Tag Archives: philosophy of science

What does Copernicus have to say about String Theory?

1 Reply

Putting aside some highly controversial exceptions, string theory has made no testable predictions. Conceivably, a world governed by string theory and a world governed by conventional particle physics would be indistinguishable to every test we could perform today. Furthermore, it’s not even possible to say that string theory predicts the same things with fewer fudge-factors, as string theory descriptions of our world seem to have dramatically many more free parameters than conventional ones.

Critics of string theory point to this as a reason why string theory should be excluded from science, sent off to the chilly arctic wasteland of the math department. (No offense to mathematicians, I’m sure your department is actually quite warm and toasty.) What these critics are missing is an important feature of the scientific process: before scientists are able to make predictions, they propose explanations.

To explain what I mean by that, let’s go back to the beginning of the 16th century.

At the time, the authority on astronomy was still Ptolemy’s Syntaxis Mathematica, a book so renowned that it is better known by the Arabic-derived superlative Almagest, “the greatest”. Ptolemy modeled the motions of the planets and stars as a series of interlocking crystal spheres with the Earth at the center, and did so well enough that until that time only minor improvements on the model had been made.

This is much trickier than it sounds, because even in Ptolemy’s day astronomers could tell that the planets did not move in simple circles around the Earth. There were major distortions from circular motion, the most dramatic being the phenomenon of retrograde motion.

If the planets really were moving in simple circles around the Earth, you would expect them to keep moving in the same direction. However, ancient astronomers saw that sometimes, some of the planets moved backwards. The planet would slow down, turn around, go backwards a bit, then come to a stop and turn again.

Thus sparking the invention of the spirograph.

In order to take this into account, Ptolemy introduced epicycles, extra circles of motion for the planets. The epicycle would move on the planet’s primary circle, or deferent, and the planet would rotate around the epicycle, like so:

French Wikipedia had a better picture.

These epicycles weren’t just for retrograde motion, though. They allowed Ptolemy to model all sorts of irregularities in the planets’ motions. Any deviation from a circle could conceivably be plotted out by adding another epicycle (though Ptolemy had other methods to model this sort of thing, among them something called an equant). Enter Copernicus.

Enter Copernicus’s hair.

Copernicus didn’t like Ptolemy’s model. He didn’t like equants, and what’s more, he didn’t like the idea that the Earth was the center of the universe. Like Plato, he preferred the idea that the center of the universe was a divine fire, a source of heat and light like the Sun. He decided to put together a model of the planets with the Sun in the center. And what he found, when he did, was an explanation for retrograde motion.

In Copernicus’s model, the planets always go in one direction around the Sun, never turning back. However, some of the planets are faster than the Earth, and some are slower. If a planet is slower than the Earth and it passes by it will look like it is going backwards, due to the Earth’s speed. This is tricky to visualize, but hopefully the picture below will help: As you can see in the picture, Mars starts out ahead of Earth in its orbit, then falls behind, making it appear to move backwards.

Despite this simplification, Copernicus still needed epicycles. The planets’ motions simply aren’t perfect circles, even around the Sun. After getting rid of the equants from Ptolemy’s theory, Copernicus’s model ended up having just as many epicycles as Ptolemy’s!

Copernicus’s model wasn’t any better at making predictions (in fact, due to some technical lapses in its presentation, it was even a little bit worse). It didn’t have fewer “fudge factors”, as it had about the same number of epicycles. If you lived in the 16th century, you would have been completely justified in believing that the Earth was the center of the universe, and not the Sun. Copernicus had failed to establish his model as scientific truth.

However, Copernicus had still done something Ptolemy didn’t: he had explained retrograde motion. Retrograde motion was a unique, qualitative phenomenon, and while Ptolemy could include it in his math, only Copernicus gave you a reason why it happened.

That’s not enough to become the reigning scientific truth, but it’s a damn good reason to pay attention. It was justification for astronomers to dedicate years of their lives to improving the model, to working with it and trying to get unique predictions out of it. It was enough that, over half a century later, Kepler could take it and turn it into a theory that did make predictions better than Ptolemy, that did have fewer fudge-factors.

