You could be wondering: Why even ask such an obvious question? The answer is clear. Physics is trying to understand the physical world around us. But what does that even mean? Doesn’t Philosophy have almost identical goal, without all the mathematical gibberish?
Throughout the history of mankind, humans have always had some picture of the world around in their minds. It was based primarily on intuitive everyday experience of interactions with the surroundings and it was subjected to individual’s everyday needs. If this model couldn’t predict consequences of what was going on fast and accurately enough, natural selection took over. Now imagine an ambitious and thoughtful person, who would attempt to formulate physical laws, which form the basis of such a picture. The first law that comes to her mind is: Everything falls towards the ground. But then she notices a flock of birds flying above her head. Hence, she must add an exception about objects with wings. It turns out though, that other exceptions will be needed for a leaf blown around by autumn wind, a cloud in the sky or a candle flame, disobediently always pointing upwards. A look at the nights sky then almost causes mental breakdown of our proto-scientist, as she realises that her law wasn’t as obvious and universal as she first imagined. When she wakes up in the morning much calmer, she begins to study her law a bit more critically. What even is a wing? How to define a flame? What does it even mean to “fall towards the ground”, when a stone thrown upwards first goes up, before finally falling down?
The trouble of our thinker does not come as such a surprise. Essentially her entire picture of the world is based on otherwise ungraspable visual image. She can name and categorise objects, but the image itself is self-contained and resilient to outside description. This problem was solved by Isaac Newton and his contemporaries. They realised that the structure necessary to unambiguously formulate physical laws has been here for millennia. It is Mathematics. In a moment, the world became 3-dimensional Euclidean space with well-defined properties, and a particle a point, a well-defined mathematical object, in this space. State of each particle can in this model be described by 3 spatial and 3 velocity coordinates. Additionally, each particle carries mass and charge, which determine its interactions with other particles through gravitational and electromagnetic forces. The last piece of the puzzle are Newton’s laws, which describe how a system of particles evolves in time. This image is a well-defined mathematical construct, which can be related back to reality and which then enables us to predict experimental results.
This leads us to another problem. How to relate a mathematical model to reality? In the case of Newtonian mechanics, the relationship of mathematical and real object is straight forward and intuitive. But even in electromagnetism, things become a bit more complicated. This theory deals with vector fields, which are functions that have magnitude and direction at each point in space. The electromagnetic field cannot be observed directly, we cannot touch it, feel it, but even so it can transfer and store energy, hence keeping our planet pleasantly warm, exert force on charged particles and hold together all atoms in the universe.
Even grater gap between model and reality came at the beginning of 20th century, when several independent experiments showed that particles are not localised to a single point, but are rather a disperse cloud, a wave. That was one of the fundamental building blocks of emerging theory of quantum mechanics. In the mathematical model of the world a point-like Newtonian particle was replaced by a concept of a wavefunction, once more a well-defined mathematical object, that lives in a so-called Hilbert space. That does not necessarily mean that a particle is the wavefunction, but rather that when we find the correct rules of translating this completely abstract object into the language of experimental results, we will be able to predict phenomena that the Newtonian model simply couldn’t describe. A set of such rules is offered by the famous Copenhagen interpretation, which, despite being very successful, contains numerous rather unsatisfying technical issues. Search for a self-consistent interpretation is therefore still under way.
Consequently, the relationship of reality and such an abstract model is by no means trivial anymore. Mathematical formulation is becoming more and more independent of our everyday experience and begins to form a new basis for predictions of previously unobserved phenomena. That is because it requires to be logically self-consistent.
This is one of the greatest mysteries to me. It is as if logic was the very fabric of the universe. Our mathematical models hadn’t had the ambition to achieve anything more than to translate the messy world into a language, which would allow us to work with it objectively and unambiguously to make sufficiently accurate predictions. It was just a tool, a simplification of otherwise hardly approachable reality. But so many times in the history of physics has it proven to be more than that. Purely theoretical arguments, arguments requiring the model to be self-consistent, lead to predictions of before unobserved phenomena. That means that the universe is at least to some extent logically consistent, which allows Newton’s trick to work so well that it up to this day forms the very core of science.
A classic example of logical inconsistency of the model leading to a complete change of our understanding of the universe is the birth of theory of relativity. Electromagnetism predicts the speed of light, but it was not clear with respect to what it should be measured. Medium of light is only the mathematical concept of electromagnetic field, which is not fixed to any observer. Einstein and his contemporaries therefore changed the 3D Euclidean space in the model for a so-called Minkowski 4D spacetime with a unique geometry that ensures that any two observers will measure the same speed of light, irrespective of their relative motion. This model has many other measurable consequences, such as time dilation of two observers moving fast relative to each other, which have all been later experimentally confirmed. This is a canonical example, but there are many more. Prediction of Higgs’ boson, gravitational waves, angular momentum quantisation have all been required by the model to be self-consistent and have later been confirmed by a measurement.
This discussion could lead to some very controversial statements. Is nature just a realisation of mathematical concepts? Aren’t these concepts finally just the forms Plato had in mind, through which our reality emerges? These are questions that physics in its current form cannot even begin to tackle. Its task is to create an effective model that we can use to make predictions with desired accuracy. Whether or not it corresponds to reality is a different problem entirely. Even though we currently have much more sophisticated models than the Newtonian one, it has not been forgotten and is still used under circumstances, when it is a good representation of reality. We are not looking for the “correct” model. Correctness can never be tested. We are looking for a model, which when interpreted appropriately does give correct predictions under clearly defined conditions.
This distinction is rather subtle. To illustrate it I will use quantum mechanics once again. Above, I have already described the representation of a particle in its mathematical construction as a wavefunction in a Hilbert space. There are however other ways to formulate quantum mechanics. One could, for instance, use the so-called path integral formulation. In a nutshell, path integral evaluates the probability of finding a particle at point B in time t, given that it has been at point A at some earlier time t’. In this model, the particle took all possible paths between A and B and each of them contributed to the final probability through a function called action, which can be evaluated for each trajectory. Both formulations are mathematically distinct, however give exactly the same predictions of experimental results. Which is the “right” one then? Which unravels the fundamental basis of reality? Maybe neither, maybe both. Maybe the basis of reality is not mathematical at all.
Despite all that, I believe that Physics does indeed give us directions to approach reality in the right way. Each new theory views the world from a different angle, transforms our naïve intuitive ideas. Does it mean that when in the 4D spacetime of theory of relativity there is no conceptual difference between the spatial and temporal dimensions, we should think about yesterday the same way we think about the room next door? Definitely not. It is clear, however, that time and space are much more intertwined than one might have imagined at first glance. This is a small obscured guidepost on the pilgrimage towards the right perception of reality, which we can now use rationally and with full responsibility. This is the case with all science. It is impossible to prove anything beyond doubt. We can however critically utilise the new information and use rational thought to put it into wider context. This is precisely what should be required of all scientists. Not to be afraid to say ideas that are not yet confirmed by the scientific method, but rather based on their lifelong experience in their field and use this experience to interpret their theories much more broadly. Then they have to honestly (with clear indication of what are just speculations) communicate all that to the general public. It is crucial for the development of mankind that the way we think about the world develops from generation to generation. That we all in general terms understand achievements of our civilisation and are able to appropriately work with scientific conclusions. Otherwise, as a society we will hardly be able to deal with the challenges of today.
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