- Thermodynamics uses a handful of laws to explain things like why perpetual motion can't happen, how engines work or why Play-Doh™ always ends up looking gray-brown if you mash it together long enough.
- Newton's laws explain things like why the Moon goes around the Earth, how you can tell if a car in an accident was speeding or how to sink the 8-ball in the corner pocket.
- Nöther's theorem demonstrates (in a way I've never quite completely grasped) a deep relation between symmetry and conservation -- if, for example, the equations describing motion don't care about direction then angular momentum is conserved and that figure skater spins faster and faster as the arms come in.
- General relativity holds that, left to themselves, objects travel in a straight line, the simplest possible path. It just doesn't always look that way because space-time isn't flat, but this is why, for example, Mercury's orbit moves just a bit every time around.
- Quantum physics ... yeah. Quantum physics.
It's not that quantum physics lacks elegance. The idea that all matter and energy, basically everything we can measure, can be explained by equations similar in form to those that describe a vibrating string is pretty astounding if you think about it. The Standard Model of quantum physics has built on this to make a large number of predictions, including predictions of new particles, that have been confirmed with outstanding accuracy.
You'd think this would be good news. Instead, a certain uneasiness has developed around the Standard Model. The basic framework is nice enough, but it can't completely describe what we know until you plug in several parameters. There are 19 in all, ranging from me (the mass of the electron, 511 keV), to θ23 (the "CKM 23-mixing angle", 2.4°) to the recently established mH, (the Higgs mass, tentatively 125.36±0.41 GeV). There aren't just infinitely many other ways to tune the knobs, there are not one, not two but 19 knobs to tune.
Tweak a few of them the wrong way and stars can never form, or worse, no kind of solid matter can form at all. We seem to be in some sort of special regime where the parameters just happen to have the right values for us to be here to observe them. Even if you adopt the view that there may be infinitely other universes out there where the knobs aren't tuned right, so where else could we be (the "weak anthropic principle"), it's still all pretty unsatisfying. Our universe is some point in a 19-dimensional space that's suitable for life forms like us to develop? That's it?
Particle physicist Sabine Hossenfelder argues in a piece called The LHC “nightmare scenario” has come true that yep, that's it, get over it. As I read it she makes two points. The smaller one is that the Large Hadron Collider which was instrumental in finding the Higgs boson has likely found all the particles it's going to find, and maybe it's time to stop trying to build bigger and bigger particle accelerators.
Fellow particle physicist Matt Strassler argues that there's no nightmare regardless of whether there are any other new particles. The LHC has produced ridiculous amounts of data which won't be thoroughly examined for years, and it can easily produce more. There might be, indeed probably are, interesting discoveries to be pulled out of that data now that it's pretty well established that the Higgs exists.
This seems reasonable, but it's more an argument against Hossenfelder's headline than the substance of the article. Disputes over what experiments to do (and, more to the point, what experiments to fund) are by no means new. Hossenfelder's and Strassler's are by no means the only views on the subject, and they may not even be particularly divergent, but in any case whether to keep building bigger particle smashers is of greatest concern to particle physicists and those who fund them.
Public policy and the sociology of science are worthy topics, but I won't be conjecturing any further about them here. I'm more interested in Hossenfelder's larger point, which as I understand it is about what makes a good theory of physics.
When people started taking a close look at Newtonian mechanics, heat transfer and other fields they started to find anomalies under extreme conditions that eventually led to the discovery of relativity and quantum physics. This is just part of a long history of progress in physics. For example:
So far no one has come up with a theory-breaking anomaly for the Standard Model analogous to the precession of Mercury's orbit, or some new phenomenon, say an unpredicted particle or force, that the Standard Model could have been expected to predict but didn't. There are a few candidates, but even after decades of effort nothing has really panned out. The experiments at the LHC found the Higgs, at an energy consistent with the Standard Model, and nothing, or at least nothing definitive, inconsistent with it.
So the Standard Model is it, right? We've described the fundamental forces and elementary particles of the natural world. There's plenty of work, probably an endless amount, to be done working out the ramifications of that, and how it all fits in with relativity, what exactly it means to "measure" a system described by a wavefunction, and on and on, but as to explaining the basis for particle physics, we're done. Right?
As I understand it, Hossenfelder's answer to that would be "looks like we could be", but that answer doesn't sit well with everyone. How can such an inelegant theory, with its 19 arbitrary parameters, be the final answer? "They just do" can't be an adequate answer to "why do those parameters have the values they do?" can it? Hossenfelder would likely say "sure it can".