String theory as a model of the universe doesn’t make novel predictions, it doesn’t have fewer fudge factors. What it does is explain, explaining spectra of particles in terms of shapes of space and time, the existence of gravity and light in terms of closed and open strings, the temperature of black holes in terms of what’s going on inside them (this last really ought to be the subject of its own post, it’s one of the big triumphs of string theory). You don’t need to accept it as scientific truth. Like Copernicus’s model in his day, we don’t have the evidence for that yet. But you should understand that, as a powerful explanation, the idea of string theory as a model of the universe is worth spending time on.

Of course, string theory is useful for many things that aren’t modeling the universe. But that’s the subject of another post.

Elegance, Not So Mysterious

2 Replies

You’ll often hear theoretical physicists in the media referring to one theory or another as “elegant”. String theory in particular seems to get this moniker fairly frequently.

It may often seem like mathematical elegance is some sort of mysterious sixth sense theorists possess, as inexplicable to the average person as color to a blind person. What’s “elegant” about string theory, after all?

Before explaining elegance, I should take a bit of time to say what it’s not. Elegance isn’t Occam’s razor. It isn’t naturalness, either. Both of those concepts have their own technical definitions.

Elegance, by contrast, is a much hazier, and yet much simpler, notion. It’s hazy enough that any definition could provoke arguments, but I can at least give you an approximate idea by telling you that an elegant theory is simple to describe, if you know the right terms. Often, it is simpler than the phenomenon that it explains.

How does this apply to something like string theory? String theory seems to be incredibly complicated: ten dimensions, curled up in a truly vast number of different ways, giving rise to whole spectrums of particles.

That said, the basic idea is quite simple. String theory asks the question: what if, in addition to fundamental point-particles (zero dimensional objects), there were fundamental objects of other dimensions? That idea leads to complicated consequences: if your theory is going to produce all the particles of the real world then you need the ten dimensions and the supersymmetry and yadda yadda. But the basic idea is simple to describe. An elegant theory can have very complicated consequences, but still be simple to describe.

This, broadly, is the sort of explanation theoretical physicists look for. Math is the kind of field where the same basic systems can describe very complex phenomena. Since theoretical physics is about describing the world in terms of math, the right explanation is usually the most elegant.

This can occasionally trip physicists up when they migrate to other careers. In biology, for example, the elegant solution is often not the right one, because evolution doesn’t care about elegance: evolution just grabs whatever is within reach. Financial systems and economics occasionally have similar problems. All this is to say that while elegance is an important thing for a physicist to strive for, sometimes we have to be careful about it.

Braaains…Boltzmann Braaaains…

10 Replies

In honor of Halloween yesterday, let me tell you a scary physics story:

Sarah was an ordinary college student, in an ordinary dorm room, ordinary bean bag chairs strewn around an ordinary bed with ordinary pink sheets. If she concentrated, she could imagine her ordinary parents back home in ordinary Minnesota. In her ordinary physics textbook on her ordinary desk, ordinary laws of physics were written, described as the result of centuries of experimentation.

Unbeknownst to Sarah, the universe was much more chaotic and random than she realized, and also much more vast. Arbitrary collections of matter formed and dissipated, and over the universe’s long history, any imaginable combination might come to be.

Combinations like Sarah.

You see, Sarah too was a random combination, a chance arrangement of particles formed only a bare few moments ago. In truth, she had no ordinary parents, nor was she surrounded by an ordinary college, and the laws of physics that her textbook asserted were discovered through centuries of experimentation were just a moment’s distribution of ink on a page.

And as she got up to open the door into the vast dark of the outside, her world dissipated, and she ceased to exist.

