There is a fascinating discussion on “Not even wrong”, about a post a couple of days ago concerning the differences between “physical intuition” and “math”, and their relative contributions to successful and unsuccessful theories in the 20th century. Peter Woit’s contention is that theoretical physics is not so much “Lost in Math”, as Sabine Hossenfelder describes it in her book with this title, as “Lost in Physical Intuition”, although he does not use this phrase explicitly. Sabine has commented with a quote from her book, to say that she agrees with him. In other words, as Peter suggests, “Physical Intuition” means “habitual use of familiar mathematics”, and Sabine uses “Math” as a snappy shorthand for this kind of “Physical Intuition”.
Woit’s most telling example I think is string theory (as you might expect), which he points out is not wrong for mathematical reasons, but for reasons of “physical intuition”. The “intuition” that elementary particles behave like tiny vibrating strings is simply wrong. The familiar mathematics of vibrating strings is not the right mathematics to use to describe elementary particles. Some other mathematics is required. But, I believe, it is mathematics that is not familiar to physicists, which is why “physical intuition” (aka “habitual use of familiar mathematics”) has not helped them to find it.
Instead, the pointers to the right mathematics must come from experiment, as they have done throughout the history of physics. The pointer to the mathematics of Special Relativity, Lorentz transformations, Minkowski space and all the rest, came from the Michelson-Morley experiment that showed that the speed of light did not transform between different observers in the way that was expected by “physical intuition”. This led to a new physical principle, namely that the speed of light in a vacuum was a constant, and from this principle the mathematics was developed.
But then experiment showed that the new “physical intuition” provided by the theory of Special Relativity was not correct, and that the speed of light is affected by gravity. So a new physical principle was required to replace the old one, to develop some more mathematics. The new physical principle is called “the” Equivalence Principle (actually, there are lots of Equivalence Principles, but we’ll come to that in a moment), and the new mathematical theory is called General Relativity. So far so good.
But experiment has shown that the new “physical intuition” provided by the theory of General Relativity is not correct, and that the equivalence of inertial and gravitational mass is affected by something else, currently unknown or unexplained. So we need a new physical principle to replace the old “equivalence principle”. We haven’t got such a new physical principle yet, because “physical intuition” has become so entrenched that it is impossible to suggest the Equivalence Principle might be wrong, without getting labelled a crackpot and sent to Coventry. Instead some “dark matter” was invented to try and save the current theory from falsification by experiment.
Well, as you know, the “physical intuition” provided by the theory of dark matter has been the mainstream of gravitational physics and cosmology for 40 years. But experiment has proved it wrong. Just as the “physical intuition” that elementary particles behave like vibrating strings is wrong, so the “physical intuition” that the universe is filled with “dark matter” is wrong. Cosmology, just as much as particle physics, is lost in physical intuition. The universe on a large (gravitational) scale is not behaving in the way that the “physical intuition” of mainstream cosmologists says it should. End of.
As I said, we need a new physical principle to replace the Equivalence Principle. I’ve made a few suggestions, such as Mach’s Principle. Asher Yahalom suggests that the Principle of Retarded Gravity is enough to underpin a theory that agrees with experiment. I am inclined to agree with him, not because I have followed all his calculations – I haven’t – but because it is a philosophically compelling principle. It is the principle that there is a finite “speed limit” for the communication of any signal, gravitational or electromagnetic, throughout the universe. The finite speed limit for electromagnetic signals (light, radio waves, X rays, etc.) is part of mainstream “physical intuition”, but not so for gravitational signals.
Which is very odd, because gravitational signals are important over vastly greater distances, in which the finite speed of propagation becomes vastly more important. The Principle of Retarded Gravity explains anomalies on the Solar System scale (flyby anomaly, Pioneer anomaly) and the galaxy scale (flat rotation curves, wide binary star rotation speeds). It is a good principle, better than the Equivalence Principle. It allows the Equivalence Principle to hold approximately, in situations in which the retardation is negligible. It allows the principle of a constant speed of light to hold approximately, in situations in which gravity is negligible. So it extends the old Einstein theory of gravity (General Relativity) to a more general theory of gravity, that works on a much larger scale.
To summarise, then, the problem with our theories of gravity and cosmology is that they are lost in the “physical intuition” of General Relativity, which is based on an incorrect physical principle (the “equivalence principle”), and are completely ignoring the experimental facts provided by our extremely detailed and extensive observations of everything we can see in the sky.
The problem in particle physics is even worse. This is partly because it too requires the equivalence principle, which is demonstrably false. But it also requires the “physical intuition” of Quantum Field Theory, which is a vast assemblage of “familiar mathematics” that habitual use has elevated to the status of incontrovertible dogma. What is the physical principle that underlies this “physical intuition”? To be honest, I don’t really know, and, to be honest, I don’t really care – because whatever it is, it clearly isn’t the right one. All I know is, that attempts to replace it by the Principle of Strings have failed. So we need a new principle. Let’s call it the X Principle.
Or we could call it the Principle of Discreteness, the principle that everything is fundamentally discrete. We do not normally see the discreteness, so continuous “physical intuition” often suffices. But the mathematics of vibrating strings and propagating waves is not the right mathematics to describe a discrete universe. So the “physical intuition” of quantum field theory is completely useless as a guide to mathematical theory of what is really going on. But the Principle of Discreteness itself tells us what the correct mathematical basis for the theory must be – it must be finite group theory. Representation theory then allows us to work with continuous approximations, and recover the old Quantum Field Theory in situations where we cannot see (or use) the discreteness.
I don’t believe in the Principle of Discreteness just because I am a finite group theorist by training. I believe in it because it is a compelling philosophical principle. It provides a “physical intuition” (aka habitual use of familiar mathematics) that I can use to interpret the universe we live in – it is mathematics that is familiar to me, that I can apply to as many examples as I like, and explain various experimental facts that quantum field theory cannot explain. Things like neutrino oscillations, and properties of entangled photon states, and where mass comes from. In other words, the Principle of Discreteness in and of itself provides me, as a finite group theorist, with the “physical intuition” to understand why these initially unexpected properties of elementary particles must be true. The “physical intuition” provided by QFT does not do this.
The standard or mainstream theories are still based on continuous mathematics, and do not embrace the Principle of Discreteness. Therefore they have to invent neutrino masses to explain neutrino oscillations, because the “intuition” provided by the “habitual use of familiar mathematics” cannot conceive of any other explanation. Just as the “intuition” provided by the habitual use of GR cannot conceive of any explanation for flat galaxy rotation curves, other than dark matter haloes. But experiment has failed to detect any such mass directly, which indicates that a better physical principle is that they have zero mass, and it is only the continuous approximation to the discrete reality that creates the illusion of a non-zero mass.
To summarize, the two fundamental principles of 21st century physics are the Principle of Retardation, and the Principle of Discreteness. Throw out the old Equivalence Principle, and Quantum Field Theory, and start again from scratch. Develop the mathematics that these two principles require, and then you will develop the physical intuition (“habitual use of familiar mathematics”) to understand why the universe is the way that experiment says it is.
