature of the electron (for which the wave function gives a probability that it will be found in a certain state). They refer only to the kinetic energy; irrespective of the type of wave-natured particle that orbits the nucleus (in fact, it also works for muonic atoms).

Dirac used the correct special relativistic term for energy E = and replaced Schrödinger’s term. However, there was no explicit justification for switching from the kinetic energy to the total energy of the particle. This conceptual problem was overshadowed somehow by the mathematical problem arising from the Delta operator in the square root, to which Dirac found an ingenious solution using the matrices named after him. The algebra of Dirac matrices transpired to be a description of spin. In the following, the opinion spread that spin was a consequence of putting relativistic energy into the basic equations of quantum mechanics.

However, the initial problem of the missing equivalence of kinetic and total energy persisted. Dirac was also disappointed that he could not deduce any concrete properties for the electron from his equation. The retrospective narrative is that the positron, undiscovered in 1928, was a ‘prediction’ of Dirac’s theory, but Dirac had rather sought to explain the huge mass relation of the proton and electron, which is 1836.15. In fact, in his latter days, Dirac distanced himself a little from his earlier findings and according to his biographer Helge Kragh, he was “disposed to give up everything for what he had become famous”.

Let us adopt another perspective regarding the nature of spin, one which is related to the properties of three-dimensional space; the world we perceive (those who perceive more dimensions should see a doctor). The group of rotations SO(3) obviously must have some significance, but its topology is a little intricate. It lacks a property called ‘simple connectedness’ because the paths in SO(3) may not be contracted. Objects connected to a fixed point with a ribbon must twist 720 degrees, not just 360 degrees, in order to perform a full rotation that leaves the ribbon untwisted (see the visualization here). It seems that nature has a predilection for the generalized rotations called SU(2), which are simpler mathematically and have a surprising feature; they represent precisely the electron’s spin – you need to perform a double twist of 720 degrees, rather than just 360 degrees, to get into the original position. However, there are no Dirac matrices and thus, I think there is an open problem. It seems that the properties of three-dimensional space alone are sufficient to cause spin to emerge – no relativity or quantum mechanics are needed. To put it another way, a direct understanding of quantum mechanics from the geometrical properties of space, if there is one, is still missing.

Why Physics Needs to Ask Questions

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File:Schopenhauer.jpgThe German Philosopher Arthur Schopenhauer once said that thequestion “Why?” is the mother of all sciences. In our era of modernity, physics offers a lot of answers, almost every day. These answers however, refer to sophisticated questions that presuppose a lot of “established” concepts. What bothers me is that some more basic problems seem to have been forgotten in this process. I want to illustrate that with two examples from particle physics and astrophysics.

Today’s neutrino experiments deliver data about the so-called mixing angles, which represent the probabilities of the three neutrino flavors (elecron, muon, tau) being transformed into each other. This is an experimental answer on the `top level’, but the underlying question “Why do three types of neutrinos exist?” (once raised by Emilio Segre) is about to fade. Today’s physicists would be even less likely to bother with the question “Why do neutrinos exist at all?”, though one may justifiably wonder why Nature had created such peculiar and elusive objects. To address such questions properly, one has to study a little bit of history (in this case, Wolfgang Pauli’s ideas of around 1930). This would lead to the still more basic question of whether energy has to be conserved during the beta decay – as discussed at the time by Niels Bohr. Also, there is still another fundamental question which seems to have been forgotten by the overwhelming importance of radioactivity in physics (indeed, its discovery triggered its biggest revolution). Why did Nature invent radioactivity after all, and why in different types? Couldn’t one just think of a world with stable nuclei? Is the very existence of radioactivity just a superfluous whim of Nature? Or is there something we still fail to understand?

When one follows the latest news in cosmology, it appears that the acceleration rate of the universe is changing (“How much?” would be the question) – in the jargon, this is called the time dependence of the cosmological constant or of dark energy. However, we have barely digested the very existence of dark energy (2011′s Nobel prize), as it means asking: “Why is the expansion of the universe accelerating?” This is a worthwhile problem to ponder, however, but on a still more basic level we can ask: “Why is the universe expanding?” Of course, Edwin Hubble’s observation of 1930 is now interpreted as indicating such expansion and there is no reason to warm up the `steady state’ model which was popular in the 1960s. However, a good reason for why the universe must expand does not seem to exist (I shall come back later to an idea of Robert Dicke in 1957). Theorists would immediately argue that Einstein’s equations do allow only for contracting or expanding solutions, which is true. But this does not answer the question in terms of a logical necessity, as Einstein used to phrase it: “I want to know if he [the creator] had a choice”.

I do not think that going to ever more sophisticated levels of questions and answers, while leaving behind the important ones, will advance physics in the long run. And surely, the pragmatic approach “Well it is as it is, let’s continue to collect more data” cannot be said to be a wise one.

What Einstein Said About Fundamental Constants

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Reality and Scientific Truth: Discussions with Einstein,von Laue and Planck is a collection of conversations between Einstein and Ilse Rosenthal-Schneider, a lady who took a PhD in philosophy in Berlin around 1920. After fleeing the Nazi regime in 1938 and settling in Australia, she continued her discussions with Einstein by letter. The book is a unique source of the views Einstein held about the fundamental constants of physics. It is worthwhile to compare them with some modern opinions on the subject.

In a letter dated May 11th, 1945, Einstein wrote that he believed that numbers “arbitrarily chosen by God” do not exist and that their “alleged existence relies on our incomplete understanding”. Similarly, he contended in a letter of March 24th 1950 that “dimensionless constants in the laws of nature, which, from a rational point of view, could have other values as well, shouldn’t exist”.

Such a statement obviously refers to numbers such as the inverse of the fine structure constant (which is about 137), which is reminiscent of Richard Feynman, who forty years later wrote in a very similar vein: “It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say, ‘the hand of God’ wrote this number, and we don’t know how He pushed his pencil.” At the same time, Feynman advised his colleagues that: “All good theoretical physicists put this number up on their wall and worry about it.”

It is interesting that both Einstein and Feynman seemed to be convinced that this was a puzzle to be tackled while at the same time being aware that such a conviction was not testable in a strict sense. Einstein, in another letter from Oct 13th, 1945, wrote: “Obviously, I can’t prove that. But I cannot imagine a reasonable unified theory which contains a number that could have been chosen differently by a whim of the creator.”

Since then, the attitude of physicists toward fundamental constants seems to have changed. Modern cosmology, for example, has terrific data, and Michael Turner of the University of Chicago explained in 2010 in Munich how these observations are accommodated using a couple of parameters by the current ‘concordance model’ of cosmology. After the talks at the Siemens foundation, there is always an ample possibility for discussion (and a very nice buffet). Turner, as he admitted frankly to me, is not very interested in the initial conditions of the universe such as density, photon to baryon ratio or similar stuff. He would be happy to find the correct equations that would make the world go, rather than bothering with how it got started. No doubt, however, these initial conditions (although Einstein would have been delighted by the data) are numbers he would have sought to explain using the theory. All these numbers make the world a little more complicated than it should be in principle. “A theoretical construction has little chance to be successful, unless it is very simple” Einstein wrote on April 23rd, 1949, and here he was certainly in agreement with Isaac Newton’s credo: “Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.”