Why the laws of physics don’t actually exist

What we call laws of physics are often just mathematical descriptions of some part of nature. Ultimate physical laws probably don't exist and physics is all the better for it, says theoretical physicist Sankar Das Sarma.

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I was recently reading an old article by string theorist Robbert Dijkgraaf in Quanta Magazine entitled “There are no laws of physics”. You might think it a bit odd for a physicist to argue that there are no laws of physics but I agree with him. In fact, not only do I agree with him, I think that my field is all the better for it. And I hope to convince you of this too.

First things first. What we often call laws of physics are really just consistent mathematical theories that seem to match some parts of nature. This is as true for Newton’s laws of motion as it is for Einstein’s theories of relativity, Schrödinger’s and Dirac’s equations in quantum physics or even string theory. So these aren’t really laws as such, but instead precise and consistent ways of describing the reality we see. This should be obvious from the fact that these laws are not static; they evolve as our empirical knowledge of the universe improves.

Here’s the thing. Despite many scientists viewing their role as uncovering these ultimate laws, I just don’t believe they exist.

A hundred years ago, an opinion like this would not have been controversial. Before then, most so-called laws of physics were all directly connected to concrete aspects of the natural world, like Hooke’s law that describes how much force is needed to stretch a spring or Boyle’s law about the relationship between the pressure, temperature and volume of a gas. But this started to change in the early 20th century when people like Albert Einstein took up the quest to find the ultimate theory of everything. He spent the last 30 years of his life searching for one to no avail. Dirac too believed in this view, having apparently said that all of chemistry can be derived just from his equation – though I think that particular remark is probably apocryphal.

There are around 86 billion neurons in the human brain. This is less than the number of stars in the Milky Way which is just a miniscule part of the known universe. The universe seems almost infinite in comparison to the finite capacity of the human brain, leaving us perhaps little chance of figuring out ultimate laws. What is amazing is that we can make sense of some aspects of the universe through the laws of physics. It may have been Richard Feynman who first said that the issue is not how clever we humans are in figuring out how nature works, it is how clever nature is in following our laws!

As we discover more about nature, we can hone our descriptions of it, but it is never-ending – like peeling an infinite onion, the more we peel, the more there is to peel.

Take string theory as an example. It is a theory that is very mathematically tight and rather magical in the way that it treats gravity and quantum mechanics equivalently, matching many of our observations of the universe. It holds a lot of promise, but so far has struggled to provide any testable concrete predictions beyond our current understanding.

It also has a rather thorny stumbling block known as the landscape problem, where literally zillions of universes (around 10500, the number is so large that it seems obscene) are acceptable solutions of the theory. If string theory is correct one can declare victory as one of those zillions of universes must be our universe, and all one needs to do is to somehow find that particular solution to figure out what the laws of physics are for us. Of course, this is an impossible task because of the exceptionally large number of possible universes existing in the landscape, and all with their own distinct laws.

This scenario is often called the multiverse. All possible laws, conceivable and inconceivable, are allowed in some possible universe, and laws of physics are no longer meaningful or unique from a fundamental sense, since they depend entirely on where in the multiverse landscape one is looking. It is ironic that the theory of everything turned out to imply an everything which is exponentially larger than any everything anybody could have imagined before.

One possible conclusion from this is that the conventional reductionist approach of particle physics, where natural laws are increasingly focused on smaller and smaller building blocks (like molecules, atoms and particles) and fundamental forces (like gravity and electromagnetism) acting between them, is no longer a fruitful way of looking at the physical world. There are no fundamental building blocks and no fundamental forces and, as such, there are no laws because thinking about ultimate reductionist laws rigorously has led to the possible existence of 10500 universes, with only one of them perhaps obeying the laws needed to accommodate Homo sapiens.

The only thing we are left with is the landscape, where the “laws” depend on the specific universe one is dealing with. This is so mind-bogglingly complex that the whole idea of natural laws must be modified. It’s an apparently strange end to a worthy journey that started with atoms as hypothetical indivisible constituents of matter 2500 years ago and witnessed a great recent triumph in the experimental discovery of the Higgs particle in 2012. In the end, our physical laws are not intrinsic at all, depending entirely on where in the landscape we happen to be.

As a theoretical condensed matter physicist I do not find this scenario discouraging at all – quite the opposite. The fact that there is an essentially infinite number of possible laws only makes doing science more exhilarating because exploring the landscape will remain an active and creative activity forever. Theoretical physics can never end because the landscape is simply too vast.

I know from my 40 years of experience in working on real-life physical phenomena that the whole idea of an ultimate law based on an equation using just the building blocks and fundamental forces is unworkable and essentially a fantasy. We never know precisely which equation describes a particular laboratory situation. Instead, we always have to build models and approximations to describe each phenomenon even when we know that the equation controlling it is ultimately some form of the Schrödinger equation!

“What about quantum mechanics?” you might ask. It has been hugely successful for close to 100 years at matching all our experiments at the quantum scale. But quantum mechanics is actually more like a set of rules that we use to express our laws rather than being an ultimate law itself. For example, the standard model of particle physics, the theory of superconductivity and the theory of atomic spectra are all built using the rules of quantum mechanics, but they have little to do with each other. In addition, space and time are variables that have to be put in by hand into the theory, when space and time should come out naturally from any ultimate law of physics. This has remained perhaps the greatest mystery in fundamental physics with no solution in sight.

It is difficult to imagine that a thousand years from now physicists will still use quantum mechanics as the fundamental description of nature. Something else should replace quantum mechanics by that time just as quantum mechanics itself replaced Newtonian mechanics. I have no idea what that something else might be, but I see no particular reason that our description of how the physical universe seems to work should reach the pinnacle suddenly in the beginning of the 21st century and become stuck forever at quantum mechanics. That would be a truly depressing thought!

Newton’s laws were extraordinarily successful for 300 years, but we had to go beyond them as we learned more about the universe, and the same should happen with quantum laws some day in the future.

Any such unknown new theory of the future must build on and incorporate the physics of quantum mechanics, just as quantum mechanics built on and incorporated classical mechanics. Our understanding of the physical world must continue indefinitely, unimpeded by the search for ultimate laws. Laws of physics continuously evolve – they will never be ultimate.

Sankar Das Sarma is a theoretical physicist based at the University of Maryland, College Park. His interests are diverse, spanning the strange properties of matter to how information should be understood in the quantum realm.