That’s the life of a Boltzmann Brain. If a universe is random and old enough, it is inevitable that such minds exist. They might have memories of an extended, orderly world, but these would just be illusions, chance arrangements of their momentary neurons. What’s more, they may think they know the laws of physics through careful experiment and reasoning, but such knowledge would be illusory as well. And most frightening of all, if the universe is truly ancient and unimaginably vast, there would be many orders of magnitude more Boltzmann Brains than real humans…so many, that it would almost certainly be the case that you are in fact a Boltzmann Brain right now!

This is legitimately worrying to some physicists. The situation gets a bit more interesting when you remember that, as a Boltzmann Brain, anything you know about physics may well be a lie, since the history of research you think exists might not have. The problem is, if you manage to prove that you are probably a Boltzmann Brain, you had to use physics to do it. But your physics is probably wrong!

This, as Sean Carroll argues is why the concept of a Boltzmann Brain is self-defeating. It is, in a way, a logical impossibility. And if a universe of Boltzmann Brains is logically impossible, then any physics that makes Boltzmann Brains more likely than normal humans must similarly be wrong. That’s Carroll’s argument, one that he uses to argue for specific physical conclusions about the real world, namely a proposal about the properties of the Higgs boson.

It might seem philosophically illegitimate to use such a paradox to argue about the real world. However, philosophers have a similar argument when it comes to such “reality is a lie” scenarios. In general, modern philosophers point out that any argument that proves that all of our knowledge is false or meaningless by necessity also proves itself false or meaningless. This is what allows analytical philosophy to carry forward and make progress, even if it can’t reject the idea that reality is an illusion by more objective means.

With that said, there seems to be a difference between simply rejecting arguments that “show” that the world is an illusion or that we are all Boltzmann Brains, and using those arguments to draw conclusions about other parts of the world. I would be curious if there are similar arguments to Carroll’s in philosophy, arguments that draw conclusions more specific than “we exist and can know things”. Any philosopher readers should feel welcome to chime in in the comments!

And for the rest of you, you probably aren’t a Boltzmann Brain. But if the outside world looks a little too dark tonight…

What are Vacua? (A Point about the String Landscape)

4 Replies

A couple weeks back, there was a bit of a scuffle between Matt Strassler and Peter Woit on the subject of predictions in string theory (or more properly, the question of whether any predictions can be made at all). As a result, Strassler has begun a series on the subject of quantum field theory, string theory, and predictions.

Strassler hasn’t gotten to the topic of string vacua yet, but he’s probably going to cover the subject in a future post. While his take on the subject is likely to be more expansive and precise than mine, I think my perspective on the problem might still be of interest.

Let’s start with the basics: one of the problems often cited with string theory is the landscape problem, the idea that string theory has a metaphorical landscape of around 10^500 vacua.

What are vacua?

Vacua is the plural of vacuum.

Ok, and?

A vacuum is empty space.

That’s what you thought, right? That’s the normal meaning of vacuum. But if a vacuum is empty, how can there be more than one of them, let alone 10^500?

“Empty” is subjective.

Now we’re getting somewhere. The problem with defining a concept like “empty space” in string theory or field theory is that it’s unclear what precisely it should be empty of. Naively, such a space should be empty of “stuff”, or “matter”, but our naive notions of “matter” don’t apply to field theory or string theory. In fact, there is plenty of “stuff” that can be present in “empty” space.

Think about two pieces of construction paper. One is white, the other is yellow. Which is empty? Neither has anything drawn on it, so while one has a color and the other does not, both are empty.

“Empty space” doesn’t come in multiple colors like construction paper, but there are equivalent parameters that can vary. In quantum field theory, one option is for scalar fields to take different values. In string theory, different dimensions can be curled up in different ways (as an aside, when string theory leads to a quantum field theory often these different curling-up shapes correspond to different values for scalar fields, so the two ideas are related).

So if space can have “stuff” in it and still count as empty, are there any limits on what can be in it?

As it turns out, there is a quite straightforward limit. But to explain it, I need to talk a bit about why physicists care about vacua in the first place.

Why do physicists care about vacua?

In physics, there is a standard modus operandi for solving problems. If you’ve taken even a high school physics course, you’ve probably encountered it in some form. It’s not the only way to solve problems, but it’s one of the easiest. The idea, broadly, is the following:

First get the initial conditions, and then use the laws of physics to see what happens next.