In the history of physics, power and elegance seem to go hand in hand. Or at least, after enough anomalies with ad-hoc descriptions turn up, eventually someone comes up with a new framework where it all makes sense again. The new theory is both more elegant and more powerful. Some would even say more "natural" and claim that nature is itself elegant, and if it doesn't seem that way we must not understand it properly.
The Standard Model seems ready to be replaced with something better, except it doesn't seem to be producing the sort of "close, but not quite" results that led us from Newton to Einstein. There may be more elegant theories around -- string theory gets a lot of attention in this regard -- but nothing, so far, clearly more powerful. If there's a more "natural" theory, nature doesn't seem keen to lead us to it.
This feeling that the world has to be more elegant than our current theories may just be an occupational hazard of physicists, and not necessarily the majority at that. Plenty of working particle physicists are content to "shut up and calculate" without worrying too much about what it all might "mean" or whether the universe has some deep hidden simplicity.
Many chemists would shake their heads at the whole business. There are around a hundred elements one can do meaningful chemistry with, each with its own particular properties. That's not going to change with a new theory of chemistry. There is a theory, namely the Standard Model, which explains why those elements are the way they are, and quantum effects definitely come into play in chemistry, but from a chemist's point of view it doesn't matter how many parameters the Standard Model has. It matters what the electrons are going to do in a particular situation.
In my own field there are several models that can define the behavior of computers, and we do refer to them (particularly state machines and stack machines) from time to time, but there is not and is never likely to be a unified theory of software engineering. And yet the servers still run. Mostly.
Even mathematics, which can almost be defined as the relentless pursuit of elegance, is full of quirky, inelegant results. What's so special about manifolds in four dimensions? Why are there 26 sporadic groups? Why is the 3N+1 problem so hard? And let's not even get started on the prime numbers.
Suppose that everything in the universe could be precisely described by three simple rules ... and a table of three quadrillion quadrillion seven-digit numbers. Even storing such a table would be completely infeasible using today's technology, but suppose we meet up with an alien race with full access to it. Our best physicists pose them questions, they consult the table and deliver a verifiable answer every time (how to reduce any measurable question and its answer to an invocation of three simple rules is an interesting question, but roll with it). Would we say the aliens have a good theory?
On the one hand, of course they do. The hallmark of a good theory is making testable predictions that hold up. On the other hand, there's something less than satisfying about a planet-sized table of numbers, each essentially its own arbitrary parameter. What happens if our aliens go away or decide that we're not worthy of True Knowledge? Maybe we should start asking questions that will reveal the nature of the magic number table and, ideally, allow us to reduce it to something our puny minds and computers can handle.
A good theory doesn't just have to be true in the sense of making true predictions. It also has to be comprehensible and usable. To this end, a theory with a thousand fairly simple rules and three or three hundred parameters with values we just have to accept is far better than the one I just described. But this is not saying anything about nature. It says something about us. Our "natural" theories are the ones that work best for us, not just in aligning with nature, but with our resources and the way our minds work.
From that point of view, 19 is not a prohibitive number of parameters the way three quadrillion quadrillion would be. If that's really how it is, we can probably live with it. But the distinction is of degree, not kind. The problem is not with arbitrary parameters themselves, but with having an intractable number of them. Consulting our hypothetical aliens with knowledge beyond our ability to process is really just another kind of experiment from our point of view. Consulting the Standard Model with its human-friendly list of parameters is better, and it would be even if its predictions weren't quite as good as they are. It's certainly better than a more "elegant" theory that doesn't fit experiment as well as it does.
Nature is what it is. A theory is only "natural" if it fits with our nature in particular as well as nature at large.
[Re-reading this, I realize I neglected to say that, although the basic equation of the standard model is fairly compact -- you can get a T-shirt with the Standard Model Lagrangian on it -- actually finding solutions for all but the simplest conditions is generally far beyond our computing ability. In one sense this is more than a bit like the aliens-with-the-numbers scenario, but instead of a hidden table of numbers we can't begin to access, we have an equation we can barely begin to compute. Except maybe with quantum computers ... --D.H.]
Re-reading Hossenfelder's piece, I see one more subtle point. The main argument doesn't seem to be that there can't possibly be an elegant theory unifying quantum physics with relativity, or even a better way of explaining the results of the Standard Model. Rather, a search for "elegance" or a "natural" theory is no longer a good way -- if it ever was -- of deciding what particle experiments to run next. If we do find such a unified theory, it's probably not going to be because we found a more elegant replacement for the Standard Model, or because we found an unexpected particle with a new, more powerful accelerator, but because we found something else entirely and a theory to explain it that happens to subsume the Standard Model.
