Gerard ′t Hooft

 Name: ′t Hooft, Gerard

 Postal address: Spinoza Instituut,

 Leuvenlaan 4

 Postbus 80.195

 3508 TD
 Utrecht.

 Voorts verbonden aan:

 Institute for Theoretical
 Physics

 Universiteit Utrecht

 Leuvenlaan 4, 3584
 CC Utrecht

 Tel.: +31 30 253 5928

 Tel.  +31 30 253 1863

 Fax:  +31 30 253 5937

  e-mail: g.thooft@uu.nl

Warning: due to severe clogging of this email post box, I can no longer guarantee that received messages will be processed and/or answered.

Warning 2: Requests to be recognized as “friend” in social networks such as Facebook or LinkedIn are only considered if they are written with some personal note, not when they seem to come from robots.

secretary: Mrs Riny de Haas, [e.dehaas@uu.nl]

Discussing Magnetic Monopoles with Rembert Duine

Professor Theoretical Physics

Click here for lectures (notes, PowerPoint files)

Research interests:

Gauge theories in elementary particle physics.
This was the topic of the 1999 Nobel Prize. An idea was proposed by C.N. Yang and Robert Mills in 1954: they suggested that particles in the sub-atomic world might interact via fields that are similar to, but more general than electricity and magnetism. But, even though the interactions that had been registered in experiments showed some vague resemblance to the Yang-Mills equations, the details seemed to be all wrong. Attempts to perform accurate calculations were frustrated by infinite - hence meaningless - results. Together with my advisor then, and my co-Nobel-laureate now, M. Veltman, I found in 1970 how to renormalize the theory, and, more importantly, we identified the theories for which this works, and what conditions they must fulfil. One must, for instance, have a so-called Higgs-particle. These theories are now called gauge theories.

It was subsequently discovered that, indeed, the observed details of all known forces exactly agree with this picture. First it was found that the so-called weak force, in combination with the more familiar electro-magnetic one, is exactly described by a Yang-Mills theory. In 1973 it was concluded that also the strong force is a Yang-Mills theory. I was among the small number of people who were already convinced of this from early 1971. During the later 1970s, all pieces fell into place. Of all simple models describing the fundamental particles, one was standing out, the so-called ‘Standard Model’.
Gauge theories are the backbone of this Standard Model. But now it also became clear that this is much more than just a model: it is the Standard Theory. Great precision can be reached, though the practical difficulties in some sectors are still substantial, and it would be great if one could devise more powerful calculation techniques. Also, in spite of all its successes, the Standard Model, as it is formulated at present, shows deficiencies. It cannot be exactly right. Significant refinements are expected soon, since the new European machine, the Large Hadron Collider (LHC) is now fully operational.

More and more data concerning the Higgs particle are being registered at CERN. The most uncertain parameter has always been its mass, which in principle could be anything between 100 and 1000 GeV. Precision checks obtained from numerous experiments suggested that the most likely mass value should be between 114 and roughly 150 GeV. Using results first from Fermilab in the USA, and now the ones pouring in from LHC, the margin of possible mass values were rapidly narrowed down. As from July 4, 2012, the value 126 GeV is being reported, with a margin less than 1 GeV. So far, everything still agrees with the simplest version of the Standard Model ! Modest modifications of the Standard Model would replace the Higgs with a multitude of particles, which will be more difficult to identify. CERN data taking will soon be interrupted by a long maintenance stop. After that, at higher energies and higher luminosities, more information with much higher precision may be expected.

Quantum gravity and black holes .
The predominant force controlling large scale events in the Universe is the gravitational one. The physical and the mathematical nature of this force were put in an entirely new perspective by Albert Einstein. He noted that gravitation is rooted in geometric properties of space and time themselves. The equations he wrote down for this force show a remarkable resemblance with the gauge forces that control the sub-nuclear world as described in the previous paragraph, but there is one essential difference: if we investigate how individual sub-atomic particles would affect one another gravitationally, we find that the infinities are much worse, and renormalization fails here. Under normal circumstances, the gravitational force between sub-atomic particles is so weak that these difficulties are insignificant, but at extremely tiny distance scales, of the order of 10^-33cm, this force will become strong. We are tempted to believe that, at these tiny distance scales, the fabric of space and time is affected by quantum mechanical phenomena, but exactly how this happens is still very mysterious. One approach to this problem is to ask: under which circumstance is the gravitational force as strong as it ever can be? The answer to this is clear: at the horizon of a black hole.

