Physical reality

As far as reality is concerned, few scientists will claim themselves to be non-realists or anti-realists. In other words, few scientists admit that they are not interested in (a non-realist position) or deny (an anti-realist position) the existence of objective reality. Thus, if realism is the tenet of believing in objective reality, almost every scientist will claim herself to be a realist.

But what, then, is physical reality? A standard answer can be traced back to René Descartes (1596-1650): physical reality is matter and the properties thereof. Moreover, matter is an extended, inert substance. These ``things'' are simply there whether somebody is watching or not. In other words, physical reality is independent of observers. More specifically, these properties (such as linear momentum, angular momentum, energy, coordinates, charge, mass, etc.) are well defined since there are methods to retrieve them and they yield the same properties every time. Let us call this the ``classical concept of physical reality.''

This belief in objective reality squares well with the classical Newtonian world view, although this view has to be subject to a great but not essential revision in the Special and General Theory of Relativity. In the Theory of Relativity, mass and energy can be converted into each other, therefore substance is not inert; moreover, physical properties are dependent on the observer at his/her space-time vantage point. Nevertheless, the ``classical concept of reality'' remains sound and valid as far as its well-definedness is concerned, for objective properties can still be retained. Specifically, gravitation -- as the curvature of space-time -- is to be contemplated from outside of space-time and is an objective property.

Even in classical statistical mechanics, in which the exact determination of momentum and position of a particle is completely out of the question, the ``classical concept of reality'' still squares well with the Newtonian world view. This is because in classical statistic mechanics the position and momentum of the particle are well-defined -- the position and momentum of the particle are objectively there, even if I (or anyone else) do not know how big they are. It is qualitatively different to say that one cannot know how big they are. In fact, what are relevant in classical statistical mechanics are the aggregate properties of particles (e.g. molecules) such as temperature or pressure. A realist position can be still retained.

When it comes to quantum mechanics, the picture of ``classical concept of reality'' encounters a real crisis. First of all there is the Uncertainty Principle stating that one cannot accurately measure momentum and position at the same time. Furthermore, the decision of what to observe may play a crucial role: either the position or the momentum can be measured, but not both. The observer has the freedom, so to speak, to choose which one she prefers and this will change the properties of a quantum system. Specifically, if the position of a particle is measured accurately, its momentum will turn out to be fully random. If, however, the momentum of a particle is measured accurately, its position will turn out to be fully random.

Before going into details, we have to mention a standard high-school ``explanation'' of the Uncertainty Principle, which is seemingly able to restore the classical view. According to this ``explanation,'' a measurement ``disturbs'' the system so that the particle is either violently pushed away (when momentum is being measured and one cannot know the exact position) or confined (when the position is being measured and one cannot know the exact momentum). Objective properties such as momentum and position are ``actually'' there. In this way one hopes that the ``classical concept of reality'' can still be maintained. But this is not correct. The disturbance ``interpretation'' has been refuted again and again, most recently by the experimental tests of Bell's Inequality (see e.g. [10]). In fact, for many there seems to be no intuitively valid models that get away from the Uncertainty Principle without resorting to non-realist (such as the Copenhagen Interpretation) or intuitively very bizarre models (such as the Many-World Interpretation [19]).

Moreover, in quantum mechanics one talks about the duality of wave and particle. The behavior of a particle is described by a complex-valued wave function. The Uncertainty Principle states that coordinates alone are enough to describe the behaviors of a quantum object. These behaviors are stochastic, however. Specifically, if the wave function of a particle is $\psi (\vec x,t)$, where $\vec x$ is a coordinate vector, the probability of finding a particle in an infinitesimal volume $S$ is:

$$\int_S {\left\vert {\psi (\vec x,t)} \right\vert^2dV}.$$ (2.1)

A bizarre implication of wave functions is that a wave function is seldom confined to a finite space. Thus the particle can be everywhere, albeit with extremely low probability in some places. Only when a measurement is performed, can a physical property manifest itself. This is a profound challenge to well-definedness, for what happens if nobody does the measurement? Are the properties still there? A standard answer is that we cannot know so we should not care. In this sense, quantum mechanics demands a fundamental revision of the ``classical concept of reality,'' if not a total abandonment.