In high school physics, this is how almost every problem works: your teacher tells you what the situation is, and you use what you know to figure out what happens next.

In quantum field theory, things are a bit more subtle, but there is a strong resemblance. You start with a default state, and then find the perturbations, or small changes, around that state.

In high school, your teacher told you what the initial conditions were. In quantum field theory, you need another source for the “default state”. Sometimes, you get that from observations of the real world. Sometimes, though, you want to make a prediction that goes beyond what your observations tell you. In that case, one trick often proves useful:

To find the default state, find which state is stable.

If your system starts out in a state that is unstable, it will change. It will keep changing until eventually it changes into a stable state, where it will stop changing. So if you’re looking for a default state, that state should be one in which the system is stable, where it won’t change.

(I’m oversimplifying things a bit here to make them easier to understand. In particular, I’m making it sound like these things change over time, which is a bit of a tricky subject when talking about different “default” states for the whole of space and time. There’s also a cool story connected to this about why tachyons don’t exist, which I’d love to go into for another post.)

Since we know that the “default” state has to be stable, if there is only one stable state, we’ve found the default!

Because of this, we can lay down a somewhat better definition:

A vacuum is a stable state.

There’s more to the definition than this, but this should be enough to give you the feel for what’s going on. If we want to know the “default” state of the world, the state which everything else is just a small perturbation on top of, we need to find a vacuum. If there is only one plausible vacuum, then our work is done.

When there are many plausible vacua, though, we have a problem. When there are 10^500 vacua, we have a huge problem.

That, in essence, is why many people despair of string theory ever making any testable predictions. String theory has around 10^500 plausible vacua (for a given, technical, meaning of plausible).

It’s important to remember a few things here.

First, the reason we care about vacuum states is because we want a “default” to make predictions around. That is, in a sense, a technical problem, in that it is an artifact of our method. It’s a result of the fact that we are choosing a default state and perturbing around it, rather than proving things that don’t depend on our choice of default state. That said, this isn’t as useful an insight as it might appear, and as it turns out there is generally very little that can be predicted without choosing a vacuum.

Second, the reason that the large number of vacua is a problem is that if there was only one vacuum, we would know which state was the default state for our world. Instead, we need some other method to pick, out of the many possible vacua, which one to use to make predictions. That is, in a sense, a philosophical problem, in that it asks what seems ostensibly to be a philosophical question: what is the basic, default state of the universe?

This happens to be a slightly more useful insight than the first one, and it leads to a number of different approaches. The most intuitive solution is to just shrug and say that we will see which vacuum we’re in by observing the world around us. That’s a little glib, since many different vacua could lead to very similar observations. A better tactic might be to try to make predictions on general grounds by trying to see what the world we can already observe implies about which vacua are possible, but this is also quite controversial. And there are some people who try another approach, attempting to pick a vacuum not based on observations, but rather on statistics, choosing a vacuum that appears to be “typical” in some sense, or that satisfies anthropic constraints. All of these, again, are controversial, and I make no commentary here about which approaches are viable and which aren’t. It’s a complicated situation and there are a fair number of people working on it. Perhaps, in the end, string theory will be ruled un-testable. Perhaps the relevant solution is right under peoples’ noses. We just don’t know.

Model-Hypothesis-Experiment: Sure, Just Not All the Same Person!

Leave a reply

At some point, we were all taught how science works.

The scientific method gets described differently in different contexts, but it goes something like this:

First, a scientist proposes a model, a potential explanation for how something out in the world works. They then create a hypothesis, predicting some unobserved behavior that their model implies should exist. Finally, they perform an experiment, testing the hypothesis in the real world. Depending on the results of the experiment, the model is either supported or rejected, and the scientist begins again.

It’s a handy picture. At the very least, it’s a good way to fill time in an introductory science course before teaching the actual science.

