“Philosophy of Science is as useful to scientists as ornithology is to birds.” – Richard Feynman

For obvious reasons this provocative quote is not very popular among philosophers of science, but Feynman certainly didn’t mean it in bad taste. The fact of the matter is that most science can be done with little to no philosophical reflection. Chemistry, Biology, and Computer Science are simple examples of fields where it is easy to entirely dismiss the role of philosophy of science. That’s not to say it can’t play a role, but it is not something one comes up against often in their work. This is in contrast to Theoretical Physics, a science where questions of the limits of empiricism, and the relationship between observation, theory and ontology are still hotly debated issues despite not being scientific questions. The constant confrontation of these questions is one of the main reasons for the popularity of the Shut up and calculate! “interpretation” of quantum mechanics. Physicists got tired of doing philosophy, and so decided to move forward despite being unable to make heads or tails of what the theory tells them about reality. This was a huge change in direction for physics: it inadvertently claims that the goal of theory is not to describe reality, but only to predict and account for observations. As progress continues, conflicting philosophies of physics are causing trouble again, in discussions on effective field theories. In order to paint the full picture, lets first look at a place where philosophy and science for the most part agree.

When General Relativity, Einstein’s revolutionary theory of gravitation took hold in 1915, people were happy to make metaphysical claims about what the theory meant for the nature of reality. Of course there is always room for debate, but people had not only begun saying, but accepting claims such as “Our Universe is a curved spacetime” and “The presence of matter, momentum and energy curve spacetime”. The quantum revolution has had far less success in this regard. Aside from wave-particle duality (matter waves) and the uncertainty principle, we as a species have had a rough time agreeing on anything metaphysical about the quantum theory of nature. Despite all this, by pushing through that period particle physicists from the late 20’s through the early 60’s developed quantum field theory, an extension of of quantum mechanics which naturally includes the laws of special relativity (nothing with mass travels faster than light) and intrinsic spin. The most precise and accurate physical theory we’ve ever had is a quantum field theory, known as the standard model of particle physics. The standard model accounts for nearly everything we’ve seen in experiments; we know it’s not entirely correct (at the very least it doesn’t account of Neutrino oscillations), but it is still the best theory of nature we have (a refresher on fields and the whole of the standard model can be found here).

Funny enough, the standard model arguably lends itself more to metaphysical conclusions than the old quantum theory, despite being born out of metaphysical ignorance. This is one of the reasons philosophy is coming back into the discussion, because there seems to be a feeling that the objects of the standard model, fields, really are fundamental in a way that the wave-functions of the old theory were not. One might get hopeful at this point and say we ought to be fair to our theories of physics, and treat the standard model how we’ve been treating general relativity for a century. However if we wish to do this we immediately run into a problem: the Higgs field.

The Higgs is easily the first point of contention among metaphysically minded theorists, for several reasons. I’ve discussed this before in The Frustrating Success of Our Best Theory of Physics (skip to the 10th paragraph if you only care for the details of the Higgs), so I’ll get straight to the problem: in order to get the field to behave the way we want it to, we must assign the field an imaginary mass (we avoid predicting an imaginary measured mass through a clever process called spontaneous symmetry breaking, which is beyond the scope of this article). We’ve never measured a particle to have anything but a positive mass, and so the fact that we can assign the Higgs field an imaginary mass, and still have the prediction that the measured value is real, is the main problem behind treating general relativity and the standard model with equal metaphysical status. For general relativity, we really only need to assume the existence of energy, and of curving spacetime. It is at least a simple theory in what it assumes of nature. If you wish to treat the standard model the same way, you need to be comfortable with allowing masses to take imaginary values in your metaphysics, or you have to bite the bullet and say that the model and what actually exists clearly differ at some point, unlike general relativity. This tension and inability to place general relativity and the standard model on equal footing, is caused by the fact that the standard model is an effective field theory.