As I have been emphasizing for more than two decades now, the text book description of quantum gravity (where the Einstein-Hilbert action is quantized using standard procedures) shows flaws here that run deeper than that it generates infinities: it does not allow a description of a black hole as a single quantum object. This is a direct contradiction, a paradox, a problem shouting for a radical solution, saying that there is something we are not doing right. For a long time I was convinced that also superstring theory, in this respect is fundamentally faulty, but two developments forced me to be more cautious here. One: it is now possible to describe at least some members of the black hole family using string theory with multidimensional membranes, called D-branes, added to it. The objects thus obtained are purely quantum mechanical and agree with naive expectations so well that many of my colleagues are convinced that “string theory solves the problem”. But why does this happen? How does string theory resolve the paradox? Curiously, string theorists themselves do not quite understand this. I think that important improvements of the theory are necessary. See later (red text).

Here come twist number two: I claim to have found how to put quantum gravity back in line so as to restore quantum mechanics for pure black holes. It does not happen automatically, you need a new symmetry. It is called local conformal invariance. This symmetry is often used in superstring and supergravity theories, but very often the symmetry is broken by what we call “anomalies”. These anomalies are often looked upon as a nuisance but a fact of life. I now claim that black holes only behave as required in a consistent theory if all conformal anomalies cancel out. This is a very restrictive condition, and, very surprisingly, this condition also affects the Standard Model itself. All particles are only allowed to interact with gravity and with each other in very special ways. Conformal symmetry must be an exact local symmetry, which is spontaneously broken by the vacuum, exactly like in the Higgs mechanism.

This leads to the prediction that models exist where all unknown parameters of the Standard Model, such as the finestructure constant, the proton-electron mass ratio, and in fact all other such parameters are computable. Up till now these have been freely adjustable parameters of the theory, to be determined by experiment but they were not yet predicted by any theory.

I am not able to compute these numbers today because the high energy end of the elementary particle properties is not known. There is one firm prediction: constants of Nature are truly constant. All attempts to detect possible space and time dependence of the Standard Model parameters will give negative results. This is why I am highly interested in precision measurements of possible space-time dependence of constants of Nature, such as the ones done by using a so-called "frequency comb". These are high precision comparisons between different spectral frequencies in atoms and molecules. They tell us something very special about the world we live in.

The Hierarchy Problem.
An important problem can now be addressed: the hierarchy problem, which is the question why particle masses are 20 orders of magnitude smaller than the Planck mass, and the cosmological constant even more than 120 orders of magnitude. Could my theory explain this? I have been studying some intriguing ideas. Could the coefficients that relate to the cosmological constant and the mass terms be due to instantons? These are known for generating exponentially suppressed amplitudes. My present theory allows me to investigate such approaches. I do have a candidate gravitational instanton that could be the culprit here, but details do not yet work out right.

Fundamental aspects of quantum physics, and their implications for (super) string theory.
My views on the physical interpretation of quantum theory, and its implications for Big Bang theories of the Universe, are rapidly evolving.
My earlier papers (see for instance Hilbert space in deterministic theories, ) may seem to be very formal, and moreover, their contents are disputed, even ridiculed, by some of my colleagues. Is there "free will" or "predestination"? What I am really saying is that, at the most basic level of Nature's equations, there is no quantum mechanics, but only classical logic. But even so, who cares?
Well, if true, this would be a very important piece of information to use in model building. My claim that it has to be true is based on considerations concerning black holes and the limited amount of quantum information they can contain. Now investigators put forward that this cannot be true because of the so-called "Bell inequalities": quantum mechanics strongly violates these inequalities while classical systems cannot do that. At the atomic scale, numerous experiments confirm the quantum mechanical predictions. Can I wiggle myself out of this one?
There are long answers and there is a short one. The long answers are complicated, and usually my opponents find weak spots in them, but the short answer is more basic:

I have mathematically sound equations that show how classical models generate quantum mechanics. It's not fake quantum mechanics, with "pilot wave functions" or other such nonsense; it's the real thing. End of argument.

However, to produce models that are classical at their most basic levels, while producing something interesting such as the Standard Model at the TeV scale, is not easy. I first derive how a standard set of canonical quantum variables p and q can emerge from classical variables, being integers P and Q . Now when I stick to mathematical rigor, I can only construct some very trivial harmonic oscillators with these. But then I take many variables p and q , like the ones describing harmonically oscillating fields. The procedure works best if these fields are non-interacting, and live in no more than 1 space and 1 time dimension. Boring? No! This also describes bosonic string theories.

