What exactly is an electron? What is it made of? How about a photon?
The Nobel Laureate physicist Richard Feynman is said to have mentioned that calculus is the language that God speaks. Students of science tend to believe that scientific theories are undying eternal truths. Apparently both the masters and the students of science have forgotten an important word that appears over and over again in science: model. In physics (which happens to be the most basic and foundational of all natural sciences) we encounter terms such as Newtonian model, general relativistic model, Bohr model, Sommerfeld model, cosmological model, big bang model, standard model. Model? But isn't a model a mock-up of the real thing?
Newton's theory of gravitation explained attraction between two massive bodies with a force that could act at a distance and make its effects felt instantaneously. The attraction part was the only real observation. The rest came from Newton's head. He imagined that there was a mysterious force that pulled the two masses together and proposed a formula to measure the force. This was a hypothesis. The name of the method used by Newton was induction: from specific to generic. Given the accuracy of the measurements that could be made in Newton's time, his formula predicted the force and its effects very precisely. But not precisely enough by the time Einstein came around. The ability to observe and measure had significantly improved in three hundred years and Newton's law needed a replacement. Similarly, classical electromagnetism, based on experiments and measurements made by Faraday, Ørsted, Ampère and others and codified by Maxwell had to be replaced by quantum electrodynamics after new observations (photoelectric effect) were made half a century later. Of course, that gave rise to quantum mechanics which in turn replaced or modified other models including Einstein's gravity and atomic physics. Atomic physics itself had several models: cubic model, Rutherford model, Bohr model. I think I've made my point: models are aplenty in physics. Models are how physicists model the universe. And if nothing else, then just the fact that model after model has been thrown away to accommodate newer models should make one wonder about the nature of scientific theories: are they really accurate depictions of the world or are they simply guesses about the universe?
Just because a model matches observations and measurements does not mean the model is the truth. The universe is a like a black box (or many black boxes, if that's easier) with lots of wires going in and coming out. We have built meters to measure the signals on these wires. We measure the inputs on a set of wires, measure the outputs on another set and then we guess what could be inside. With time our meters have grown more sophisticated and we can measure with more precision. We can also measure signals we couldn't measure before. And as we get more details, we keep modifying our guess of what's inside that black box. We derive relationships between the various wires, we slice and splice them and come up with fascinating theories. But we don't really know what's inside that box. I don't think there is any serious scientist worth his or her weight in salt who would want to debate that point. Sorry Professor Feynman, God probably doesn't speak in little squiggly lines. Calculus is a tool that contemporary terrestrial scientists use to model physical phenomena. Ironically, Newton, who invented (or discovered) calculus, didn't use calculus in his models at all. He used geometry. In future, someone might invent (or discover) yet another clever way to model the universe.
How does an electron behave? How do photons behave? Or to back up even further what is an electron? Is it spherical? What is it made of? What shape is a photon? What is gravitation? What is matter? What is energy? I don't believe there are any definitive answers to these questions. In fact even these terms are not definitive. We merely experience the world and attempt to model it. In our model, we introduce several items that we call by different names. Furthermore, the models are just guesses based on our current ability to observe this world. What is a galaxy after all? It is merely a name we give to a shape: a shape filled with stars, planets, dust... What is a star or a planet? It is merely a name we give to shape filled with atoms. What is an atom? It is merely a name we give to a shape filled with electrons, protons and neutrons. What is a proton? It is merely a name we give to a shape that is filled with quarks. What is a quark? We can't see that far yet. Just like three hundred years ago we couldn't see at the level of atoms.
Scientific theories are not absolute truths. They are models and frameworks that we create or guesses that we make to understand reality. The true nature of reality is unknowable through the methods of physical science.
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