Has physics become a “classical” science?
I was prompted to write this post by reading Leo Breiman’s article “Statistical Modeling: The Two Cultures” (http://projecteuclid.org/euclid.ss/1009213726). The XXth century physics has developed as a consequence of appreciating the limits of what we could learn about nature, imposed by the finite speed of interactions, small size of objects such as atoms and molecules, and the limited amount of information that we can store and operate. The respective fields of relativity theory, quantum mechanics and statistical physics all owe their existence to acknowledging that these limitations were of fundamental nature rather than merely due to the imperfection of the available technology.
The physics, that had existed before the three above-mentioned fields came to life, is conventionally referred to (with some condescension) as “classical physics”. I am going to suggest below that physics itself has become a “classical” science in the sense that its very basic paradigm of building models of natural phenomena – the paradigm which for many of us has been defining the very concept of what science is – may have become outdated. That physics has become a “classical” science, as opposed to modern “data sciences”.
Let us first review the three paradigm shifts that ushered in the age of modern physics.
Relativity
Relativity, as paradoxical as the conventional wisdom holds it, is anything but paradoxical to a physicist. Once you accept the Einstein’s postulate that the interactions propagate with a finite speed (the speed of light), all the conclusions of relativity immediately follow by simple logical reasoning (or math), including shrinking of length, the distortion of time, etc. These conclusions, of course, contradict to our conventional understanding of time and space. This is why, although many of these conclusions were derived well before Einstein appeared on the stage, the transformations of relativity were thought of as convenient calculation tools, reflecting our inability to measure faster than light. If only we could measure faster, the conventional classical mechanics would be recovered.
Einstein’s courage was in declaring that, if we couldn’t measure faster than light, we shouldn’t base our world-view on the idea of instantaneous measurement. That the limitation was fundamental and required a philosophical shift of mind, rather than the sophisticated efforts to bring reality in agreement with conventional thinking.
Quantum mechanics
Just like relativity arose from acknowledging the limit on how fast we could measure, the quantum mechanics came from acknowledging the objective limitations on our ability to study small objects. It was not because we didn’t have a good enough microscope that the atoms behaved so strangely, but because, in order to study such a small object as an atom, we had to bring it in contact with a much larger one, such as the microscope (more precisely, the stream of photons or electrons), and this larger object inevitably affected the small one in unpredictable ways.
If we couldn’t directly study small objects, there was no reason to assume that they behaved according to our everyday expectations. And, indeed, they were found to be described by the laws of quantum rather than classical mechanics. The main point here is not the particular strange form that the quantum theory has taken – this can be debated and perfected – but that, once we accepted that we could not directly observe something very small, there was very little reason to expect that it would behave in the way fitting our previous experience.
It is worth noting that this philosophical shift was not immediate either: Schroedinger’s wave mechanics and Bohr’s quantization rules first appeared as attempts to reconcile the behavior of atoms with classical ideas.Statistical physics, decoherence, phase transitions
Statistical physics deals with the fact that, in order to describe an object with 10^23 or more degrees of freedom, we need a computer with at least as many (or likely many more) degrees of freedom. This puts a limit on how precisely we can describe things and ushers in the uncontrollable: the “noise.” In the extreme limit, to describe the Universe we would need to have an alternative Universe or even something bigger. One can elaborate more on the details of how the information is stored, transferred and how the computation is performed, but the limitation will always exist – because this limitation is conceptual, it nothing to do with our current level of technology.
Surprisingly, my experience shows that many of my colleagues do not appreciate the fundamental nature of this limitation. And who can blame them? – statistical physics books provide us with smooth derivation of statistical distributions from very basic mechanics, and it is easy to continue to think that the whole of statistical physics is just an approximate way to do calculations. That we do it because we don’t have a powerful enough computer. That we could, at least in principle, have such a computer…
We fall here in the same trap of trying to extend our conventional thinking in the realm, where we could not possibly verify that this thinking is correct or not. In other words, we are committing the same mistakes as those who searched hopelessly for the universal reference system in order not to acknowledge relativity, and those who tried to save the determinism of Newtonian mechanics from making it quantum.
The reality is that the noise will always exist. And this is why no powerful computer will ever be able to predict the future. This is why the free will exists – because of our fundamental inability to take all the influences into account.
Data science
The one thing that the physicists have never questioned is whether we could create models of the natural phenomena. Models such as: relativity, quantum mechanics, statistical physics etc. Indeed, creating models is what we mean when we talk about discovering the laws of nature. Creating models is something that we associate intimately with the scientific method, of which physics is the most successful example. If we study a phenomenon without creating a model, can we really say that we understand this phenomenon? Can we really call it science?
At this point I would like to direct you again to the Leo Breiman’s article that I mentioned in the beginning: describing a complex phenomenon, dependent on many parameters and resulting in a wealth of data, requires a complex model. But, as the number of the parameters and the amount of data increase, can we plausibly claim that there is a unique model relating the data and the parameters? And, if we can never have enough data and computational power to resolve between several models producing similar results, can we really claim that resolving them is possible in principle? Is it scientific to make such a claim?
I am not talking here about the data science as applied to analyzing financial markets or social behavior, but rather about something as physical as biological systems. My short experience in biology has taught me that we simply don’t know enough to model biological processes with the same level of rigor that we use to construct models in physics. This is why biophysicists and bioinformaticians make a heavy use of modern statistical techniques, such as hidden Markov models, machine learning, neural networks etc. But is this just a matter of convenience? Will we ever be able to model gene transcription as unambiguously as a movement of a particle in a magnetic field? Are we better off thinking that such modeling is possible in principle?
I am not claiming to have a definite answer to these questions. But I am asking for your intellectual courage to contemplate the very possibility that some things cannot be modeled. That physics, the field that has reached perfection in modeling phenomena, may not be anymore at the forefront of our knowledge. That it has become a “classical science” in the same sense as classical physics, which still forms the basis of modern engineering when it comes to launching satellites or developing micro-fluidic devices, but which is no more the place where the mysteries of the Nature are being uncovered.