Some real progress was made.
This opens up the way to find constraints on theories such as the Standard Model to make them deterministic at high energies but apparently quantum mechanical -- just the real thing -- at low energies. Such models form discrete classes, so one of my conclusions is that there may be better ways to explain the values of coupling strengths than those ugly 'anthropic principles'.
- added May 15, 2020.
General 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 200 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 125.1 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 was be interrupted by a long maintenance stop. After that, at higher energies and higher luminosities, more information with much higher precision may be expected.
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 10-33 cm, 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.
Quantum gravity and
black holes .
For an important discussion of my recent work, see its
lecture note format in this link.
As I have been emphasizing for more than three 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 below (red
text).
Conformal invariance. Here comes 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 what I am claiming 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. Producing 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. Therefore, the long answers are complicated, and usually my opponents find weak spots in them, but the short answer is more basic. Here is the core of it:States usually considered are called “physical states”. Any normalised “quantum” superposition of physical states is again a physical state. Atomic physics, elementary particle physics, are all based on considerations of physical states.