Zürich, Switzerland. Even a small amount of randomness can be amplified without limit, a finding with broad implications for physical and the biological sciences.

The effects of this research could be considerable, given the importance of understanding random mutations on human development. Currently, there has been no proof either that the world is purely deterministic and all randomness is due solely to a lack of knowledge about certain events, or that everything happens purely by chance.


Free choice is decisive for a representative outcome. Experiments in physics always depend on a large number of variables. To obtain a representative result, the choice of the variables — like the selection of the people questioned in an opinion survey — must be completely free and random. The entirely free (or random) choice of variables is also important for efficient simulations in information technology. It is also extremely important for encoding messages, (i.e., cryptography), and for the random number generators in a wide variety of scientific disciplines. Even gambling casinos can be affected if such generators are unworkable and a fraudster exploits vulnerabiities for advantage.

Classical physics is deterministic: for example, we can determine the position and velocity of a particle at any time in the future.

But quantum theory states that fundamentally random processes exist: for instance, the outcomes of measurements of quantum particles seem to be determined entirely by chance.

The latter is the basis for an argument by Einstein in 1935 that quantum theory is incomplete, and yet another kind of higher theory must exist. However, up to the present time there has been no proof either that the world is purely deterministic and all randomness is due solely to a lack of knowledge about certain events, or that everything happens purely by chance.

Pondering this problem, Roger Colbeck and Renato Renner, physicists at the Swiss Federal Institute of Technology Zurich (ETH Zürich), have now constructed a thought experiment that shows randomness can be amplified.

Their results appear in the journal Nature Physics, may also have practical applications.How random is a choice of variables?

Roger Colbeck, postdoctoral researcher, and Renato Renner, Professor, are physicists at the Swiss Federal Institute of Technology Zurich (ETH Zürich). In their study, they investigated which minimum conditions must be fulfilled in order for a selection of variables to count as absolutely free, and for this selection not to be already practically “pre-programmed” through earlier events. In this study the physicists defined that a variable counts as being chosen freely and at random if it is not correlated with other variables at this or an earlier moment in time.

In 1964 the physicist John Stuart Bell developed what is known as Bell’s inequality, which in simple terms states that there are measurements whose results are not pre-determined and are thus random. The experiments proposed by Bell to prove his theorem, which are based on measuring the entanglement of quantum-mechanical particles, did indeed show this, but only subject to the fundamental condition that the measurements performed during the experiment were chosen completely freely and at random. It is like arguing in a circle: the existence of randomness is again presupposed.

Making use of quantum mechanical laws

The scientists now made use of entanglement and locality — the fact that for example a local event on the Earth does not exert any direct influence on another planet — to show that beyond a certain point “weakly” indeterministic situations can be amplified to such an extent that they are completely random.

This is achievable for example with two entangled quantum particles that are strongly coupled but are then measured independently of one another. The scientists’ calculations showed that the quantum correlation between the bits can be so strong that they cannot be correlated with anything existing previously. This means that the results are completely random, whereas only weak randomness is needed for the choice of the measurement.

The two scientists stress that they have not thereby proved that the world is non-deterministic. However, they say there is nothing in between. The existence of weak randomness automatically implies that there must be an unlimited amount of strong randomness. However, Colbeck says it is first of all necessary to achieve a particular “randomness threshold”: “Our method allows randomness to be amplified once a certain threshold has been reached.

It would now be interesting to know whether this threshold can be made arbitrarily small by using improved methods.” This would then mean that an arbitrarily small amount of indeterminism would be sufficient to generate an unlimited amount of randomness.