But science is a big area. And just as no two sports have the same league setup, no two areas of science use the same method. While the central principles behind the method still hold (the idea that predictions need to be made before experiments are performed, the idea that in order to test a model you need to know something it implies that other models don’t, the idea that the question of whether a model actually describes the real world should be answered by actual experiments…), the way they are applied varies depending on the science in question.

In particular, in high-energy particle physics, we do roughly follow the steps of the method: we propose models, we form hypotheses, and we test them out with experiments. We just don’t expect the same person to do each step!

In high energy physics, models are the domain of Theorists. Occasionally referred to as “pure theorists” to distinguish them from the next category, theorists manipulate theories (some intended to describe the real world, some not). “Manipulate” here can mean anything from modifying the principles of the theory to see what works, to attempting to use the theory to calculate some quantity or another, to proving that the theory has particular properties. There’s quite a lot to do, and most of it can happen without ever interacting with the other areas.

Hypotheses, meanwhile, are the province of Phenomenologists. While theorists often study theories that don’t describe the real world, phenomenologists focus on theories that can be tested. A phenomenologist’s job is to take a theory (either proposed by a theorist or another phenomenologist) and calculate its consequences for experiments. As new data comes in, phenomenologists work to revise their theories, computing just how plausible the old proposals are given the new information. While phenomenologists often work closely with those in the next category, they also do large amounts of work internally, honing calculation techniques and looking through models to find explanations for odd behavior in the data.

That data comes, ultimately, from Experimentalists. Experimentalists run the experiments. With experiments as large as the Large Hadron Collider, they don’t actually build the machines in question. Rather, experimentalists decide how the machines are to be run, then work to analyze the data that emerges. Data from a particle collider or a neutrino detector isn’t neatly labeled by particle. Rather, it involves a vast set of statistics, energies and charges observed in a variety of detectors. An experimentalist takes this data and figures out what particles the detectors actually observed, and from that what sorts of particles were likely produced. Like the other areas, much of this process is self-contained. Rather than being concerned with one theory or another, experimentalists will generally look for general signals that could support a variety of theories (for example, leptoquarks).

If experimentalists don’t build the colliders, who does? That’s actually the job of an entirely different class of scientists, the Accelerator Physicists. Accelerator physicists not only build particle accelerators, they study how to improve them, with research just as self-contained as the other groups.

So yes, we build models, form hypotheses, and construct and perform experiments to test them. And we’ve got very specialized, talented people who focus on each step. That means a lot of internal discussion, and many papers published that only belong to one step or another. For our subfield, it’s the best way we’ve found to get science done.

Anthropic Reasoning, Multiverses, and Eternal Inflation (Part One of Two)

Leave a reply

You and I are very very lucky. Human life is very delicate, and the conditions under which it can thrive are not in the majority. Going by random chance, neither of us should exist.

I am referring, of course, to the fact that the Earth’s surface is about 70 percent ocean. Just think how lucky you are not to have been born there: you would have drowned! Let alone if you were born beneath the Earth’s crust!

If you understand why the above is ridiculous, congratulations: you’ve just discovered anthropic reasoning.

There are some situations we find ourselves in because they are common. Most (all) of the Earth is in orbit around the Sun, so if you find yourself in orbit around the Sun you should hardly be surprised. Some situations, on the other hand, keep happening not because they are common in the universe in general, but because they are the part of the universe in which we can exist. Recognizing those situations is anthropic reasoning.

It’s not weird that you were born on land, even though land is rarer than water, because land, and not water, is where people live. As long as there was any land on the earth at all, you would expect people to be born on it (or on ships, I suppose) rather than on the ocean.

The same sort of reasoning explains why we evolved on Earth to begin with. There are eight planets in the solar system (yes, Pluto is not a planet, get over it), and only one of them is in the right place for life like us. We aren’t “lucky” that we ended up on Earth rather than another planet, nor is it something “unlikely” that needs to be explained: we’re on Earth because the universe is big enough that there happens to be a planet that has the right conditions for life, and Earth is that planet.