Tweak a few of them the wrong way and stars can never form, or worse, no kind of solid matter can form at all. We seem to be in some sort of special regime where the parameters just happen to have the right values for us to be here to observe them. Even if you adopt the view that there may be infinitely other universes out there where the knobs aren't tuned right, so where else could we be (the "weak anthropic principle"), it's still all pretty unsatisfying. Our universe is some point in a 19-dimensional space that's suitable for life forms like us to develop? That's it?
Particle physicist Sabine Hossenfelder argues in a piece called The LHC “nightmare scenario” has come true that yep, that's it, get over it. As I read it she makes two points. The smaller one is that the Large Hadron Collider which was instrumental in finding the Higgs boson has likely found all the particles it's going to find, and maybe it's time to stop trying to build bigger and bigger particle accelerators.
Fellow particle physicist Matt Strassler argues that there's no nightmare regardless of whether there are any other new particles. The LHC has produced ridiculous amounts of data which won't be thoroughly examined for years, and it can easily produce more. There might be, indeed probably are, interesting discoveries to be pulled out of that data now that it's pretty well established that the Higgs exists.
This seems reasonable, but it's more an argument against Hossenfelder's headline than the substance of the article. Disputes over what experiments to do (and, more to the point, what experiments to fund) are by no means new. Hossenfelder's and Strassler's are by no means the only views on the subject, and they may not even be particularly divergent, but in any case whether to keep building bigger particle smashers is of greatest concern to particle physicists and those who fund them.
Public policy and the sociology of science are worthy topics, but I won't be conjecturing any further about them here. I'm more interested in Hossenfelder's larger point, which as I understand it is about what makes a good theory of physics.
When people started taking a close look at Newtonian mechanics, heat transfer and other fields they started to find anomalies under extreme conditions that eventually led to the discovery of relativity and quantum physics. This is just part of a long history of progress in physics. For example:
- Ptolemy explained the motions of the planets with a system of cycles and epicycles centered around the Earth.
- Copernicus explained those motions more simply with a system of cycles and epicycles centered around the sun.
- Kepler did away with epicycles using the notion that the planets moved in ellipses, not circles
- Newton explained elliptical orbits in terms of a universal gravitational force following an inverse square law
- and Einstein explained gravitation as a property of space-time itself
(I'm always a bit leery about ascribing a particular landmark result to a particular person, as in "Ptolemy explained ...". There is more to each of these than a single person making a single discovery even when we know a particular person had a particular key insight. But this will do for now.)
In all these cases, the new theory didn't just explain everything the old theory did, albeit in a new way. It either made sense of something that had seemed arbitrary in the old theory, explained new things the old theory couldn't, or both. Copernicus and Kepler dealt with epicycles, first simplifying them and then doing away with them altogether. Newton's mechanics explained why the planets followed elliptical orbits as described by Kepler's laws and not some other shape. It also explained why the Moon doesn't actually follow an exactly elliptical orbit, why the daily tides rise and fall, and much more.
Einstein's theory of relativity did away with gravitation as a force. Objects under the influence of gravity still follow Newton's first law, just in a more subtle form. It also gave better predictions for the motions of the planets and made a number of new predictions that were later confirmed, such as the direction and frequency of light being affected by gravity and why the orbits of stars in a binary system containing a pulsar can be seen to be slowing.
It's not just that the new theories were more powerful than the old ones. That's to be expected. Otherwise why adopt them? In all these cases, and many others, the new theory was also, in some sense, more elegant than the old. Elegant, in this sense, largely means simpler. Fewer epicycles. One universal force. No universal force at all. There is also a sense of reducing seemingly unrelated things to different aspects of the same thing. The tides and the motions of the planet are both just effects of gravity. Space and time are just components of a the space-time continuum.
Which brings us back to the Standard Model.
So far no one has come up with a theory-breaking anomaly for the Standard Model analogous to the precession of Mercury's orbit, or some new phenomenon, say an unpredicted particle or force, that the Standard Model could have been expected to predict but didn't. There are a few candidates, but even after decades of effort nothing has really panned out. The experiments at the LHC found the Higgs, at an energy consistent with the Standard Model, and nothing, or at least nothing definitive, inconsistent with it.
So the Standard Model is it, right? We've described the fundamental forces and elementary particles of the natural world. There's plenty of work, probably an endless amount, to be done working out the ramifications of that, and how it all fits in with relativity, what exactly it means to "measure" a system described by a wavefunction, and on and on, but as to explaining the basis for particle physics, we're done. Right?
As I understand it, Hossenfelder's answer to that would be "looks like we could be", but that answer doesn't sit well with everyone. How can such an inelegant theory, with its 19 arbitrary parameters, be the final answer? "They just do" can't be an adequate answer to "why do those parameters have the values they do?" can it? Hossenfelder would likely say "sure it can".