This leads to the consideration of string theories where target space (that is, real space-time) is a lattice. Adding fermions appears to be easy, so my analysis will include superstrings. I am led to a startling result: quantized superstrings can be mapped mathematically to classical strings living on a lattice. The equations of motion of these strings are straightforward; they're obviously finite, discrete, and classical. At the classical level, Lorentz invariance is reduced to lattice-Lorentz invariance - indeed, this is the first such model, and I have been searching for such models for some time!

My fellow Nobel laureate David Gross has stated at several occasions his expectation that the logic of superstring theory will be "even crazier than ordinary quantum mechanics", and that we will have to revise our sense of logic once again. My theory now makes me think the opposite:
The logic of Superstring Theory will be even easier than that of classical mechanics!
Classical mechanics is based on variables that are real numbers, hence they require infinite series of decimal places, to be recalculated infinitely many times during any time interval. This leads to the well-known phenomenon of chaos : regardless how accurately you specify the initial conditions, after a certain amount of time the evolution of a classical mechanical system becomes unpredictable. Superstring theory will be based on integers living on a lattice. Only finite amounts of information are progressed, during finite time steps. No chaos.
Large amounts of work remains to be sorted out here. I think this subject is fascinating.

To me, Nature is a big jig-saw puzzle, and I see it as my task to try to fit pieces of it together. Click and cut the pieces you see here from the screen and see how they fit, or: read more about it in my book: ‘Bouwstenen van de Schepping’ (Prometheus/Bert Bakker, ISBN 90 351 1327 6) or its English version: 'In Search of the Ultimate Building Blocks', Cambridge Univ. Press, Paperback, ISBN 0 521 578833; hardback, ISBN 0 521 550831) . In ‘Planetenbiljart’, a personal view is described of the potentials of scientific and technological developments in the future. Which possibilities are there and are there things that will be impossible forever? Maybe you enjoy SF novels as much as I do, but don’t mistake those for predictions of the future. My book appeared in English: Playing with Planets, World Scientific, ISBN 978-981-279-307-2 (hard cover), ISBN 978-981-279-020-0 ( pbk), 2008.

Important message for autograph collectors: Some people are afflicted with the desire to collect photographs and autographs of Nobel Prize winners. I am very flattered when I receive such requests, but I think I have done my share. I am sold out now. No more photographs or autographs, with apologies.

July 4, 2012: Important announcement at CERN: a bosonic particle with all the properties expected for the Higgs particle has been detected. This most likely will fill up the last blank spot in the Standard Model. As of December 2012: this still seems to be our Higgs particle!

June 5, 2012: Honorary Doctorate from the National Polytechnical University of Odessa, Ukraine.

There is so much wrong with modern software, see my fulmination page (mopperpagina)

Tijd in machten van Tien, door Gerard ’t Hooft en Stefan Vandoren, Uitgave Natuurwetenschap & Techniek, onderdeel van Uitgeverij Veen Magazines B.V., ligt nu in de boekwinkels.

"Time in Powers of Ten " is written in Dutch, but we certainly plan to produce a version in English as soon as possible. The idea is simple: Physicists and astrophysicists have produced various popularized descriptions of the enormously varying length scales in the Universe, in books and films. The Universe is some 50 billion light years across, that's nearly 10²⁹ cm. The smallest conceivable objects are superstrings, somewhere around 10^-32 cm. At every scale in powers of ten, our world looks different and very special. So now, we do the same thing with time. In fact, the variations in the time scales are even bigger. The time scale for super strings is 10^-43 seconds, and age of the Universe is less than 10¹⁸ seconds, but there are phenomena that outlast our Universe by gigantic factors. The lifetime of the most fundamental particle in our world, the proton, is expected to be something around 10⁴¹ seconds, and large black holes can last much longer than that. At nearly every time scale, things happen in our world, and we describe them, starting with just one second, then 10 seconds, 100 seconds and so on, until in the middle of the book, where we switch to the fastest time scales conceivable, until at the end we return to one second.

Appointment as Universiteitshoogleraar beginning July 1, 2011.

A (very tiny) stamp collection.

Birth of first grandson, Rowan B.A. van Deutekom, son of Ellen ′t Hooft and Roland van Deutekom, February 5, 2011. Some pictures of my family.

January 29, 2011: Erice Prize 2009 ("Ettore Majorana Prize - Erice - Science for Peace"). Here is the citation.

Lomonosov Medal:
The Russian Academy of Sciences has awarded the Lomonosov Large Gold Medals to a Full Member of the Academy Spartak Beliayev of Russia, and to a Dutch Professor Gerardus t Hooft.