The philosophy behind effective field theories is one of pragmatic freedom. You have a theory which works for a certain range of values, and in that range of values, your theory is allowed to say anything it wants about its constituents, so long as its expectation values of any observable quantities, are always real. You can have fields that are imaginary in mass, fields which have infinite coupling strength between them, and even theories which exist in non-integer dimensions. The only requirement is that every observable be a real number. A simple example of this is that physicists will often impose momentum cut-offs on their theories; they declare no interactions can occur beyond some chosen large momentum. This stops expectation values from being infinite, but also breaks some symmetries of the theory because in reality you can have arbitrarily high momenta, while your theory assumes a maximum possible momentum (specifically, boost/translation symmetry is broken).

While some theorists consider effective field theories the only viable strategy to guarantee progress, others find this is hideous. “We’re not going to make progress by hacking the math until it spits out what we want! The core theory we have is ugly enough. Masses should be real! Infinities don’t exist in nature! Dimensions have to be integer to make any sense!” Even if one doesn’t fully agree with this camp, it is hard not to sympathize with them. The road to progress outlined by this “Symmetry and Simplicity” camp, is to go back to the drawing board, and hope that by enforcing more symmetries and demanding a certain level of simplicity from our theories, the correct laws of physics will fall out (some examples of this working are special relativity, which falls nicely out of 2 very basic assumptions, and gauge theory where interactions are a simple consequence of imposing more symmetries on our theories of physics). This is how you get theories like Super Symmetry, and String Theory. Now there is no experimental evidence for Super Symmetry, and String theory has its own load of (debatably) ad-hoc assumptions (why should all but 3 spacial dimensions be wrapped up very tightly? etc), but these theories are no doubt more promising as a basis for a metaphysics, than effective field theories are.

No one disagrees that it would be nice to have a clear picture of what is going on at the most fundamental scales, but the effective field theorists simply concede that we do not and probably will not ever understand, in some intuitive sense, what is happening on the level of quantum field theory, and so see this “symmetry and simplicity” camp as a misguided effort to understand something that may very well be ineffable. For all we know, they may have a point. If nature isn’t sensible (to us) at the quantum level, then why on earth should we demand our theory to be? Many of these effective field theories are not even mathematically well defined, but that doesn’t stop them from working. It is truly the logical conclusion of Shut Up and Calculate! Simply give up on trying to understanding what your theory tells you about reality, and just find a theory which gives the correct predictions and fits the data, to all our experiments and observations, within the range of energies we can access. Perhaps this leaves you a bit glum if you care deeply about metaphysics, but this thinking certainly trims the fat and allows for progress to take place.

One elucidating example in all of this, is the case of renormalization via Gerard ‘t Hooft’s dimensional regularization (renormalization just means “getting rid of infinities in our theory”). As said before, in order to stop calculations from going off to infinity, one thing theorists will often do is put arbitrary cut-offs on their calculations, and so their theory will work for for a certain range of energies or momenta etc. ‘t Hooft found another clever way to avoid these infinities: start by saying we live not in 4 dimensions, but 4-ε dimensions, where epsilon is just some real number. Then we do all our math, and when we get our final results we’ll find epsilon (ε) shows up in them. If we can set ε equal to 0, then our job is done! If when we try to do that everything blows up, we make our various coupling constants in the theory have epsilon terms in them as well, in a such a way so that all the epsilons go away in our results. Unfortunately this gets rid of any physical meaning for our coupling constants, and now they are just free parameters of our theory. Despite this, the above method of renormalization has been enormously successful. Why? Because it respects the symmetries of nature. It still let’s us have arbitrarily high momenta, among various other things. Depending on who you ask, this progress is an argument in favour of both camps: No, we don’t live in a non-integer number of dimensions, but if we just pretend we do we can make great progress! vs. If we can find a more beautiful way to renormalize, that respects the symmetries of nature, we can make great progress!

This is the ornithology that the birds are still doing. They may not be arguing about the metaphysical nature of reality quite like Bohr and Einstein did, but there is still intense discussion being had about the role of models in science, not only in a pragmatic sense, but in metaphysical and aesthetic senses as well. Whether or not effective field theories are the best way to progress in physics is something only time will tell, but if there is one takeaway from this discussion, it is that philosophical values and beliefs are far from unimportant in the construction of our models in theoretical physics. Two physicists with the same education but particularly distinct metaphysical and aesthetic commitments will end up doing physics very differently, with different goals in mind. The discussion is nowhere near finished, and in my opinion makes this an exciting time to be both a physicist and philosopher of science.