Everything is motion. You may want to interpret this as Heraclitus’ panta rhei principle. That’s fine. However, this idea is much older than that – think of the thoughts that are attributed to Simplicius and Plato himself, for example – and, in any case, physicists cannot do much with an idea without an equation. In other words, don’t engage in too much philosophy here.
A force is that what changes the state of motion of an object. Mass is a measure of inertia—resistance to a change of the state of motion. When we choose a natural unit to measure force, we choose a natural unit to measure mass. Also, energy and mass are equivalent according to Einstein’s E = mc2 equation, so energy can be understood in terms of motion too. [I offer an intuitive interpretation of the mass-energy equivalence relation in terms of Wheeler’s concept of ‘mass without mass’ in my book on QED.] So the force law – or force laws, plural – are very fundamental.
But what is a force? A force has to grab onto something. So let us think about what a force can grab onto. We may say that mass comes in one ‘color’ only: it is just some scalar number. Hence, Einstein’s geometric approach to gravity makes total sense. An object with some mass comes with its own space, so to speak: a light beam that gets bent by the Sun goes along a geodesic. So we can establish an equivalence between a description in terms of curved spacetime and gravity. [This may sound deep and profound, but if you think about it for a while, you’ll understand it intuitively—somewhat, at least! Or so I hope.]
In contrast, the electromagnetic force is based on the idea of an electric charge, which comes in two ‘colors’, so to speak: black or white, or + or -, or whatever other dichotomy you want to use. Maxwell’s equation(s) seemed to cover it all until it was discovered the nature of Nature – sorry for the wordplay – might be discrete and probabilistic. However, that’s fine. We have been able to modify the classical theory to take that into account. We’re all good. It’s just a different sector in the Standard Model. Gravity talks about big stuff. Quantum electrodynamics (QED) talks about small stuff: electrons and photons, and how they interact.
And then we have the strong force to describe what goes on inside of the nucleus. So that’s quantum chromodynamics: QCD. The strong force effectively grabs onto stuff (quarks) that comes in three colors, so to speak, and the rules for mixing those colors are quite particular. So that some version of color television. [You may find it interesting to know that our eyes actually do respond to three types of color only—using three types of cone receptors—and that, yes, color television works the same!]
And then we have the weak force which we don’t really understand but we’ve got some kind of theory that matches the results from whatever experiment we’re doing.
In short, we have different sectors in the Standard Model, and they’re separated by very different force laws: some linear, some non-linear, and all acting on different stuff. So we might say we have a Theory of Everything already. In fact, with the addition of the Higgs sector, we may say the Standard Model is a Theory of Everything. The only problem is that it looks rather ugly.
So… What do we want to do with this blog? We want to examine its ugliness and see what might or might not make sense. 🙂
Note: Physicists will probably cry wolf when I say we don’t really understand the weak force: Weinberg, Salam and Glashow got a Nobel Prize for unifying the weak and electromagnetic forces in 1979, right? Right. I just feel it’s nothing more than an ad hoc theory. I am with Dirac: if a theory isn’t beautiful, then it can’t be right. To paraphrase Dirac’s words: if God exists, then he’s a mathematician—not a plumber.