Noether's Theorem and Causality in Physics

The translation from physical problems to geometric problems also allows us to understand the origin of some conservation laws in physics. For example, if the laws of the physical system do not depend on their spatial orientation, this means they possess rotational symmetry, i.e., rotating the entire system by an arbitrary angle will not change its evolution. Noether's theorem states that this symmetry with respect to rotations is the origin of the conservation of angular momentum. Similarly, if the physical laws of the system are independent of translations, i.e., from displacements in space, we will have that this translational symmetry in physical laws will translate into the conservation of momentum. And finally, if the physical laws of the system are independent of time, then the quantity to be conserved will be Energy. In practice, among its particular cases, Noether's theorem explains the intimate relationship existing between physical laws and Energy. As long as the laws of Physics remain invariant in time, Energy is conserved; conversely, an alteration in the conservation of Energy is the sign of a temporal dependence in the laws governing the system's evolution. This is the central core to keep in mind for the discussion we are about to undertake and which will allow us to better understand some philosophically important nuances of the next paragraph. Causality and Chance The third great category of thought, after Space and Time, is represented by Causality. This represents the fundamental element of Physical description as we know it. It establishes a constraint between distinct phenomena, allowing the transfer of the reason for being of one, the effect, to another, the cause. In the context of a physical theory, we can therefore say that the effect is explained by the cause. In turn, this cause will be explained as the effect of one or more causes and so on according to a causal chain or causal branching. This process of causal description is opposed by what is called the random element, i.e., a part or component of phenomena that is not only unexplained but even considered unexplainable. A causal description of the Universe is a description made of inviolable laws, known or unknown, that govern the mechanism of the Universe. Conversely, a random description of the Universe is a description formed by indicative guidelines on how the Universe should unfold. In the first case, the Universe, governed by laws of absolute causality, already has a determined future, even if not known, and the flow of time would be nothing other than the progressive sliding of the veil that wraps the scene of the world in mystery. Conversely, if there is something unexplainable in the Universe, if there is a realm of indetermination, then the future is in perennial formation and time represents the wave front of this formation. These are the two positions exasperated to paroxysm. Between these two extremes, there are then an infinity of other moderate ways. For example, the observation that given that macroscopically the world seems to be governed by absolute causality and only microscopically this is violated, may suggest that the guidelines of universal development are already outlined, like an image already present, and that the flow of time is nothing other than a focusing or specification of this image. In reality, the antithesis between causality and chance dominated the world of Physics and Philosophy throughout the first half of the twentieth century and then went out of fashion. Emblematic in this sense are the figures of Bohr, proponent of the Copenhagen interpretation, and Einstein, proponent of some hidden variable. While Bohr sustained the real and effective indetermination of the system below the values of Heisenberg's principle, Einstein maintained that this principle was simply an estimate of our ignorance and that there had to exist some hidden variable not yet identified. Actually, the debate between hidden variables and real indetermination was never definitively resolved but simply went out of fashion. In the 1960s, physicist John Bell proposed an experiment that would have allowed determining the presence or absence of a local hidden variable (i.e., a hidden variable that influences only objects close to it), hoping thus to definitively resolve the question. Indeed, the experiment decreed the absence of such a hidden variable and thus seemed to have put an end once and for all to the argument in favor of real indetermination. In fact, after years of work, physicist David Bohm demonstrated that even this victory of quantum mechanics was actually ephemeral and that in reality an entire theory with a non-local hidden variable (in which distant objects can influence each other) could be formulated ambivalently, completely equivalent to quantum mechanics. Bohm's formulation, sometimes called the causal or ontological interpretation, provides an interpretation of Quantum Mechanics, just like the Copenhagen interpretation, being, from an experimental point of view, completely equivalent to it. The difference between the two positions lies precisely in the philosophical interpretation, i.e., between the causal interpretation described by Bohm's theory and the indetermination interpretation described by the Copenhagen interpretation. Bohm's formulation, based on De Broglie's work, is a causal interpretation (knowing the causes univocally, one can determine the effects univocally), non-local (distant causes can influence effects), and the origin of this dispute lies in a principle formulated by Heisenberg, called indetermination.