## Counter - A theory of everything should only deal with certainties
by Prof. G. 't Hooft

## ACKNOWLEDGEMENT

Published in the Dutch language science magazine "Natuur Wetenschap & Techniek", issue January 2008 as part of a collection of articles from leading scientists describing a common idea in their field they disagree with. Translation below is by Korneel van den Broek with permission from Prof. G. 't Hooft and Natuur Wetenschap & Techniek.

## ABSTRACT

An issue where I disagree with almost all of my colleagues, deals with the question what one may expect of a complete theory of all natural phenomena, the "Theory of Everything".

## ARTICLE

Issues we mostly agree upon (apart for some details):

1) It is very unlikely that mankind will ever be able to formulate the exact universal laws of nature, although this just might nonetheless be possible. We believe this because combining the laws of quantum mechanics and gravity suggests that there is a 'smallest distance'. At even smaller scales, the concepts 'space' and 'distance' loose their meaning. This is similar to zooming in on a digital image: once one is able to distinguish the individual pixels, zooming in becomes useless and it doesn't make sense to attribute individual properties to one half or one quarter pixel. At that level there could exist a fundamental, universal equation of motion which determines with infinite precision what happens. From there, everything follows using induction and mathematics.

2) We cannot expect that one can describe with infinite precision all macroscopic phenomena with such a theory, let alone predict. We will still be forced to use approximation techniques with very limited precision. In practice, such a fundamental theory would therefore only have a limited impact.

Now the disagreement:

3) Will an equation of motion completely determine all events in the universe or, just as we are used to from quantum mechanics, will it only provide probabilities of what could possibly happen? This is what current theories do. For every experimental setup studying small particles such as atoms, quantum mechanics can only provide probability distributions.

According to current understanding, it is fundamentally unpredictable when a radioactive atom will decay. The theory only provides the probability per unit of time that it will decay (as such the theory is very precise once one deals with a macroscopic amount of material). For all practical purposes, this works so well that nobody complains anymore. If one would have a deterministic theory for atoms and molecules, it would not provide better predictions since for experiments dealing with millions of atoms one cannot know the initial state, so one would have to rely on statistical techniques anyway.

I am one of a few who claim that a complete theory should only deal with certainties. While I expect that nature contains so many moving cogwheels that it will remain impossible to capture them with infinite precision, the issue deals with the principles on which such theory should be based. If one knows for all the dynamical variables the exact initial state, the final state should be completely determined and not a probability distribution.

Most of my colleagues tell me, with varying amounts of tactfulness, that my ideas are outdated since the beginning of the last century, and that it is naive to try turn back time. Quantum mechanics is too beautiful to reject. They believe that nature, including the most fundamental laws to which any phenomena can be reduced, are fundamentally quantum mechanical. My suspicion is that not nature, but our understanding of nature is quantum mechanical. The laws we know only provide probabilities since we don't know the actual laws (yet?).

My colleagues confront me with theorems by John Bell and others, which purportedly show that my point of view is untenable. What those theorems do show instead is that their interpretation of my ideas is untenable. The 'reality' I talk about does not consist of atoms, electrons or other particles that have energy levels and rotate around their axes, but instead little cogwheels which are billions and billions of times smaller. Their collective behavior implies that one can use the quantum mechanical language for atoms and electrons. However, the behavior of atoms or electrons can never be considered completely independent from what happens at that much smaller scale. This could be an explanation for the odd phenomena we call 'quantum mechanics'.

The major difficulty of my point of view, which I indeed realize, is that I am unable to demonstrate the mathematical laws which would underlie this special situation.

Gerard 't Hooft

Professor Theoretical Physics

Utrecht