What anthropic reasoning has a harder time explaining (but what some people are working very hard to make it explain) is the question of why our whole universe is the way it is. Our universe is a pretty good place for life to evolve. Granted, that’s probably just a side effect of it being a good place for stars to evolve, but let’s put that aside for a second. Suppose the universe really is a particularly nice place for life, even improbably nice. Can anthropic reasoning explain that?

Probably. But it takes some work.

See, the difficulty is that in order for anthropic reasoning to work, you need to be certain that some place hospitable to life actually is likely to exist. Earthlike planets may be rare, but there are enough planets in the universe that some of them are bound to be like Earth. If universes like ours are rare, though, then how can there be enough universes to guarantee one like ours? How can there be more than one universe at all?

That’s why you need a multiverse.

A multiverse, in simple terms, is a collection of universes. If you object that a universe is, by definition, all that exists, and thus there can’t possibly be more than one, then you can use an alternate definition: a multiverse is a vast universe in which there are many smaller universe-like regions. These sub-universes don’t have much (or any) contact with eachother, and (in order for anthropic reasoning to work) must have different properties.

Does a multiverse exist, though? How would one work?

There are several possibilities, of varying degrees of plausibility. Some people have argued that quantum mechanics leads to many parallel universes, while others posit that each universe could be like a membrane in some higher dimensional space. The multiple universes could be separated in ordinary space, or even in time.

In the next post, I will discuss one of the more plausible (if still controversial) possibilities, called eternal inflation, in which new universes are continually birthed in a vast sea of exponentially expanding space. If you have no idea what the heck I meant by that, great! Tune in next time to find out!

In Defense of Pure Theory

3 Replies

I’d like to preface this by saying that this post will be a bit more controversial than usual. I have somewhat unconventional opinions about the nature and purpose of science, and what I say below shouldn’t be taken as representative of the field in general.

A bit more than a week ago, Not Even Wrong had a post on the Fundamental Physics Prize. Peter Woit is often…I’m going to say annoying…and this post was no exception.

The Fundamental Physics Prize, for those not in the know, is a fairly recently established prize for physicists, mostly theoretical physicists.  Clocking in at three million dollars, the prize is larger than the Nobel, and is currently the largest prize of its sort. Woit has several objections to the current choice of award recipient (Alexander Polyakov). I sympathize with some of these objections, in particular the snarky observation that a large number of the awardees are from Princeton’s Institute for Advanced Study. But there is one objection in particular that I feel the need to rebut, if only due to its wording: the gripe that “Viewers of the part I saw would have no idea that string theory is not tested, settled science.”

There are two problems with this statement. The first is something that Woit is likely aware of, but it probably isn’t obvious to everyone reading this. To be clear, the fact that a certain theory is not experimentally tested is not a barrier to its consideration for the Fundamental Physics Prize. Far from it, the purpose of the Fundamental Physics Prize is precisely to honor powerful insights in theoretical physics that have not yet been experimentally verified. The Fundamental Physics Prize was created, in part, to remedy what was perceived as unfairness in the awarding of the Nobel Prize, as the Nobel is only awarded to theorists after their theories have received experimental confirmation. Since the whole purpose of this prize is to honor theories that have not been experimentally tested, griping that the prizes are being awarded to untested theories is a bit like griping that Oscars aren’t awarded to scientists, or objecting that viewers of the Oscars would have no idea that the winners haven’t done anything especially amazing for humanity. If you’re watching the ceremony, you probably know what it’s for.

Has this been experimentally verified?

The other problem is a difference of philosophy. When Woit says that string theory is not “tested, settled science” he is implying that in order to be “settled science”, a theory must be tested, and while I can’t be sure of his intent I’m guessing he means tested experimentally. It is this latter implication I want to address: whether or not Woit is making it here, it serves to underscore an important point about the structure of physics as an institution.

Past readers will be aware that a theory can be valuable even if it doesn’t correspond to the real world because of what it can teach us about theories that do correspond to the real world. And while that is an important point, the point I’d like to make here is a bit more controversial. I would like to argue that pure theory, theory unconnected with experiment, can be important and valuable and “settled science” in and of itself.