In the history of physics, power and elegance seem to go hand in hand. Or at least, after enough anomalies with ad-hoc descriptions turn up, eventually someone comes up with a new framework where it all makes sense again. The new theory is both more elegant and more powerful. Some would even say more "natural" and claim that nature is itself elegant, and if it doesn't seem that way we must not understand it properly.
The Standard Model seems ready to be replaced with something better, except it doesn't seem to be producing the sort of "close, but not quite" results that led us from Newton to Einstein. There may be more elegant theories around -- string theory gets a lot of attention in this regard -- but nothing, so far, clearly more powerful. If there's a more "natural" theory, nature doesn't seem keen to lead us to it.
This feeling that the world has to be more elegant than our current theories may just be an occupational hazard of physicists, and not necessarily the majority at that. Plenty of working particle physicists are content to "shut up and calculate" without worrying too much about what it all might "mean" or whether the universe has some deep hidden simplicity.
Many chemists would shake their heads at the whole business. There are around a hundred elements one can do meaningful chemistry with, each with its own particular properties. That's not going to change with a new theory of chemistry. There is a theory, namely the Standard Model, which explains why those elements are the way they are, and quantum effects definitely come into play in chemistry, but from a chemist's point of view it doesn't matter how many parameters the Standard Model has. It matters what the electrons are going to do in a particular situation.
In my own field there are several models that can define the behavior of computers, and we do refer to them (particularly state machines and stack machines) from time to time, but there is not and is never likely to be a unified theory of software engineering. And yet the servers still run. Mostly.
Even mathematics, which can almost be defined as the relentless pursuit of elegance, is full of quirky, inelegant results. What's so special about manifolds in four dimensions? Why are there 26 sporadic groups? Why is the 3N+1 problem so hard? And let's not even get started on the prime numbers.
Suppose that everything in the universe could be precisely described by three simple rules ... and a table of three quadrillion quadrillion seven-digit numbers. Even storing such a table would be completely infeasible using today's technology, but suppose we meet up with an alien race with full access to it. Our best physicists pose them questions, they consult the table and deliver a verifiable answer every time (how to reduce any measurable question and its answer to an invocation of three simple rules is an interesting question, but roll with it). Would we say the aliens have a good theory?
On the one hand, of course they do. The hallmark of a good theory is making testable predictions that hold up. On the other hand, there's something less than satisfying about a planet-sized table of numbers, each essentially its own arbitrary parameter. What happens if our aliens go away or decide that we're not worthy of True Knowledge? Maybe we should start asking questions that will reveal the nature of the magic number table and, ideally, allow us to reduce it to something our puny minds and computers can handle.
A good theory doesn't just have to be true in the sense of making true predictions. It also has to be comprehensible and usable. To this end, a theory with a thousand fairly simple rules and three or three hundred parameters with values we just have to accept is far better than the one I just described. But this is not saying anything about nature. It says something about us. Our "natural" theories are the ones that work best for us, not just in aligning with nature, but with our resources and the way our minds work.
From that point of view, 19 is not a prohibitive number of parameters the way three quadrillion quadrillion would be. If that's really how it is, we can probably live with it. But the distinction is of degree, not kind. The problem is not with arbitrary parameters themselves, but with having an intractable number of them. Consulting our hypothetical aliens with knowledge beyond our ability to process is really just another kind of experiment from our point of view. Consulting the Standard Model with its human-friendly list of parameters is better, and it would be even if its predictions weren't quite as good as they are. It's certainly better than a more "elegant" theory that doesn't fit experiment as well as it does.
Nature is what it is. A theory is only "natural" if it fits with our nature in particular as well as nature at large.
[Re-reading this, I realize I neglected to say that, although the basic equation of the standard model is fairly compact -- you can get a T-shirt with the Standard Model Lagrangian on it -- actually finding solutions for all but the simplest conditions is generally far beyond our computing ability. In one sense this is more than a bit like the aliens-with-the-numbers scenario, but instead of a hidden table of numbers we can't begin to access, we have an equation we can barely begin to compute. Except maybe with quantum computers ... --D.H.]
Re-reading Hossenfelder's piece, I see one more subtle point. The main argument doesn't seem to be that there can't possibly be an elegant theory unifying quantum physics with relativity, or even a better way of explaining the results of the Standard Model. Rather, a search for "elegance" or a "natural" theory is no longer a good way -- if it ever was -- of deciding what particle experiments to run next. If we do find such a unified theory, it's probably not going to be because we found a more elegant replacement for the Standard Model, or because we found an unexpected particle with a new, more powerful accelerator, but because we found something else entirely and a theory to explain it that happens to subsume the Standard Model.