First off, let’s talk about how such a theory can be science, and in particular how it can be physics. Plenty of people do work that doesn’t correspond to the experimentally accessible real world.  Mathematicians are the clearest example, but the point also arguably applies to fields like literary analysis. Physics is ostensibly supposed to be special, though: as part of science, we expect it to concern itself with the real world, otherwise one would argue that it is simply mathematics. However, as I have argued before, the difference between mathematics and physics is not one of subject matter, but of methods. This makes sense, provided you think of physics not as some sort of fixed school of thought, but as an institution. Physicists train new physicists, and as such physicists learn methods common to other physicists. That which physicists like to do, then, is physics, which means that physics is defined much more by the methods used to do it than by its object of study.

How can such a theory be settled, then? After all, if reality is out, what possible criteria could there be for deciding what is or is not a “good” theory?

The thing about physics as an institution is that physics is done by physicists, and physicists have careers. Over the course of those careers, those physicists need to publish papers, which need to catch the attention and approval of other physicists. They also need to have projects for grad students to do, so as to produce more physicists. Because of this, a “good” theory cannot be worked on alone. It has to be a theory with many implications, a theory that can be worked on and understood consistently by different people. It also needs to constrain further progress, to make sure that not just anyone can create novel results: this is what allows papers to catch the attention of other physicists! If you have all that, you have all of the relevant advantages of reality.

String theory has not been experimentally tested, but it meets all of these criteria. String theory has been a major force in theoretical physics for the past thirty years because it can fuel careers and lead to discussion in a way that nothing else on the table can. It has been tested mathematically in numerous ways, ways which demonstrate its robustness as a theory of quantum gravity. In this sense, string theory is a prime example of tested, settled science.

Why I Am Not A Mathematician

2 Replies

(No relation to Russel’s Why I Am Not A Christian. Well, not much.)

I am a theorist. I study theories. Not the well-supported theories of the AAAS definition, but simply potential lists of particles, and lists that, further, are almost certainly not “true”.

Most people find that disconcerting. Used to thinking of scientists as people who investigate the real world, people whose ideas are always tested in the fire of experiment, the idea of a scientist whose work has no direct connection to the real world is a major source of cognitive dissonance…for at least a few minutes. After that, a light dawns in most people’s heads, as they turn to me with a sigh of relief and say,

“Oh. So you’re a Mathematician.”

No.

No, I am not a Mathematician. There is a difference, subtle but vast, between what I do and a mathematician does.

An illustrative example: Quantum Electro-Dynamics, or QED, is the most successful theory in the entirety of science. Yes, I do mean the entirety of science. Quantum Electro-Dynamics, the theory of how electrons and light behave, agrees with experiments to ten decimal places. Ten digits of detail, predicted then observed. That’s more confirmed accuracy than anything else in physics, in science at all, has ever achieved.

And if you ask a mathematician who specializes in this sort of thing, they’ll tell you that QED probably doesn’t exist.

Now, by this they don’t mean that electrons don’t exist, or that light doesn’t exist. What they mean is that, if you follow the theory’s implications all the way, you get a contradiction. You can calculate each step of the way, getting reasonable results each time, results that keep agreeing perfectly with experiments…but if you were to go all the way, off to infinity, you get results that make your whole theory stop making any sort of reasonable sense.

But as physicists, we keep using it. Because before reaching infinity, for any real calculation, it works. Perfectly.

That’s the difference between a theoretical physicist and a mathematician: for a mathematician, everything must be completely rigorous, and every implication, out to infinity, has to be vetted. For a physicist, if a theory gives reasonable results, we don’t really care whether it is completely clear how it works mathematically. We use physical reasoning, using concepts that work in the physical world, even if we’re studying a theory that doesn’t actually exist in the physical world. And while that sounds like a poor way to study abstract ideas, it allows us to take risks mathematicians can’t, which sometimes means we can make discoveries that even the mathematicians find interesting.